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The Effects of Aft Cavity Inset and Boat Tail
Angle on Drag Reduction of Tractor Trailers
D. Maragno
K. D. Visser
Department of Mechanical and
Aeronautical Engineering
Clarkson University
Potsdam, NY
13699-5725
Report No. MAE-365
May 2003
i
Abstract:
The flow behind a moving tractor trailer is characterized by circulating regions of low pressure
which occupy a region referred to as the wake. This low pressure region is responsible for
aerodynamic pressure drag, and the size of the wake region is proportional to the drag force that a
tractor trailer experiences. Geometric manipulation of the rear of tractor trailers was attempted to
narrow the wake region and reduce drag. Specifically, plate-cavity devices were examined due to
their practicality and ease of use in industrial and commercial settings.
Previous work suggests that orthogonal plate designs are very effective in reducing drag
at zero degrees of yaw, however such designs become less effective with increasing yaw angles.
This study investigates the effect of yaw by angling the side plates inward by various amounts
and determining which angled plate geometry produces the largest reduction in drag for typical
highway conditions. Models for use in Clarkson University’s subsonic wind tunnel are examined
to determine which plate-cavity configuration statistically reduces drag by the greatest amount
between negative three and positive nine degrees of yaw. A force balance was utilized to
measure side forces and drag forces acting on the wind tunnel models. Results have been
acquired for 26 devices that compare the effects of three different lengths, two inset dimensions,
and five plate angles.
Results indicate that plates with a full scale length of four feet—the maximum length
tested—are most successful in reducing drag, and that for any positive plate angle, an inset
dimension of zero performs best. At zero degrees of yaw, the four foot, zero inset device having
a plate angle of 10 degrees reduced the drag coefficient by the greatest amount, while the device
having the same length and inset dimension but an angle of 15 degrees was most effective at yaw
angles greater than three. Both of these devices reduced drag more effectively than the optimum
devices tested with no plate angle, and all devices tested reduced drag at all yaw angles by
varying, positive amounts.
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Table of Contents:
Abstract i
Acknowledgments ii
Table of Contents iii
Table of Figures iv
List of Tables v
Nomenclature vi
1. Introduction 1
1.1 Motivation 1
1.2 Environmental conditions 2
1.3 Device Specifications 3
2. Background Information 5
2.1 Mathematical Background 5
2.2 Previous drag reducing efforts 5
2.2.1 Front End 5
2.2.2 Aft End 6
2.3 Aft Modification by Plate-Cavity designs 7
2.4 Scope of Current Research 12
3. Research Methodology 15
3.1 Clarkson University wind tunnel facility 15
3.2 Wind tunnel base model specifications 16
3.3 Bi-Axial force balance 17
3.4 Other instrumentation 19
3.5 Plate device construction and preparation 20
3.6 Calibration 22
3.7 Wind tunnel operation procedure 23
4. Results 24
4.1 Solution Method 24
4.2 Summary of zero yaw results 26
4.3 Summary of results at all yaw angles 28
4.4 Effects of top plate removal 31
4.5 Results of select special cases 32
5. Conclusions 34
5.1 Data Observations 34
5.1.1 Impact of inset dimension 34
5.1.2 Impact of plate length 34
5.1.3 Impact of boat tail angle 35
5.1.4 Impact of top plate removal 35
5.2 Future recommendations 35
Appendix A: Uncertainty analysis 38
References 40
iv
Table of Figures:
1.1 Wind velocity components over a tractor trailer 21.2 Probability of exceeding a given yaw angle for a truck
traveling 25 m/s. 3
2.1 Examples of rounded boat tail (a), pointed boat tail (b), and truncated boat tail (c). 7
2.2 Mason and Beebe add-on devices. a) Vertical and HorizontalSplitters, b) vanes, c) cavities. 8
2.3 MAKA Innovations design 92.4 Flow around a plate-cavity device with inset dimensions 9
2.5 Prototype of Coon plate-cavity design 102.6 Percent reduction in drag coefficient vs. yaw angle for
optimum Coon device 112.7 Stream line diagram at the rear of a tractor trailer 11
2.8 Flow surrounding vehicle with angled plates 132.9 Effective plate angle based on yaw 14
3.1 Interior Wind Tunnel illustration 153.2 Model positioning in wind tunnel 17
3.3 Force Balance with Load Cells Shown 183.4 Data acquisition board 19
3.5 Examples of device models tested. a) variation in wall length. b) variation in narrowing angle. c) Variation in inset dimension.
d) variation of all parameters 213.6 Device model, attached to trailer model 21
3.7 Calibration device 223.8 Sample calibration curve 23
4.1 Side force and Drag schematic 25
4.2 Drag coefficient reduction vs. narrowing angle for: a) 2’ models, b) 3’ models, c) 4’ models. 27
4.3 Drag coefficient reduction vs. narrowing angle for all zero inset cases 284.4 The effects of yaw on all zero inset models: 29
4.5 Best cases compared 304.6 Percent drag reduction of best performers 31
4.7 Effects of top plate removal 324.8 MAKA and Visser and Coon performance plots 33
v
List of Tables:
1.1 Percent contribution of drag components to overall drag 1
1.2 Dimensional Constraints 43.1 Plate-cavity design geometries investigated 20
A1 Experimental Uncertainties 40
vi
Nomenclature
A Projected frontal area
A1 Cross sectional area of inletA2 Cross sectional area of test section
Ac Area contraction ratioAf Frontal area of vehicle
As Area of one side of vehicleCD Coefficient of drag
CDbase Reference drag coefficient
DCD Reduction in coefficient of drag
D Drag force
DT Drag measured by drag force load cellDD Component of drag measured from drag load cell that
contributes to overall vehicle dragDSF Component of overall drag that is measured by the side
force load cellF Force due to pressure
i Inset dimensionL Plate length
P or Ptotal Atmospheric pressure
DP Differential pressure
R Universal gas constantSFT Side force measured by balance
T TemperatureUx Uncertainty of quantity x
V Velocityf or phi Boat tail angle
r Density of air
y yaw angle
1
1. Introduction
The purpose of this study was to passively reduce the pressure-induced wake drag oftractor trailers through use of an added aft-end cavity style device. Specifically, theeffects of cavity inset dimension and cavity plate angle were investigated.
1.1 Motivation
The US department of transportation reports that there were 1,997,345 combinationtrucks, including nine-axle tractor trailers, in service in 19981. Between all of them,approximately 128.4 billion miles were traveled, resulting in 21.1 billion gallons of fuelconsumed by these vehicles for the year. This translates into an average of 6.1 milestraveled per gallon of fuel consumed. Considering the average cost of fuel per gallon of$1.285 in 1998, and the average number of miles traveled per combination truck of64,265 for the year, each vehicle required on average approximately $13,538 for fuelexpenditures in 1998.
Given the figures above, there is an obvious economic motivation to reduce thefuel consumption of tractor trailers on the road today. Reduction of fuel consumptionwould save enormous dollar amounts for transportation businesses that use hundreds oftractor trailers for freight delivery at any given time. However, there are alsoenvironmental motivations for reducing fuel consumption of large vehicles. It has beenapproximated that tractor trailers emit an average of 6.1 grams of hydrocarbons per mileand 61.07 grams of carbon monoxide per mile. Considering the total mileage of alltractor trailers in 1998, the total emissions for that year were 7.83*108 kg ofhydrocarbons and 7.84*109 kg of carbon monoxide1. Because carbon monoxide is aproduct of engine exhaust, and the quantity of engine exhaust is directly related to theamount of fuel consumed, it is assumed that a reduction of fuel use would reduce thequantity of pollutants emitted into the atmosphere. With an increasing push for federalregulations of vehicular and other emissions, there may become an increasing legalincentive to reduce fuel consumption as well.
Vehicle weight, engine and drive train efficiency, friction, fuel properties, andvehicle geometry are some of the factors that affect the fuel efficiency of a vehicle. Theprimary focus of this study is to reduce fuel consumption by reducing the pressure-induced wake drag of tractor trailers, which is a function of geometry. Table 1.1illustrates the contribution of tractor trailer geometric features to its overall drag.
