An Easy Way To Select an Electric OutrunnerMotor Power System for an ARF, Kit or Plans Built

Glow Powered Prop Plane (Heck of a title, eh?) 

By Ken Myers, May 2011 Updated: September 2012 with all links checked

September 2011 Update: Revised and easier to use Excel workbook. Spelling and grammatical errors corrected in text. The screen captures of the spreadsheets have been updated to the latest version.

Note: There are MANY ways to choose an electric power system for a glow conversion to electric power.

This is just ONE way to do it!

     Converting a glow powered almost ready to fly (ARF), plans built or kit built, prop propelled, model aircraft to an electric power system may seem like a daunting task to someone with no electric power system experience.

     "How can the motor, and the other electric power system components, the battery, electronic speed control (ESC) and propeller, be selected by someone with little prior knowledge of electric power systems?"

 

     Why is picking an engine so 'easy' for a glow plane and a motor so 'hard' for an electric?

     When suppliers of glow engine airframes recommend a certain cubic inch (cu.in.) displacement 2-stroke or 4-stroke engine, it is not just a power recommendation. They are not only recommending the engine 'size', but they are also recommending the prop diameter and pitch.      For any given glow engine, there are only a handful of prop sizes (diameter and pitch) that will work well within the engine's power range.

Prop Chart from www.flyurbana.com/media/Chart.PDF

     A typical sport 1.20 4-stroke might use a 14x8, 15x6, 15x8, 16x6,16x8, 17x6, 18x5, or 18x6 prop. (See Prop Chart for Four-Stroke Engines.) Various prop brands may 'work better' or 'worse' on a given engine, but the size (diameter and pitch) is quite limited.      On the other hand, varying an electric motor's cell count within an acceptable range, and varying the 'acceptable' level of input power, a given electric motor may use many, many different props within its acceptable power range.

     A Scorpion SII-3020-890 (3846-890, 166g) motor, using a 3S Li-Poly battery, is in its useful power range using a 10x5 prop through a 15x6 prop. There are roughly a dozen or more diameters and pitches that fall within the useful power range when a 3S pack is used. The motor is rated up to a 5S Li-Poly. Using a 4S or 5S pack adds a whole array of different props to the mix resulting in well over 25 different prop sizes that may be useful within the motor's power range. Using "A123" 2300mAh LiFePO4 cells instead of Li-Poly cells adds even more usable props to the mix!

     To keep the process as simple as possible, a glow to electric Excel workbook, with spreadsheets for Li-Poly and "A123" 2300mAh cells, has been designed to use as a guide.      The technique presented here is based on limiting the prop selection. First, the required power in (watts in) is determined. The required power in is based on the supplier provided information for the glow powered ARF, kit or plans. Next the prop size is determined and the rest of the power system components are matched to the prop power requirements.

Step 1: Estimate a Suggested Power In.

     The Suggested Power In unit of measurement is watts in (watts = volts times amps) as displayed by a power meter connected between the battery and electronic speed control (ESC) at full throttle. It isExtremely Important to verify that the current and power do not exceed the capabilities of the motor, ESC and battery. Exceeding the capabilities of any of the power system components will cause catastrophic failure to one or more of the power system

components! A power meter is essential when working with electric power systems!

The Example Model:

 Balsa USA 1/4 Scale EAA Bipe

     The spreadsheet is designed so that user inputs are placed in cells with green backgrounds and results are presented in cells with red backgrounds. The spreadsheet input cells are noted in parenthesis after the Manufacturer or Supplier recommended maximums (Max.).

Name of Plane: 1/4 Scale EAA Bipe (B6) Max. 2-stroke: 0.80 cu.in. (B7) Max. 4-stroke: 1.20 cu.in. (B8) Max. wt. 8 lb. (must be in pound) (B9) Wing area: 1018 sq.in. (B10)

The Wing Cube Loading (WCL), presented in result cell (B13), is 6.81oz./cu.ft.

     Knowing what wing cube loading (WCL) is or how it works is not important to the use of the spreadsheets. 

More information on WCL.

 Average and Median watts in/cu.ft.

     There is a table on the spreadsheet, similar to the one shown above, that shows the average and median watts in per cubic foot of wing area. It also indicates the WCL Level number and typical types of missions. The lower the WCL level number, the "easier" the plane is to fly. The easier a plane is to fly, the more susceptible it becomes to increasing wind speeds.

     The example plane has a WCL of 6.81; Level 3 'typical park flyer'. Even though the 'typical' mission is 'park flyer', the example plane is too big and fast to actually fly in a park, but it will fly like a 'typical park flyer', very easily.

     The Suggested Power result is 975 watts in.

     The weight range is the first motor characteristic determined. The Lightest OUTRUNNER motor result is 390g. The Heaviest OUTRUNNER motor result is 610g.

Step 2: Determine prop diameter

Prop Chart from www.flyurbana.com/media/Chart.PDF     The electric prop diameter is based on a relationship to the 4-stroke Standard Propeller diameter. To determine the prop diameter, add 2 inches in diameter to the 4-stroke recommended Standard Propeller.      The example model's recommended 4-stroke engine is a 1.20. The chart shows a 16" diameter propeller as the Standard Propeller for this engine. 16" + 2" = 18" (Input B20)      If only a 2-stroke displacement is given by the supplier, multiply it by 1.5 for a 4-stroke equivalent displacement. It will be close enough. Round to nearest actual 4-stroke displacement found in the chart.      No 4-stroke .30 is shown in the chart, but a 10" diameter prop would be standard.

What if the suggested 4-stroke diameter doesn't allow enough ground clearance?

     If the plane has a tricycle landing gear configuration, or for some other reason, a prop with the suggested diameter can't be used using the 4-stroke method, add 2 inches of diameter to the suggested 2-stroke glow engine prop diameter.

