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The Coilover Bible - Part 1

By Bill "BillaVista" Ansellwith Ben "Bigger Valves" Langford

Photography: Bill Ansell, Dan Dibble, & Fox Racing ShoxCopyright 2008 - Bill Ansell

(click any pic to enlarge)

Coilover Bible Part 1 - The Basics

Suspension design and engineering are extremely complex. So muchso that it has been said that it would take several encyclopedia-sizedvolumes to cover it all, and even then there may not be more than adozen engineers on the planet who would understand it all. That said,we can still learn a great deal from an examination of the basics; andwith a firm grasp of those basics and a little testing and evaluation,almost anyone can build a decent working coilover suspension. Theaim of this series of articles is to help you towards that goal.

Acknowledgements

I am enormously indebted to Benny "Bigger Valves" Langford for his assistance with the production of thisarticle. Without his incredible wealth of technical knowledge, considerable expertise, generosity, and immensereserve of patience in answering my seemingly endless questions, it would not have been possible. For hiskind support and expert advice I am profoundly grateful. Benny - you are the master and I the humblemessenger - thank you! Thanks also to Frank Alioto for his kind assistance with the section on shock valving.

Very Special Thanks

An undertaking of this magnitude would not be possible without the assistance of others, most notably mywonderful wife Laurie and my kids Mitchell and Jessie. To them, a huge thank you for your patience andunderstanding through the countless late nights.

Introduction

Because of the complexity, we will be tackling the subject of coilover tech in several parts – this is the first. Inthis first part we’ll be reviewing basic shock and spring tech, examining the types of coilovers and their parts,going over their use and advantages, covering the concepts of installation ratio, wheel rate, and suspensionfrequency, then concluding with some preliminary spring-rate selections. Future articles will cover moreadvanced topics such as: spring length selection and tuning, coilover adjustments / tuning, spring selectionusing spring force modeling, re-valving, and hands-on tech procedures such as rebuilding a shock.

There is much to learn – even if you’re a seasoned coilover user as there exists a lot of misinformation aboutcoilovers. This is because, more than with any other style of shock & spring, the coilover user is presented withalmost limitless options regarding setup. Mounting, valving, spring rates, spring lengths, gas pressure andmore are all completely in the hands of the installer and can be easily changed from one extreme to another.When those hands are expert – the result is phenomenal performance. When those hands are not so expert –the unfortunate result is that we novices really just have a huge amount of rope with which to hang ourselves. Instead of a huge number of ways we can tune, we are faced with a huge number of ways we can get it wrong,and sometimes badly wrong at that.

To make matters worse, after we’ve unknowingly gotten it wrong (or someone else has) and we're observingthe results, without a proper grounding in the basics, we lack the ability to properly interpret the results we areobserving. The unfortunate result is that, instead of passing on wisdom, we unintentionally contribute to mythand misinformation. Again, without the proper grounding to accurately communicate our observations andconclusions, and despite our best intentions, we end up spreading myths and misinformation across theInternet – preventing the next hands from becoming as expert as they could be. And the cycle begins again.

My aim with this article is to help break that cycle, to help your hands become just a little bit more expert, totake back some of that rope yer fixin’ ter hang yerself with.

One last thing before we begin. We are going to have to be extremely clear about the definitions of the termswe use – and disciplined in their application. There are so many terms that get bantered around, often withcompletely different meanings, that confusion is virtually guaranteed. If nothing else, we need to agree to striveto use the correct terms, and use them consistently, to avoid adding to the confusion.

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A word about design philosophy.

All design, including suspension design, is a compromise of factors to achieve a desired result that will bejudged by some criteria. Those criteria are numerous, often subjective, and may range from cost andcomplexity to performance and even appearance. With this in mind, my philosophy is that there are very few, ifany, absolutes – very few “rights” or “wrongs”. Some will have you think otherwise – especially the so-called“band-aid” accusers. For example, some will say that the use of an anti-roll bar is a band-aid for poor springrate selection. Some will say that a limit-strap is a band-aid for poor link geometry. Some will say a “helper coil”is a band-aid for improper spring length. There are many other examples. In my opinion, very few are valid.There are many tools in the box of design, and if they are applied with reason and understanding, then theyare certainly valid. Only if they are applied from lack of understanding of a better way do they become aconcern. May this article expand your understanding so that any and all “tools” you use from the box ofsuspension design, you use with knowledge and confidence. Good luck!

Table of Contents

Part 1 - The Basics

Suspension ReviewHow Shocks WorkShock Design

Gas ChargingTwin-tube DesignMono-tube DesignVariable Damping / ValvingExternally Adjustable BypassShocks

Modes of Travel, Ride Height, SuspensionHeight, & Wheel TravelCoilovers

Remote ReservoirPiggybackEmulsion

Coilover OperationThe Seven Goals of Suspension DesignSpring TheoryDual-Rate SpringsKey Suspension Definitions

Leverage TheoryThe Angle FactorInstallation RatioMore DefinitionsMeasuring d1, d2, & alpha -Practical Calculation of the IRMeasuring CSWSuspension FrequencyThe Basis For SelectingPreliminary Spring RatesPreliminary Spring RateCalculations - The BVCalculatorWhat to Shoot For -Correlating the BV CalculatorInputs With VehiclePerformanceInterpreting the BVCalculator's Results - Prepareto Tune (or Start Over)SummaryClosing NotesResourcesReferencesSources

Suspension Review

An off-road vehicle's suspension system is designed to perform these basic functions:

Support vehicle weight / maintain correct vehicle ride height.1.Keep the tires in contact with the trail.2.Provide comfortable ride for driver & passengers.3.Prevent or reduce damage to chassis from force of impacts with obstacles (including landing afterjumping).

4.

Maintain correct wheel alignment (locate the axles).5.

The first function requires no explanation. The remaining four are best illustrated by the simple example of avehicle traveling down the trail and hitting a bump.

When a tire hits a bump the wheel moves up. Without suspension this motion would be transferred directly tothe chassis, causing the vehicle and it’s occupants to go up. When gravity takes over, the vehicle comes backdown, and the force of the impact with the ground would again be transferred directly to the chassis and itsoccupants. Depending on the size of the bump, without suspension the tires could lose contact with the road,traction is lost, it would certainly be uncomfortable, the chassis would be subjected to damaging shock loads,and directional / steering control could be lost.

In other words, the ride & handling would be awful.

We’re going to be using the terms “ride” and “handling” a lot, so let’s define them now:

Ride is a qualitative description of what it feels like to ride in the vehicle – it’s a description of“comfort level” if you like. In other words, it describes the vehicles ability to soak up uneven terrain,isolate the occupants from the road, and provide a comfortable ride.

(The term “ride” also has another distinct and important definition in suspension theory. It is theterm used to describe the motion, or travel, of the suspension when both wheels on an axle travelequally together in the same direction, as in when both wheels on a solid axle hit a bump at the





same time. Normally, context alone will be sufficient to determine which definition of “ride” isimplied. Where there may be any doubt or confusion, I shall use the term “ride quality” for thequalitative description of what it feels like to ride in the vehicle, and “ride travel” to describe themovement of the suspension when both wheels on an axle travel together equally.)

Handling is the ability of the vehicle to keep all four tires firmly in contact with the ground. Doingso maximizes the vehicle’s ability to accelerate, brake, and corner. In an off-road rig we also haveto be concerned with the vehicle’s ability to climb, descend, and side-hill. Technically, climbing anddescending are just different forms of acceleration, and side-hilling (driving along the side of a hillin an off-camber manner) is similar to cornering in terms of vehicle dynamics. Ultimately,“handling” is the term used to describe how the vehicle performs.

When a rig climbs or accelerates weight is transferred from the front to the rear causing a suspension motioncalled “squat”. This increases the traction at the rear wheels but reduces it at the front. When a rig descendsor brakes, weight shifts from the rear to the front, causing a suspension motion called “dive”, and the oppositeoccurs – traction increases at the front wheels and decreases at the rear. When a rig corners or side-hills,weight transfers from the inside or uphill side of the vehicle to the outside or downhill side of the vehicle, whichcauses a motion called “sway” or “body roll”.

Without suspension, all this weight transfer would not only be incredibly uncomfortable, but depending on theseverity, could quickly and easily lead to loss of traction and / or control.

Enter suspension.

All the components of the vehicle's suspension work together to achieve the five functions and provide thedesired ride and handling. These basic suspension components are:

TiresLinks (or control arms)SpringsShocks

Tires

Tires are really just an air spring that supports the entire vehicle. I’ll not go into great detail about tire tuninghere, but you should be aware that the tires, and the pressure in them, have a huge impact on vehicle ride andhandling – regardless of the style of suspension used. This can be a complication in suspension tuning, butcan also be used to advantage. For example, a stiff suspension set up for high-speed work can be made morecomfortable and pliable in really rough terrain simply by adjusting the air pressure in the tires. The otherreason I mention tires is because you often don’t see them mentioned when people are swapping suspensionadvice and experience. That’s a mistake. To properly understand and use the experience of another you needto be aware of, and account for, the type of tires they run and at what pressure.

Links

For the purposes of this article, the suspension links (or control arms) locate the axles, and define thesuspension’s geometry. That is, they define the arc through which the suspension will cycle as it moves up andown. The geometry of the links also defines a host of other properties such as the vehicle’s roll axis,anti-squat, etc. Since this is not an article on suspension link design, we shall leave the discussion of linkshere for now, and return to them in a later part when we discuss roll and roll resistance.

Springs

The springs support the weight of the vehicle, maintain ride height, absorb road shock, and keep the tires incontact with the ground. By doing so they allow the chassis to ride relatively undisturbed while the tires followthe bumps and pot-holes in the road.

There are many different types of springs, including: air springs, leaf springs, coil springs, and torsion bars. They all do the same job, with their own advantages and disadvantages. We shall be concentrating on coilsprings, specifically those designed to be mounted on a coilover shock. The advantages of coil springs arenumerous. They are:

lightcompactinexpensivefriction freeunaffected by heateasy to construct in various rates, length and diameterswhen properly constructed, will not loose free height or installed length

When a wheel hits a bump, a force is applied to the wheel. That force causes a vertical acceleration of thewheel – the wheel goes up. The springs will absorb the load by compressing, converting the kinetic energy ofthe wheel’s motion into potential energy stored in the now-compressed spring. This potential energy is thenreleased, causing the spring and wheel to rebound.





The rate at which the springscompress and rebound is calledthe suspension frequency. Leftundamped, the spring willcompress and rebound at thesuspension's natural frequencyuntil all of the energy originally putinto the spring by the force of thebump is used. Of course, energycan neither be created nordestroyed; it can only beconverted from one form toanother. Unassisted, a spring willbounce up and down convertingkinetic energy to potential andback again for a very long time. Obviously this would translate toterrible ride and handling, as thewheels would bounce up anddown uncontrollably.

What is needed, then, is some sort of energy-converting device to assist the springs – something that candamp the compression and rebounding of the spring.

Enter the shock absorber, or shock.

Shocks

Shocks control spring motion, that is, they slow down and reduce the magnitude of the spring’s oscillation. Theprocess is known as damping. In technical terms, a shock controls the frequency and amplitude of thesuspension's oscillation. In layman’s terms, a shock controls how fast and how much the suspensioncompresses and rebounds.

This:

a) is important in keeping the tires in firm contact with the road (providing handling); and

b) helps isolate the passengers from road shocks (providing a good ride).

By damping the movements of the suspension, the tires remain in contact with the trail surface. This preventsthe tires from bouncing and skipping with every bump and dip in the trail. Tires that do not stay in contact withthe trail can’t provide good traction, steering stability or braking friction. Damping the movements of thesuspension also results in resistance to vehicle bounce, roll, and sway during weight transfer and thereforeresistance to brake dive and acceleration squat.

How Shocks Work

A shock absorber is basically a hydraulic piston pump that converts the energy of motion (kinetic energy) intoheat energy. One end of the shock, the shock body or “tube”, is the cylinder of the pump, the other end of theshock is the rod and piston. One end of the shock is connected to the chassis and the other end is connectedto the suspension. As the wheels move up and down relative to the chassis the piston pumps up and down inthe cylinder.

The cylinder (shock body) is a tube filled with hydraulic oil. When the piston pumps up and down through thehydraulic oil, the oil is forced through holes in the piston, called orifices. The flow of the oil through the orificesis further regulated by the deflection of special spring-loaded metering valves, or deflection discs, located oneither side of the piston.

Assembled shock.

Cylinder (shock body) is uppermost, rod (shock shaft) protrudesbelow.





Rod and piston being removed from cylinder.

Rod and piston being removed from cylinder.

Rod and piston removed from cylinder.

Because of the valves and the fact that the piston orifices are so small, only a small amount of fluid, undergreat pressure, passes through the piston as it pumps up and down. The resulting resistance slows down thepiston and creates heat from friction. This in turn slows down spring and suspension movement and convertsthe spring’s kinetic energy to heat in the oil that is then dissipated as the oil cools.

The amount of damping a shock absorber provides depends on the number and size of the orifices in thepiston as well as the valving. By changing the design of the valves, the pressure at which they open and closecan be altered and a shock’s damping characteristics can be tuned as needed. The higher the openingpressure, the firmer the shock. The lower the opening pressure, the softer the shock.

Obviously, shock absorbers must work in two directions - compression and rebound. The compression strokeoccurs as the shock gets shorter and the piston travels into the cylinder. The rebound stroke occurs as theshock lengthens and the piston extends from the cylinder. The compression stroke controls the motion of thevehicle's unsprung weight, while the rebound stroke controls the heavier sprung weight. Accordingly, a typicalcar or light truck shock will have valving designed to provide more resistance during rebound thancompression.

Close-up view of shock piston.

(photo courtesy of Dan Dibble)





Compression valving discs are on the rod-side of the piston.


Rebound valving discs are on the free-end of the piston.


Rebound valving discs removed from free-end of the piston.

Looking very much like a series of washers (and often referred toas such) they are stamped spring steel deflection discs that reactto pressure and velocity to meter, or regulate, the amount of fluidthat flows through the piston and thus the amount of resistance ordamping the shock provides. A particular number, size, andarrangement of valving discs is often referred to as a "shimstack".


Heat and Shock Fade

Because of the tiny orifices in the piston, the viscosity of the shock oil has a large effect on the resistance theoil presents to the piston’s movement, and hence the damping the shock provides. Viscosity changes withtemperature –hot oil is “thinner” and pours more easily than cold oil (which is why you change your oil whenthe engine is warm). It stands to reason then, that to provide consistent damping, we would want the shock oilto maintain a consistent viscosity. However, we just said one of the purposes of the shock is to dissipate thespring’s kinetic energy by converting it to heat that is absorbed by the hydraulic oil, so we can see the potentialfor trouble here. If the shock is used hard enough, it will eventually heat the oil to a point where its viscositychanges (becomes less). This thin, overheated shock oil now offers less (possibly much less) resistance to thepiston’s movement, and the shock’s damping capability is reduced – sometimes drastically. This is called“shock fade.” There are strategies to combat shock fade that we will cover shortly.

Shock Design

Most shocks produced today are either of twin-tube or mono-tube design. Before we look at each individually,let’s look at another important aspect of modern shock design that is often applied to both twin-tube andmono-tube shocks – gas charging.

Gas Charging

The primary function of gas charging is to minimize aeration and foaming of the hydraulic fluid by reducing thechance of cavitation. When the shock cycles, the motion of the piston through the oil creates an area of highpressure ahead of the piston and an area of low pressure behind it. If the pressure of a fluid is reduced belowits vapour pressure, the fluid will spontaneously change state from a liquid to a gas. This means that tiny airbubbles can form in the low-pressure area directly behind the piston. The process is called cavitation. Leftunchecked, the tiny air bubbles that form will mix with the oil - a process called aeration. The resultant mixtureof oil and air inhibits the functioning of the shock as the piston and valving are designed to produce therequired damping by operating in a column of incompressible oil. Once the oil is mixed with air, or aerated, it isno longer incompressible. The faster the piston pumps up and down, the more rapidly cavitation aerates the oilon both sides of the piston, and eventually the oil will be churned into foam. The resulting foam offers littleresistance and causes extreme fade of the shock’s damping ability.

The addition of pressurized nitrogen gas to the shock helps to prevent the low-pressure zone behind themoving piston from falling below the vapour pressure of the oil, reducing the chance of cavitation, aeration,foaming, and eventual fade.





In addition to reducing foaming and fade, the gas charge allows greater flexibility in valving design. Without thegas charge, valving design would have to be compromised to allow for the possible eventual aeration of the oil.

Depending on the pressure used and the diameter of the rod, gascharging can also cause the shock to provide a small increase inthe spring rate of the suspension (in fact, if the vehicle were lightenough, the rod diameter large enough, and the pressure highenough, the pressurized nitrogen alone could act as the spring –hence airshocks, but I digress). This mild boost in spring rate iscaused by the pressurized gas acting on the rod through whichthere are, obviously, no orifices; as shown at left. Therefore, thelarger the rod is in diameter, the larger the area for the pressureto act against. This gas pressure acting on the rod through thecentre part of the piston is also the reason why an uninstalled,unloaded, gas-charged shock absorber will extend on its own.

Despite the effective spring rate of the pressurized shock, in a normal hydraulic shock, pressure shouldprobably not be used to compensate for incorrect spring rates or worn / broken springs. However, it can helpreduce body roll, sway, brake dive, and acceleration squat compared to a vehicle with identical springs butnon-gas-charged shocks.