Table 1.1: Percent contribution of drag components to overall drag2
Skin friction 5 %
Fore-body 20 %
under-body 50 %
Base 25 %
2
As is seen in the above table, the base, referring to the cross-sectional area at the rear,contributes approximately 25% to overall drag. As is discussed in the next chapter, muchwork has been done to decrease the contribution of the fore-body to overall drag, whilecomparatively little effort has been made to reduce the contribution of the aft-end tooverall drag.
1.2 Environmental conditions
The majority of large vehicle traffic occurs on highways and interstates. As such, there islittle acceleration experienced, and typical speeds are between 25 and 30 m/s. Forstagnant wind conditions, the air flow over a vehicle tends to be approximated as one-dimensional, moving from the front of the vehicle and toward the rear. The wind speedover the vehicle is directly related to the traveling speed of the vehicle.
If a crosswind is experienced, the flow can no longer be approximated as one-dimensional. Figure 1.1 illustrates the way in which the flow can be represented bycomponents. The component from the truck velocity and the cross-wind component areadded to form the resultant velocity, and its angle y is referred to as the yaw angle. The
probability of exceeding a wind-induced yaw angle in typical highway conditions by atruck traveling at typical highway speeds is represented by the distribution in Figure 1.2.3
From the data plot in Figure 1.2, it is noted that yaw angles in excess of 9 degrees occurabout 10 percent of the time. The data represented in the plot was gathered from 30Canadian weather stations in 1982, and the average wind speed for the year was found tobe 11.3 km/h. This velocity can induce a maximum yaw angle of 7.3 degrees for a trucktraveling 25 m/s, as indicated in the figure.
Figure 1.1: Wind velocity components over a tractor trailer
3
Figure 1.2: Probability of exceeding a given yaw angle for a truck traveling 25 m/s. 3
1.3 Device Constraints
The objective of this study was to reduce the drag of tractor trailers in typical highwayconditions. This was intended to be accomplished by attaching a plate-cavity style deviceto the rear of existing trailers in order to manipulate the flow field in such a way that thepressure-induced drag is reduced. The physics behind this process is explained in chaptertwo.
When considering the geometry of a device to attach on existing vehicles, thereare dimensional and other physical constraints to be mindful of. Some of theseconstraints are governed by legal issues while others are governed by practicalityconcerns. The practicality concerns consider the usual operations of a tractor trailer,including: methodology for loading and unloading the trailer, space requirements fordocking and parking, rear door operation and safety, fork lift access, and others. Materialproperties and construction cost issues are not within the scope of this research aretherefore neglected. Some specifications for a rear device are listed in Table 1.2.Specifications having to do with practicality concerns are labeled with a “P,” whilespecifications having to do with legal issues are labeled with an “L.”
4
Table 1.2: Dimensional Specifications List
L The total length of the tractor and trailer combination vehicle must notexceed 53 feet. Until 2009, this condition does not apply in Canada tovehicles manufactured prior to 1999.4
L A performance enhancing attachment such as this must not extend thelength of the vehicle by more than 5 feet
L The vehicle height may not exceed 13.5 feet.L,P The rear doors must be able to latch securely, preferably with the same
ease as currently experienced with an unaltered trailer.P The doors must be able to open fullyP Docking procedures should remain unaltered, and fork lift access to the
cargo region must not be restricted
Given the above issues, it was decided that a plate-cavity device would be themost suitable. Such a device can be easily collapsed to allow unhindered access to therear doors, and such a device can be easily manufactured. Previous research, discussed inchapter 2, suggests that such a device is also effective in reducing drag and is desirablefor this function.
5
2. Background information
A review of previous drag reducing efforts on tractor trailers and justification of usingaft-end plate-cavity devices is presented below.
2.1 Mathematical Background
Drag force of any object is typically expressed as:
fD AVCD 2
2
1r= (1).
Velocity and air density are generally fixed parameters and are not altered in the designof vehicles to reduce drag. The remaining parameter then is area, which if lowered mayreduce drag. Area refers to projected frontal area to an on-coming flow. The projectedfrontal area considers body dimensions, wheels, undercarriage protrusions, lights, andmirrors. Assuming that measurements of the frontal area of the vehicle Af are obtained,as well as the area of one side of the vehicle As, the expression for projected frontal areaat any yaw angle may be obtained as:
yy sincosexp sfosed AAA += (2),
where the side area accounted for is assumed to be facing the onward flow.
Since drag is often known or measured for an object, equation 1 is solved for thecoefficient of drag. For an altered geometry, the base or original CD is compared to thenewly obtained CD to calculate the percentage drag savings, as follows:
100100% xC
Cx
C
CCsDragSaving
basebase
devicebase
D
D
D
DD D=
-= (3).
It is desirable in this study to maximize the percent drag savings. The methodology formeasuring drag changes is described in chapter 3. For an average Class 8 tractor trailer,weighing approximately 80,000 pounds, the base drag coefficient is approximately 0.6.5
2.2 Previous Drag Reducing Efforts
2.2.1 Front End
Little attention was given to the aerodynamic design of large ground vehicles to improvefuel efficiency prior to the oil crisis of the 1970's. Since then a great deal of modificationhas occurred to the design of the front cabs of tractor-trailers in order to reduce themagnitude of pressure induced drag acting on the vehicle. Such modification hasincluded the addition of deflectors and roof fairings, front edge rounding, and changes inthe front bumper and engine grill designs.
6
A survey of 965 tractor trailers in the western United States in 1975 revealed thatapproximately 79 percent of cab configurations were of the cab-over-engine (COE) type6.Since then, a gradual transformation has occurred such that the predominant cabconfiguration today is the conventional, or long nose, type. Many cabs of this type aremanufactured with aerodynamic fairings above and behind the cab, which essentiallyshield the entire front face of the trailer from on-coming flow and narrow the gapbetween the cab and trailer. The fairings gradually increase the cross-sectional area, asopposed to suddenly increasing it as with its absence. This helps the flow field to remainuniform and attached, keeping pressure at a desired lower value at the front.
Over the past decade, the profiles of tractor trailer cabs have become increasinglysmooth and many of the severe slope discontinuities present in older vehicles havedisappeared. These modifications have significantly reduced the fore-body contributionto drag, and this trend continues today. Several representatives at a workshop held inPhoenix, Arizona in January of 1997 have agreed on a goal of reducing the coefficient ofdrag on tractor trailers to .25. For comparison, a perfectly rectangular vehicle tested byNASA6 in 1974 at a speed of 60 miles per hour had a drag coefficient of .89, asdetermined by coast-down tests. While front end modifications have reduced dragcoefficients to lower than .3, it is recognized that aft-end modifications must be employedto reduce the drag coefficient to lower values than the goal set in Phoenix.
2.2.2 Aft End
The NASA experimentation discussed in the previous section included research on theeffects of some aft-end modification. The baseline vehicle with a drag coefficient of .89was used for comparison against modified geometries. Some important findings fromtheir research are listed below:
1. The addition of a truncated boat design to the end of the baseline vehiclereduced the coefficient of drag to .242, which is lower than the expressed goalof .25.
2. As fore-body drag is reduced, after-body drag increases. This trend wasnoticed for van-type trailers, but full scale testing on tractor trailercombinations is recommended for verification.
3. Assuming the second conclusion is true, aft-end modification of large vehiclesis necessary to reduce the drag coefficient to less than .25. This is because thefore-body drag and the aft-end drag components are additive.
4. A full aft-end boat-tail device reduced the overall drag coefficient to .238
A full boat-tail device, it should be noted, is one which gradually reduces the crosssectional area of the aft end to a single point. Such designs help to keep the flow behindthe trailer attached. Flow separation is a primary cause of large pressure gradientsbetween the front and rear of the vehicle, or aerodynamic drag. It should also be notedthat the truncated boat tail case is nearly as effective as the full length boat tail. In thetruncated case, the tail is shortened to maintain the vehicle to within legal length limits.
7
Figure 2.1 illustrates an example rounded boat tail, pointed boat tail, and truncated boattail.
Figure 2.1: Examples of rounded boat tail (a), pointed boat tail (b), and truncated boattail (c).