Prop Chart from www.flyurbana.com/media/Chart.PDF     A typical tricycle landing gear, high-wing or shoulder-wing, glow 40 trainer might use a .40 or .45 2-stroke engine using a 10-inch diameter prop. (see table) A 12-inch prop diameter should be a usable.

Step 3: Determine prop pitch

     This is the 'hardest' part of the whole process, and I can't help you with it. Basically, you can't go wrong, as any of the suggested pitches will provide the information required to find the correct motor, ESC and battery combination. I use APC E thin electric props and base my selection on the pitches they have available for the chosen diameter and the plane's mission.

     The pitch suggestion box (cells A37 through B40) shows suggested pitches for the WCL levels after the prop diameter is input. The prop diameter, for the example plane, is 18" and was input previously in B20.

     For Cub-like planes, biplanes and other civilian light aircraft with a WCL level of 4, it might be better to use the WCL 1-3 pitches.

     If more speed is desired of a WCL level 3 plane, a pitch may be chosen either between the WCL 1-3 pitches and the WCL 4-7 pitchesor at the lower end of the WCL 4-7 pitches.

     The example plane is a WCL Level 3.      Choosing the recommended middle pitch, 10", allows the static current draw to be adjusted slightly down using the lower pitch or slightly up using the higher pitch.      A 10" pitch was chosen for the example and input into B21. The APC Web site was used to verify that there is an APC 18x10E thin electric prop.      The final choice of which prop pitch to use may depend on the availability of possible props and may require rounding.

A Word About Props

     Not all props are created equal! Zinger props should be avoided. They are relatively inefficient, compared to other brands, when used in electric motor applications and draw too much current.      APC slow flier (SF) props and GWS RS props are not designed for this purpose.      APC sport, pattern and thin electric (E) props are appropriate. APC props are listed at www.apcprop.com/pindex.asp.      Master Airscrew wood props and G/F 3 series props also work well in electric power applications, but NOT the Master Airscrew electric props!

     Once the prop diameter and pitch have been input, the resultant Target RPM of 5500 and pitch speed of 52 mph are displayed. The Pitch Speed to Stall Speed ratio of 3.31:1 is displayed. Anything greater than 3:1 is quite good.

Pitch Speed Conformation:

 Pitch Speed Table

     For reference, the pitch speed table can be used to compare the pitch speed to both average and median electric and glow powered planes. The table indicates that a predicted pitch speed of 52 mph for the example plane is a bit 'faster' than the typical Level 3 electric and a bit 'slower' than the typical Level 3 glow plane.

Recap:

1. Motor needs to handle at least 975 watts in 2. Motor weight range between 325g - 610g 3. Chosen prop is an APC 18x10E

     At this point, an important motor number is missing. It is the Kv (RPM/volt) number. Don't worry if you don't know what it is or how it affects a motor's operation. It just needs to be determined and used for final motor selection.      More information on the motor constant Kv

Step 4: Determining which Kv (RPM/v) to use

     Manufactures and suppliers provide one more important piece of information about their motors. It is called the Kv (RPM/v). Kv is a motor constant that is best thought of as RPM per volt out. It is not the expected RPM per volt applied at the ESC!      The chosen prop combined with the number and chemistry of the cells contained in the battery pack determines the appropriate Kv.      The useful amp draw range is used to select the number of cells. For Li-Poly cells, the useful amp draw range for most glow to electric conversions is between 30 amps and 60 amps.      The spreadsheet Estimated Kv (RPM/v) provides a useful starting

point. Motors within a range of about 5% of the predicted estimate should be considered. On the spreadsheet, the range is indicated in yellow cells under the Estimated Kv. Kv numbers at the high end of the range may have a higher than Anticipated Amp Draw. Kv numbers at the lower end of the range may have a lower than Anticipated Amp Draw.

     For the example plane, 5-cell (5S) through 9-cell (9S) Li-Poly packs should be considered.      In general, the lower the amp draw, the higher the system efficiency is.

How to locate a motor - the hard part:      Where do you look if you don't know what you are looking for?      A good place to start is a Web site called RCBOOK.      It does not have all the manufacturers and suppliers of electric outrunner motors in its database, but it does have a lot of them. Manufacturers' and suppliers' Web sites may also be used for specific 'brands.'

How to use RCBOOK to locate possible outrunner motors

1. From the RCBOOK index page, select Parts from the tabs across the top of the screen.

 2. From the left column menu, select Engine

 3. Using the Engine filter on the right side of the engine screen, select electric from the Power type drop down menu. Fill in the weight range (390g - 610g) for the example plane. Select Apply and several pages of possible motors are presented. Not all of the listed motors will beoutrunners.

4. Finding possible outrunner motors:

     Make a list noting the number of cells and Kv range. (Using the workbook can be helpful! Select the spreadsheet in the workbook named motor notes and do the note taking there.)

For the example plane:

5S Kv 360 - 400 6S Kv 300 - 330 7S Kv 250 - 280 8S Kv 220 - 245 9S Kv 195 - 215

     Go through the returned results on RCBOOK looking for outrunnersthat fit the various Kv ranges and note them. Don't worry about the nomenclature of the various brands. The only thing that is important is the weight, which was set by the Engine filter and the Kv. The Kv for all brands is not always shown on the info page. A click on the photo link for the motor may be necessary to find the Kv.      Note the outrunner motors for each Kv range and their weight (wt.) in grams. After the RCBOOK search, the motor notes spreadsheet looks like this for the example plane:

     While 28 possible motors for this plane is significant, it is a lot less than hundreds of possible motors!!!      Next, use Google search to locate a supplier for the motor and note the supplier's Web site address and price on the motor notes spreadsheet. After the Google search the motor notes spreadsheet looks like this. (Web addresses truncated in this screen capture.)