Twin-tube Design

Most modern OEM passenger vehicle shocks are of thetwin-tube design. The twin tube design has an inner tubeknown as the working or pressure tube and an outer tubeknown as the reserve tube. The pressure tube holds the oilthrough which the piston moves. However, because the oil isincompressible, it must have somewhere to go during shockcompression as the piston rod displaces a certain volume offluid. The reserve tube provides a place for this hydraulicfluid that is displaced as the rod travels into the pressuretube. The reserve tube also creates a space for the fluid asits volume expands due to heat during use. The reserve tubemay also contain a low-pressure charge of nitrogen. Thepressure of the nitrogen in the reserve tube normally variesfrom 100 to 150 psi.

Twin-tube shocks have a valve located at the bottom of thepressure tube called the base valve. The base valve is thecompression valve - it controls fluid movement during thecompression stroke of the shock by metering the flowbetween the pressure tube and the reserve tube.

Because they use a “tube within a tube”, twin-tube shocksare compact in length, making them easy to fit or package,particularly on OEM cars where space is extremely limited.Their design also lends itself to relatively cheap massproduction while retaining effective performance withoutrequiring the strict tolerances (and associated manufacturingcosts) of a mono-tube design.

Twin-tube shocks also have some limitations. They tend to trap heat within the pressure tube as it is insulatedfrom cooling air by the outer reserve tube, making them prone to heat buildup and fade under hard use.Because the base valve is inside the pressure tube they are also not designed for the user to be able to alteror customize the valving. Finally, gas-charged twin-tube shocks can only be mounted in one orientation – theywill not function properly if mounted upside down.

Mono-tube Design





Mono-tube shocks have only one tube, the pressure tube. They are longer thantwin-tube shocks because the single pressure tube must have sufficient length tostore the hydraulic oil that is displaced as the rod travels into the pressure tubeas well as provide space for the fluid as its volume expands due to heat duringuse.

If a mono-tube shock is gas charged, as most are, it must also have a place tostore the high-pressure nitrogen charge. There are two methods ofaccomplishing this. In some shocks, the nitrogen is stored with the oil in thepressure tube. The gas and the oil are, in effect, mixed together in an emulsion.Not surprisingly, this style of gas-charged mono-tube shock is known as anemulsion shock.

A better way to contain the nitrogen charge is to separate it from the oil with afloating piston, also called a dividing piston. The floating piston moves up anddown as the piston moves up and down in the cylinder, keeping the oil andnitrogen from mixing. However, the shock must now be much longer because thetube must be of sufficient length to accommodate the full stroke of the piston, allthe hydraulic oil, the heat expansion of the oil, the gas charge, and the floatingpiston. If the shock is a long-travel shock, (meaning the piston stroke alone is 12inches or more), the total tube length required can become prohibitive. In thiscase, an external reservoir is used to house the nitrogen charge, the floatingpiston, and some of the hydraulic oil. Mono-tube gas charges normally rangefrom about 150 psi to 350 psi.

A mono-tube shock does not have a base valve. Instead, all of the valving during both compression andextension takes place at the piston. Since the piston and rod are easily removed from the shock, themono-tube design lends itself to independent tuning of the compression and rebound damping by providing foreasy valving changes by the end-user. As a result, mono-tube shock users can individually customize theirvalving for improved ride and handling.

In addition, non-emulsion mono-tube shocks can be mounted in any orientation, including upside down.

Because a mono-tube shock doesn’t require a “tube-within-a-tube”, for a given outside diameter, a mono-tubeshock will have a larger bore, and thus be able to use a larger piston than a twin-tube design. This can bebeneficial when designing a shock to extract the maximum possible damping from the smallest diameterpackage.

Mono-tube design also allows the heat in the oil to transfer directly to the outer surface of the shock body,which is in direct contact with cooling airflow, where it can dissipate more efficiently. This reduces heat-inducedfade, allowing the shock to maintain full damping characteristics as temperatures rise with hard use.

Finally, mono-tube shocks must be designed and built to exacting tolerances in order to function properly. Thisresults in a high-quality product.

In the mono-tube shock, note the larger diameterpiston, and the floating piston.

In the twin-tube shock, note the "tube-within-a-tube" construction and the base valve.

(Diagram courtesy of Polyperformance)

Shock Diameter

The larger a shock is in diameter, the larger its bore can be. The bore is the diameter of the piston and theinside diameter of the pressure tube. The larger the piston’s diameter, the larger its surface area. Sincepressure is force divided by area, it stands to reason that the larger the area, the smaller the pressuregenerated by a given force. Inside a shock, the lower the pressure, the lower the temperature. In addition, alarger diameter shock can contain more oil to absorb and dissipate the heat generated, resulting in reduced





internal operating temperatures for a given force. The result is, the larger the shock diameter, the cooler it willrun and therefore the harder the shock can be worked before fading.

Variable Damping / Valving

In street / track driving, maximum performance demands shocks that provide both firm, crisp handling and asmooth comfortable ride. In offroad rigs we have the additional demands of soaking up small and large bumpsat speed while allowing a degree of flexibility for slow crawling. No environment is as demanding of shocks asoffroad racing. A shock with relatively stiff valving can provide firm, responsive handling and control roll, dive,and squat. But stiff valving creates ride harshness and increases feedback to the driver through thesuspension. Conversely, a shock with relatively soft valving smoothes out the bumps, roughness and vibration,and allows great flexibility but can fall short of the required suspension control required for responsive handlingand damping the pounding experienced in high-speed offroad driving.

One solution to this apparent dilemma is to use adaptive, or variable, damping - that is, valving that adaptsautomatically to changing road / trail conditions. There are different strategies, all aimed at perfecting thatmagical balance between ride and handling for a wide range of driving conditions. Among the more commonstrategies are:

Velocity sensitive dampingPosition sensitive dampingAcceleration sensitive damping

Each have their particular strengths and weaknesses, but they all operate on a similar principle: variablevalving senses some condition and changes to react to that condition – be it the speed of the shock stroke, theposition of the shock in its stroke, or some other factor. Theoretically, the shock can therefore adjust tochanging road or trail conditions and deliver improved suspension control and better handling withoutincreasing ride harshness.

Velocity sensitive damping involves valving changes that occur in response to the speed, or velocity, of theshock’s stroke. This strategy provides relatively soft valving for driving on smooth surfaces, but when thewheel hits a bump, the sudden change in piston velocity causes the velocity sensitive valve to open, alteringthe damping to control the suspension’s oscillation. The same thing happens when the wheel rebounds fromthe bump. When the driving surface smoothes again, and the piston velocity slows, the valve closes and theshock's damping automatically alters for greater ride comfort. The reason I say "alters" instead of saying itgets "softer" or "stiffer" is because the precise details get quite complicated. For example, when the valvesopen or close, depending on the shock and valving design, the rate at which the damping becomes softer orstiffer per unit of shock velocity increase depends on if the valving is linear, progressive, or digressive. As thename suggests, in linear valving the rate at which the damping changes with the velocity of the shock isconstant. If the valving is progressive, the rate of change of stiffness increases as velocity increases; and if thevalving is digressive, the rate of change of damping gets less as the shocks velocity increases. Whether thevalving is linear, progressive, or digressive depends on several factors including the particular shim stack andpiston design. The specifics are beyond the scope of this article, but will be explored in greater detail in a laterissue. For now, the key point is that velocity sensitive valving alters the shocks damping depending on thevelocity of the rod and piston; it is simple, effective, and fairly rugged which makes it popular in motorsportsand is the form of variable valving of most interest to off-road coilover users, albeit sometimes in combinationwith some form of internal or external bypass valving, described below.

The disadvantage to velocity sensitive damping is that the velocity of the piston often slows as it reaches thelimit of its stroke, just before it changes direction (the same way the velocity of a ball thrown in the air slows tozero at the peak of its height before it begins to fall). The problem is, it may be that, at this point of maximumstroke (rebound or compression), the shock needs more damping, not less. One approach to mitigating thislimitation is to use position sensitive damping.

Position sensitive damping takes a slightly different approach. Instead of using valving that opens and closesin response to piston velocity, the shock’s pressure tube is specially modified. Several small grooves aremachined into the side of the pressure tube to create a different "zones" in the shock’s travel. The groovescreate a leak path for oil to bypass the piston when the shock is operating in a particular zone. By carefullycontrolling the size and location of these internal grooves, more or less oil can be allowed to bypass the pistonin different zones, increasing or decreasing damping as required. A shock using this strategy is often called an"internal bypass" shock. A typical example used in street cars has grooves machined in the normal operatingmidrange of the shock’s travel, creating a "comfort zone". Oil is allowed to bypass the piston when the shock isoperating in this comfort zone,resulting in less damping and a softer ride. When the piston travels more than afew inches in either direction, as it does when the wheels hit a bump, it goes past the grooves and dampingincreases to control the suspension.

Inertia sensitive damping is still another strategy. One manufacturer has developed what it calls an "inertiaactive system" that it says continuously meters the rebound stroke and can instantly switch from firm to soft asconditions dictate. When high rebound damping is needed, as when cornering or braking hard on a smoothsurface, the inertia valve is closed. This "closed-valve" (stiff) state is the normal default condition in whichhandling is greatly improved. When low rebound damping is needed, as when a wheel hits a bump or pothole,the inertia valve opens to reduce damping. The system is designed to allow the wheel to better follow theterrain and the suspension to absorb jolts without transmitting them to the chassis for a smoother ride.

A similar strategy is acceleration sensitive damping. With this strategy, a specialized compression valve isused. This compression valve is a mechanical closed-loop system, which opens a bypass to fluid flow aroundthe compression valve when it senses a bump in the road, automatically adjusting the shock to absorb the





impact. As soon as the impact is overcome, the valve closes and returns to the normal setting. It is claimed thevalve can react in 15 milliseconds and that it operates anytime an impact or acceleration of 1.5 g’s or more isexperienced. This ability to instantly switch from firm to soft is claimed to provide a noticeably smoother ride aswell as better handling.

Externally adjustable bypass shocks

No matter what the strategy or the claims of the manufacturer; each variable damping strategy is in itself acompromise of sorts. The current pinnacle of variable damping shock design, the externally adjustable bypassshock, attempts to maximize performance and minimize compromise by blending velocity sensitive pistonvalving with position sensitive external bypass tubes. The piston valving uses velocity sensitive meteringvalves (deflection discs) but the shock also uses external bypass tubes that function in a similar manner as theinternal grooves of a position-sensitive shock – they allow precisely metered amounts of oil to bypass thepiston. Because the bypass tubes are external to the pressure tube, they are easily adjusted to vary theamount of bypass. The result is a shock that combines the best properties of velocity and position sensitivedamping with the provision for quick and easy external adjustment. Depending on the number, size, andlocation of the bypass tubes, a vast amount of shock tuning is possible. Normally, when using external bypasstubes, the first 2/3rd's of the shock’s compression stroke can be lightly damped to soften the ride while the last1/3rd is stiff to keep the suspension from bottoming. On the rebound stroke, the first 1/3rd is stiff to control therebounding spring and stop the vehicle from bouncing while the last 2/3rd's can be lightly damped to allow thewheels to droop quickly before the next bump.

Fox 2.5 inch externalbypass shock withremote reservoir.

(Photo courtesy of Fox Racing Shox)

Massive 4.4 inch external bypassshock with piggyback remotereservoir.


Modes of Travel, Ride Height, Suspension Height, & Wheel Travel

Now that we have basic understanding of suspension components and their function, let’s covera some key suspension terms and definitions. These definitions, and indeed this entire article, isunapologetically written assuming the vehicle has solid axles installed at both front and rear of thevehicle. Unless otherwise specifically mentioned to the contrary, you should read this articleassuming we're discussing solid axle suspensions.

Travel: In the strictest sense, travel is just the movement or motion of some component of thesuspension, or of the suspension as a whole. All moving components of the suspension havetheir own travel, thus we have wheel travel, spring travel, shock travel, and suspension travel.

We can speak of either "total" travel, meaning the entire range of motion from one extreme toanother - e.g. "total wheel travel"; or we can speak of some portion of travel -e.g. "up-travel"

If we're talking about only some portion of travel, we qualify it in one of two ways:

If we're talking about the wheels or suspension as a whole we describe it by direction - e.g.up-travel or down-travel; or

1.

If we're talking about the shocks or springs, we describe it by the effect on the component -e.g. shock compression.

2.

If we're talking about the travel of the shocks or springs we have:

Compression: Travel of the spring or shock that occurs as it gets shorter.Spring compression is also known as deflection, crush, displacement fromfree length, or simply, displacement.

Rebound: Travel of the spring or shock that occurs as it gets longer. Alsoknown as extension.

If we're talking about the travel of the wheels or suspension as a whole, before wequalify the direction of the travel, we must first distinguish the "mode" of travel. Thereare three modes of travel, distinguished by how the wheels and chassis are movingrelative to one-another. They are:





Ride: The vertical travel that occurs when both wheels on an axle movetogether the same distance at the same time, relative to the chassis. If bothwheels on a solid axle hit a speed-bump at the same time the resultingwheel or suspension travel would be ride travel. During ride travel, the axleremains parallel to the ground and both wheels on that axle remain, moreor less, perpendicular to the ground. Sometimes ride is also called heave.Ride travel can be subdivided into:

Compression / Up-travel / Bump - terms that describe the ridetravel that occurs when the wheels get closer to the chassis.

Rebound / Down-travel / Droop - terms that describe the ridetravel that occurs when the wheels get farther away from thechassis.

Flex: The suspension travel that occurs when one wheel on an axle movescloser to the chassis and the other wheel on that axle moves farther awayfrom the chassis. During flex the wheels on the other axle move in thesame direction as their diagonal opposites. In other words, if you stuff theright front wheel, you also stuff the left rear wheel, while the other twowheels droop. Also known as warp travel or articulation. Flex travel can besubdivided into:

Compression / Up-travel / Bump / Jounce / Stuff - terms thatdescribe the motion of the wheels that get closer to the chassis.

Rebound / Down-travel / Droop - terms that describe themotion of the wheels that get farther away from the chassis.

Roll: Roll is the motion that occurs when all four wheels remain more orless fixed in position and the chassis moves relative to the wheels. In roll,the chassis pivots about an imaginary longitudinal axis in such a way that itgets closer to the wheels on one side of the vehicle, and farther away fromthe wheels on the opposite side. Also known as body-roll or sway, roll isgenerally an unwanted motion that is related to, but not the same as, flex.

The following diagrams should help clarify the different modes of travel:

Ride Travel.

Axle remains parallel to theground as it travelsvertically.

Flex Travel.

Rear axle shown. Frontaxle will be articulating inopposite direction.

Roll.

Note distinction betweenflex and roll.

In flex, wheels at oppositecorners are doing thesame thing (both gettingcloser too, or farther awayfrom, the chassis).





Whilst in roll, wheels on thesame side are doing thesame thing (both gettingcloser to, or father awayfrom, the chassis).

You may be wondering about the distinction between wheel travel and suspension travel. Theterms are very closely related and often used interchangeably. However, there is a distinctionworth noting:

Wheel travel generally refers to the motion of one wheel on an axle, and can be usedto describe that motion either with or without springs / shocks installed.

Suspension travel generally refers to the motion of both wheels on an axle, and is onlyever used to describe the motion with springs / shocks installed.

For example, wheel travel can have two different "values":

- a theoretical maximum value, in both ride and flex modes, that is limitedby link geometry, driveline angles, and tire to chassis / body clearance; and

- an actual installed value, measured or calculated with the springs andshocks (and bumpstops and limit straps) installed.

In contrast, suspension travel, meaning the motion of the entire suspension as awhole, has only an actual installed value measured or calculated with the springs andshocks (and bumpstops and limit straps) installed.

Clearly many of these travel terms are interchangeable and may be used in more than onecontext. Care is required when both reading and writing so that confusion may be eliminated or atleast reduced to a minimum. With regards to this article, I shall attempt, as far as possible, to stickto the following conventions:

Referring to shock travel - compression & rebound

Referring to spring travel - compression / deflection & rebound

Referring to ride travel - bump & droop

Referring to flex - bump & droop

Oscillation: Oscillation is a back-and-forth motion. A spring compressing and rebounding is anexample of oscillation.

Force: A force is simply a push or a pull. When we apply a force to something, we push it or pullit. Force = Mass times Acceleration. Load is synonymous – when something experiences a load,it has a force applied to it. Weight is a particular load or force, it is the mass of an objectmultiplied by the acceleration due to gravity, measured in pounds.

An Important Note on Ride Travel

Ride travel is the simplest mode of travel to model and to understand. Modeling the suspension interms of ride travel forms the basis for understanding shock and spring geometry. Once we havea firm grasp of the basics, we can then move on to modelling and design in the other modes oftravel, which are more complicated. For this reason, Part 1 of the Coilover Bible is writtenprimarily with ride travel in mind, unless otherwise specified.

Ride Height (RH)

The height of the chassis or frame above the ground, measured in inches when the vehicle is atstatic rest - i.e. sitting still on level ground.

Ride height is a fundamental component of vehicle design and is arrived at through carefulconsideration of the compromises between ground clearance, suspension travel, and stability.

Suspension Height (SH)

The position in the suspension's travel where the vehicle sits at ride height, expressed as theamount of droop travel available from static rest, quantified by either:

the number of inches of available droop, orthe percentage of total suspension travel that is available for droop.

In the latter case, the following examples illustrate the concept:

Suspension Height 0% = suspension at full droop. No more droop available.





Suspension height 50% = suspension in the middle of its travel. Equal amounts of droop andbump available.

Suspension height 100% = suspension at full compression. No bump available.

Suspension height for high speed desert applications usually varies from 30% to 50%. Suspension height for slow speed rockcrawler applications usually varies from 50% to 70%.

Wheel Travel (WT)

The total vertical travel of the wheel as the wheel goes from full droop to full bump. Can beexpressed for ride travel or flex travel, with values often varying between the two. In this article weshall concern ourselves with wheel travel in ride mode, and discuss other modes in later issues.Wheel travel is a separate value for front and rear axles, although these values can be equal.