Boat tail concepts such as these have been patented by Lechner7, Keedy8, Davis9,Mulholland10, and others, often with slightly modified geometric characteristics.
2.3 Aft modification by plate-cavity designs
While the results of boat-tail after-body vehicle modifications are quite positive, thesemodifications fall short from a practical stand point. Boat-tail designs are difficult andexpensive to manufacture, and they severely restrict access to the cargo doors at the rearof all tractor trailers. A detachable boat-tail design may be of some value, butconsidering their necessary size, they would likely be both awkward and heavy to move.Also, such devices risk extending some vehicles beyond the legal length of 53 feet asthey require a considerable length to be most effective.
By contrast, the plate-cavity design is easily manufactured, can be attached to anyexisting trailer with two cargo doors in the rear which swing open, and is easilycollapsible so as not to interfere with typical operations. While the boat tail concept isdesigned to minimize flow separation along the trailer edges, passive manipulationconcepts involving the use of plates have been designed to allow separation off of the
8
trailer edges to guide the subsequent direction of flow. Mason and Beebe11 experimentedwith orthogonal vertical and horizontal splitters, vanes, and non-ventilated cavities,which are illustrated in figure 2.2.
Figure 2.2: Mason and Beebe add-on devices. a) Vertical and Horizontal Splitters, b)vanes, c) cavities.
The splitters in Figure 2.2a were intended to trap vortex structures in defined regionsbetween the trailer edges and the plates, but a negligible reduction in drag was reported.The vanes in Figure 2.2b were intended to direct flow inward toward the low pressureregion, but a drag increase was reported for these designs. The cavity devices shown inFigure 2.2c had the best results, reducing drag by 5%, presumably because of an increaseof pressure inside of the cavity.
Hucho12 performed research with four walled cavities in the late 1970’s, witheach plate flush with the edges of the trailer (inset dimension of zero). For a plate lengthto vehicle length ratio of 0.22, an approximate 6% reduction in drag was observed.Bilanin13 patented a device with plates orthogonal to the rear of the trailer with non-zeroinset dimensions from the top and side edges of the trailer, but not from the bottom edge.As with the Mason and Beebe devices, the intent of the inset dimensions is to trap vortexstructures, resulting from flow separation from the trailer, between the trailer’s edges andthe plates. Figure 2.4 illustrates the expected flow pattern around such a device.
9
Figure 2.4: Flow around a plate-cavity device with inset dimensions (From Coon14).
Bilanin claims that a drag reduction of 10% has been achieved for his device, howeverresults have not been published in the literature.
More recently, MAKA Innovation, based in Quebec, Canada, has patented andmarketed a plate-cavity device in which each plate is angled inward 16 degrees from aplane normal to the trailer face. The device uses three plates, mounted flush to the topand side trailer edges. Each plate is 20-24 inches in length14. Figure 2.3 offers anillustration of the MAKA device.
Figure 2.3: MAKA Innovations design
Insetdimension
10
The angled plates of the MAKA device separate the flow at their edges and guide theresulting vortices toward the low pressure region behind the trailer, thus narrowing thesize of the low pressure region.
Figure 2.5 illustrates a full scale prototype tested by Coon and Visser14. Coon andVisser experimented with Hucho and Bilanin type devices in that they created cavitieswith four plates, each perpendicular to the rear of the trailer. Various plate lengths andinset dimensions were investigated.
Figure 2.5: Prototype of Coon and Visser plate-cavity design
Highway results from the Coon and Visser research suggest that as much as an 8.5percent reduction of drag may be had with a four-walled device of this type. Figure 2.6illustrates the reduction in the drag coefficient vs. yaw angle for the optimal Coon andVisser device based on current measurements taken at zero degrees of yaw. It is seen thatthe drag coefficient is reduced by about .085 for this device at zero degrees of yaw, whichrepresents an 8.5 percent reduction in overall drag for this device. The optimum Coonand Visser device at zero yaw had wall lengths of four feet, with an inset dimension ofsix inches from the top, left, and right sides of the trailer. Note that at increasing yawangles, the performance of the device diminishes.
11
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-4 -2 0 2 4 6 8 10
Yaw angle (degrees)
CD R
ed
ucti
on
Figure 2.6: Reduction in drag coefficient vs. yaw angle for optimum Coon and Visserdevice
Some of the drag reduction illustrated above may be attributed to the reduction of cross-sectional area at the rear, however some other physical characteristics of the flowsurrounding the device may be responsible even more so for the reduction of drag.
Figure 2.7 is a suggested stream-line diagram surrounding the profile of a tractortrailer without an attached device, based on observations by Mason and Beebe11.
Figure 2.7: Stream line diagram at the rear of a tractor trailer (From Coon14)
As is seen in the figure, there is a large recirculation bubble directly behind the trailer.This is a region of turbulent flow, which is characterized by low pressure. The turbulentflow continues for a large distance downstream of the trailer in a region referred to as the
12
wake. The aerodynamic wake drag may be thought of as the difference between pressureforces pushing at the front of a moving tractor trailer and the pressure forces pushing inthe opposite direction at its rear. The force due to pressure, F, is given by:
PAF ª (4),
however the projected areas of the front and rear of the trailer are equal, thus the forcedue to pressure acting along either of these faces of the tractor trailer is directlyproportional to the magnitude of the pressure along that face. Because the pressurewithin the wake region directly behind the trailer is comparatively low to the pressurealong the front face of the trailer due to flow separation at the rear, the magnitude of thepressure force pushing against the front of the vehicle is larger than the correspondingforce pushing against the rear. The difference between these forces accounts for pressureinduced aerodynamic wake drag.
It is suggested by the Coon and Visser research and by previous research byHucho, Bilanin, and others that rear plate attachments minimize flow separation in thewake region, thus reducing the size of the wake overall, and that the flow may even besucked into the cavity to increase its static pressure. These effects would reduce thepressure drag. Note from Figure 2.7 that a low-pressure separation bubble forms fromthe bottom surface of the trailer, while the flow from the top surface forms no suchbubble. The four plate design may be simplified to account for this.
2.5 Scope of current research
While the Coon and Visser, Hucho, and Bilanin tests considered orthogonal plate designsthat attach perpendicularly to the rear surface of the tractor trailer, the currentinvestigation examined the effects of angling the vertical side plates inward to mitigatethe effects of yaw, as with the MAKA design. The angle of these side plates is referredto as the boat tail angle, and the desired effect is to narrow the wake region, thus reducingthe overall size of the wake. It was hypothesized that similar results experienced byCoon and Visser for zero degrees of yaw will be experienced by the current designstested at yaw angles of the same magnitude as the corresponding boat tail angles. Figure2.8 illustrates this phenomenon.
13
Figure 2.8: Planform view of vehicle geometry with angled plates
In the above case, the angled plates do not cause separation of the flow and may evenforce it to remain attached at higher yaw angles. Also, the plates configured as such donot increase the vehicle area exposed to the flow.
Because yaw angles above 10 degrees are rare in highway conditions, themajority of angled plate designs were angled to a lesser degree. However, someinvestigated designs include boat tail angles as high as 20 degrees. For a yaw angle of 10degrees, a boat tail angle of 20 degrees would effectively be angled inward 10 degreesfrom the oncoming flow. Figure 2.9 illustrates this. The effective plate angle withrespect to yaw is given in the figure as f-y, where the plate angle with respect to the rear
of the trailer is f. Since air is a viscous fluid, it is expected that a flow along the side of
the trailer would stick to the plate at the rear which is angled inward until it is shed fromits tip. As the flow sheds from the plate, its flow direction is inward at an anglecomparable to the angle of the plate. As such, the flow separation region behind thetrailer is narrowed, and thus so is the region of associated low pressure. This assumptionis valid for small angles as it is assumed that the flow will not remain attached to a platethat is angled excessively inward.
14
Figure 2.9: Effective plate angle based on yaw
15
3. Research Methodology
The methods employed to measure drag reduction resulting from various aft-end plategeometries are presented below.