     The motors may now be compared by Kv, weight, supplier and price.

Outrunner Supplier Notes:      Hobby King and Hobby Partz have notoriously poor customer service. Hobby King has quality control issues with some of their products. NEVER order anything that is not in stock at Hobby

King!      Before making a final decision on a motor, consider the battery and electronic speed control (ESC).

Batteries:      As I seldom use Li-Poly batteries, no particular brand is recommended. Use the Approx. Li-Poly capacity as a guide. Round up to the nearest available size. All of the batteries listed, based on their capacity and expected amp draw, will fly a plane for approximately 9 to 10 minutes. Capacities are based on those recommended in Row 31 or the spreadsheet, Approx. Li-Poly capacity.

A word about electronic speed controls:

     You can't go wrong with Castle Creations (CC) ESCs. The following CC ESCs are appropriate for the example plane based on the recommended ESC amp draw in Row 33 of the spreadsheet.      The list prices are noted. They may be found at a discount online.

9S (Row 33 31.0 amps) Phoenix Ice HV 40 $129.95 8S (Row 33 39.8 amps) Phoenix Ice 50 (not lite version) $99.95 7S (Row 33 39.8 amps) Phoenix Ice 50 (not lite version) $99.95 6S (Row 33 46.4 amps) Phoenix Ice Lite 75 $119.95 5S (Row 33 55.7 amps) Phoenix Ice Lite 75 $119.95

Putting it all together:

     All of the systems will work with the example plane when the selected prop is an APC 18x10E thin electric. Here is a recap of what is required for the battery, ESC and motor.

5S 5800mAh Li-Poly battery (5500mAh, 5600mAh and 5700mAh are not as common), 70-amp ESC, 360Kv to 400Kv outrunner motor weighing between 390g and 610g

6S 4900mAh or 5000mAh Li-Poly battery (4700mAh and 4800mAh are not as common), 60-amp ESC, 300Kv to 330Kv outrunner motor

weighing between 390g and 610g

7S 4000mAh Li-Poly battery, 50-amp ESC, 250Kv to 280Kv outrunner motor weighing between 390g and 610g

8S 3600mAh Li-Poly battery (3500mAh is not as common), 45-amp ESC, 220Kv to 245Kv outrunner motor weighing between 390g and 610g

9S 3200mAh Li-Poly battery (3100mAh is not as common), 40-amp ESC (most likely will need to be a high voltage (HV) type), 195Kv to 215Kv outrunner motor weighing between 390g and 610g

A word about using "A123" 2300mAh cells

     The Excel Workbook also contains a spreadsheet for "A123" 2300mAh cells. The process for finding a motor and prop is the same as when using Li-Poly cells.      "A123" 2300mAh cells work 'best' at about 35 amps for a 1P (parallel) application and 70 amps for a 2P application. This limits the quantity of cells that may be used in series with these cells.      With all of the same inputs as for the Li-Poly cells using the example plane, the results for the number of cells, amps, etc. looks like this.

     9, 10 or 11 "A123" 2300mAh cells could be considered for use with the example plane. The motor notes results look like this.

     My purchased power system choice for my 1/4-scale BUSA EAA Bipe; 9S "A123" 2300mAh battery pack, Castle Creations' Phoenix Ice HV 60 and a Scorpion S-4035-250.

What to do if Microsoft Excel in not on the computer

     For computers that do not have Microsoft Excel, the FREE Open Office Suite may be used.

Wing Cube Loading (WCL) Information

What it is and how to use it

WING CUBE LOADING (WCL) by FRANCIS REYNOLDS

WING CUBE LOADING, by Roger Jaffe

3D Wing Loadings: a Better Way to Scale Models

WCL Calculator online at Electric Flight UK

Return to articleGeneric Motor Naming

     Unlike glow engines, there is no standard way of 'naming' an electric motor. Using a generic name for all outrunner motors allows for direct comparisons. The generic name for the outrunners used in this article is the first two digits indicate the outside diameter in millimeters (mm) with the next two digits noting the can length in mm, then a dash followed by the Kv (RPM/v). A comma separates the weight in grams from the rest of the motor description. The Scorpion SII-3020-890, used to illustrate the versatility of an electric outrunner motor, has a can diameter of 38mm, can length of 46mm, Kv of 890 and weighs 166g. Its generic name is 3846-890.

More on "generic" motor naming here

Return to article

Electric Motor Kv or RPM/volt By Ken Myers Updated: November 2012

Ampeer Articles Regarding Motor Kv

Finding R and K, December 1989

Kv for Robbie 600, Aug. 1999

Motor Kv Question, January 2005

Measuring Kv Using the Drill Press Method, January 2009

It Is Not Just the Kv, May 2009

Ke variation, November 2010   (note: not a typing error; Ke is related to Kv)

Identifying the Usefulness of an Unknown Brushless Outrunner, October 2011

     Kv is a motor constant and is directly related to Kt, the motor torque constant. Kv is most often expressed as RPM/Volt or RPM/v. Kt is often expressed in the units inch ounces per amp. Kv (expressed as RPM/v) * Kt = 1352. (Note: Some sources uses 1355 as the constant.)

     The Kv motor constant is part of the motor's physical makeup. The voltage used to multiply the Kv constant by, to determine the RPM, isNOT the input voltage at the motor, for a brushed motor, or the input voltage at the Electronic Speed Control (ESC) for a brushless motor.

     There is a voltage drop from the input voltage. It is caused by the resistance of the motor. For brushless motors, there is an additional voltage drop caused by the resistance of the ESC.