There are two "values" for wheel travel – “max theoretical” and “actual installed”.

Maximum theoretical wheel travel is measured with shocks and springs disconnected. It is limitedby link geometry, tire to body clearance, or steering and driveshaft bind.

Actual installed wheel travel is the wheel travel achieved by the complete, installed suspension,including shocks, springs, limit straps and bumpstops.

To measure wheel travel:

Support the vehicle chassis with a lift or jack-stands so that the sprung weight is not on thesuspension.Working on one axle at a time, remove the shocks, springs, and any anti-roll bar if installed(for measurement of "max theoretical" wheel travel only). In ride travel mode, bring the axle (i.e. both wheels) to full droop, measure from the floor tothe centre of the wheel hub, and note the distance. In ride travel mode, bring the axle (i.e. both wheels) to full bump, measure from the floor tothe centre of the wheel hub, and note the distance.Make sure that no suspension link binds with wheels turned to full left and full right. Alsocheck that the desired tire to body clearance is maintained, check all other components(brake components, brake lines, wires, sensors, drive-axles, drive-shafts, CV joints, U-jointsand etc.) to make sure they can function properly and that there are no clearance issues.The difference between the two noted distances is the wheel travel.

Droop Travel (DT)

The amount of wheel travel, measured from static rest, available for suspension droop. May beexpressed as a length, in inches, or as a percentage of total available wheel travel. Whenexpressed as a percentage of total available wheel travel, it is known as suspension height.

Droop travel is also known as down travel, droop, or rebound travel,

Bump Travel (BT)

The amount of wheel travel, measured from static rest, available for bump, or compression. Maybe expressed as a length, in inches, or as a percentage of total available wheel travel. Equal tototal wheel travel minus droop travel (suspension height).

Coilovers

A coilover shock is a high quality mono-tube shock that includes provisions to mount coil springs on the shock.The springs and shock are therefore combined in a single, compact package. There is nothing particularlymagical about coilover shocks – their use requires strict attention to mounting geometry, spring rates, andshock valving the same as any other system. However, they do offer a number of advantages:

High quality, long-travel, mono-tube shock.Completely rebuildable - parts are available separately at very reasonable cost.Easy to package - compact, easy to fit, frees room for link geometry and steering.Revalveable - easy to adjust or modify valving to suit needs.Tuneability - with a vast array of spring lengths and spring rates available, coilovers allow you to selectspring rate for a specific target suspension frequency, and then use spring length and the built in adjusterto achieve a target ride height / suspension height.Multiple spring rate - easy to set up for use with a combination of springs, providing a soft initial springrate that transitions to a firmer spring rate as the suspension compresses.Adjustability - built in adjustable top spring seat provides ability to adjust ride height, suspension height,& preload as well as accommodate different length springs with different amounts of spring travel.Adjustable stop ring provides ability to adjust position where spring rate transition occurs.

Don’t worry if not all of those statements make complete sense to you at this stage – they will by the end.





Let’s go over the different types of coilovers and then dig in to the parts and their functions.

Most coilover shocks will fall into one of the following three categories:

Remote reservoirPiggybackEmulsion

Remote Reservoir coilover shocks are the most common. They arenitrogen-charged mono-tube shocks and are commonly available withup to 18” of travel. They use a remote reservoir to house the nitrogencharge and floating piston, allowing the use of a shorter tube than wouldotherwise be necessary. The reservoir is connected to the pressure tubewith a short, flexible hydraulic hose. Swivel fittings and different lengthhoses are easily installed providing flexible mounting options for thereservoir.

Depending on the position of the piston in its travel, there will also be acertain amount of oil in the remote reservoir. Theoretically, depending onthe mounting location of the remote reservoir, this could provide aslightly improved cooling capability – but this is not the primary purposeof the remote reservoir. Then again, if the reservoir is mounted too closeto a heat source (engine, exhaust) this could cause a detriment tocooling.


A piggyback coilover shock is identical to a remote reservoir shockexcept that the reservoir, instead of being attached to the shock with aflexible hydraulic hose, is mounted directly on the shock with a bracketthat incorporates the necessary hydraulic passage between the cylinderand the reservoir. Because of this they can be more of a challenge tofit. Technically, both a remote reservoir shock and a piggyback shockcan be mounted upside down and still work – although there’s noreason to do so and every reason not to, as the reservoirs would bevery vulnerable in that position.


An emulsion coilover shock has no reservoir and no floating piston. It isstill a gas-charged mono-tube shock, but the nitrogen charge iscontained in the pressure tube along with the oil in an emulsion. Lessresistant to aeration, foaming, and fade than the external reservoirstyles, they are best suited to light weight and / or low-speed use. Theyare more compact and therefore easier to fit than the other styles. Alsomore economical than the other styles, they are usually adequate forrockcrawling use. An emulsion shock can only be mounted right side up.


There are also a few non-emulsion, non-reservoir mono-tube coilover shocks available on the market. Thisstyle incorporates the reservoir and the floating piston into the main shock tube, and is sometimes called an"internal reservoir" shock. They are normally available only in shorter to medium travel (up to about 14") as somuch cylinder length is required to internally accommodate the reservoir and floating piston. This style ofcoilover is most commonly seen for application (make / model) specific replacement or upfit.

Shock diameter

Most styles and brands of coilover are available in either 2” of 2.5” diameter. This is the diameter of thepressure tube or shock body. 2.5” shocks are larger and heavier than 2” shocks. Their larger diameter canmake them more of a challenge to fit without limiting clearance between tire and chassis / fender. 2.5” shocksare also more expensive. Either shock can be valved the same, but the larger 2.5” shock will run cooler.Having said that – this is really only important for lengthy higher-speed desert or rock racing type use, asrockcrawling, street use, and trail riding are unlikely to overheat a 2” shock.





The 2” shock uses 2.5” ID springs and the 2.5” shock uses 3” ID springs. 3” ID springs are heavier, moreexpensive, and their availability in numerous different rates (particularly lighter rates favoured by rock crawlers)is more limited than the smaller 2.5” ID springs.

Coliover Operation

There are a great number of tuning and adjustment factors to consider when using coilovers, which we shalldiscuss in detail shortly. For now, it is sufficient to understand that a coilover shock with springs mountedfunctions as a unit that provides both springing and damping. One end of the shock has a fixed, integratedspring seat and is mounted to the axle or suspension. The other end, which incorporates an adjustable upperspring seat, is mounted to the chassis. The springs are installed over the body and shaft of the shock betweenthe fixed lower spring seat and the adjustable upper spring seat. Springs of many different lengths and ratescan be accommodated, which combined with the ability to alter the shock's internal valving, gives a wide rangeof tuneability.

Since the shocks have a great deal of travel (to permit the large amounts of wheel travel needed for offroaduse) a great deal of spring travel is also required to prevent the springs from bottoming before the shock. Inorder to achieve the necessary spring travel a very long spring is required. However, because there is apractical limit to how long a spring can be made before it will tend to buckle, multiple springs are stacked inseries on the shock (one on top of the other) in order to achieve the required spring length.

The most common configuration consists of two springs stackedtogether in series, and is called a "dual-rate" system as frequently thetwo springs have different rates. The upper spring is called the "tender"spring or coil, and the bottom spring is called the "main" spring or coil.

(From this point forward I shall use the terms "spring" and "coil"interchangeably.)

A nylon sleeve, known as the dual-rate slider (DRS), "floats" on thebody of the shock between the two springs. As the springs compressand rebound, the dual-rate slider slides up and down the shock body.

When multiple springs are stacked in series in this manner, the result isa variable spring rate that begins as the (normally softer) rate of thecombined springs and progresses to the (normally stiffer) rate of just themain spring.

The rate is initially soft because both springs are compressing together.When the springs compress far enough, the DRS slides up until it hitsthe stop ring and is prevented from sliding further. At this point, the dualrate slider effectively becomes the upper spring seat, locking out theupper spring. From this point, remaining spring travel occurs at the rateof the lower, main spring alone.

We shall discuss dual-rate systems in great deal, including relevantformulae later. For now it is sufficient to know that stacking multiplesprings gives us the required spring length and allows us to use a softerinitial spring rate that transitions to a firmer rate at some point in thesuspension's travel.

With a basic grasp of how they operate, let's now examine the coilover shock and it components in detail.

(Note: As we've discussed, because a non-emulsion mono-tube shock can be mounted either way up,technically there is no "top" or "bottom" , "upper" or "lower" to the shock. However, the normal method ofmounting the shock is with the cylinder up, attached to the chassis. This protects the cylinder and reservoirfrom damage. There is no practical reason to mount the shock the other way up. In addition it will make my lifeas a writer, and yours as reader, an awful lot easier and less complicated if we agree at the outset that the"top" or upper-end of the shock is the body- or cylinder-end, and that the "bottom" of the shock is the shaft- orrod-end.)





The Schrader valve, located at the end of theremote reservoir is used to charge the shock withnitrogen.

This remote reservoir is 2" in diameter, and 11"long.

The remote reservoir is connected to the shockcylinder with a braided stainless steel hydraulichose; this one is 14" long.





The top end of the shock has a spherical bearingfor mounting to the chassis.

The cylinder is threaded for a portion of its length,allowing adjustment of the position of the topspring seat.

This adjustability of the top spring seat is a keyfeature of coilovers, and allows us toaccommodate different length springs as well asadjust ride height, suspension height, and springpre-load - each of which we will define anddiscuss in detail later. The top spring seat is alsofrequently know as the "adjuster."

There is a locknut to lock the adjuster in position.

In addition to allowing adjustability of the topspring seat, the threaded portion of the cylinderalso allows the position of the stop ring to beadjusted.

The position of the stop ring is used to define thepoint where the dual rate slider will stop sliding. Atthis point in the shocks / springs travel, the springrate transitions from the softer initial combinedspring rate to the stiffer, final rate of the mainspring.

The point in the shocks travel where this transitionoccurs is called the transition point. Thus, we cansay the stop ring is used to set the transitionpoint.

Once its position has been determined, on a Foxshock the stop ring is secured in position with twosmall Allen-head grub screws that engage agroove machined along the length of the threadedportion of the cylinder.

Other shocks may use a different arrangement forthe stop ring, such as two nuts that lock againstone-another.

The dual-rate slider "floats" on the body of theshock. It is positioned between the main andtender springs. As the springs compress andrebound, the dual-rate slider slides up and downthe cylinder. When the springs compress farenough, the dual-rate slider slides up until it hitsthe stop ring and is prevented from sliding further.At this point, the dual rate slider effectivelybecomes the upper spring seat, locking out thetender spring. At this point, remaining spring /shock travel occurs at the rate of main springalone.





The shock body (a.k.a. the cylinder or the tube)and associated hardware.

View of the rod, or shaft, where it enters thecylinder.

The bearing cap incorporates a wiper seal toclean the shaft of contaminants as it enters thecylinder, and an internal rod guide to keep theshaft supported and aligned.

At the rod-end of the shock there is anotherspherical bearing for mounting the shock to theaxle or suspension.

The lower spring seat is fixed at this end.

There is a small rubber bumper mounted on theshaft and resting on the lower spring seat. It is nota true bumpstop designed to handle the forces ofbottoming the suspension at speed. Instead, it ismerely designed to prevent damage that couldotherwise occur from the lower spring seatcontacting the bearing cap at full shockcompression.





View of an installed shock without springs.

The springs are installed on the shock betweenthe lower spring seat and the top spring seat or"adjuster".

Because the coil springs are mounted on theshock, spring travel must equal the shock travel.That is, the amount the springs change lengthfrom full bump to full droop must equal theamount the shock changes length from full bumpto full droop.

If the shock is setup to provide a great deal ofdroop, often the main and tender springs are notlong enough to span the gap between the springseats when one wheel is at full droop.

The result is, the springs fall away from the topspring seat and rattle around, possibly damagingthe shock.

The solution is to install a small spring, called a"helper coil" between the top spring seat and theother springs. Another slider, called the "triple rateslider", fits between the helper coil and the tendercoil.

Technically, with a helper coil installed, there arenow three springs installed on the shock, and theconfiguration is known as a "triple-rate" setup.

The helper coil is a short, flat-wound spring withvery little stiffness. It can easily be compressed byhand. Resting between the top spring seat andthe tender coil, it is compressed completely flat oninstallation. However, once the suspension nearsfull droop, it expands, exerting just enough forceto keep the tender and main coils in place andprevent them from rattling around.

Use of a helper-coil is an important considerationin selecting spring rates and lengths that we shallcover in detail later.

Typically a helper coil will have a free length of 5”,a compressed height of 0.5” and a rate of only 2lbs/in.





A complete triple-rate coilover setup.

This picture shows a complete triple-rate coiloversetup installed on the rig. Note how, at rest (calledstatic ride height), the helper coil is compressedflat.

Upper end of the installed coilover at static rideheight.





Installed main and tender coils separated by thedual-rate slider.

Installed triple-rate coilover at full droop. Note theextended helper coil between the top spring seat(adjuster) and the tender coil. Also note thetriple-rate slider between the helper coil and thetender coil.

Here the helper coil is exerting just enough force tokeep the springs seated.

Additional hardware required for a coilover setupincludes:

The shock mounting bushings, which installbetween the vehicle's mounting tabs and theshock's spherical bearings, to provide adegree of misalignment capability to the endsof the shock; andThe rubber mounts and clamps used tosecure the remote reservoir to the chassis.

Interim Summary:

We've covered a lot of ground to this point, so let's do a brief summary before we forge on.

Suspension provides ride and handling - it's chief jobs are to prevent the wheels from loosing contactwith the ground over rough terrain and to isolate occupants from that rough terrain.Springs support the weight of the vehicle and absorb the road shock of bumps and holes by compressingand rebounding.Shocks damp the oscillation of the springs by pumping a piston through a column of hydraulic oil.The amount of damping a shock provides depends on its valving.Springs and shocks combine to determine whether a suspension is firm or soft.Spring and shock selection is a careful compromise between ride and handling.Coilovers are an ingenious way to package shocks and springs as one convenient assembly.Coilovers are long-travel, high quality, revalveable, gas-charged, mono-tube shocks.Coilovers use two or more coil springs in dual- or triple-rate setups, allowing a soft initial spring ratefollowed by a firmer spring rate as the suspension compresses.





Great. So how do we go about getting the best performance from our coilover shocks? How do we mostclosely approach that magical balance between ride and handling, between firm and soft suspension? Whatare our goals?

The Seven Goals of Suspension Design

Designing suspension is a matter of achieving the best balance between these often competing goals:

Desired suspension frequency1.Desired suspension height2.Desired ride comfort3.Acceptable roll resistance4.Desired flexibility*5.Matched wheel, spring, and shock travel6.Desired ride height7.

(* by flexibility we mean the ability of the rig to apply enough force (weight) at each corner to flex / articulatethe suspension enough to make use of all the wheel travel (bump) available. If springs are too stiff, wheel willstuff, then start lifting corner before full bump is reached)

While avoiding

Bottoming out the shocks1.Coil-binding the springs2.Springs coming loose and falling out on full shock extension3.

Before we design our coilover system, though, the following preliminary work must be completed. With theexception of the last point, for the purposes of this article, I shall assume these have all been completed:

Chassis fabricatedTire size decidedMulti-link suspension designed and builtRide height decidedMax theoretical wheel travel calculatedCoilover mounting geometry decided and checked for clearances between shock / spring and tires /chassis

With all that done, we have the information required to begin our coilover system. The first steps are:

Decide on the size (diameter) of the shock required. We already covered the differences between 2" and2.5" coilovers - most of us will be best served by a 2" coilover. If you choose a 2.5" or larger shock, beaware that you may have to revisit this decision later if the springs you require are not available for thatsize shock.Based on the wheel travel you have and the mounting points chosen, calculate the length of shockrequired to give the total wheel travel. DO NOT choose a super-long shock just because it sounds cool -if it's longer than you need it will cost more, weigh more, be more expensive to buy springs for, will likelybe more difficult to fit and may even limit the compression travel of the suspension.

The next step is to select some preliminary spring rates. There are many factors that go into any suspensiondesign intended to satisfy the seven goals, including: spring rates, shock length, spring length, shock / springmounting geometry, link geometry, shock valving, and the use of tools such as bumpstops, limit straps, andanti-roll bars. Spring rate, or how stiff the spring is, will affect all seven of the suspension design goals, sopicking spring rates seems a logical place to start. This is normally what we do. But first, there is one very, veryimportant point I wish to make, and that is:

The problem with spring rate is that so many people treat it as it was the goal, instead of anecessary calculation to arrive at the seven goals stated above. Keep in mind that spring rateselection is a means to an end, not the end itself.

Of course, before we go about picking spring rates, we must first understand some basic spring theory.

Spring Theory

A coilover spring is a compression coil spring, that is, a spring that is designed to carry a load by compressing.

It will have the following properties - as illustrated in the diagram:





Inside Diameter (Di)Wire Diameter (Dw)Mean Diameter (Dm)Number of Active Coils (Na)Spring Rate (k)Free Length (Lo)Block Height (Lc)Travel (max defection) (Sc)Force Limit (Fc)

Let’s examine each property in turn:

Inside Diameter (Di)

A spring’s diameter may be measured as the outside or inside diameter. Because coilover springs aredesigned to fit over a particular size of shock, we are most concerned with the inside diameter. For clearancewhen compressing and extending, a 2.5” ID spring goes on a 2” shock , and a 3” ID spring goes on a 2.5”shock.

Wire Diameter (Dw)

The spring’s wire diameter is the diameter of the wire from which the spring is wound.

Coil Mean Diameter (Dm)

The spring’s coil mean diameter is the diameter of the spring measured between the centres of the coils. It isequal to the inside diameter plus the wire diameter.