3.1 Clarkson University wind tunnel facility
Many of the potential aft-end design combinations with parameters described in section2.5 have been fabricated for fitting on a 1:15.25 scale tractor trailer model constructed byCoon and Visser14 for use in the Clarkson University indraft, open circuit, subsonic windtunnel. The wind tunnel test section has cross section dimensions of 48in. by 36in. and alength of 65 inches. The inlet contraction ratio is 4.67:1.
As recommended by the Society of Automotive Engineers,15 a smooth simulatedroad bed at an elevated height of 12 inches (allowing model positioning at test sectioncenter) is included in the tunnel. It is constructed with a 0.5 inch thick impermeableboard and spans the dimensions of the wind tunnel test section. Its purpose is tominimize the boundary layer thickness which reduces error in the wind tunnelmeasurements since there ordinarily wouldn’t be a boundary layer growth from the roadresulting from vehicle traffic in physical conditions. The tractor trailer model is attachedabove the simulated road bed, as seen in Figure 3.1.
Figure 3.1: Interior of Wind Tunnel
The road bed is supported by 8 threaded rods that are each 0.5 inches in diameter, whichallows for adjustment to assure that the road bed is parallel to the top and bottom walls ofthe tunnel test section at all locations. The bed is stationary at all times and does not havea moving belt simulating vehicle travel as used by Beauvais16, however Beauvais reportsthat such a mechanism is not necessary to quantify performance differences betweenmodified devices.
Road bed
16
During testing, the maximum velocity achieved by the wind tunnel is 48 mph, orabout 21.5 m/s. Based on trailer width, the Reynolds number produced by this velocity isabout 2.3x105. If it is assumed that a full scale tractor trailer experiences an average windspeed of 28 m/s in standard sea level conditions, and that the usual width of a tractortrailer is 2.46 meters, the resulting full scale Reynolds number is 4.5x106. The SAEWind Tunnel Test Procedure for Trucks and Buses15 suggests a minimum experimentalReynolds number of 0.7x106, which is above the values seen with the current wind tunnelsetup. According to Coon and Visser14, the scaled dimensions of the wind tunnel basemodel (having no attachments) were selected based on resulting blockage of the testsection cross sectional area, satisfying requirements set forth by Mason et al17. Reynoldsnumber conditions set forth by the SAE Wind Tunnel Test Procedure15 are not satisfied,meaning that the drag measured in the tunnel may not be considered equivalent to thedrag a full scale vehicle would experience at the same velocity, but varies by a scalefactor.
3.2 Wind tunnel base model specifications
The wind tunnel base model (having no cavity device attached) was 1:15.25 scalerepresenting a 1990’s generation Peterbilt model 379 tractor trailer. The cab wasconstructed with light weight foam and is covered with a layer of polyurethane in order tominimize its porosity and maximize its rigidity. The tractor trailer model has a frontalarea of 61.7 in2 and a side cross-sectional area of 372.6 in2. This area includes the detailsof a 1990’s generation Peterbilt model 379 cab with a standard trailer having a full scalelength of 48 feet, excludes mounted lights, mirrors, door handles, and many underbodyobstructions, and accounts for a tractor-trailer combination of typical dimensionsdescribed in chapter one. The tractor trailer frontal area obstructs an area of 3.49% of thecross-sectional wind tunnel test section area at zero degrees of yaw, which is less than 5%as recommended by Mason et al17.
The cab is connected rigidly to the trailer by a wooden beam, and the trailer wasconstructed from plywood. A gap of 2.5 inches (38 inches full scale) exists between thecab and trailer. Undercarriage protrusions include mounting devices for a set of nineaxles and 18 fixed rubber wheels. The total length of the model is 51.35 inches, with thetrailer comprising approximately 37.75 inches of the total length. The model wasmounted at the center of the test section.
A .75 inch diameter steel mounting sting was attached to the undercarriage of themodel at its center of gravity, which was determined by finding the balancing point of themodel. The location of the mounting sting on the trailer model minimizes bendingmoment contributions of the model on measured drag data. The process used formeasuring drag is described in section 3.3. The portion of the sting residing inside thewind tunnel is shielded by a 1.25 inch diameter PVC pipe in order to minimize measuringerrors due to shedding vortices from the sting. The sting does not contact the PVC pipeor the simulated road bed at any time. Figure 3.2 illustrates the wind tunnel setup andpositioning of the trailer model.
17
Figure 3.2: Model positioning in wind tunnel
3.3 Bi-Axial Force Balance
Side force and drag measurements are recorded through use of an in-house customizedforce balance. The force balance is a device which sits below the wind tunnel test sectionand consists of two nearly frictionless IKO International linear translators with crossedroller bearings, allowing for two degrees of freedom in horizontal directions.Propagating from these translators and into the wind tunnel test section is a sting onwhich the trailer model rests. The drag forces acting on the trailer model as a result of theflow through the tunnel cause it to displace along with the attached translators. Restingagainst the translators via customized brackets are load cells which are essentiallyaluminum cantilevered beams that can flex and have a built-in electronic strain gaugewhich is used to measure forces applied to it. As drag forces cause movement of thetranslators, the translators push against the load cells causing them to flex. The flexcauses a change in the electrical resistance of the cells, which thus changes the voltageoutputted by them. LabVIEW software was used to write a program using graphicallanguage G in order to interpret the change in voltage outputs by the load cells as ameasure of the change in drag forces acting on the trailer. The resulting dragmeasurements recorded by LabVIEW are based on inputted calibration coefficients. Thecalibration procedure is described in section 3.5.1, and other instrumentation used fordata acquisition is described in section 3.3.2. Figure 3.3 shows the load cells in relationto the translators.
Bi axial balance
Data acquisition board
Powersupply
Flow direction
Sting guard
Splitter plate
18
Figure 3.3: Force Balance with Load Cells Shown
The load cells used with the force balance shown above are both Precision Transducersmodel PT1000. Both require an excitation voltage of 10 V and have a precision of 2.0mV/V. The manufacturer specified instrument error for both cells are 0.0300% of theapplied load. The drag load cell has a range of 0-3 kg and the side force cell has a rangeof 0-5 kg, which is acceptable as the forces measured during experimentation was on theorder of 0.5-1.5 kg and 0.0-2.0 for the drag and side force directions, respectively.
3.4 Other Instrumentation
A differential pressure transducer is used to measure the pressure drop inside the tunnelassociated with the tunnel velocity. Equation (5) is used to determine the wind tunnelvelocity V at any time.
totalc
PA
PRTV
D=
2 (5)
In the above equation, R is the universal gas constant, T is temperature in degrees Kelvin,
DP is the pressure differential inside the tunnel (Bar), and Ptotal is the total atmospheric
pressure (Bar). Coupled with equation (1), the drag coefficient may be obtained fromequation (5). The area contraction factor, Ac, is a function of the contraction ratio of thewind tunnel and is given by equation (6):
2
1
21 ˜̃
¯
ˆÁÁË
Ê-=
A
AA
c (6),
where A1 and A2 are the cross sectional area of the tunnel inlet and the cross sectionalarea of the test section, respectively.
Side force Loadcell
Drag forceload cell
Linear translator(side force direction)
19
The unknown quantities of equation (5) are temperature, pressure differential, andtotal pressure. An Omega EWS-TX temperature transducer is used to obtain temperature,the pressure differential is obtained with a Modus model DT differential pressuretransducer, and the atmospheric pressure is measured with a Setra model 276 barometricpressure transducer. The uncertainties associated with these transducers are 0.6 °C,
0.0491 in.H2O, and 0.750mb for the temperature, pressure differential, and atmosphericpressure transducers, respectively.
A National Instruments data acquisition board, illustrated in Figure 3.4, was usedto communicate the voltage outputs of the load cells and the three other transducersdescribed above to the Dell 800 MHz computer. The computer was equipped with aNational Instruments data acquisition card model PCI-6024E. LabVIEW was then usedto convert transducer voltage outputs to desired quantities with appropriate units, basedon calibration coefficients provided by the transducer manufacturers or obtainedaccording to section 3.5.1.