The Math

Volts = I (current) * Resistance The voltage out (Vout) equals the input voltage (Vin) minus the current times the resistance (the voltage drop). Vout = (Vin - (I * R))

     Rm is a term that was used with brushed motors. It meant the motor resistance. The term Rm, as used here, means the motor resistance plus the ESC resistance, so that it may apply equally to brushed and brushless systems.

Measuring Motor Constants

     Two data points are required to determine the Rm and Kv of a motor. The data points are gathered using a power meter (aka watt meter) and tachometer. Either an optical tachometer or phase tachometer will work. An accurate phase tachometer is much easier to use.

All measurements are taken at FULL THROTTLE! Do NOT use partial throttle readings! Data should be gathered as quickly and accurately as possible. The motor should not be run for any extended period of time, ever!

One of the earliest iterations of this method was presented in theDecember 1989   Ampeer . Unfortunately, I didn't really understand the concept and math at the time, but THE electric columnists, Bob Kopski and Mitch Poling, did.

Data Points 1 Select and mount as large a propeller as the supplier recommends for the motor with the number of cells to be used. (For help in selecting the prop, review "Selecting the CORRECT Supplier Recommended Props". You should try to get as close to the maximum current rating of the motor as possible, without going over it. The readings should be as close as possible to the same instant in time. Record the current, voltage, and RPM readings. They will be known as I1 (current), V1 (volts), and RPM1 (RPM).

Data Points 2 Next affix a very small propeller or even small, flat 'stick' just large enough to get a tachometer

reading. Servo arms have been used on small motors. With a phase tachometer, nothing needs to be attached to the motor, as the phase tach will yield the no load RPM, which is even better. Measure the light load or no load current, voltage, and RPM. They become I2 (current), V2 (volts), and RPM2 (RPM).

The math is completed using the Excel workbook spreadsheet titled Rm. Kv & Rm Spreadsheet

     The Io (no load current) is also a valuable constant. Measure the volts and amps using a power meter with no propeller attached to the motor. For a no load test to calculate the Io, it is best to use a battery or power supply that applies only about 80% of the voltage that the motor is expected to run at. DO NOT ATTEMPT TO CONTROL THE VOLTAGE USING AN ESC! Getting the measurement at 80% of the expected voltage is sometimes difficult to do. If that cannot be done, just use the pack that has been used to do the Rm testing, but don't recharge it, unless it is extremely low.

     A major problem with many suppliers' is that they give an Io without noting the voltage. Io varies somewhat with the volts applied. This causes a problem when the Io is used to estimate 'iron loss' in the power out formula.

Power Out Formula Pout = (Iin - Io) * Kv (Vin - (In * Rm))

     While called constants, the Rm and Io are not truly constant. They vary slightly with the applied voltage.

Some Examples

     It is important to note that the Rm derived in the following examples is NOT the Rm that is often provided by the suppliers.

Cobra C2203/52, wt. 17.5g I1 = 6.93, V1 = 7.4, RPM = 6740 I2 = 0.36, V2 = 8, RPM = 12,080* *Adjusted to yield a Kv of 1540 - found in the Examples on the Rm sheet.

Results from spreadsheet: Rm = 0.4363 ohms, Kv = 1540 Io was given as 0.36 amps at 8 volts

The maximum amp draw is given as 7 amps. 80% of the maximum is 5.6 amps. On the Innov8tive Designs' prop test table the APC 7x5SF draws 5.6 amps. The voltage drop at 5.6 amps with 7.4Vin. 7.4Vin - (0.4363ohms * 5.6 amps) = 4.96Vout RPM at 5.6 amps = 4.96Vout * 1540Kv = 7638 RPM 

The actual measured data for the APC 7x5SF is, 7.4Vin, 5.60 amps,7,620 RPM The Vout is 67% of the Vin. That is not unusual for such a small motor (17.5g).

The Io is used to calculate the Pout in watts. (5.6 amps - 0.36 amps) * (7.4 - (0.4363ohms * 5.6 amps)) = 26 wattsout Efficiency = 26 watts out / (7.4v * 5.6 amps) watts in = 0.627 or 63% Again, this is pretty typical efficiency for such a small motor.

Cobra C4130/14, wt. 400g I1 = 58.26, V1 = 29.6, RPM = 10581 I2 = 1.46, V2 = 20, RPM = 8940* *Adjusted to yield a Kv of 450 - found in the Examples on the Rm sheet.

Results from spreadsheet: Rm = 0.1049 ohms, Kv = 450 Io was given as 1.46 amps at 20 volts

The maximum amp draw is given as 60 amps. 80% of the maximum is 48 amps. 46.04 amps is used for the example as the measured APC 12x8E draws 46.04 amps at 29.6v. The voltage drop at 46.04 amps with 29.6v in. 29.6Vin - (0.1049ohms * 46.04 amps) = 24.77Vout RPM at 46.04 amps = 24.77Vout * 450Kv = 11,146 RPM The actual measured data for the APC 12x12E is, 29.6Vin, 46.04 amps,11,063 RPM The Vout is 83.7% of the Vin. That is not unusual for the larger motor (400g).

The Io is used to calculate the Pout in watts. (46.04 amps - 1.46 amps) * (29.6 - (0.1049ohms * 46.04 amps)) = 1104 watts out Efficiency = 1104 watts out / (29.6v * 46.04 amps) watts in = 0.81 or 81% Again, this is pretty typical efficiency for this larger motor.

     The examples chosen were not arbitrary. They demonstrate some general trends that can be applied to all motors. 'Smaller, lighter' motors have a higher Rm than 'larger, heavier' motors and therefore a higher voltage drop. In general, for the way that they are used, 'Smaller, lighter' motors have a lower efficiency than 'larger, heavier' motors.