Dm = Di + Dw

Number of Active Coils (Na)

The number of active coils in a spring is the number of coils that are free to compress under load. Normallythis is equal to the total number of coils minus two (i.e. minus the coil at each end). This is because the coil ateach end is fixed against its spring seat and therefore unable to compress.

Spring Rate (k)

Coil springs have a rate – a description of how stiff they are. The rate describes how much the spring willdeflect (compress) for a given load (weight) placed on it. The rate is measured in pounds per inch. The greaterthe rate, the stiffer the spring, and the more pounds of load it takes to compress the spring one inch.

Four things determine a coil spring’s rate:

The material from which it is made (the “torsional modulus” of the material, in psi)1.The diameter of the wire from which the spring is wound (Dw)2.The diameter into which the coils are wound – the Coil Mean Diameter (Dm); and3.The number of active coils in the spring (Na)4.

Virtually any spring that is of interest to us will be made from chrome silicone steel, which has a torsionalmodulus of about 11,250,000 psi, so that when we calculate a spring’s rate based on its dimensions, thetorsional modulus becomes a constant.

The equation for calculating a spring’s rate from its dimensions is:

k = 11,250,000 * (Dw)^4 / 8 * Na * (Dm)^3

By examining this equation, we see that the only dimensions affecting the spring rate of a steel coil spring areits wire diameter, coil mean diameter, and the number of active coils it has.

The following table illustrates how altering these dimensions affects a spring's rate:

Dimension Change Effect onRate

Wire Diameter (Dw) Increase Increases

Decrease Decreases





Coil Mean Diameter (Dm) Increase Decreases

Decrease Increases

Number of Active Coils (Na) Increase Decreases

Decrease Increases

Since coilover springs have to have a fixed ID to fit on a given shock, the coil mean diameter for every springfor a certain shock is essentially fixed. This means, for coilover springs, the only two remaining factors that canbe adjusted to create different rate springs are the wire diameter and the number of coils.

For a given diameter shock, a stiffer spring will have fewer coils and / or be made from thicker wire.Conversely, a softer spring will have more coils or be made from thinner wire.

Similarly, for a given rate spring, a larger diameter spring (for a larger diameter shock) will have fewer coils and/ or be made from thicker wire than a spring with the same rate for a smaller diameter shock.

In practical terms this results in the following rules of thumb:

For a given diameter and length, a softer spring will have more coils and therefore possibly less traveland a higher block height.For a given rate and length, a larger diameter spring (as required by a larger shock), will have fewer coilsand therefore possibly more travel and a lower block height.

That said, springs are available commercially in a huge variety of lengths, diameters, and rates. The differencebetween a 2.5” and 3” spring of the same rate and length is so little that it should not be used as thedetermining factor in deciding which size shock to buy.

To measure actual spring rate, we use the equation:

Spring Rate (lbs./in.) = Load (lbs) / Deflection (in.)

A coil spring’s rate can either be constant or progressive. In a constant-rate spring (also called a linear spring),the spring’s rate is consistent* throughout the spring’s travel (deflection). In a progressive rate spring, thespring rate changes throughout the spring’s deflection. Progressive rate springs are easily identified as thecoils will not all be wound the same diameter. We shall confine our remaining discussion to constant-ratesprings, as they are the type used on coilover shocks.

* Technically, even a “constant rate” spring doe not have a truly constant rate throughout its entire deflection,but in a good spring the rate will be constant for at least 80% of the spring’s travel, excluding perhaps the firstand last 10%. During the first part of its travel the rate is lighter until the ends touch. During the last part of itstravel the rate will increase because not all the coils bottom out at the same time - the end coils tend to bottomout first. However, since we rarely use the spring dynamically in the first or last 10% of its travel (the first 10%is consumed when we set the vehicle’s weight on the spring, and we don’t load the springs to totalcompression (block height) often enough to worry about the last 10% of travel) we may consider the spring tobe linear or “constant rate” for our purposes.

Free Length (Lo)

A spring’s free length is the length it is when at rest with no load on it. Also called “free height”.

Theoretically, it is only limited by when the manufacturer stops winding the wire into coils.

There are practical limitations as to how long a coil spring can be made, though, depending on its diameter.Excessively long, small-diameter springs tend to buckle under load. This is the reason why most 18” longsprings are only available in 3” ID and not 2.5” ID.

To build a spring with a different free length while maintaining a given rate, the distance between full turns ofthe coil (the space between each coil of the spring) is increased or decreased to increase / decrease the freelength. In this manner, all the factors that affect spring rate (coil mean diameter, wire diameter, and number ofactive coils) remain the same so the rate doesn't change but we get a different length spring.

Properly engineered and manufactured suspension coil springs should not lose free length or installed heightunder normal conditions.

Block Height (Lc)

A spring’s block height is it’s length or height when it can be compressed no more. When a coil spring is atblock height it is compressed to its maximum and all its coils will be squished up together and touching. This isreferred to as “coil bind”. Block height is also known as “solid stack height”.

Spring Travel (Sc)





A spring’s travel, or maximum possible deflection, is the difference between it’s free length and its block height.Also known as maximum displacement.

Force Limit (Fc)

A coil spring’s force limit is the force (or load or weight) on it when it is at block height. It is the maximum loadthe spring can withstand without damage. It is also the load that must be applied to fully compress the spring –i.e. to use all of its travel. This is important to us for two reasons – it tells us how much load we can place onthe spring, but just as importantly it tells us the load we must place on the spring to use all of its travel. This isparticularly important in designing long-travel suspension where we are trying to make the most of all thespring travel we have to match the amount of wheel travel we have from using long-travel shocks and linkedsuspensions.

Dual-Rate Springs

As we've discussed, suspension design is a precise balancing act. On one hand, the spring system should besoft enough to allow required flex for rock crawling and to compensate for road and trail irregularities, assuringmaximum traction and providing a comfortable ride. On the on the other hand the spring system must be firmenough to control the wheels over big and fast bumps, and provide adequate resistance to roll, squat, and diveduring climbing, descending, side-hilling, cornering, acceleration, and braking.

An advantage to coilover suspension is that this perfect balance can be more closely approached by using adual-rate system.

By selecting two springs from amongst hundreds of individually available springs and combining them inseries, a huge number of possible initial and final spring rates is achievable.

The position of the stop-ring is set to stop the travel of the DRS before the tender spring binds, reducing wearon the tender spring, but, more importantly, allowing the user to tune where in the vehicle’s wheel travel thetransition from soft initial rate to firm final rate occurs. In general the stop ring is located so that the final ratecomes into effect in the last 20% to 40% of the shocks compression travel. This way the suspension will havea higher wheel rate for the last 20% to 40% of total travel before the shock bottoms out.

The initial spring rate of a dual-rate system is calculated as the product of the individual spring rates divided bythe sum of the individual spring rates, according to the following formula:

Ki = (Km * Kt) / (Km + Kt)

Where:

Ki = Initial Spring Rate (of combined springs)Km = Spring Rate of Main SpringKt = Spring Rate of Tender Spring

The final spring rate (effective after the tender spring binds or the DRS has hit the stop) is simply the rate ofthe main spring.

Kf = Km

Terms

You may read many different names for different springs in a dual-rate coilover system.

For example:

The main spring is sometimes called the: primary spring, lower spring, bottom spring, or heavyspring

The tender spring is sometimes called the: secondary spring, top spring, upper spring, or lightspring

The helper spring is sometimes called the: droop spring, flat spring, spacer spring, or sometimeseven the tender spring (really confusing).

I prefer to stick with the following names: from top to bottom on the shock - helper spring / tenderspring / main spring.

You may also see where sometimes the initial spring rate (of the two springs) is called the:primary spring rate or combined spring rate; and the final spring rate is called the: secondaryspring rate or main spring rate.

I prefer to avoid confusion between the names of the springs and the names of the rates.Therefore I use main and tender springs to achieve initial and final spring rates. This has theadded benefit that the name of the rate is descriptive of where it occurs in the suspension's travel.

In particular, I think the terms primary and secondary should be avoided when referring to thesprings, because we may otherwise end up saying “The primary rate is the combination of the





primary and secondary spring rates and the secondary rate is the same as the rate of the primaryspring (the primary spring rate?)” - very circular and confusing!

Now that we have a good understanding of spring theory, we are almost ready to move on to selecting springrates. But before we do, we must first cover a a few more key definitions and explore the concepts of leverageand the "installation ratio".

Key Suspension Definitions

Corner Weight (CW)

The total weight of the vehicle at that corner. I.e. the weight shown if that corner were to beweighed by driving only that corner’s tire onto a scale.

Corner Sprung Weight (CSW)

The weight of the vehicle, at that corner, that is supported by the springs.

Corner Unsprung Weight (CUW)

The weight of the vehicle, at that corner, that is not supported by the springs and moves with thewheel. Equal to the weight of the tire, wheel, and brakes at that corner, plus half the weight of theaxle, plus half the weight of the links, shocks, and springs at that corner.

CSW = CW – CUW

Step-up Ratio (SUR)

The percentage by which the spring rate jumps at the transition from the initial (combined) springrate to the final (main) spring rate.

SUR = main spring rate / combined spring rate * 100% = (Kf / Ki) *100%

Shock Travel (ST)

The maximum possible travel of any shock is determined by the difference between the fully openand fully closed lengths of the shock. Coilover shocks are normally specified by the OD of thecylinder (e.g. 2.0”) and their max travel (e.g. 14", 16", 18”)

To calculate the max shock travel of any shock, subtract the length of the fully compressed shockfrom the fully open shock (or refer to the manufacturers literature).

To calculate the shock travel you require (i.e. what length shock to buy):

Support the vehicle chassis with a lift or jack-stands so that the unsprung weight is not onthe suspension.Working on one axle at a tim, remove the shocks, springs, and any anti-roll bar if installed. In ride travel mode, bring the axle (i.e. both wheels) to full droop.Measure between the upper and lower shock mounts and note the distance as extendedshock length.In ride travel mode, bring the axle (i.e. both wheels) to full bump .Measure between the upper and lower shock mounts and note the distance as compressedshock length.Make sure that during the axle's full range of travel, in both flex and ride modes, nosuspension link binds with wheels steered to full left and full right. Also check that thedesired tire to body clearance is maintained, check all other components (brakecomponents, brake lines, wires, sensors, drive-axles, drive-shafts, CV joints, U-joints, etc.)to make sure they can function properly and that there are no clearance issues.Extended shock length minus compressed shock length equals the shock travel required.

Shock travel should not be confused with wheel travel. Shocks should be installed so as to notlimit wheel travel. Depending on the position and angle at which they're installed, wheel travelcan be much greater than shock travel. The relationship between shock travel and wheel traveldepends on the installed position and angle of the shock, and is called the installation ratio. Weshall explore the concept in detail shortly.

Finally, although shocks should be selected and installed in such a way that the shock travelallows the most possible wheel travel, the shocks themselves should not be relied upon toactually act as the physical limiters to wheel travel - that is a job for limit straps and bumpstops. Inother words, we must avoid using a length of shock or shock installation that could lead to shocktop-out or shock bottoming.

Shock Top-out

Shock top-out occurs when droop travel (at the wheel) exceeds the shock’s available droop traveland the shock is forced to be the physical limit to droop. At top-out, internally, the shock piston





bottoms against the bearing cap which will likely cause damage.

Shock Bottoming

Shock bottoming occurs when bump travel at the wheel exceeds the shock’s available bumptravel and the shock acts as the bumpstop. This should be avoided to prevent harsh ride andshock damage. The small rubber snubbers that come installed on the shaft of many coilovershocks are intended to prevent shock body to lower spring-seat contact but are not sufficient tobe used as a true bumpstop.

Rising Rate

The term "rising rate" as it relates to suspension, refers to some component whose rate increasesas its travel increases. Typically it refers to springs, damping, or the suspension as a whole thatgets stiffer as it compresses. For example, a bumpstop or position-sensitive shock may have arising rate. Also known as progressive rate.

Falling Rate

Falling rate is the opposite of rising rate and refers to some component whose rate decreases asits travel increases. Typically it refers to springs, damping, or the suspension as a whole that getssofter as it compresses. Also known as digressive rate.

As we've just discussed, there is an important relationship between shock travel and wheel travel, known asthe installation ratio, that depends on the position relative to the wheel and the angle at which the shock isinstalled. Because the springs are co-located with the shock in a coilover, this ratio is also important inunderstanding the difference between the force at the wheel and the force on the spring, and by extension, thespring rate at the wheel and the actual rate of the spring as manufactured.

In other words, how, where, and at what angle we install the coilover shock with its installed springs causesthere to be a difference between shock travel and wheel travel, spring force and wheel force, and spring rateand wheel rate (wheel rate being the effective spring rate "seen" or "felt at the wheel.

This is a very important consideration for us because it is the wheel travel, wheel force, and wheel rate thatactually define the characteristics of the suspension and how it will perform. We really don't give a darn aboutthe actual values of shock travel and spring rate (i.e. what's printed on the side of the components), except inthat they contribute to the wheel travel and wheel rate.

For example, if someone says "I have 12 inch shocks and a spring rate of 250 lbs/in" that tells us exactlynothing about their suspension and how it might perform. On the other hand, if someone were to say "I have18 inches of wheel travel, an initial wheel rate of 100 lbs.in and a final wheel rate of 275 lbs.in" now that wouldtell us something. But we're getting ahead of ourselves.

In order to be able to understand (and design with, or compensate for) the differences, we must understandwhere they come from. The answer is "leverage between wheel and shock / spring." and so to fully understandlet's first review some basic leverage theory.

I must make clear one very important point, before we begin:

In the following discussion we shall be talking about ratios, dimensions, and angles. Obviously, a rig'ssuspension is a dynamic, moving thing. But dynamic, moving things are horribly complicated things tomeasure and analyze - especially if you're just starting out. So to begin with, we pick some given fixed staticpoint at which to take our measurements and make our calculations. Normally, and in this article, we use staticride height. This is perfectly adequate for initial design purposes and perfectly adequate for the purposes ofmeasuring the dimensions the BillaVista spring rate calculator (BV Calculator) requires as inputs. But, for thesake of complete technical accuracy - I would be remiss if I didn't point out that in a real working dynamicmoving suspension, dimensions and angles and such can, and do, change - changing the results of anycalculations on a pretty-much continuous basis.

Similarly, in the following discussion, when we speak of wheel travel, we are talking about ride-travel (bothwheels moving up and down together) as opposed to roll travel. With roll travel, there are a whole 'nuther setof variables and angles to consider, which would make things entirely too confusing at first. And again, for ourpurposes at this stage, ride travel is a perfectly adequate, clear, and simple model to use - so we do.

Later in the series we will get into roll travel and it's attendant difficulties. But for now, back to the basics.

Leverage Theory

Leverage is an important concept for us to understand because quite often the wheel will exert some leverageon the shock and spring, which we must account for in our calculations and design. If we could mount thespring on the vehicle at the centre of the wheel hub, perfectly vertical, and the suspension only ever travelledperfectly vertically, we wouldn't have to worry about the effect of leverage and angles in the suspension.Clearly this is impossible, and so we must be concerned with leverage.

The leverage affects displacement (travel), force (load), and rate. The leverage means that wheel travel will bedifferent from spring or shock travel, that wheel rate will be different from spring rate, and that the force felt atthe wheel will be different from the force on the spring. Clearly, important stuff. But let's not get ahead of





ourselves.

We'll begin by exploring the affect of leverage on displacement. That is, we're going to discover why it is thatwheel travel differs from shock travel because of the effect of leverage. In other words, why the position andangle at which the shock is installed means there is a difference between wheel travel and shock travel.

Work is force times distance. W = F x d. By looking at the equation we can see that if work remains constant,increasing force decreases distance or increasing distance decreases force. A lever is a simple machine thattrades force for distance or vice versa. We all use levers every single day. The simplest example is a door.Imagine you open a door by pushing near the hinges. Now imagine you open the same door by pushing nearthe handle. In either case the same amount of work is done. But, when you push near the hinges you mustpush harder (force is greater) but over a smaller distance (distance is less). When you push near the handleless force is required, but you must push for a greater distance. The door is a lever that trades distance forforce - putting the handle on the opposite side of the door from the hinges makes it easier to open.

Normally this is how we think of using a lever - to make things easier. For example, a lever makes it possibleto lift a heavy object with low input force, but requires us to apply the input force for a greater distance than theobject will be lifted. Nothing in life is free - the lever costs us distance and pays us back in force. Let's look atthe parts of a lever and how it works.

The force applied to the lever is called theeffort, or F2. The force the lever produces iscalled the load, or F1. The pivot about whichthe lever acts is called the fulcrum. Thedistance from the effort to the fulcrum is calledthe effort arm or d2. The distance from thefulcrum to the load is called the load arm, ord1.

The Law of the Lever states that:

Load * Load Arm = Effort * Effort Arm, or

F1*d1 = F2*d2

We can rearrange this to calculate F1 if weknow the effort, F2, and the dimensions of thelever (d1 and d2):

F1 = (F2 * d2) / d1.

We can further simplify this equation to develop a ratio that describes the output of the lever for any giveninput force or effort. This multiplication of effort is called the mechanical advantage (MA) of the lever:

MA = d2/d1.

The mechanical advantage is a ratio that describes how much the lever multiplies input force.

Example: Suppose F2 = 100 lbs, d2 = 4 feet, and d1 = 2 feet.

The mechanical advantage of the lever would be d2 / d1= 4 / 2 = 2.

Therefore, for any effort applied, the load will be 2 times as much. In our example the effort, F2, = 100 lbs,therefore the load would equal 2 x 100 lbs or 200 lbs. We can confirm with

F1 = (F2 * d2) / d1 = (100 * 4) / 2 = 400 / 2 = 200 lbs.