Figure 3.4: Data acquisition board
3.5 Plate device construction and preparation
Wind tunnel tests for the configurations outlined in Table 3.1 below and the optimumCoon and Visser device were performed at five yaw angles: -3, 0, 3, 6, and 9 degrees.The yaw angle was accomplished by angling the truck model inside the tunnel to exposethe model sides to the oncoming flow. The series of yaw angles does not increasebeyond nine degrees because, according to Figure 1.2, yaw angles experienced in naturerarely exceed this amount. While negative three and positive three degrees of yaw should
Load cellinputs
Computer output
20
produce the same reduction of drag forces for each device, both were tested to check forsymmetry.
Several plate geometries were constructed and tested for wind tunnel use and aresummarized in Table 3.1 below. The dimensions indicated are the equivalent full scaledimensions.
Table 3.1: Plate-cavity design geometries
Geometric Parameter Experimental QuantityNumber of plates 3 (bottom and sides only), 4Side inset dimension i 0, 6 inchesTop inset dimension j 0Bottom inset dimension k 0boat tail angle f 0, 5, 10, 15, 20 (degrees)
Top plate angle g 0
Bottom plate angle z 0
Plate length L 24, 36, 48 (inches)Plate thickness t .9 inches
The test parameters specified above offer a potential of 60 combinations of widelyvarying specifications. An inset dimension of six inches for the side plates was selectedin order to compare with the Coon and Visser optimum device having the same insetdimensions.
Figure 3.5 illustrates examples of the array of device models that were tested inthe wind tunnel. The models shown illustrate the varying inset dimensions, wall lengths,and boat tail angles. Figure 3.5a illustrates models having the same boat tail angle andinset, but with plate lengths of 2, 3, and 4 feet, to scale. The plate length refers to thelength of the side plates. The lengths of the top and bottom plates are adjusted to extendthe same distance as the side plates from the rear trailer face so that the trailing edges ofeach plate lie within the same plane. Figure 3.5b illustrates models with 4 foot platelengths and zero inset with varying boat tail angles from zero to 20 degrees, shown infive degree increments. Figure 3.5c illustrates variation only in inset dimension, showinga zero inset model and a model with a 6 inch inset, to scale. The inset dimension is withrespect to the side edges of the trailer only. It was determined by Coon and Visser14 thatit is more beneficial in a drag reducing sense to maintain the bottom plate at an inset ofzero. In the current investigation, the top and bottom plates remain flush with the traileredges. Figure 3.5 d illustrates four models, each with varying parameters. The modeledplates are built using polystyrene, chosen for its relative strength and ease ofconstruction. The base plate, which attaches to the rear of the trailer model, is made ofPlexiglas and has magnetic strips for easy attachment and removal to the trailer model.The magnetic strips adhere to the steel backing of the trailer model and do not leave gapsthat might disturb surrounding flow. Figure 3.6 illustrates how the device models lookafter being attached to the trailer model inside the wind tunnel.
21
a) b)
c) d)
Figure 3.5: Examples of device models tested. a) variation in wall length. b) variationin boat tail angle. c) Variation in inset dimension. d) variation of all parameters
Figure 3.6: Device model, attached to trailer model
22
3.6 Calibration
Prior to each set of data collected, calibration of the load cells is required. Thecalibration process involves loading the force balance along the side force and dragdirections by known amounts and determining the linear relationship between the appliedloads and the outputted voltage reading. A weight-application mechanism wasconstructed and is shown in Figure 3.7.
Figure 3.7: Calibration device
As can be seen in the above figure, a series of weights are applied to an inelastic string ina downward direction, and by a series of assumed frictionless pulleys, the weight isshifted horizontally to pull against the force balance in the drag or side force directions.An output voltage V vs. applied weight W graph is generated as in Figure 3.8, and theequation of the line having the form V=AW+B is determined with Microsoft Excel. Thecoefficients A and B are calibration coefficients inputted into LabVIEW to translatevoltage measures into force measures.
Applied load
23
Sample Drag Calibration Curvey = 1969.6x + 9.4154
R2 = 0.9999
-5
0
5
10
15
20
25
-0.006 -0.004 -0.002 0 0.002 0.004 0.006
output voltage (V)
Ap
plied
fo
rce (
N)
Figure 3.8: Sample calibration curve
In the above plot, the equation of the line is provided in the upper right corner. In thiscase, the calibration coefficients are A=1969.6 and B=9.415.
3.7 Wind tunnel operation procedure
After calibration is complete and the trailer model is securely set to a specific yaw angle,a base test is run to determine the quantity of drag experienced with no device attached.Each geometry is then attached at the particular yaw angle for a series of data collection.The wind tunnel motor runs at full speed with the vanes fully open, achieving velocitiesin the tunnel approaching 48 miles per hour. During all tests, 40 voltage readings, orpoints of data, are collected at a rate of 1 second per point with a sample rate of 1000readings per second. That is to say, 1000 readings are recorded and averaged into asingle data point, and the process is repeated 40 times over 40 seconds. The wind tunnelis powered down and then run back up to speed between points 20 and 21 to reduce anyeffects of backlash in the load cell system. The 40 data points are then averaged into asingle reading for drag and side force, yielding a statistical measure of forces acting uponthe truck model. A resultant drag force is obtained for each device tested and iscompared against the base drag measurements to determine the potential of each devicefor drag reduction. The process of obtaining a resultant drag force is described in section4.1.
It should be noted that base conditions are tested periodically to check forconsistency of force measure. If it is found that the measurements of the drag forces forthe base case taken at different times are diverging, recalibration and possible adjustmentof the trailer model position becomes necessary. Also, to account for possible errors inthe calibration curves, an occasional “wind-off” test is performed to be sure that the sideforce and drag measurements in these cases are zero. All non-zero measures indicated inthese tests are averaged and treated as an offset when observing the other data.
24
4. Results
A summary of all experimental findings are outlined below.
4.1 Solution Method
The wind tunnel is operated such that data is recorded 40 times for each experimentalrun. For each data output, LabVIEW reports room temperature (C), wind tunnel pressuredifferential (mbar), ambient pressure (Pa), tunnel velocity (mph), side force in thedirection of the side force load cell (N), and drag force in the direction of the drag loadcell (N). Each of these conditions are measured with instrumentation described insections 3.3.1 and 3.3.2. An average of the 40 measurements obtained for each quantityduring each experimental run is determined so that these results might be comparedagainst results from other experimental runs more easily.
After each calibration, a series of data is collected with the wind tunnel poweredoff. In these cases, the wind tunnel pressure differential, tunnel velocity, side force, anddrag force are zero and should be reported as such. However, calibration approximations,room vibrations, and instrument white noise frequently cause non-zero values to bereported for each of these quantities. To correct for this, the 40 “wind-off” valuesreported for each condition are averaged and are treated as offsets for the data collectedlater with the tunnel run at full speed.
The side force and drag quantities reported, after adjusted with offset values,represent components of these forces that act in the directions of the respective load cellson the bi-axial force balance. For measurements taken at zero degrees of yaw, side forceand drag indeed act on the trailer model in the same directions as the load cells, howeverfor any non-zero yaw measurements, the force balance components reported must beresolved along the side force and drag axes of the vehicle model. Figure 4.1 illustratesthis point.
25
Figure 4.1: Side force and Drag schematic
In the above figure, if flow is moving in the positive X direction, then the resulting sideforce on the vehicle is described by the SAE wind tunnel test manual16 as negativebecause it acts in the negative Y direction. Equations 7-8 describe how to resolve themeasured balance forces onto the drag axis of the vehicle. The process may be adaptedto determine forces acting along the side force axis of the vehicle, however drag is theprimary concern of this study.
ycosTD
DD = (7)
ysinTSF
SFD -= (8)
In the above equations, DD refers to the portion of drag acting in the drag load celldirection that contributes to the overall drag on the vehicle, and DSF refers to the portionof side force, as measured by the side force load cell, that contributes to the overall dragacting on the vehicle. The drag and side forces measured by the force balance arerepresented by DT and SFT, respectively. As there are no other components to consider,the overall drag acting on the vehicle is the sum of equations (7) and (8), or:
yy sincosTT
SFDD -= (9).