     One thing that was not demonstrated by the examples is that the highest Kv motor in a series will be the most efficient and have a lower Rm. Why? A higher Kv is created by using larger diameter wire for the windings compared to a lower Kv version of the same series motor with the same type of termination. Not all suppliers provided different Kv motors of the same 'size'.

     The Cobra C2203/34, which is in the same series of motors as the first example, has a Rm of 0.2255ohms (about 1/2 the resistance of the /52) for a voltage drop of 1.55V at 6.89 amp yielding 5.85Vout. (Shown in the Examples on the Rm spreadsheet). At 6.89 amps the Vout is 79% of the Vin and the efficiency is about 72.6%. The /52 is a 52-wind and /34 is a 34-wind. The fewer winds of larger gauge wire on the /34 means that it has a lower resistance and higher Kv than the /52.

     One of the results of the previous testing method is the Kv.

     Another way to derive the Kv is with a phase tachometer and voltage measurement. An optical tachometer cannot be used for this measurement as the motor needs to be 'unloaded'. The Emeter II with the RDU or MDU and the phase tach lead can be used or a device like the AEO Tech KV Meter K0. The motor is run with no load, while the voltage and rpm are recorded. While not the 'true' Kv, it is close enough. For this type of measurement, RPM / volts = Kv. i.e. 8940 RPM / 20V = 447Kv, which is close enough compared to the 450Kv in the previous example

     Kv is also known as the generator constant or dynamo constant. When any electric motor's shaft is physically spun, it generates electricity. It doesn't matter whether it is a brushed or brushless motor.

     A typical hobby brushed motor can be spun by a drill press at a constant speed. By measuring the DC voltage across the terminals, with brushes set to neutral timing, and knowing the RPM of the drill press, the Kv can be calculated. i.e. 1560 RPM / 1.6v DC measured volts = 975 RPM per volt. (To see how timing affects a motor, read Timing Test.)

     A brushless motor isn't quite as simple to test. A bit of math is required.

     A brushless motor has three possible lead combinations that need to be measured using AC voltage.

First, determine the constant drill press RPM (1560 in this example). Measure the AC voltage on each pair of leads. There are three possible combinations with a brushless motor. Lead combination A - 2.08 Lead combination B - 2.08 Lead combination C - 2.08 Note, most cheap brushless motors do not have all three lead combinations come out exactly the same, but they do on the better quality motors. Use the average of the three voltage numbers if the measurements are slightly different.

Find the V-peak by multiplying the average AC volts by 1.414 In this example 2.08 * 1.414 = 2.94v Divide 1000 (a constant) by the RPM (1560 in this case) = 0.64 Ke = V-peak ((2.94) * (in this case 0.64))/1000 = 0.00188 Find the inverse of Ke (1/Ke) (1/0.00188 in this case) = 531 Divide the inverse of Ke by 0.95 = 559 RPM/v or the approximate Kv expressed as RPM/v

Brushless Kv formula using drill press Kv = (1 / ((Vac * 1.414) * (1000 / drill press rpm)) / 1000) / 0.95 Kt = 1352.4 / Kv

     The Kv Spreadsheet (sheet Kv) can do the math for you.

     It should be noted that many manufacturers/suppliers, even the good ones, provide inaccurate information about the motor's Kv, so if you can, measure it to be sure you have the motor you want. Using this method, nothing really needs to be done to the motor to measure the Kv, so it should be easily returnable if the Kv is not suitable, as the shaft will only have been chucked into a drill press that is set up with a known RPM.

     Advancing the timing on a brushed motor (using rotation of the brushes) or brushless motor (via an ESC setting) changes the apparent Kv, increases the RPM and Io (no load amp draw), increases the heat (wasted energy) more than neutral timing, but increases the power out.

Getting Started in Electric Flight An Introduction and Some BASICS By Ken Myers kmyersefo@theampeer.org Updated: Oct., 2012

Warning! The many facets of Electrically Powered Flight ARE Addictive

 Indoor - living room flyer

 Backyard

 Park Flyer - Scale

 3D

 Sport

 Scale

 Electric Ducted Fan (EDF)

 Electric Helicopter

 Old Timer

 Thermal Sailplane

 F5B

 Race

 Multi-motors

 Foamie

 QuadCopter controlled by iPhone or iPad

And MUCH, MUCH MORE!

Table of Contents

Wing Cube Loading Defines Aircraft Types and Missions

Recommended First Purchase - Power Meter

How to Use a Power Meter

Chargers

Li-Poly Batteries      How to read a Battery Label or Battery Specifications      Li-Poly Storage and Safe Handling

Other Flight Power Batteries

Li-Poly Batteries for use in Transmitter

Temperature Effects on Batteries

Connectors - Power Leads

The 4 Major Balance Plugs, Taps, Nodes or Node Connectors

Brushless Electronic Speed Controls (ESC) Basics      The Speed Control      The Lov Voltage Cutoff - LVC      The Battery Eliminator Circuit - BEC

Motors for Electric Flight      Kv or RPM/v      Timing and Apparent Kv      Power In versus Power Out      Prop Shaft Rotation

Props

Selecting the CORRECT Supplier Recommended Props

Power Chart

Tips for Being Successful with Electrically Powered Flight

Safety Precautions

Other Resources

Ken Myers' Modeling Background

Wing Cube Loading Defines Aircraft Types and Missions

     Wing cube loading is a much better comparative number than the commonly used wing area loading.