By simple algebra we have confirmed what we know from experience: the longer the effort arm (d2) relativeto the the load arm (d1), the more mechanical advantage the lever has.





But remember that nothing in life is free. If alever multiplies force, it costs us distance, ordisplacement.

The ratio of input displacement to outputdisplacement is the opposite, or inverse, ofthe ratio between effort and load. That is, bywhatever factor we increase force, wedecrease distance.

The lever allows us to lift 200 lbs with an effortof only 100 lbs, but in order to lift the 200 lbs 1foot, we must apply the effort for 2 feet. Totalwork done (Work = Force *distance) remainsthe same, the lever just allows us to tradedistance for force.

The difference between the inputdisplacement and the output displacement weshall call the displacement ratio (DR).

We've said that the mechanical advantage and displacement ratio are equal but inverse. That is, if:

MA = d2 / d1 then DR = d1/d2

In the above diagram, using the same lever as in our previous example: d2 = 4 feet, and d1 = 2 feet.

The displacement ratio is: DR = d1/d2 = 2/4 = 1/2 or 0.5.

Meaning the displacement we get out of this lever is half what we put in. Or put another way, in order to geta certain displacement as output, we must put in twice that displacement.

Summary: a lever trades force for distance in equal but inverse ratios.

Not all levers trade distance for force though.Some trade force for distance - that is, theycost force and payout in distance.

By looking at the equations for mechanicaladvantage and displacement ratio, we cansee that the key to how the lever works is therelative length of d1 compared to d2. In otherwords, it matters a whole lot where we put thefulcrum.

Here we have the same type of lever asabove, but the fulcrum has moved - d2 is nowless than d1. This means that this lever willcost us force but pay back in displacement. Inother words, the effort will be greater than theload, but the input displacement will be lessthan the output displacement.

Example: Suppose, as in the picture above, we move the fulcrum so that now d2 = 2 feet and d1 = 4 feet.Suppose also that F2 remains 100 lbs.

MA = d2 / d1= 2 / 4 = 1/2 or 0.5.

DR = d1/d2 =4/2 = 2

Therefore for any effort applied, the load generated will be half as much and for any input displacement theoutput displacement will be twice as much.

There are three different types or "classes" of levers. So far we have looked only at the first class, where thefulcrum is positioned somewhere between the effort and the load. We have seen that, in a first class lever,the lever can either trade displacement for force or vice versa, depending on the position of the fulcrum andthe resultant relative lengths of d1 and d2.





In a second class lever, the fulcrum ispositioned at the end of the lever, the effort isapplied some distance from the fulcrum, andthe load is applied somewhere between thetwo.

However, the law doesn't change, and neitherdo the definitions. Ahhh the beauty of mathand physics!

Remember how, with a first class lever, thelever could either increase or decrease effort?In contrast, if you study the diagram at left andthe equations:

MA = d2/d1 & DR = d1/d2

you should be able to see that the secondclass lever can only trade distance for force. Itcosts distance and pays out force. That is,load will always be >= effort and outputdisplacement will always be <= inputdisplacement.

Mathematically, MA >=1 & DR <=1.

(For the advanced student in the class - if you're wondering why the heck I'm dragging you through all this -look at the second class lever above and imagine the effort is the wheel, the fulcrum is the suspension pivotpoint, and the load is the coilover! Ah-ha! Don't worry, we'll get to it all in good time!)

At the other end of the scale is the third classlever, pictured at left.

In a third class lever, the fulcrum is at the endof the lever, the load is applied some distancefrom the fulcrum, and the effort is appliedsomewhere between the two.

Once again, neither the law nor the definitionschange.

MA = d2/d1 & DR = d1/d2

Again, by studying the diagram at left, youshould be able to see that the third class levercan only trade force for distance. It costs forceand pays out in distance.That is, load willalways be <= effort and output displacementwill always be >= input displacement.

Mathematically, MA <=1 & DR >=1.

Summary of lever types:

Class Cost Payback Note Examples

1 Displacement ForceIf fulcrumpositioned so thatd2 > d1

Bottle opener,crowbar.

1 Force DisplacementIf fulcrumpositioned so thatd2 < d1

Catapult.

2 Displacement Force Diving board , wheelbarrow, door, 4-link with shockmounted on lower control arm.

3 Force Displacement Broom, baseball bat.

Bottom line: a lever trades force for distance in equal but inverse ratios. If we know one ratio, we knowthe other. Depending on shock mounting geometry, if there is a lever created between wheel (effort) andshock (load), then the displacement of the wheel (wheel travel) will differ from the displacement of the shock(shock travel).

The Angle Factor





Just as leverage between wheel and shock (created by where we mount the shock) can create a differencebetween wheel travel and shock travel, so to does the angle at which we mount the shock. That is, the angle atwhich me mount the shock creates a difference between wheel travel and shock travel.

If we mounted the shock vertically, (at an angle of 0° fromvertical) then there would be no difference between shocktravel and wheel travel.

For every inch the wheel goes up, the shock compressesone inch.

Using a ludicrously extreme example for illustrativepurposes:

if we mounted the shock laying flat (at an angle of 90° tovertical) then shock travel would equal 0, regardless ofwheel travel.

In this configuration, no matter how much the wheeltravels vertically, the shock would just pivot on itsmountings, but wouldn't compress at all.

Although this example is completely impractical, itdemonstrates that as the angle increases the shock traveldecreases compared to wheel travel.

If we mount the shock at 45° from vertical, the relationshipbetween shock travel and wheel travel is not soimmediately apparent, although we know it depends onthe angle, and we know the shock travel will be somethingless than the wheel travel.

But by how much? Wouldn't it be great if there was a ratiothat related shock travel to wheel travel in terms of theangle?

Well, there is. I'll save you the trigonometric derivation, butit turns out that the shock travel depends on the cosine ofthe angle between the shock and vertical. We call theangle 'alpha'.

That is, the ratio that describes the relationship betweenshock travel and wheel travel is cos(alpha). We call thisratio the "angle correction factor" or ACF.

ACF = cos(alpha)

That's it. We now understand the two factors that describe the relationship between wheel travel and shocktravel in terms of the mounting position and angle of the shock.

Mounting position of the shock creates leverage. Leverage modifies the shock travel compared to the wheeltravel by the displacement ratio (DR). You may see the displacement ratio referred to in some circles as the"motion ratio" or MR.

Mounting angle of the shock modifies the shock travel compared to the wheel travel by the ratio we call anglecorrection factor (ACF).

DR = d1/d2

ACF = cos(alpha)

For simplicity and elegance, we combine both of these factors into a single factor, or ratio, that describes therelationship between wheel travel and shock travel for any position or angle at which the shock / spring ismounted.

We call it the installation ratio, or IR.





IR = DR * ACF

For conciseness I shall forthwith refer to the "position and angle at which the shock / spring is mounted" assimply the "shock geometry".

Installation Ratio

So the installation ratio is a dimensionless ratio that relates wheel travel to shock / spring travel, as follows:

shock travel is equal to wheel travel multiplied by the installation ratio; or

ST = WT * IR, and therefore, WT = ST / IR, and IR = ST / WT

and since IR = DR * ACF; and

DR = d1/d2; and

ACF = cos(alpha)

All we need to know are the dimensions d1 & d2 and the angle alpha and we can calculate shock travel fromwheel travel or wheel travel from shock travel; for the particular shock geometry.

Since IR is a ratio of displacement, or travel, the most obvious uses then would be:

calculating the max theoretical wheel travel that can be achieved for any given shock length and / orshock geometrycalculating the length of shock required to achieve a certain wheel travel for a given shock geometrycalculating the required shock geometry to achieve a certain wheel travel for a given length shock

The IR's usefulness doesn't end there though.

Just as there is a difference between between wheel travel and spring travel due to leverage and angle, sothere is also a difference between the actual spring rate of the installed coil, and the spring rate experienced atthe wheel due to this leverage and angle. This "effective" spring rate at the wheel is called the wheel rate(WR). Most people like to quote and compare spring rates. Stopping them from doing this is one of the mostimportant objectives I had in mind when starting this project. I want to get people to stop asking, "What springrate are you running?" and start asking, "What wheel rate are you running?". Why? Because essentially, springrate alone is completely meaningless without knowing how the spring / shock are installed. Now, we could say,"What's your spring rate and where is the shock located, and at what angle, and what are your d1 & d2dimensions?", but that would be painful. Instead, we have the term "wheel rate" which takes all that intoaccount - it describes the effective spring rate at the wheel by taking into account the shock / spring'sinstallation. Before we look at exactly how it does that, we should understand that it is the wheel rate, and notthe spring rate that:

determines ride height & suspension height (or frequency) for a given corner sprung weight, ANDdefines how the suspension will perform. Wheel rate tell us how the wheel will react to being loaded bybumps and potholes. Wheel rate dictates how the vehicle's ride feels as well as how it handles andperforms including its roll stiffness and how well the axle will articulate (is there enough unsprung cornerweight to fully stuff the wheel with the given wheel rate?).

So what is the relationship between wheel rate and spring rate and what does the difference between wheeltravel and shock travel (the installation ratio) have to do with it?

Recall that the wheel acts on the spring through a lever and a lever trades force for displacement in equal butinverse ratios. The lever created between wheel and shock / spring trades wheel travel for wheel force (or viceversa, depending on the class of lever the suspension geometry matches) - just like a simple lever. If we knowone ratio, we know the other.

In other words, if we know the ratio by which wheel travel and shock / spring travel differ, we also know theratio by which wheel force and spring force differ. And of course we know this ratio - it is the installation ratio.

We can measure the d1, d2, and alpha of our spring installation (an example of how will follow shortly) andcalculate IR from

IR = DR * ACF = (d1/d2) * cos(alpha)

Now, remember what we were originally after was the difference between the wheel rate and the spring rate.

Well, since rate = force / distance, and we know by how much the distance differs (the IR), we also know howmuch the force differs - it's the same ratio.

So, to calculate wheel rate from spring rate - if we know the original spring rate (and we ought to as we boughtthe springs!) and we know the force ratio and the distance ratio we can calculate the wheel rate. And of coursewe know the ratios - they're the same, namely, the installation ratio. Since the ratio affects both force anddistance (remember the lever example) we must apply it to the spring rate twice to get the wheel rate. Theequation is:

WR = k * IR * IR





orWR = k * IR^2

where:

WR = wheel rate (lbs/in)

K = spring rate (lbs/in); and

IR = installation ratio.

Summary

In summary, because of the way a lever works, the difference in travel tells us all we kneed to know tocalculate the difference in rate between the spring and the wheel.

We know a lever has a ratio that depends on the placement of the fulcrum. We know this ratio affectsboth force and displacement - the longer the lever - the more our force input is multiplied and the moreour displacement input is reduced.

1.

We know suspension geometry creates a lever between wheel and spring, and that the placement of thespring and the angle both play a role in defining the lever.

2.

We know this suspension lever has a measurable and calculable ratio (IR) that affects force anddisplacement.

3.

We know that a rate, such as a wheel rate, is force / displacement.4.Since the IR affects force AND displacement, it affects a RATE twice - once for force and once fordisplacement.

5.

So it is intuitive to understand that to go from one rate to another when there is a lever between them (asis the case between spring rate and wheel rate), the ratio of said lever (i.e. the IR) must be applied toboth force and displacement. That is IR must be applied twice and thus WR = k * IR * IR = k* IR^2.

6.

The following says the same thing algebraically, for the mathematically inclined:

Summarypoint Math Words

1.MA = d2 / d1 Mechanical advantage = effort arm divided by load arm

DR = d1/d2 Displacement ratio = load arm divided by effort arm

2.

DR = d1/d2The displacement ratio of our suspension's lever is the distance from thespring (load)to the suspension pivot (fulcrum) divided by the distance from thewheel centre (effort) to the suspension pivot.

ACF =cos(alpha) The greater the angle of the spring, the softer it will seem to be at the wheel.

IR = DR *ACF

The total "leverage ratio" of our suspension is the displacement ratiomultiplied by the angle correction factor

3.

WT = ST / IRDisplacement at the wheel = displacement at the spring/shock divided by theIR. Wheel travel = shock travel divided by IR. This is the affect of oursuspension lever on displacement.

Fw = Fs * IR Force at the wheel = Force at the spring times the installation ratio. This is theaffect of our suspension lever on displacement.

The leverage ratio, IR, affects force and displacement in equal but opposite ways.

4.Fs = k * ST Force at the spring in pounds = spring rate in lbs/in multiplied by deflection at

the spring (or spring travel, ST) in inches.

Fw = WR *WT

Similarly, force at the wheel in pounds = wheel rate in lbs/in multiplied bydeflection at the wheel (or wheel travel, WT) in inches.

5.

WR = k *IR^2

OK, let's prove this algebraically, using the above equations:

Starting with the definition of rate being force divided by displacement, at thewheel we have:

WR = Fw / WT - wheel rate = force at the wheel divided by wheeltravel.

Now, Fw = Fs * IR - force at the wheel = force at the spring times theinstallation ratio (the leverage ratio applied to force)

So, substituting for FW, we now have:

WR = Fs * IR / WT

Now, WT = ST / IR - wheel travel = spring travel divided by the instillationratio (the leverage ratio applied to displacement)





So, substituting for WT, we now have:

WR = (Fs * IR) / (ST / IR)

By algebra, dividing by something is the same as multiplying by its inverse, sowe can rearrange to:

WR = (Fs * IR) * (IR / ST)

Remove the brackets as they were for clarity and not order of operations, wehave:

WR = Fs * IR * (IR / ST)

Rearranging without violating order of operations, we get:

WR = Fs / ST * IR * IR

Since Fs / ST is force at the spring divided by spring travel (deflection of thespring) it is, by definition, spring rate, or k. So substituting k for Fs/ST wehave:

WR = k * IR * IR

And simplifying gives us:

WR = k * IR^2

Wheel Rate = spring rate multiplied by the installation ratio squared. Ta-da!!

Q.E.D.

The Big Five

All this theory simply uses the laws of leverage (force and displacement ratios) to relate six things:

the displacement at the wheel and the displacement at the shock / spring (wheel travel vs. shock / springtravel)the force at the wheel and the force at the spring

and combining these two

the spring rate at the wheel and the spring rate at the spring (wheel travel vs. k)

These relationships can be boiled down to what we call the "big five" equations. These equations are the base,root equations for almost all spring / suspension work. They are the equations boiled down to their most basicform - from which all other equations can be derived. The "big five" and their descriptions are:

IR = Ds / Dw -- installation ratio equals displacement at the spring/shock divided by displacement at thewheel (i.e. IR = ST/WT -- installation ratio equals shock travel divided by wheel travel.)

1.

Fw = Fs * IR -- force at the wheel equals force at the spring times the installation ratio.2.Dw = Ds / IR -- displacement at the wheel equals displacement at the shock / spring divided by theinstallation ratio (technically, just a rearrangement of equation 1)

3.

Fs = k * Ds -- force at the spring equals the spring rate times the displacement at the spring (arearrangement of the definition of spring rate: k = force / displacement)

4.

Fw = WR * Dw -- force at the wheel equals wheel rate times the displacement at the wheel (again, arearrangement of the definition of spring rate: k = force / displacement, but at the wheel instead of at thespring)

5.

Let's summarize our new terms and then proceed to a concrete example.

More Definitions

Displacement Ratio (DR)

Displacement ratio is the mathematical ratio that expresses the relative lengths of the parts of a lever(effort arm and load arm). This ratio describes the relationship between wheel travel and shock travelthat results from the lever between wheel and shock created by the mounting position of the shock.

DR = d1/d2

You may see the displacement ratio referred to in some circles as the "motion ratio" or MR.

The most common example of such a configuration occurs when the shock is mounted on the lowercontrol arm as opposed to on the axle (which creates a second class lever between the wheel and theshock). In suspension terms:





d1 = the distance between the lower shock mount and the suspension pivot point.

d2 = the distance between the wheel centre and the suspension pivot point.

Angle Correction Factor (ACF)

A factor that describes the relationship between wheel travel and shock travel that results from theangle at which the shock is mounted. If the shock is mounted at any angle other than vertical, wheeltravel will be greater than shock travel.

ACF = Cosine(alpha), where:

alpha = the angle of the shock, measured as follows:

If the shock is mounted on the axle: alpha = the angle between the shock axis and vertical

If the shock is mounted on the lower link (control arm): alpha = the angle between the shock axis and aline drawn perpendicular to the lower link (when viewed from the side).

Installation Ratio (IR)

The IR is the ratio of wheel travel to spring / shock travel. IR combines the displacement ratio and theangle correction factor into a single ratio that relates wheel travel to shock travel by accounting for thelocation and angle of the shock mounting (the shock geometry).

IR = MR * ACF

Wheel Rate (WR)

The wheel rate is the effective spring rate at the wheel. It is the spring rate "seen" by the wheel, i.e. thespring rate corrected for the shock geometry. Wheel rate is the spring rate multiplied by the square ofthe installation ratio

WR = K * (IR)^2

In a dual-rate setup, just as there are initial and final spring rates, so there are also initial and final wheelrates. The initial wheel rate is the wheel rate during the initial (combined) spring rate. The final wheelrate is the wheel rate after the spring rate transitions to the final (main) spring rate. The equations are:

Initial Wheel Rate (WRi).

WRi = Ki * (IR)^2

where Ki = the initial (combined) spring rate, IR = installation ratio

Final Wheel Rate (WRf).

WRf = Km * (IR)^2

where Km = the final (main) spring rate, IR = installation ratio

Finally, if you mount the shocks on the axle close to the centreline of the axle, and you mount themstraight up and down (or very close to it), for practical purposes the terms wheel rate and spring ratecan be interchanged. That is, WR ~ K for values of IR close to 1.