Finally, the coefficient of drag is determined with equation (1). Because the drag forcewas resolved along the longitudinal axis of the vehicle, the area referred to in equation (1)is the frontal area of the vehicle only. The tractor trailer model has a frontal area ofapproximately 0.040 m2.
Refer to Appendix A for an uncertainty analysis of all data.
Direction offlow
Balancecomponent
of side
force, SFT
Drag, measuredby balance, DT
Vehicle
component
of side
force
Trailer, top
view
Resolved drag onthe vehicle, D
y
26
4.2 Zero yaw results
It was observed that for every device tested that the largest drag savings occurred at zerodegrees of yaw. The test procedures performed in this investigation for all devices aresimilar to those performed by Coon and Visser14 for devices having a boat tail angle ofzero, with the exception of performing tests at yaw angles of -3, 3, 6, and 9 degrees,largely not investigated by Coon and Visser. The optimum Coon and Visser device wasderived based on performance at zero degrees of yaw only. The current devices werecompared with the Coon and Visser device to indicate whether there is an advantage toangling the vertical side plates for zero yaw conditions and at other yaw angles. Theresults of tests performed at zero yaw are summarized first, followed by results from theremaining tests in section 4.3.
A summary of the drag reducing performance for each of the 2 feet, 3 feet, and 4feet models is given in Figures 4.2a-c. The coefficient of drag reduction, DCD, is
compared against the boat tail angle for each plate length, with the two investigated insetdimensions plotted on the same axes for each length. The reduction of drag coefficient isrelative to a base drag coefficient, or the coefficient obtained for the trailer model havingno attached device. Note that the inset dimension refers only to the side plates withrespect to the left and right trailer edges, with the exception of the four foot device with aboat tail angle of zero, which has an inset dimension of six inches from the left and rightsides of the trailer edges and an inset of six inches from the top trailer edge. This is theCoon and Visser14 optimum device at zero yaw. The Coon and Visser device wasinvestigated along with all current devices using the original model constructed by Coonand Visser for the current wind tunnel trailer model. The reported drag reduction for theCoon and Visser device was also determined during the same set of tests as the otherreported devices in this document.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0 5 10 15 20 25
Boat tail angle (degrees)
CD r
ed
uc
tio
n
zero inset
6" inset
a) 2 foot models
27
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14 16
Boat tail angle (degrees)
CD r
ed
uc
tio
n
zero inset
6 inch inset
b) 3 foot models
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 5 10 15 20 25
Boat tail angle (degrees)
CD r
ed
uc
tio
n
zero inset
6" inset
c) 4 foot models
Figure 4.2: Drag coefficient reduction vs. boat tail angle for: a) 2’ models, b) 3’models, c) 4’ models.
It can be seen from Figures 4.2 a-c that the zero inset cases reduce the drag coefficientmore than the six inch devices in nearly every case, with the only exceptions being thethree foot length with zero boat tail angle and the two foot length with a boat tail angle of20. It may, however, be reasonably interpolated from Figure 4.2 a that, had a set of twofoot devices with a boat tail angle of zero been constructed, the one having an insetdimension likely would have performed better here as well. This perhaps is not the casefor the four foot models with a boat tail angle of zero because the inset device in this casewas relative to the top and side trailer edges, whereas the other inset devices were withrespect to the side trailer edges only.
As the zero inset cases look more promising upon initial investigation, Figure 4.3compares all zero inset cases on the same set of axes so that the impact of plate lengthmay be seen more clearly.
28
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 5 10 15 20 25
Boat tail angle (degrees)
CD r
ed
ucti
on
4' length
3' length
2' length
Figure 4.3: Drag coefficient reduction vs. boat tail angle for all zero inset cases.
From the above figure, it can be observed that the four foot model with a boat tail angleof 10 degrees reduced the drag coefficient of the vehicle by the greatest amount at zeroyaw.
4.3 Summary of results at all yaw angles
While the probability distribution of Figure 1.2 favors zero yaw conditions in nature,higher yaw angles occur frequently enough to warrant consideration in the final selectionof a device for recommended highway use. Figures 4.4a-c illustrate the reduction of CD
for all zero inset devices as a function of yaw angle. Non-zero inset devices are notshown as the effects of inset at zero yaw, shown in Figures 4.2a-c, was consistent at allyaw angles. The two foot devices are shown in the first of these figures, followed by thethree foot devices and the four foot devices.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
-4 -2 0 2 4 6 8 10
Yaw (degrees)
CD r
ed
ucti
on
Boat tail angle = 5
Boat tail angle = 10
Boat tail angle = 15
Boat tail angle = 20
a) All 2 foot models
29
0
0.02
0.04
0.06
0.08
0.1
0.12
-4 -2 0 2 4 6 8 10
Yaw (degrees)
CD r
ed
uc
tio
n
Boat tail angle = 0
Boat tail angle = 5
Boat tail angle = 10
Boat tail angle = 15
b) All 3 foot models
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-5 0 5 10
Yaw (degrees)
CD r
ed
uc
tio
n
Boat tail angle = 0
Boat tail angle = 5
Boat tail angle = 10
Boat tail angle = 15
Boat tail angle = 20
c) All 4 foot models
Figures 4.4a-c: Effect of yaw on all zero inset models
For the two foot devices, a boat tail angle of 15 degrees seems most effective at everyyaw angle except for 9 degrees, achieving a maximum drag coefficient reduction of0.088. For the three foot models, the most effective boat tail angle is five degrees,performing best at zero and three degrees of yaw with a maximum drag coefficientreduction of 0.098. The four foot models are less well defined, with a boat tail angle of10 performing best at the lowest yaw angles and a boat tail angle of 15 performing best atangles of three or greater. Recall that the curves may not be simply integrated todetermine the best performing device; rather, the probability of occurrence of yaw mustbe considered as well.
It is interesting to note that, particularly for the two and three foot devices in theboat tail angle range of five to 15 degrees, the drag reduction at nine degrees of yaw tendsto exceed that at six degrees of yaw. For the four foot plate cases, this is noted for higher
30
boat tail angled devices. This is likely related to the effective boat tail angle relative toyaw. For the three foot device having a boat tail angle of 15, tested at nine degrees ofyaw, the relative angle of the plate to the wind is about five degrees, which is theoptimum angle observed for the three foot devices at zero yaw. This supports that thefluid is drawn by the plates inward toward the wake even at higher yaw angles. The fourfoot, 20 degree boat tail angle at nine degrees of yaw likewise supports this, as therelative angle of the plates to the oncoming wind is about 10 degrees, which was theoptimum device at zero yaw. The 20 degree device performs better at nine degrees ofyaw than at three or six degrees, and nearly as well as it does at zero degrees of yaw.
Figure 4.5 separates what appears to be the best performing devices from theabove plots and includes them on the same set of axes so that the effect of plate lengthmay be observed and a single best-performing device may be selected.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-4 -2 0 2 4 6 8 10
Yaw (degrees)
CD r
ed
uc
tio
n
L=4, i=0, phi = 10
L=4, i=0, phi = 15
L=3, i=0, phi = 5
L=2, i=0, phi = 15
Figure 4.5: Best cases compared
Notice that the trends for all of these cases are similar, with the most drag reductionachieved at zero yaw and a general downward concavity at all locations for every plot. Itmay be inferred from the above plots that performance tends to improve with increasingplate length, within the confines of the length parameters observed.
The four devices from Figure 4.5 are presented in Figure 4.6 in terms of a percentreduction in drag relative to the base drag. The graph in Figure 4.6 leads one to betterappreciate the magnitude of drag reduction associated with these devices. As expected,the trends observed in Figure 4.6 are very similar to those of Figure 4.5.
31
0
2
4
6
8
10
12
-4 -2 0 2 4 6 8 10
Yaw (Degrees)
Pe
rce
nt
Dra
g R
ed
uc
tio
n
L=2, i=0, phi=15
L=3, i=0, phi=5
L=4, i=0, phi=10
L=4, i=0, phi=15
Figure 4.6: Percent drag reduction of best performers
Wind tunnel test results illustrate relative trends among models that are expectedin a full scale test regime; however, the quantitative reduction in drag may be less in fullscale due to unknown Reynolds number scaling effects and other factors, such asturbulence levels. It is also possible that a thicker boundary layer presence could increasedrag reduction in full scale. The overall effect is unknown.