 Wing Cube Loading Table

Online Sources for WCL

"Cubic Wing Loading: What it is and how to use it." Also known as - Wing Cube Loading by Ken Myers

"MODEL DESIGN & TECHNICAL STUFF:  WING CUBE LOADING (WCL)"  by Frances Reynolds, Model Builder - September 1989

"Aircraft Performance Parameters Revisited : WING CUBE LOADING", by Roger Jaffe, Model Builder - June 1994

"3D Wing Loadings: a Better Way to Scale Models and Compare different size models easily", by Larry Renger, Dec. 1997

Online WCL Calculator: Electric Flight UK

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Recommended First Purchase

     The very first item to purchase when getting into electric power is a power meter. It is also known as a wattmeter, watt meter and Whattmeter (Astro Flight brand and first in RC the market). It is connected between the battery pack and electronic speed control (ESC) and usually

displays the volts at the input of the ESC, amps drawn by the power system, energy delivered over time (Ah - amp hour or mAh - milliamp hour) and the watts input at the ESC.

Watts equals volts times amps. W=V*A

     The purpose of the power meter is to provide the actual information about the power system (battery, ESC, motor & prop). The information provided by the meter allows the user to adjust the prop (load) so that all parts of the power system are within a safe operating range.

     The meter is ALWAYS used at full throttle. Partial throttle readings mean nothing. A power meter measures watts in (power in), not watts out (power out)!

     The Power Meter by E-flite is NOT RECOMMENDED. It does not display all of the essential information on one screen.

Online sources:

 Progressive RC PowerLog 6S

     This meter also includes an optical tachometer and has the ability to log data to a file on a computer. It also has a 'Hold' button to keep the information onscreen. Hyperion Emeter 2 (expensive, but HIGHLY recommended!!!)

 P1 from Hobby Partz and similar meter at Hobby King

 Watt's Up Meter

BP Hobbies has several choices

Other power meters can be found online at Tower Hobbies and additional sources.

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How to Use a Power Meter

The Manual for the Watts Up meter may be applied to all types and is found on the PowerWerx site.

Power Meter Videos: Video 1 Video 2 Video 3

     When I previewed this information at the December EFO meeting, everyone one nodded and agreed that this is an essential first purchase. Get one ASAP!

Hint! If you do not have a power meter with a hold feature, video the data and then record the data when playing back the video.

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Chargers

     A high power, balancing, multi-chemistry charger with discharge function is the 'best' choice. It should charge and discharge Lithium Polymer (Li-Po/Li-Poly), Li-Ion (Li-Io), Lithium Iron Phosphate (LiFe), NiCad, NiMH, and Pb (lead acid).

 My chargers - FMAdirect Power Lab 8 (new) & CellPro 10S (well used!)

 Progressive RC is a great source for decent chargers.

Another good charger is the TME (Tejera Microsystems Engineering) Xtrema. The Xtrema has a built in wattmeter, so there is no need to purchase a separate wattmeter. TME also has a neat adapter board for charging single Li-Poly cells.

 12-volt DieHard Deep Cycle Marine/RV battery, battery case from NAPA, Walmart 12-volt charger - also shown AF Whattmeter

     Decent chargers require an external power source such as a Deep Cycle Marine/RV battery or power supply - NOT a car battery! There are NO decent chargers with a built-in power supply. They are too limited in power to be useful for most purposes.

     It is very handy to have a charger that will discharge so that a storage charge can be put on Li-Poly batteries when storing for extended periods of time. A storage charge is approximately 3.7v to 4v per cell with most chargers. When set to storage charge, many chargers automatically charge to 3.85v per cell.

     It is best not to plug a charger's input connector into a 12-volt socket in a vehicle. A vehicle battery is not designed for that use. Li-Poly batteries should NEVER be charged in or on a vehicle.

     The photo shows a safe way to charge a Li-Poly battery with a car plug type connector. The charging is done in the middle of a cement driveway, away from all combustibles. The adapter hooked to the battery is from Radio Shack. The manual was removed before the actual charging took place.Return to Table of Contents

Li-Poly Batteries

     Lithium Polymer batteries are the most common type of power battery in use today.      A single cell is not technically a battery, but they are used with some small electrics and called a battery.

How to read a Battery Label or Battery Specifications

     Li-Poly cells are said to have a nominal voltage 3.7v per cell. Actually, with a resting voltage of about 3.7v per cell, they are almost empty.

11.1V is the nominal voltage of 3 Li-Poly cells assembled in series (aka 3S). The charged voltage is 12.45v (4.15v per cell) to 12.6v (4.2v per cell) for a 3S pack depending on the charger.

2200mAh (milliamp hours) is the capacity (C) of this battery. 2200mAh is 2.2Ah (amp hours).

25C means that the supplier or manufacture implies that the longevity and performance of the pack will not degrade quickly if the battery is DISCHARGED up to this C-rate. The maximum amp draw for the battery is calculated using the capacity in Ah (amp hours) times the rate multiplier. The rate multiplier is the number preceding the letter C. In this instance it is 25 (rate multiplier) times 2.2Ah (C) or 55 amps. There is no industry standard regarding the C-rate and a manufacturer or supplier may claim whatever they want as the C-rate.

Charge current 2C normal 4.4 amps (approximately 30 minutes to charge completely discharged pack) 4C fast 8.8 amps (approximately 15 minutes to charge completely discharged pack) 5C max 11 amps (approximately 12 minutes to charge completely discharged pack)

The burst amps really mean nothing.

     Charging this battery at 5C requires a charger that can output a bit more than 12.6v at 11 amps. (12.6 * 11 = 138.6 watts) The charger needs to be rated for at least 155 watts or more for a 5C charge.

 C-Rate in minutes

     The chart shows approximately how long it will take to fill an empty pack or deplete a full pack at the C-rate. High charge rate Li-Poly batteries, mated with a good charger, reduce the time spent in the immediate area of a charger. When the charge time is shorter, there is less waiting time for the battery to completely charge.

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Li-Poly Storage and Safe Handling

     Li-Poly batteries contain a lot of potential energy. They require special attention and care when in use and in storage.