Measuring d1, d2, & alpha - Practical Calculation of the IR

The BillaVista spring rate calculator (BV Calculator) requires the installation ratio in order to calculate therecommended preliminary spring rates required to arrive at a target wheel rate. It is designed to calculate theIR from the following user inputs: d1, d2, and alpha. The following practical examples should solidify ourunderstanding of the IR and illustrate how to measure the required dimensions for a common 4-link rearsuspension. However, if you understand the theory, you can figure out and measure d1, d2, and alpha for anystyle suspension. As a side note - all suspensions will have an IR, but it may be that the IR is 1.

Before we continue, I must re-emphasize that all of our discussions to this point regarding DR's, ACF's, andIR's have been with regards to some fixed static point in the suspension's travel - namely static ride height.Things begin to change, and get exponentially more complicated, when we attempt to analyze a rig'ssuspension as a dynamic, moving thing. So to begin with, we take our measurements and make ourcalculations. at static ride height. This is perfectly adequate for initial design purposes and perfectly adequatefor the purposes of measuring the dimensions the BV Calculator requires as inputs. But, for the sake ofcomplete technical accuracy - I would be remiss if I didn't point out that in a real working dynamic movingsuspension, dimensions and angles and such can, and do, change - changing the results of any calculationson a pretty-much continuous basis. Just keep in mind that, for now, we're sticking to the basics -measurements and calculations at static ride height and wheel travel modelled as ride travel.





Side View

Example 1: 4-link rear, shock mounted on axle.

In "lever" terms we have:

Setup:second class leverLever: lower control arm (link)Effort: wheel centreLoad: lower shock mountFulcrum: suspension pivot - in this case the frame attachmentpoint of the lower link.Load arm = d1 = wheel centre to suspension pivotEffort arm = d2 = wheel centre to suspension pivot

since d1 = d2, DR = d1/d2 = 1

In other words, the wheel has no lever through which it appliesforce to the springs. This situation is shown at left.

The angle alpha is measured with an angle finder, and is theangle from vertical at which the shock is mounted.

The ACF = cosine(alpha). If alpha = 20°

IR = DR * ACF = 1 * ACF = Cos(20°) = 0.94

In other words, for every inch of wheel travel, the shock will travel0.94"

WR = k * (0.94)^2 = 0.88(k)

In other words, the wheel rate will be 88% of the spring rate.

The BV Calculator will make the calculations, the user simplyneeds to enter values for d1, d2, and alpha. Strictly speaking,because d1 = d2, any value can be entered for d1 and d2 as longas it's the same for both.

Side View

Example 2: 4-link rear, shock mounted on lower link.

In "lever" terms we have:

Setup:second class leverLever: lower control arm (link)Effort: wheel centreLoad: lower shock mountFulcrum: suspension pivot - in this case the frame attachmentpoint of the lower link.Load arm = d1 = shock mount to suspension pivotEffort arm = d2 = wheel centre to suspension pivot

DR = d1/d2

In other words, if the coilover is mounted on the lower link(control arm), there will be a displacement ratio, as shown at left.

Since the DR is a dimensionless ratio, d1 and d2 can actually bemeasured in any plane and at any angle, as long as you areconsistent with both measurements. i.e. if you measure d2parallel to the ground, be sure to measure d1 also parallel to theground.

Conversely, you could also measure both dimensions parallelwith the link.

Because of the shock mounting location on the link, the anglealpha is not measured between the shock axis and vertical, butinstead between the shock axis and a line perpendicular to thelink, as shown at left. This accounts for angle between the linkand the ground. Obviously, if the link is parallel to the ground, the





line perpendicular will be vertical.

The ACF = cosine(alpha). If alpha = 20°, d2 = 48", and d1=36"

DR = d1/d2 = 36 / 48 = 0.75

ACF = Cos(20°) = 0.94

IR = DR * ACF = 0.75 * 0.94 = 0.705

In other words, for every inch of wheel travel, the shock will travel0.7" You will notice many desert race truck setup similar to this,which is how they achieve 30+ inches of wheel travel, eventhough no 30" shocks exist.

WR = k * IR^2 = 0.50(k)

In other words, the wheel rate will only be 50% of the spring rate.

Front or Rear View

Compound values of alpha:

The angle alpha will normally be because the shock leanstowards the centre of the vehicle, when viewed from the side, asin the above two diagrams; OR

as shown in this diagram, it may be because the shock leanstowards the centreline of the vehicle when viewed from the frontor rear.

Of course, the shock may be installed leaning in both directions -in which case the angle alpha will be a combination of bothangles, and is best measured with an angle finder.

If, however, for planning purposes, you wish to calculate thecombined angle produced when you lean the shock sidewayssome angle x and lean it forward some angle z, you would do soas follows:

alpha = arccos((cos(x) * cos(z)))

E.g. If I lean the shock sideways 20° and forwards 30°, theresultant angle from vertical is

arccos((cos(20) * cos(30))) = 35.5°

There is, of course, one other way to calculate IR, and that is by direct measurement. Suppose we have theshock already installed on the rig, since:

ST = WT * IR, then

IR = ST / WT

In other words, the IR is the shock travel, divided by the wheel travel.

If we therefore take several measurements of WT and ST we can calculate an average value for IR, using aprocedure called a "linear fit"..





To do this, we would have to jackup the axle so that both wheels aretravelling vertically at the sametime (ride travel) and take severalmeasurements of both ST and WTat different points in thesuspension's travel.

If we did this by say, taking ameasurement of shock travel forevery inch of wheel travel, wewould end up with a number ofdata points each consisting of twonumbers - the wheel travel and thecorresponding shock travel.

If we then plot those points on agraph, with shock travel on the y(vertical) axis and wheel travel onthe x (horizontal) axis we thendraw a line on the graph that bestfits all of the points. This line iscalled a "linear fit", an example ofwhich can be seen at left.

The slope of the best-fit line, orlinear fit, is the installation ratio.

To calculate the slope of the linewe divide the rise by the run - inother words the amount the linerises vertically by the amount theline travels horizontally.

(plot diagram courtesy of Ben Langford)

In the example above, we have: slope = rise / run = (7.650 - 0.675) / (10-1) = 6.975 / 9 = 0.775

Therefore, the slope of the line is 0.775 and the IR is 0.775. In other words, for every inch of wheel travel, theshock travels approximately 0.775"

Measuring CSW

The last thing we must accurately measure before using the BV Calculator is the corner sprung weight at eachcorner of the vehicle. There are a number of different ways to measure corner sprung weight.

If you have access to a small portable scale of appropriate capacity (like a race car scale) you can place itunder the tire and measure the corner weight of the rig. Be sure to block up the other 3 tires the same heightas the scale though, otherwise your result will be inaccurate due to weight transfer. Then, leaving the tire onthe scale, use a Hi-Lift jack to jack up that end of the rig until the suspension goes slack and the sprung weightis not on the suspension. Read the scale again and record the value of the unsprung weight. Subtracting theunsprung weight from the total weight will give you the sprung weight at that corner.

If you don't have a portable scale, you may be able to do the same thing at a truck scale, but the difficulty willbe taking the sprung weight off the suspension in order to measure the unsprung weight.

If you have access to neither, you can attempt to rig up a system using a bathroom scale, like this:

Good Lord it's an upside down second class lever! See, I told you physics and math were useful!

Recall: mechanical advantage = effort arm / load arm.In this case the effort arm is y and the load arm is x+y.Therefore, the weight the scale will see is the weight onthe tire, multiplied by y/y+x.

You can vary x and y to avoid exceeding the capacityof the scale.

For example, if x = 3 ft. and y = 1 ft., the scale will see1/4 of the weight on the tire.





Be aware that the beam will have to be very strong andrigid.

It's a little hokey, but may be better than simplyguessing.

The easiest way to explain finding CSW is this.We know force is modified by IR. In this case the force is just the CSW. So use the equations we introduced.

Measure the deflection of the spring and find the force on the spring using the definition of spring rate Force onthe spring = spring deflection * spring rate You know your spring's rate, you measure deflection so you multiplythe two and have the force on the spring.

Now you use the definition of IR in terms of what it means to force.Force at the wheel = Force on the spring * IR You just found the force on the spring, so modifying that at thewheel by IR by multiplying so it gives you force at the wheel.Force at the wheel is just the CSW of the vehicle.

So find force on spring ---> Fs = ks * ds Find that force at the wheel ---> Fw = Fs * IR Fw is corner sprungweight.

We've already explained all that, so no need to introduce anything new, just apply what we know. Make sense?

If you already have coil springs installed, you can calculate the CSW by measuring the deflection of thesprings at ride height and multiplying this by the spring's rate and the IR at that corner. If you don't know thespring rate, you calculate it by measuring the coil's dimensions and using the formula and definitions given inthe previous section on spring theory. (i.e. k = 11,250,000 * (Dw)^4 / 8 * Na * (Dm)^3).

The reason you have to multiply the spring rate by the IR is because of the effect of suspension leverage onforce. We can prove this to ourselves algebraically, because the corner sprung weight is actually just the forceat the wheel:

Recall from the "big 5" the equation for force at the wheel:

Fw = Fs * IR

And force at the spring equals the spring rate times the spring displacement (deflection)

Fs = k * Ds

So, if we substitute this equation back into the equation for force at the wheel (CSW) we get:

Fw = k * Ds * IR; or

Corner Sprung Weight = spring rate times spring deflection at ride height time the installation ratio.

If you have a single coil at the corner multiply the spring rate by IR then multiply by the measureddeflection of the spring (how much it compresses with the vehicle's weight on it at ride height) to get theweight on the spring, or CSW..If you have two springs in series (dual-rate setup), because any number of springs in series all resist thesame weight, theoretically you should get the same CSW whether you measure the deflection of thetender spring, main spring, or both, and multiply by the appropriate tender, main, or combined spring'srate and IR. Just remember that whichever deflection you measure, multiply by the correspondingspring's rate - that is to say, apply the installation ratio to the spring rate in question before multiplying bythe deflection to get the weight.

The BV Calculator has a sheet to perform the calculations for you if you enter the appropriate variables (d1,d2, alpha, spring rate, the free length of the spring, and the installed length of the spring). In practice I havefound that the results vary a little, depending on if you measure the deflection of tender, main, or combinedspring stack - probably due to limitations on accurately measuring the spring's length at ride height. As such,the calculator will also produce an average if you have values for more than one spring to enter.

Suspension Frequency

What is suspension frequency?

Traditionally, rockcrawlers and trail riders have thought of suspension chiefly in terms of suspension height -the amount of droop travel and bump travel the suspension provides. And traditionally we have designed oursuspension with suspension height as the foremost goal.

There is, however, another core property of any suspension, a property that is essential in defining low speedperformance and that becomes increasingly important as speeds increase.

The property is suspension frequency (Fn).





Recall from our very early discussion of suspension; we said that "when a vehicle's wheel hits a bump, the rateat which the (undamped) springs compress and rebound is called the suspension frequency". If you were toremove the shocks from a car and then push down and release a corner, that corner would bounce up anddown, or oscillate, at the suspension's natural frequency. If you did it to a luxury car with soft springs, like aCadillac, the car would bounce up and down fairly slowly - the suspension frequency would be comparativelylow. If, on the other hand, you did it to a stiffly sprung sports car, the car would bounce up and down morequickly - the suspension frequency would be higher.

We also know that the softly sprung luxury car provides a comfortable ride and soaks up small bumps andpotholes well, but that it is prone to excessive body roll when cornering, acceleration squat, and brake dive.Conversely, the stiffly sprung sports car exhibits excellent handling, but can provide a stiff, jarring ride. Sointuitively we already know that the suspension frequency is an indicator of both ride quality and handling. Thisis one of the characteristics that makes it so useful in suspension design.

Suspension frequency is as important in describing an off-road rig's performance as it is in describing a car'sride and handling. A rig with a low frequency suspension will be flexible and comfortable, but may lack rollresistance and the ability to soak up large bumps and potholes at speed without bottoming. A rig with a higherfrequency suspension may be able to blast through the whoops, but at what cost to ride quality, and will it beflexible enough to use all it's wheel travel when crawling through a field of boulders? As with anything, the"right" frequency is a matter of balance.

The front to rear balance of a rig's suspension frequency is also extremely important in defining how the rig willperform - especially in the faster rough stuff. If you have ever seen a rig bucking back and forth from front torear axle while crossing rough terrain at speed, you have seen an example of poor front to rear suspensionfrequency balance.

Suspension frequency also gets exponentially more important the faster we go. This is becoming increasinglysignificant as rock sports like rock racing, rock cross, and King of the Hammers type events grow in popularityand begin to blur the line between traditional rockcrawling and off-road desert racing.

In traditional rockcrawling, suspension performance is typically slow and quasi-static as the rig crawls. Whencrawling slowly over a boulder the wheel reacts slowly - in technical terms the wheel is excited at a slowvelocity. Think of our car corner pushing again, and push down and release very slowly - nothing terriblyexciting happens, and because we do it slowly, the differences between the Caddy and the coupé aren'tterribly noticeable or important.

However, when you hit a bump / dip / log at speed or land from a jump at speed you excite the wheels at ahigh velocity. The reaction of the suspension and wheels, and consequently vehicle handling, following highvelocity excitation is very dependent on the natural frequency of the suspension. Back to our car cornerpushing experiment - imagine that when you push down and and release the corner, you do it quickly andrepeatedly. Now the difference between the two is readily apparent. The Caddy will dip and sway and wallow,the sports car will bounce and jiggle quickly. This is the suspension frequency at work. The ability to soak upbumps at speed depends heavily on suspension frequency - certain frequencies will help keep the vehiclestable as its front hits a bump and a split-second later the rear hits the same bump. Research, development,and testing develop ranges for suspension frequencies, front and rear, that work well for particular rigs inparticular terrain. For now, we should be convinced that suspension frequency is an important property insuspension design.

You may be thinking to yourself, "Yea, but you said the suspension frequency was the undamped rate ofoscillation, and we know the shocks provide damping - that's what they're designed to do". And you'd be right,the shocks do have a big effect on the suspension's performance - BUT it is critical to get the springs andtherefore the suspension frequency right first - otherwise the shocks will end up"fighting" the springs and anyattempt at valving the shocks will be a frustrating exercise in futility. Let me put it this way - if the spring ratesand suspension frequency are wrong and you attempt to dial in the shock valving it would be like trying to setignition timing when the valve timing is off! I know I began the article by stating that there are very few hardand fast "rules" in suspension design. This may be the exception. If you don't get the suspension frequencyright, you will never get the ultimate performance you seek.

In fact, I would argue that it is so important, it is THE goal in suspension design.

By thinking and designing in terms of suspension frequency we don’t have to know the sprung weight or wheelrate to compare the suspensions of different vehicles, be they luxury cars, f1 racing cars, rock crawlers orloaded 30 ton trucks, as the suspension frequency takes these factors into account. Seldom will you seesuspension height or "amount of droop available" referred to in circles outside the rock-crawling world butsuspension frequencies are frequently discussed in all arenas of suspension design. Learning to think andcalculate in terms of frequency can open up to us a whole world of valuable data and experience - experiencefrom which we can draw valuable design insight.

Unlike suspension height, suspension frequency includes an intuitive assessment of ride comfort and handling.If I say “I have 6 inches of droop” it is hard to visualize or imagine the overall ride and handling – is that soft orstiff? On the other hand – if we say a flexy competition rock buggy has a suspension frequency of perhaps0.85 to 1.0 Hz, a luxury car has a suspension frequency of 1.0 to 1.3 Hz, a sports car 1.3 to 1.7 Hz, and aFormula 1 racing car 2.7 to 3.3 Hz , we can intuitively relate frequency to ride and handling. In fact, by usingfrequency we can even relate to non-automotive information - for example, the frequency of a person walkingnormally is usually about 2.0 Hz and a boat gently rising and falling with long swells may have a frequency aslow as 0.5 Hz or less. The lower the frequency the softer the ride feels, the more flexy the suspension will be,





but the less effective it will be at keeping the wheels in contact with the ground at higher speeds, and the lesscapable it will be of soaking up bumps at speed with bottoming or serious wallowing that can lead to a loss oftraction and / or control. As suspension frequency increases the suspension becomes more stiff andresponsive, more capable of handling the impact of bumps at speed and jumps, but the less flexible it will befor boulder crawling and the harsher the ride will be. There's a point between the extremes of low and highfrequency that strikes the best balance for any given vehicle and its intended use. Just as importantly, bystudying the suspension frequencies of different vehicles with known performance characteristics we can nowintuitively understand what we may achieve by designing our rig for a particular suspension frequency.

By quoting suspension frequency we can describe and compare suspensions across different vehicles, withouthaving to know sprung weight or spring rate. If my 1-ton trail buggy has a suspension frequency of 1.1 Hz, andso does my buddy's pro lightweight moon buggy, we know that they will have similar performancecharacteristics and will feel similar in ride quality - even though they have dramatically different weights, springrates, spring lengths, etc.

Of course, despite its many virtues, suspension frequency alone is not the beginning and the end ofsuspension design - not least of all because it is the undamped natural frequency and the use of shocks,variable or adaptive valving, and other components like anti-roll bars and rising rate bumpstops create thecomplete suspension system that, as a whole, dictates the vehicle's ride and handling. Still more factors, suchas unsprung weight, also play a part in ride and handling, particularly as speeds increase. Suspensionfrequency is just one part of the equation - but it happens to be the most important, and in my opinion, the bestbasis on which to select preliminary spring rates.

In short, rockcrawlers, trail riders, and rock racers need to begin to think and design in terms of suspensionfrequency, to build up a body of experience of what frequencies work well for different types of rigs andterrains, so that we can then easily select spring rates to achieve wheel rates to achieve the desiredsuspension frequency.

How do we calculate suspension frequency?