4.4 Effects of top plate removal:
The Mason and Beebe stream line diagram of Figure 2.4 suggests that flow off of the topedge of the trailer remains parallel to the trailer longitudinal axis for a considerabledistance downstream of the trailer. It is possible then that a top plate on the cavity designis not critical to the overall drag reducing effects of the device. To investigate thishypothesis, the top plate was removed from four devices that were considered to perform“very well,” and the devices were then tested in the wind tunnel in the same way as all ofthe others. Only select yaw angles were observed for the comparison, as any differencesin the performance between the three walled device and its complimentary four walleddevice should remain constant at all yaw angles.
The three walled devices observed were the 15 degree boat tail angled four footand two foot devices, each having an inset of zero, as well as the four foot device havinga boat tail angle of 10 degrees and an inset of zero. Each of these were investigated atzero yaw, and the four foot model with a boat tail angle of 10 was observed at six degreesof yaw. Figure 4.7 summarizes the impact of top plate removal on the reduction of dragcoefficient.
32
Comparison of 4 walled devices and
complimentary 3 walled devices
00.020.040.060.080.1
0.120.14
0 yaw 6 yaw 0 yaw 0 yaw
L=4, phi =10 L=4, phi =15 L=2, phi =15
Model description
CD R
ed
ucti
on
4 walled
3 walled
Figure 4.7: Effects of top plate removal
In every three walled case tested, the performance was significantly less than that of thecomplimentary four walled device. The most drastic reduction occurred with the fourfoot model with a boat tail angle of 10 at zero yaw, with the coefficient of drag reductionreduced by 0.053, or about 45 %.
4.5 Select Special Cases:
In addition to the original devices that were constructed for the purpose of thisexperiment, designs by MAKA Innovations and Coon and Visser were observed forcomparison. The MAKA Innovations design, seen in Figure 2.3, has a top plate and twoside plates, all with an inset of zero and a boat tail angle of 16 degrees. The deviceextends 20 inches from the rear trailer face. The optimum Coon and Visser device has aplate length of four feet, a boat tail angle of zero, and an inset from the side and toptrailer faces of six inches. The bottom plate of the Coon and Visser device has an insetdimension of zero. The MAKA and Coon and Visser devices are compared with eachother and are compared with the L = 4 feet, i = 0, and phi = 10 and 15 degree devices inFigure 4.8.
33
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-4 -2 0 2 4 6 8 10
Yaw (degrees)
CD R
ed
ucti
on
Maka Innovations model
Optimum Visser and Coon model
L=4, phi=10, i=0
L=4, phi=15, i=0
Figure 4.8: MAKA and Coon and Visser performance plots
It is seen above that, in general, the best of the current models achieve larger dragreductions at all yaw angles than the MAKA and Coon and Visser devices, with theMAKA device at nine degrees of yaw being an exception.
34
5. Conclusions
5.1 Data observations
The independent parameters investigated in the experimentation were inset dimension,plate length, and boat tail angle. The inset dimension refers only to the vertical sideplates with respect to the side edges of the tractor trailer. The top and bottom plates weremounted flush with their respective trailer edges. The plate length refers to the length ofthe side plates, which are angled inward at a given boat tail angle. The impacts of thelength, inset, and boat tail angle parameters are discussed separately.
5.1.1 Impact of inset dimension
Devices having inset dimensions of zero and six inches were observed in theexperimentation. In nearly every case the zero inset designs reduced significantly moredrag than the corresponding non-zero inset designs. The only occasions where this isarguable are at zero yaw for devices having a boat tail angle of zero. In the case of thefour foot plates, the zero angle devices reduce drag by approximately the same amountregardless of which inset dimension is observed. For the three foot plate case, the sixinch inset device with a boat tail angle of zero performs better than its zero insetcounterpart, and while zero angled two foot designs were never built, it can be reasonablyinterpolated from Figure 4.2a that an inset dimension would benefit here as well.
The reason for this may be due to the resulting vortex structures which formbetween the plates and the trailer edges, whose effect is to draw the flow inward and thusreduce the size of the wake region. At higher yaw angles, however, it perhaps becomesmore difficult for the oncoming flow to negotiate the increasingly sharp cornering aboutthe trailer edges for these designs, and the flow is thus not directed inward as much as itis at zero degrees of yaw. This explains why the performance drops sharply for thesedevices as compared to those with zero inset and a positive boat tail angle.
5.1.2 Impact of plate length
In general, larger reductions of the drag coefficient occur for increasing plate lengthwithin the range of lengths tested. It is conceivable that increasing the plate length suchthat the side plates arrive at a common edge would reduce drag by a greater amount, aswith full boat tail devices tested by NASA. However, this study aspires to highlight apotential design for actual road use, and thus legal constraints must be satisfied.
The impact of length is closely related to the boat tail angle of a given device.The device having a length of two feet and a boat tail angle of 15 degrees, for instance,out performs the three foot device with the same boat tail angle at zero yaw. This is trueeverywhere except for at nine degrees of yaw. For a boat tail angle of five degrees,however, the three foot length performed better at zero yaw than the complementary twofoot device, and about as well as the corresponding four foot device, however thisparticular three foot device falls short of the other most effective designs between yaw
35
angles of zero and six. The devices having a length of four feet tended to reduce moredrag than their complementary two foot and three foot devices at most yaw angles.
5.1.3 Impact of boat tail angle:
For every length parameter investigated, there is a notable boat tail angle for that lengthwhich is clearly the optimum angle for the given length. As observed from the zero yawdata, the most effective boat tail angle for the two foot length devices is 15 degrees, andfor the three and four foot lengths, the optimum angles are five and 10 degrees,respectively.
Some exceptions at other yaw angles are worth noting. The optimum two footdesign at zero degrees is less effective than the optimum three and four foot designs at thesame yaw angle, however at a yaw of six degrees, this device performed better than theother optimum devices at the same angle. Also, the four foot device having a boat tailangle of 10 performed best at zero yaw, while a boat tail angle of 15 for that lengthperformed better than the 10 degree case at all other yaw angles tested.
5.1.4 Impact of top plate removal
The top plate was removed from three of the models for testing in order to gauge itsaffect. In every case, the removal of the top plate significantly reduced the drag savingsfor the respective device. The worst case occurred with the four foot device having aboat tail angle of 10, which saw a reduction in drag savings of nearly 50 percent at zeroyaw. At six degrees of yaw, the device was only compromised by 32 percent, suggestingthat perhaps the losses are less significant at higher yaw angles. The two foot device hadthe smallest reduction at zero yaw, only losing about 30 percent of its performance.Given this, it does not seem that the three plated devices ought to be recommended formanufacture, however the extra cost of producing a fourth plate for every deviceproduced would have to be balanced with the loss of performance to determine the mostprofitable venture.
5.2 Future Recommendations:
While it is reasonable to assume that the upper limits of each of the experimental trendswill remain as currently indicated, a more complete trend may be developed for eachparameter if additional devices are constructed for wind tunnel testing. Gaps in thecurrent plots should first be investigated, including those caused by devices that werenever constructed due to material limitations. These include three foot models with boattail angles of 15 degrees and higher and two foot models with boat tail angles of less thanfive. Intermediate dimensions for each parameter may also provide for a finer dataresolution, perhaps better indicating which specific parameter dimensions cause largerdrag reduction. Construction of additional devices can help verify established trends andperhaps reveal anomalies in the trends.
36
An expansion of the number of geometric parameters investigated could revealadditional ways to enhance drag reduction. Only the side plates were angled in thisinvestigation, however the effects of top and bottom plate angles are worth studying.Similarly, adjusting the inset dimensions of the top and bottom plates could improvedevice performance.
While an expansion in the number of aft cavity models tested may be beneficial,so might expanding the number of front cab devices. Currently one cab model, describedin section 3.2, was used for all tests. This cab design is thought to best represent themajority of tractor trailers in service as it was the most popular design sold in the 1990s.Newer cab designs, however, are becoming increasingly streamlined and are becomingmore popular on the road. Developing new cab designs is beyond the scope of thecurrent research, but for experimental purposes it is worthwhile to see what impactchanging cab designs has on aft devices in the reduction of drag. New cab models forwind tunnel use should be representative of newer vehicles in service today.