Good charging practices include Using the balance connector for all charges, even when using power leadsCharging only out of the airframe Charging only in an area free of combustibles Remaining in the immediate area of a charging Li-Poly battery 

Keeping the battery and charger under close observation *High charge rate Li-Poly batteries make staying in the immediate area of a charging Li-Poly battery much easier. The charge time is muc hshorter.

     It is best to charge in a REAL Li-PoSack brand charging sack. Some off brands have been known to burn! Really. Distributors of the REAL Li-PoSack can be found on their Web site.      The Li-PoSack Plus is a good storage vessel and can be used for storage and transportation. A fireproof safe, ceramic dish with lid or ammo box make decent storage vessels.

 My ammo box with charge leads going into the box and a hole for the balance connector.

     Another storage and charge safety system is the LiPoLocker. The LiPoLocker.com Battery Charging Security System Review can be found on RC Groups. It is another Li-Poly safe charging and storage system.

     Li-Poly packs puncture easily. Keep them away from sharp objects. Do not allow bolts, screws or other sharp objects to protrude into the battery area of the aircraft. Protrusions will puncture a Li-Poly in a crash. Be sure the battery is secured very well in the aircraft.

Dispose of punctured or puffed packs immediately.

     Lithium Polymer disposal instructions from Common Sense RC

1) Discharge the battery to 0 volts. 2) Puncture each cell and immerse in saltwater for 24 hours. 3) Wrap the battery in a bag and place in an appropriate disposal canister. 4) The pack can now be thrown in the garbage - there are no special disposal requirements for Li-poly batteries.

     Put a storage charge on Li-Poly packs that will not be used for weeks or months and store in a safe container away from all combustibles.

     It is best to purchase Li-Poly packs just before they are to be put into service. They don't have as long a 'shelf life' as other types of batteries.

     To preserve long life for Li-Poly batteries, they should not be flown to the LVC of the ESC or too deeply discharged. It is best to use the "80% of the capacity rule" to avoid premature death of a Li-Poly pack.

Here are a few examples of the 80% of capacity rule: Stated capacity 4500mAh * 0.8 = 3600mAh flight capacity Stated capacity 3000mAh * 0.8 = 2400mAh flight capacity Stated capacity 2250mAh * 0.8 = 1800mAh flight capacity

Learning the 80% Capacity Point of a Pack and Flying Style

Step 1: fly the aircraft in a normal manner for 3 minutes using timer Step 2: Land, remove pack & charge pack. Note the Ah/mAh returned to the pack

If the mAh/Ah returned to pack is greater than the 80% capacity number, reduce the flight time. Repeat Step 1. or If the mAh/Ah returned to pack is less than the 80% capacity number, increase the flight time. Repeat Step 1

Repeat Steps 1 & 2 until the normal flight time for use of 80% of the capacity is established for the plane, flying style and individual pilot throttle management.

What happens if it is slightly over the 80% point, say 82%? Nothing, that is close enough.

     The actual capacity and manufacturer or supplier's capacity may not be exactly the same. Capacity changes over time. As a battery ages, the capacity decreases. It is important to be aware of this factor.

Online Resources:

Understanding RC LiPo Batteries   Proper Li-Poly management

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Other Flight Power Batteries

     Some electric power modelers use power batteries made up of cells from A123 Systems, Inc. The A123 cells are only available in 1100mAh and 2300mAh capacities. They have a nominal cell voltage of 3.3v per cell and a charged voltage of 3.85v per cell. Most people who use them 'harvest' them from DEWALT Lithium battery packs for power tools. A123 cells are Lithium Iron Phosphate (LiFePO4) chemistry. They are heavier than an equivalent Li-Poly cell, but much lighter than NiCads or high-energy NiMH cells. Many people consider them much safer than Li-Poly cells.

More Information on A123 cells

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Li-Poly Batteries for use in Transmitter

     While many modelers are using Li-Poly batteries in transmitters, it is BEST not to use them for this purpose. Li-Poly batteries may require a voltage regulator and the battery must be removed from the transmitter before charging them outside the transmitter. If the transmitter is accidentally left on, the pack will be ruined because it will be too deeply discharged.

     The Sanyo Eneloop low self-discharge (LSD) NiMH cells make excellent batteries for transmitters. They come in a 2000mAh capacity. Once fully charged, they'll hold that charge for weeks.      The cells can be purchased at COSTCO or pre-made packs for specific transmitters at No BS Batteries.      Ray'O' Vac call their type of LSD NiMH a Hybrid.

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Temperature Effects on Batteries

     Batteries work best at room temperature. Operating batteries at a high temperature shortens their useful life. At low temperatures, the performance of all battery chemistries drops substantially. A battery may be capable of operating at cold temperatures, but it may not allow charging under those conditions. The charge acceptance for most batteries at low temperatures is extremely limited. Most batteries need to be brought up to temperatures above the freezing point for charging. Even then, they will not charge well until they are at room temperature.

Battery Resources regarding temperature

Battery University.com Electric Wingman: Lithium Polymer Battery Guide

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Connectors

Power lead connectors from the battery to ESC

     There are many types to choose from. An article by Stefan Vorkoetter gives the statistics and reasons for using many of the connectors discussed here.

     The most common power lead connector is the Deans Ultra, which is usually just called Deans. There are Deans Micro Plugs as well.

 Handy "Gripper" Covers for Deans Ultra Plugs from HDi

     The Deans Ultras are similar to the XT plugs sold by Progressive RC, except that the XT is ribbed for gripping. The Progressive plugs come in three sizes, T-plug, Mini T-plug and Micro. These are NOT Deans plugs.

 

 Anderson Power Poles (APP) aka Sermos

 Crimper for APP connectors

 The EC3 and its larger relative EC5 (EC3 shown)

 BEC

     The JST plug is used for small planes and low current applications. It is also often called the BEC plug or P connector.