Before we describe the calculation of a vehicle's suspension frequency, it is helpful to explore the calculation ofnatural frequency using a simplified model or system. We shall use a simple spring and mass system, aspictured below.

The natural frequency of any system is given by the equation:

Fn = (sqrt(k/m)) / 2pi where;

Fn = natural frequency in Hz k = spring rate in the direction of interest for the system m = mass of the system2pi = conversion factor to convert angular frequency in radiansper second to linear rate in cycles per second, or Hz

Since we are not used to working with mass, if we re-write the equation so that we can use weight instead, weget:

Fn = sqrt ((386.088*k) / W ) / 2pi

If, for a moment, we strip away some of the math and get rid of the constants (the sqrt, the 386.088, and the2pi) we are left with:

Fn "depends on" k / w

The natural frequency "depends on" the spring rate divided by the weight. In other words, if we increase thespring rate (use a stiffer spring), or decrease the weight (on the spring), the frequency will go up.

This confirms the intuitive conclusions about natural frequency that we were able to draw from our simpleexperiment of bouncing the corners of the luxury and sports car.

In other words, two systems can have equal frequencies, even if one has a stiff spring with a large weight on it,and the other a soft spring but with a smaller weight on it.

A note of caution here. Because it is more convenient and logical for us, we have substituted weight for massin the equation. However, this comes at a price. Because weight is a force, and F = m * a, in order to useweight in place of mass, we must divide it by the acceleration due to gravity. Since this acceleration alwaysoccurs in a vertical direction, for the equation to be accurate, the weight and spring must be oriented vertically,as illustrated in our simple model above.





What happens when we substitute a real-world suspension, where we know the spring is quite often notvertical, for the simple model? Can we still use the equation to calculate the frequency of a suspensionsystem? We can indeed apply the equation to a suspension system by using the wheel rate instead of thespring rate.

By calculating a wheel rate using the installation ratio, weeffectively create an "imaginary spring" between the wheeland chassis. This imaginary spring, the "wheel rate spring"is oriented vertically, and the weight it carries is the cornersprung weight of the rig.

Therefore, we can calculate the Fn of our actualsuspension using the wheel rate and the corner sprungweight.

By substituting into the equation for Fn, we arrive at:

Fn = sqrt ((386.088 * WR ) / CSW ) / 2pi

So we can calculate the Fn of our suspension if we know the wheel rate and the corner sprung weight.

Working in the other direction then, we can easily select a target suspension frequency, and work theequations backwards to calculate, for our given CSW, the wheel rate we need to get our selected Fn. Ofcourse, we can similarly continue to work the equations backwards and determine the combination of springrate (k) and shock geometry (IR) we need to get that wheel rate.

And that is just what we're going to do! That is, we are going to select preliminary spring rates that, combinedwith our shock / spring geometry, will achieve a certain wheel rate that, combined with our corner sprungweight, will give us our target suspension frequency.

Fortunately, the BV Calculator will do all the math for you, all you need is a tape measure, an angle finder, andan accurate corner sprung weight.

Fn can be calculated for any individual corner or the front or rear suspension. To calculate Fn for a corner, usethe corner sprung weight and the wheel rate at that corner. To calculate for the front or rear you would use thesum of the corner sprung weights at that end and the additive wheel rate of both wheels on that axle. If weightis distributed evenly side to side, and the wheel rates are the same for both wheels of a given axle, thefrequency of the suspension at that end will match the Fn of the corners.

Equal suspension frequencies at both corners of the front or rear is a highly desirable state. It is easy toachieve if weights are evenly distributed side to side - but this is often not the case. Consider the case of alightweight moonbuggy with a heavy driver sitting to one side (Bigelow, are you reading this? ;-) The beauty ofdesigning suspension in terms of frequency is that, as we have just learned, we can alter the wheel rates ateach corner to compensate for the different weights at each corner to achieve equal suspension frequencies ateach corner of an end, and thus a balanced suspension side to side(or even front to rear if so desired) - eventhough weight distribution is not equal.

The Relationship Between Fn and SH

"But what about suspension height?", you may be asking.

Because the wheel rate (spring rate and IR) affects both suspension frequency and suspension height, there isobviously a relationship between Fn and SH. That is, the spring rate we select (for a given sprung weight andshock geometry), will determine not only the suspension frequency, but also have an effect on the suspensionheight.

The spring rate affects suspension height because setting the corner sprung weight on the springs causesthem to deflect a certain amount and the shock compresses an equal amount because the springs areinstalled on the shock.

This shock compression due to the weight on the springs contributes to how much droop travel will beavailable. It is not, however, the only factor that does - which is why Fn and SH are related but not equivalent.

Recall that the amount of droop travel available, aka the suspension height, is some portion of the total wheeltravel (obviously the portion where the wheel goes down, or droops, from static ride height). Recall also, thatwheel travel and shock travel are related by the installation ratio - the installation ratio is the ratio of wheeltravel to shock travel, or

IR = ST / WT

We can rearrange this equation to read:

WT = ST / IR

That means that, for a given shock geometry wheel travel available is controlled by the shock travel (assumingbumpstops and limit straps are set so as to not limit the wheel travel more than the shock would).





This is true for total wheel travel, as well as for some portion of it, like droop travel. Obviously, the wheel canonly droop as far as the shock will let it. How much will the shock let the wheel droop? The answer is: by theamount of shock shaft in the shock body at ride height, divided by the IR. Recalling that we define shock travelas starting from a fully open shock (i.e. fully open shock = travel of 0), we can re-write this as:

The amount of droop travel available is equal to the shock travel at ride height divided by the IR.

So what determines the shock travel at ride height? Part of the shock travel at ride height is caused by theweight on the springs - when the weight is set on the springs they deflect a certain amount and the shock shaftgoes into the shock body the same amount.

But this shock travel at ride height due to spring deflection under the sprung weight is not the sole source ofshock travel at ride height. In fact, the only situation where it would be the sole source of shock travel at rideheight is if the springs just fit perfectly between the spring seats with the shock fully open (i.e. at zero travel). If,however, we used springs of such a length that they were either longer or shorter than the space between thespring seats with the shock fully open, then the shock travel would be modified accordingly. For example,suppose we installed springs that were 3" shorter than the space between the spring seats with the shock fullopen, we would get 3" of shock travel before the springs even began to deflect under the sprung weight. Inother words, our shock travel at ride height, which determines how much droop we have available, would bethe amount the springs deflect under the sprung weight, PLUS the 3" the shock compressed before thesprings could fill the span between the spring seats and begin to support the weight.

But we're getting way ahead of ourselves now. For now, the point I want to leave you with is this:

With regards to the relationship between suspension frequency and suspension height: both are affected bywheel rate (spring rate and IR) but suspension height is further affected or modified by spring length, whereassuspension frequency is not.

In other words, once we've picked a spring rate, we cannot change the Fn unless we change the CSW or pickanother spring rate. On the other hand, although the spring rate obviously plays a role in suspension height,we can also alter the suspension height by adjusting shock travel at ride height - which we do with springlength, the position of the adjuster, and preload and which we will discuss in detail in Part 3.

In other words, spring rate affects Fn and SH, but of the two, spring length ONLY affects SH. Which isimportant to understand before we can decide whether we wish to select preliminary spring rates to arrive at atarget suspension frequency or a target suspension height.

The Basis For Selecting Preliminary Spring Rates

So it seems as if we could use either method to select our spring rates. With a measured sprung weight andan idea of shock geometry, we could either select the spring rate that will give us a certain suspension height,or we could select a spring rate that would give us a certain frequency.

This is quite true, and for many years we have been happily (if somewhat ignorantly) doing the former - pickingspring rates to give a certain droop travel. In fact, if you look around at most of the on-line "spring ratecalculators" this is exactly, and all, that they do (albeit while making other errors, such as not properly applyingthe IR).

Here's the problem with that approach though - if you simply pick a spring rate to get a suspension height andjust install those springs and go, you're going to be stuck with whatever suspension frequency, whatever rideand handling, you get. If you pick a spring rate to achieve a target suspension height, you can't then dial in atarget suspension frequency with spring length and preload. In effect, if you do it this way, you're probablygetting less than half the performance from the coilover that you should be.

On the other hand, the beauty of using suspension frequency as our primary target for spring rate selection, isthat you can do just that - that is, achieve your target suspension frequency and then tune for suspensionheight with spring length and preload. Indeed, this gets at the heart and the beauty of coilovers and Fn. Thatis:

Using a combination of: spring length, the coilover's adjustable spring seat, preload, and helper coilswe can adjust ride height and suspension height without affecting suspension frequency. Springlength, the adjuster, preload, and helper coils do not affect Fn, only CSW and wheel rate (spring rateand shock/spring geometry) affect suspension frequency. The coilover design, with it's myriadavailable spring rates in different lengths and built-in adjustment make it relatively simple to design forfrequency, then adjust for ride height and suspension height. Certainly far easier than with any otherspring / shock system. Add the ability to customize and tune both compression and rebound valvingplus the fact that the coilover springs are unaffected by heat, and that's the beauty of coilovers. Youcan't easily do that with a leaf spring, torsion bar, airbags, regular coils and shocks, or airshocks!

In a nutshell, with a good coilover shock and quality springs you can choose your suspension frequency andride height / suspension height independently.

Clearly selecting preliminary spring rates on the basis of hitting a target Fn is the best way to go. However, Ihave included in the BV calculator provisions to allow the user to select spring rates on the basis of hitting atarget SH as well. I do this because the concept of Fn is new and foreign to many and plenty of folks will bemore comfortable proceeding on the basis of suspension height, despite the drawbacks discussed. Also, for astrictly slow-speed rockcrawler, using SH as the primary target may well produce satisfactory results with the





attendant Fn merely a matter of intellectual curiosity.

Depending on the method chosen, then, the calculator operates on the basis of one of the following.

Fn

It will calculate a target wheel rate that will result in the target suspension frequency according tothe equation:

Wheel Rate = (Suspension Frequency / 3.128)^2 * Corner Sprung Weight or

WR=(Fn / 3.128)^2 * CSW

SH

It will calculate a target wheel rate that will result in the target suspension height (droop travel),assuming shock travel before we set the weight on the springs = 0 (i.e. that the spring lengths aresuch that they just fit between the spring seats with the shock fully open). It does this by dividingthe corner sprung weight (lbs) by the number of inches of droop travel required (in.), with the resultbeing a target wheel rate (lbs/in.). The calculation it does is:

Wheel Rate = Corner Sprung Weight / (Wheel Travel * Suspension Height %) or

WR=CSW / (WT * SH)

But note: this equation is only valid when shock travel before we set the weight on thesprings = 0 (i.e. that the spring lengths are such that they just fit between the spring seatswith the shock fully open)

Then, in either case, it will calculate the required preliminary spring rate to get the target wheel rate, accordingto the equation:

Wheel Rate = Spring Rate * (IR)^2 or WR = k(IR)^2

Summary

Suspension frequency is the closest thing we have to a mathematical expression of the age old question "howdoes the car ride and handle?". It is universal and cross-platform comparable. It depends only on the CSWand the WR, and therefore can (and should) be the primary suspension design goal. Fn is a superior primarygoal, as it works well for both slow speed and high speed use. In addition, front-to-rear Fn balance goes a longway to determining how the rig will handle over the bumps and through the whoops at speed.

There is a relationship between Fn and SH, but not a dependence. You can set each independently. You canselect spring rates to give a wheel rate for a target Fn, and then use spring length, spring seat adjustment,preload, and helper coils to dial in the ride height and suspension height you want. The beauty of coilovers isthat they make this so easy to do, what with the many different rate and length springs available, the widerange of adjustment of the top spring seat, and the ability to stack two or three springs in series and use ahelper coil.

Despite its many virtues, however, suspension frequency alone is not the beginning and the end of suspensiondesign - not least of all because it is the undamped natural frequency and the use of shocks, variable oradaptive valving, and other components like anti-roll bars and rising rate bumpstops create the completesuspension system that, as a whole, dictates the vehicle's ride and handling. Ride frequency is just one part ofthe equation - but it happens to be the best basis on which to select preliminary spring rates. Looking ahead,once we have selected preliminary spring rates, then chosen spring lengths to get our suspension height, wewill still need to consider some other factors such as what those spring lengths are doing at full bump anddroop (are the coils binding? do the springs fall loose on the shock?) and how much those characteristics mayor may not be important to us, and then how we adjust and compensate for them. But those are a matter forlater discussion.

For now, let's proceed by calculating the preliminary spring rates.

Preliminary Spring Rate Calculations - The BV Calculator

Regardless of whether you choose Fn or SH as your primary target, the following is the process used to selectpreliminary spring rate estimates:

Measure corner sprung weight and suspension geometry.1.Determine installation ratio (to account for shock geometry)2.Select desired suspension height or suspension frequency3.Calculate wheel rate to give selected SH or Fn4.Select desired step-up ratio5.Calculate spring rates required to give target wheel rate and step-up ratio.6.

The BV calculator, provided below in MS Excel spreadsheet form, performs all the calculations for you, andincludes extensive notes on its use and how the variables and equations work.

The user simply enters the following vehicle specs:





CSW (lbs) Corner sprung weight = the weight on that corner supported by the springs.

WT (in) Actual measured total wheel travel available from full droop to full bump in ride mode withshocks installed but no springs.

d1 (in) Length of suspension-lever load arm = distance from shock mount to suspension pivot point.

d2 (in) Length of suspension-lever effort arm = distance from wheel centre to suspension pivotpoint.

alpha (˚) Angle between shock axis and vertical (if shock mounted on axle) or angle between shockaxis and lower link (if shock mounted on lower link), measured with angle finder.

and then enters one of the following design criteria, either:

A desired suspension height (SH) (as a percentage of total wheel travel desired for droop)

or

A desired suspension frequency (Fn)

and finally the desired step-up ratio (SUR).

The BV Calculator then uses these inputs to calculate the required spring rates for the main and tendersprings.

Based on the calculated spring rates for main and tender springs, the user then selects the closest match fromcommercially available coil springs that fit on their shock of choice.

Finally, the BV Calculator will take these "actual" chosen spring rates and back-calculate the followingsuspension properties:

Ki (lbs/in) The initial (combined) spring rate of the selected springs.

WRi (lbs/in) The initial wheel rate achieved by the selected springs. Equal to the initial spring rateadjusted for installation ratio (DR & ACF).

WRf (lbs.in)Final wheel rate - the wheel rate after the transition from the initial spring rate to thefinal spring rate. Equal to the selected main spring rate, adjusted for installation ratio(DR & ACF).

SUR (%) Step-up ratio between the initial wheel rate and the final wheel rate.Fn(i) (Hz) The initial suspension frequency achieved by the selected springs.Fn(f) (Hz) The final suspension frequency achieved by the selected springs.

DT (in) Droop travel available with the selected springs - assuming springs just fit betweenspring seats with shock fully extended.

BT (in) Bump travel available with the selected springs - assuming springs just fit betweenspring seats with shock fully extended.

SH (%) Suspension height given by use of selected springs - assuming springs just fitbetween spring seats with shock fully extended.

The BV Calculator also includes four other tools:

A tool to calculate corner sprung weight from the deflection of installed springs.1.A matrix with columns of tender spring rates and rows of main spring rates, the intersections of whichgive the combined spring rate. Useful for highlighting several possible spring rate options and viewing ata glance the resultant combined spring rates.

2.

A tool to calculate required front-to-rear suspension frequency balance to optimize anti-pitching of thesuspension for a given speed.

3.

A reference chart of equations and variables.4.

One final caution on the use of the BV Calculator. The results it provides are only as accurate as the data theuser enters. The old adage "garbage in = garbage out " applies. For example, if you only guess your cornersprung weight, it can only guess spring rates for you.

Click on the picture at left to download the BillaVistaPreliminary Spring Rate Calculator





A few notes on using the BV Calculator:

~ Play with the corner sprung weights and observe what a huge difference they make. Accurate weightsare VITAL. If you guess your weights, the BV Calculator will guess your spring rates!~ Adjust the shock mounting angle (alpha) and observe the results.~ Adjust the SUR between 200-300% and observe the effects.~ BV Calculator may not provide spring rates commercially available in your chosen brand / length / I. D.Pick the closest available and plug into "Result Inputs" to see actual results.~ You can plug various commercially available spring rates into the "Result Inputs" section to see therange of possibilities. Particularly useful if you are choosing to buy a "range" of springs with which to test& evaluate.

What to Shoot For - Correlating the BV Calculator Inputs With Vehicle Performance

After playing with the BV Calculator a bit, you will no doubt notice that there are two types of inputs in thecalculator, which I call "measured data" and "subjective targets" respectively. The two are distinguished by thecolour of the text.

Green inputs are measured data - CSW, wheel travel, d1, d2, and alpha.

The blue inputs are what I call subjective targets. They are the suspension height or suspension frequency andthe step-up ratio. The choice of what to enter for the blue values is at the heart of the question of whatsuspension will work well on different vehicles for different terrain and use.

There are no easy answers to that question, and no formula that will tell you what to use. The experience ofothers and our own testing will best help us to arrive at suitable values to enter into the BV Calculator,depending on our rig and its intended use.

The following information may provide a place to start:

Rig Use Suspension Height (% Droop)

Front Rear

Slow, flexycrawler

85 70

All purposeTrail Rig

50 40

High Speed /Street

30 25

Rig Use Suspension Frequency (Hz)

Front Rear

Slow, flexycrawler

0.849 0.935

All purposeTrail Rig

1.107 1.237

High Speed /Street

1.429 1.565

Step-up ratios normally vary from 200-300%





Anti-Pitch

For medium to high speed use, normally suspension frequency will be 10-20% higher in the rear than the front.