The wind tunnel set up may be better configured to provide for increasedconsistency, starting with construction of a permanent calibration rig. Additionally, theforce balance may be raised to shorten the required length of the mounting sting. Thiswould reduce bending moment contributions to the drag and side force data. Moreaccurate yaw positioning may be attained by constructing removable pegs in the splitterplate which would force exact positioning of the trailer model at a particular angle.
Instrumentation may be substituted or replaced to reduce uncertainty in theanalysis. Refer to Appendix A for a table relating the uncertainty associated with eachtransducer used in the experimentation and for the propagation of each uncertainty intothe overall drag coefficient uncertainty. The largest contributor to the overall uncertaintycomes from the wind tunnel pressure differential transducer, with an uncertainty of
0.02015 in.H2O. Replacing this device with one having a higher resolution could
significantly reduce overall uncertainty.
Pressure taps located within and surrounding the plate cavities for each devicecould offer complimentary data to the force balance. In this way, a pressure profile mapmay be obtained to understand the flow characteristics surrounding each device.Additionally, a flow map obtained in this way could reveal any hidden and unforeseendangers associated with passive flow manipulation on the surrounding traffic. It isconceivable that turbulence intensity may increase within a certain region as a resultwhich could combat the intended direction of travel for other vehicles, thus creating asafety hazard. Though the prospect is unlikely, the risk is severe enough to warrantexamination.
To obtain a better estimate of the overall impact of a device on drag reductionacross the entire yaw spectrum, the weighted integral method proposed by Cooper18
should be applied to the plots of sections 4.2 and 4.3. This would reveal, for instance,whether the larger drag reduction of the optimum two foot device at six degrees of yawwould compensate for its significantly less drag reduction at zero yaw compared to the
37
other optimum devices of figure 4.5. In this way, a single “best” device may be selectedfor large scale production.
Lastly, examination of full scale prototypes of the best performing devices ontypical tractor trailer combination trucks in typical highway conditions would fully revealthe most practical device for use at full scale Reynolds numbers. A more complete senseof the best device to market is obtained for more prototypes tested, but given financialconstraints, it is recommended to first test prototypes of the optimum four foot devices asthe optimums at this length performed better than all other devices in the wind tunnel,and then expand testing into the other optimum devices for a given length if time andmoney allow.
38
Appendix A: Uncertainty Analysis
The following experimental uncertainty analysis is adapted from Coon and Visser14.
Recall that drag reduction was reported in terms of DCD, given as:
devicebase DDDCCC -=D (A1).
The associated uncertainty is then
22
**˜˜
¯
ˆ
∂
D∂+
˜˜
¯
ˆ
∂
D∂=D Ddevice
device
Dbase
base
E C
D
D
C
D
D
CU
C
CU
C
CU =
22
deviceDbaseD CCUU +
(A2),
assuming that UCDbase = UCDdevice = UCD.Solving equation A2 requires the uncertainty for the drag coefficient. The drag
coefficient is given by:
qA
DCD = (A3),
where the dynamic pressure q is calculated from measured quantities according toequation A4.
˜˜
¯
ˆ
ÁÁ
Ë
Ê D+==
PA
PTRVq
front
)273(2
2
1
2
1 2 rr (A4)
The uncertainty of the drag coefficient, by equation A3, is:
˜̃¯
ˆ++=˜
¯
ˆ
∂
∂+˜̃
¯
ˆ
∂
∂+˜
¯
ˆ
∂
∂=
2
2
2
2
2
2
2
22
222
1
AqDA
D
q
D
D
D
C UA
DU
q
DU
AqU
A
CU
q
CU
D
CU
D
(A5).Equation A5 requires the uncertainty of the dynamic pressure, given by:
222
˜¯
ˆ
∂
∂+˜
¯
ˆ
D∂
∂+˜
¯
ˆ
∂
∂= D PPTq U
P
qU
P
qU
T
qU
2
2
22
)273()273(
˜˜
¯
ˆ
ÁÁ
Ë
Ê D+-+
˜˜
¯
ˆ
ÁÁ
Ë
Ê ++
˜˜
¯
ˆ
ÁÁ
Ë
Ê D= D P
front
P
front
T
front
UPA
PTRU
PA
TRU
PA
PR rrr (A6).
The following is a table of uncertainty values which will assist in solving equations A6and A5. These are based on instrument resolution.
39
Table A-1: Experimental UncertaintiesUT = 0.600 °C
UDP = 0.02015 inH2O
UP = 0.3022 inH2O
UA = 0.00123 m2
UD = 0.0003*D
Considering the device having L = 4, i = 0, and f = 10 at zero yaw, equations A5 and A6
are solved. The device had a drag force of 8.27 N.Uq = 5.708 kg/ms2
UCD = 0.0149
Referring to equation A2:
UDCD = 0.0211.
40
References:
1 “National Transportation Statistics 2000.” www.bts.gov. Bureau of TransportationStatistics. 2000.
2 Aerodynamic Database: Ground Vehicles Drag. www.aerodyn.org/Drag/. A.Filippone, 2002.
3 Cooper, Kevin R. “The Wind Tunnel Testing of Heavy Trucks to Reduce FuelConsumption.” SAE Technical Series. November 8-11, 1982. SAE Paper # 821285.
4 “Vehicle Load and Size Limits.” http://www.mtq.gouv.qc.ca/. Gouvernment duQuebec, 1999.
5 McCallen, Rose, et al. “Progress in Reducing Aerodynamic Drag for Higher Efficiencyof Heavy Duty Trucks (Class 7-8).”
6 Saltzman, Edwin, and Meyer, Robert. “A Reassessment of Heavy-Duty TruckAerodynamic Design Features and Priorities.” NASA-Dryden Report # 19990047711.June 1999.
7 Lechner, Anton. “Device for Reducing the Aerodynamic Resistance of a CommercialVehcicle.” U.S. Patent # 5,375,903. 1994.
8 Keedy, Edgar L. “Vehicle Drag Reducer.” U.S. Patent # 4,142,755. 1979.9 Davis, Grover M. “Retractable Streamlining Device for Vehicles.” U.S. Patent #
4,236,745. 1980.10 Mulholland, Frank J. “Drag Reduction Fairing for Trucks, Trailers, and Cargo
Containers.” U.S. Patent # 4,458,936. 1984.11 Mason, Jr., W. T., and Beebe, P.S. “The Drag Related Flow Field Characteristics of
Trucks and Buses.” Aerodynamic Drag Mechanisms of Bluff Bodies and RoadVehicles. General Motors Research Laboratories, 1978. pp. 45-93.
12 Hucho, Wolf-Heinrich. “Aerodynamics of Road Vehicles.” Butterworths, London.1987.
13 Bilanin, Andrew J. “Vehicle Drag Reducer.” U.S. Patent # 4,682,808. 1987.14 Coon, Jamison and Visser, Kenneth. “The Effects of Non-Ventilated Plate Cavity
Devices on Drag Reduction of Tractor Trailers.” MAE Report 361, ClarksonUniversity, June 2002.
15 “SAE Wind Tunnel Test Procedure for Trucks and Buses.” SAE International. 1981.16 Beauvais, F.N., Tignor, S.C., and Turner, T.R. “Problems of Ground Simulation in
Automotive Aerodynamics.” Automotive Aerodynamics. SAE Progress inTechnology Series, Volume 16. 1978. pp59-70.
17 Mason, Jr, W.T., Beebe, P.S., and Schenkel, Franz K. “An Aerodynamic Test Facilityfor Scale-Model Automobiles.” International Automotive Engineering Congress,Detroit, MI, Jan. 8-12, 1973. pp 1-12.
18 Cooper, Kevin R. “The Effect of Front-Edge Rounding and Rear-Edge Shaping on theAerodynamic Drag of Bluff Vehicles in Ground Proximity.” International Congress &Exposition, Detroit, Michigan. February 25 – March 1, 1985. SAE Paper # 850288.