The reason the rear suspension should normally be higher frequency (stiffer / quicker) in the rear than the frontis to help combat pitching. Pitching is a front-to-rear up and down motion when one end of the vehicle is goingup while the other end is going down. In other words, it is a nose up / nose down oscillation. It is an extremelyunpleasant sensation that is, at best, uncomfortable, and at worst can lead to a complete loss of control.Depending on the suspension in question, the speed, and the frequency of the bumps, unchecked pitching willcause the vehicle to porpoise up and down and may even lead to it somersaulting out of control. Best to beavoided then!

Pitching is caused by the front of the vehicle rising over a bump, then the front comes down just as the reargoes up over the bump, then the rear comes down. That's bad enough over a single bump, but If there is aseries of bumps the cycle continues, often amplifying as it goes, and the car can quickly get out of control.

What's needed then, is different frequencies front to rear so that the rear is "quicker" than the front, allowing itto "catch up" over the bump so that the front and rear suspension tend towards working together instead ofpitching up and down. Essentially, we want the front and rear suspension to move simultaneously becausewhen they do there can be no pitching. Of course, we can't alter time and space, so the front is going to hit thebump first. But if the front has a lower frequency, it will take longer to react over the bump, meanwhile the rearcomes over the bump, and because of its higher frequency catches up to the front and the front and rear tendback towards working simultaneously. Obviously, the wheelbase and the car's speed play a factor here asthey determine the time between the front and the rear hitting the bump, and therefore the amount by whichthe rear should be stiffer (higher frequency) than the front.

You can actually calculate the amount by which the rear should be higher frequency, but the calculation is onlyvalid for a single speed. If you have a common or average speed in mind, a speed at which you wish tominimize pitching, then you can calculate front to rear frequency difference as follows:

The time between front and rear hitting a bump is the time it takes the car to travel its own wheelbase. Thiscan be calculated as:

Twb= (0.0568 * WB) / S

Where:

Twb = Time to travel wheelbase in seconds

WB = wheelbase in inches

S = speed in mph.

e.g. at 40 mph, the time it takes my 105" wheelbase buggy to travel its own wheelbase is:

Twb = (0.0568 * 105) / 40 = 0.1491 seconds.

So, in order for the front and rear to work simultaneously (at 40 mph), I need the rear suspension to react orcycle 0.1491 seconds faster than the front.

The time it takes the suspension to cycle is called the "period" and is easily calculated from the frequency.

The period is one,divided by the frequency:

P = 1 / Fn.

Therefore, if we know the frequency of the front, we can calculate the period, and then the period of the rearshould be that number MINUS the time to travel the wheelbase, and once we have the period of the rear, wecan calculate the required frequency for the rear.

Let's do an example:

Data:

Wheelbase (WB): 105"Typical Speed (S): 40 mphFront suspension frequency designed to be Fn(f): 1.107 Hz

What should the rear frequency be?

Time to travel wheelbase in seconds:Twb = (0.0568 * WB) / S = (0.0568 * 105) / 40 = 0.1491 seconds.

Period of front suspension:P(f) = 1/1.107 = 0.9033 seconds





Period of rear suspension:P(r) = P(f) - T = 0.9033 - 0.1491 = 0.7542 seconds

Frequency of rear suspension:Fn(r) = 1 / P(r) = 1 / 0.7542 = 1.326 Hz

So my resulting frequencies would be Front - 1.107 Hz, Rear - 1.326 Hz; with the rear 19.8% higher than thefront.

A moments reflection should show us that the time to travel the wheelbase is key, and therefore the shorter thewheelbase, or the higher the speed for which we optimize, the smaller the required difference between frontand rear suspension frequency.

Also, remember that this calculation is valid only for a single speed, so it isn't a magic number. Obviouslypicking the speed is critical, but again there's no magic answer, you have to pick the speed at which you wishto minimize pitching - it could be average course speed or comfortable cruising speed or some other figure andthen balance this against the competing fact that the higher the speed, the less the frequencies need to differbut the more detrimental to handling the effects of pitching will be.

The same is true of wheelbase. Obviously we don't tend to intentionally change wheelbase during a race orrun, but the shorter the wheelbase the less the frequencies need to differ while at the same time the shorterthe wheelbase the more detrimental to handling the effects of pitching will be.

And of course, this is only one method, and is by no means a rule. There may be perfectly valid designreasons for having equal front to rear frequencies, or even higher frequencies at the front. Certainly in aracecar on a good surface the search for optimal aerodynamics and weight balance will likely completelyoutweigh this anti-pitching design criteria. Once again, we see that the search for optimal suspension design isa matter of balance and that a certain amount of testing and evaluation will be necessary - I can't give you theanswers - just place from which to start.

Of interest, and in out favour though, is the fact that we don't need to alter the suspension in any way to testand evaluate different frequencies - we can do so simply by adding or removing weight. Recall that theequation for frequency is:

Fn = sqrt ((386.088 * WR ) / CSW ) / 2pi

and therefore depends only on the wheel rate and corner sprung weight. If we leave the wheel rate alone, bychanging the corner sprung weight we can alter the frequency and test that way.

In summary, here are the basic equations and units again for anti-pitching suspension frequency calculations:

Time to travel wheelbase (Twb) = (0.0568 * WB) / S

Where:

Twb = Time to travel wheelbase in seconds

WB = wheelbase in inches

S = speed in mph.

Period = 1 / Frequency

Rear Period (Pr) = Front Period (Pf) - T

Front period (Pf) = Rear Period (Pr) + T

Frequency = 1 / Period

The BV calculator includes a worksheet to calculate different front to rear suspension frequency requirementsto optimize ant-pitching for a given speed. Below is a table of results generated from the tool that shows theinteresting trend that the faster the speed, the less the difference between front and rear frequencies needs tobe for anti-pitch.

Wheelbase(in) 105 105 105 105

Speed(mph) 20 40 60 80

Fn(front)(Hz) 1.107 1.107 1.107 1.107

Twb (s) 0.2982 0.1491 0.0994 0.0746





Pf (s) 0.9033 0.9033 0.9033 0.9033Pr (s) 0.6051 0.7542 0.8039 0.8288

Fn(rear)(Hz) 1.6525 1.3258 1.2439 1.2066

%Difference 49.3% 19.8% 12.4% 9.0%

Trends

In the past, the general trend for performance cars was to use frequencies as high as tolerable (i.e. wheelrates as high or stiff as practicable). More recently the trend as reversed and wheel rates are kept as soft aspossible to better allow the tires to follows road irregularities. The situation is reversed in off-road vehicles. Inthe early days of ramp-crazy flex-mania, wheel rates were designed as soft as possible - so much so thatsome rigs would practically flop on their sides while the wheels remained on the ground. This trend hasrecently begun to reverse as well, so that stiffer wheel rates (higher frequencies) are being used to betterbalance high and low speed performance as well as deliver a reasonable amount of roll resistance duringoff-camber driving. As with all things - balance and compromise are key, and the solution for off-road rigs isprobably something like "as soft as possible while being as firm as necessary".

It is my fervent desire that this article serves to introduce many of us in the off-road world to the concept ofsuspension frequency, so that we can begin to build a body of knowledge and experience about whatfrequencies work well in different situations - the beauty being that I don't have to know your spring rates orcorner weights to compare my frequency to yours.

Interpreting the BV Calculator's Results - Prepare to Tune (or Start Over)

OK, so you've accurately measured your rig's weights and dimensions, decided on a target suspensionfrequency, and have played with the BV Calculator and its inputs to get some results - some preliminaryspring rate calculations. Is that it? Do you rush out and buy some springs and install them and go?

Unfortunately not. You will have noticed that I keep referring to the calculator's output as preliminary springrate calculations. That's because we're only just getting started. It is important to understand the limitations ofthe results the calculator provides - particularly if you're using suspension height as your input or if you're justtaking a SWAG at the frequency you want. What if the spring rates generated by the calculator fall short insome other area? For example, what if the spring rates suggested by the BV Calculator will result in a wheelrate that is too soft to provide any appreciable roll resistance or too firm for ride comfort?

Recall the seven goals of suspension design: is a matter of achieving the best balance between these oftencompeting goals:

Desired suspension frequency1.Desired suspension height2.Desired ride comfort3.Acceptable roll resistance4.Desired flexibility5.Matched wheel, spring, and shock travel6.Desired ride height7.

If you use the Calculator with SH as your primary target, the results generated by the BV Calculator addressonly the second of these. If you use Fn as your target, then the calculator's results can potentially addressmultiple goals - depending on the accuracy of the match between what you enter as a target Fn and what it isthat you are actually aiming for in terms of ride & handling. Either way, selecting preliminary spring rates is nota magic solution to the entire problem of suspension design.

Some of the design goals to be considered in spring rate selection cannot easily be quantified with equationsin a spreadsheet, even of you use suspension frequency as the target. Chief among these factors are thedesired roll resistance and even the all-important assessment of ride quality, both of which can be highlysubjective. Consider:

What feels soft to one person may feel firm to another.What is an acceptable level of roll resistance to one person may be too little for another.Other factors in the rig's overall suspension design will affect how it performs and how it feels. Forexample:

A link suspension with rod ends will likely require more roll resistance from springs or anti-roll barsthan one that uses bushings that have a degree of roll resistance on account of their internalfriction.Anti-roll bars can be very effective at providing roll resistance without increasing wheel rate orappreciably altering suspension frequency.

The more multi-purpose a rig is, the greater the compromise must be in its suspension design. Onlypersonal testing or a thorough understanding of different suspension frequencies is likely to determine afinal wheel rate that will satisfy the individual driver's needs.And, of course, the final assessment of satisfactory ride & handling will very much be a matter ofpersonal preference.





The good news is, there's plenty we can do about it. Again, if we begin with Fn, the next step is tuning forsuspension height by using spring length options, the adjustable top spring seat, preload, and helper coils.After that we still have to consider shock valving and use of other tools such as anti-roll bars and bumpstops. It isn't easy and there is no simple answer or magical formula I can give you to arrive at the perfect setup tomeet all seven goals. It is inevitable that from this point forward a good deal of testing and evaluation andtuning will be required if you are to extract the maximum performance from your coilovers. However, there is agreat deal more tech for us to consider, which we shall in Part 3 and beyond. Combined with a solidunderstanding of the contents of this article, you can significantly reduce the time and effort (and funds!) youwill have to expend reaching the magic balance.

What the BV Calculator does is provide you with a pretty good place to start.

So, where do we go next? The short answer to that is: spring length choice and spring seat adjustment. Thelong answer, however, will have to wait for part 3 - coming soon so stay tuned.

Summary

OK, so we've covered a lot of ground in Part 1, and hopefully covered all of the basics that will serve as a firmplatform for when we explore more advanced topics. Don't worry if it takes a fe reads to get it all down - I didn'twrite it all in one shot! That said, let's recap the major points:

The suspension's job is to keep the wheels in contact with the road / trail for maximum handling, andkeep the occupants isolated from the road / trail for maximum comfort. The right balance between rideand handling s the key to suspension success.The springs allow the wheels to move independently of the chassis, and the shocks damp their motion.A coilover is a clever component designed to package the shock and springs as a single system.When designing our suspension, we may think of its softness or firmness in these following ways - listedin ascending order of usefulness:

By spring rate - but this is not useful without knowing corner weights and shock / spring installationgeometry.By wheel rate - takes into account shock / spring geometry, but we still need to know cornerweights .By suspension height - takes into account geometry and corner weights - but also depends onspring lengths.By suspension frequency - takes into account geometry and corner weights, and is not affected byspring lengths.

The beauty of a coilover is that it allows us to design for a given frequency, and then easily tune toachieve a desired suspension height.Coilovers use multiple springs stacked in series, which results in an initial (normally softer) combineswheel rate that transitions at some point in the suspension's travel to a final (normally firmer) main wheelrate. By manipulating tender and main spring rates, we can achieve a soft, compliant ride for the majorityof our suspension's travel, and then a much firmer wheel rate in the last 20-40% of compression travel tosoak up the big hits without bottoming.Using the BV Calculator to pick preliminary spring rates is just the beginning of our journey!

Closing Notes

It is, of course, entirely possible to use the BV Calculator with SH as the goal, have no grasp of Fn, generatesome preliminary spring rates and then rush right out and buy springs and start installing things. In fact, peoplehave been using this approach since coilovers began appearing on offroad rigs - with decidedly mixed results!I began the article by suggesting that there are not really any "invalid" approaches to suspension design(although some are certainly better than others) so I am somewhat obliged to say that you may, if you wish, dojust this. I certainly don't recommend it though. If, however, you're the terribly impatient kind, and you're sojazzed at this point you simply must run out and buy springs and get at it - there are a few points I must leaveyou with so that you may at least avoid total disaster:

Spring Length

Spring length is a really big deal, and part of the intricate balance that will deliver the top performance weseek. If you can't wait for Part 3 then I recommend you buy a main spring with a length equal to the travel ofthe shock (so the DRS doesn't fall of the body at full droop) and a tender spring with a length that will put yourcoilover top spring seat in the middle of its adjustment range - which usually means a spring 2-4" shorter thanthe main spring, plus a helper coil and a triple-rate slider. If you go this route, you will be faced with manycompromises, even if you're not aware of them, but it will get you on the road and if you're willing to spend a lotof time and money testing and swapping different springs, you may eventually end up with a decent setup. Forthe rest of us, understanding the tech in Part 3 will provide a much more solid foundation for our eventualtesting and tuning.

Buying Coilover Shocks

There's plenty of choice in the market, I have experience with a few brands, but certainly not all. Personally, Ihave been running 16" 2.0 remote reservoir Fox Racing Shox for a number of years and they have performedextremely well and stood up amazingly to my abuse and neglect in a harsh 4-season environment. In fact, Ionce bent a rod quite badly, but continued wheeling on it for several trips without a leak, and as luck wouldhave it, some time later tagged a tree pretty hard and bent it back to darn near straight and that's how it hasstayed - it was pretty impressive. I particularly appreciate the quality of the hardware and the finish. The





one-page "manual" you get is less than impressive - but I guess that's why I get to write articles like this. Theiryears of experience, the fact that the company is virtually guaranteed to be around in the future, and the factthat you can buy any conceivable part at very reasonable cost are all good qualities too.

Buying Coil Springs

The quality of the springs you use are every bit as important as the shocks. Cheap springs will waste your timeand frustrate your efforts if they "take a set" or change length after use. A properly engineered andmanufactured quality coil spring should not lose free length or installed height under normal conditions. Also,cheap coils tend to have less travel before they coil bind than quality springs. There's simply no way you canproperly design and tune a coilover suspension without knowing the exact specifications of the springs -particularly the Free Length (Lo), Block Height (Lc), Travel (max defection) (Sc), and Force Limit (Fc). Everyspring is sold with a rate specified, but many do not include these other vital specs. We haven't covered thepractical application of all the specs yet, but trust me, they are critical. I have been using Eibach springs foryears, and can tell you that even after many years under a heavy, frequently abused rig any change in lengththat might have occurred is less than I can measure with a tape measure. Also, Eibach have an excellentcatalogue, a copy of which is linked below in the "resources" section, that clearly lists every spec you need toknow for every spring they sell - that is damn useful information and I'm impressed with how they publish it.

Where you buy your shocks and springs is an important consideration too. If you're going to rush ahead tobuying and installing, or if perhaps you don't have the time or inclination to learn all the tech, you need avendor with knowledge and experience. I've been using Dave Schlossberg and his company PolyPerformancefor years and have nothing but good things to say about them.

What's Next?

We've come a long way - and have plenty of road left to travel. Next is Part 2 where I'm going to cover somehands-on tech - it's good to break up the mental gymnastics with a good greasy-hands shop session.Following that, in Part 3 we'll pick the theory back up starting with spring length, suspension height tuning,preload and helper coils. Until then...

Resources:

Fox Shox 2.0 Series Valving Specs (pdf)

Fox Shox 2.5 Series Valving Specs (pdf)

Fox Shox Remote Reservoir Shock Rebuild Sheet (pdf)

Fox Shox Emulsion Shock Rebuild Sheet (pdf)

Eibach Springs Coil Spring Catalogue & Specs (pdf)

Eibach Springs Spring Application Guide (pdf)

References:

Chassis Engineering. Herb Adams, 1993, (HP Books)

Competition Car Suspension: Design Construction Tuning, Allan Staniforth, 1994, (Haynes Publishing)

Engineer to Win. Carroll Smith, 1985, (Motorbooks International)

How to Make Your Car Handle. Fred Puhn, 1981, (HP Books)

Machinery’s Handbook, 24th Edition. Gren, Robert E., Oberg, E., Jones, F.D., Horton, H.L., Ryffel, H. H.(Editors), 1992, (Industrial Press, Inc)

Race Car Engineering & Mechanics. Paul Van Valkenburgh, 1992, (HP Books)

Racing And Sports Car Chassis Design, Michael Costin And David Phipps, 1961, (B. T. Batsford Ltd.)

Tune to Win. Carroll Smith, 1978, (Motorbooks International)

Sources

PolyPerformance(805) 783-2060

http://www.polyperformance.com/[email protected]

Suppliers ofcoilovershocks,springs,bumpstopsand other highquality,brand-namesuspensioncomponents.

Shock tuning



http://www.polyperformance.com/

mailto:[email protected]



and rebuilding.

Manufacturersof customshockabsorbers.

Fox racing Shox(800) FOX-SHOX

http://[email protected]

Manufacturersof high quality,race-readycoilovershocks.

Full line ofemulsion,remotereservoir,internalreservoir, andexternalbypassshocks.

Eibach Springs1-800-507-2338

http://www.eibach.com

Manufacturersof high qualityprecisionengineeredcoiloversprings.

Get a GoStats hit counter



http://www.foxracingshox.com

mailto:[email protected]

http://www.eibach.com



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