 Bullet type

     Bullet connectors are available in various sizes ranging from 2mm diameter and up. The larger ones are used for larger amp loads. They are not really interchangeable by brand. They are used most often for the motor to ESC connection, but they are occasionally used for the battery to ESC connection.

     There is often controversy raging on RC Groups as to what is the best connector. Here is a current thread on that topic.

 Multi power plug adapter from Progressive RC - $16.99

     It is a good idea to have an adapter for the various power plugs. It will come in handy at the field someday to help others or yourself when unexpected charger problems arise and you may need to 'borrow' a charge or someone wants to 'borrow' some electrons from you.

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The 4 Major Balance Plugs, Taps, Nodes or Node Connectors

Please NOTE: The following listing may no longer be current.

Polyquest (PQ) taps are used on: Enermax, E-tec, Extreme Power, Fliton, Hyperion, Impulse, MaxAmps, Pache, Poly RC, Polyquest, True RC and Xcite battery packs.

 

     Note that the PQ types use the same connector for several battery configurations and skips pins that aren't required. 2S and 4S packs shown. The 3S also uses the same connector.

Thunder Power (TP) taps are used on: Apex, Danlions, EVO, Flight Power, Kong Power, MPX, Outrage, Tark Power, Thunder Power and Vislero battery packs.

Align JST XH (AL) taps are used on: 3E Models, ABF, Air Thunder, Align, Common Sense RC V2, DN Power, Dualsky, Dynam, E-flight, Electric Power, Electrifly, Energy EC, Esky, E-Watts, Exceed RC Fusion, Fully Max, GE Power, Grayson Power, Hextronix, HI Model, Hobby City, Hobby Loong, Hurricane Flight Systems, Imax, LOSI, Mega Power, Mystery, PowerSource, Protec, Rhino, Tenergy (rev polarity), Tower Hobbies, Trinity, Turborix, Vampower (new), Venom and WOW RC, X-Caliber and Zippy battery packs.

Kokam JST XE taps are used on: Apogee (but you need to remove lock), Core, Graupner, Kokam, New / Neu Motors, Orion Avionics and Vampower (old) battery packs.

     Suppliers of Chargers also supply adapter boards for various types balance connectors for use with the chargers they sell. A look at the balance boards shows how the 4 major balance plugs are configured and how many pins each connector has.

     This is the adapter board for a CellPro 10S for the Kokam JST XE (top) and Align JST XH (AL) (bottom) balance taps. Note that each connector size is only used once and has one more connection than cells in the battery.

     This is the adapter board for a CellPro 10S for the Thunder Power (TP) (bottom) and Polyquest (PQ) (top) balance taps. Polyquest uses the same connector for 2S, 3S and 4S packs and different connectors for 5S and 6S. Thunder Power uses the same connector for 2S and 3S packs and then a different one for 4S and 5S packs and double connector for 6S packs.

More balance plug information

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Brushless Electronic Speed Controls (ESC) Basics

     Many of today's brushless ESCs have three distinct parts or circuits built into them.

The speed control - There are a lot of electronic 'things' happening, but basically it is an electronic on/off switch that is turning on and off extremely rapidly. When it is On the voltage and amperage are at maximum. When it is off, there is no voltage or current passing. The RPM is controlled by how long the On cycle is on compared to how long the Off cycle is off.

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The Low Voltage Cutoff (LVC) circuit was originally designed to stop or reduce power to the motor to reserve battery power for the receiver and servos for a safe landing. It is even more important today because it can save Li-Poly batteries from being ruined by being too deeply discharged. Li-Poly batteries should never be flown to the point where the safety LVC circuit kicks in. Always time electric flights with either the transmitter timer or a typical kitchen timer.

 Kitchen timer that I use

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The Battery Eliminator Circuit (BEC) is another circuit designed into an ESC that allows the power battery to be used to power the receiver and servos. It is basically a step down voltage regulator.

The two types of BEC circuits found in ESCs

Linear (most common, cheap): It works by converting the excess voltage into heat. The higher the input voltage, the more heat generated in the BEC circuit. If there is too much heat, the BEC will either 'fry', or shut down! With a 3S Li-Poly the linear BEC is only able to provide about 0.5A before it overheats. That's only good for about 3 standard servos and the receiver. Many people overstress this type of BEC. Most ESC manufacturers don't recommend the use of a linear BEC with a 4S Li-Poly battery.

The Castle Creations Thunderbird and Phoenix lines of ESCs contain linear BEC circuits.

Switching (best type, expensive): A switching regulator works by taking small chunks of energy from the input voltage source, and moving them to the output. This is done with an electrical switch and a controller. They regulate the rate at which the energy is transferred to the output. That's why it is called a "switching regulator". A switching regulator can typically have and efficiency of 85%. A switching regulator can easily power heavy loads from a high voltage source.

The Castle Creations ICE line of ESCs contain switching BEC circuits.

     Today's Brushless ESCs, with the onboard BEC disabled (easy to do), or Brushless ESCs that do not have a built in BEC can also use NiCad or NiMH receiver packs, A123 Systems Li-Fe receiver packs, and stand alone switching BECs like the Castle Creations BEC or BEC Pro.

Sources for more BEC Information What is a BEC? A beginner's guide to switching regulators Lucien Miller, of Innov8tive Designs, provides information of the types of BEC units and which type is appropriate for which application.

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Motors for Electric Flight

     Today, brushless inner runner motors are mainly used in electric ducted fan (EDF) applications and helicopters.      Brushed motors are still used in specialized applications, especially very small planes.

     One of the main characteristics of the brushless outrunner is that its magnets are housed in a bell. The stator or armature is on the inside of the motor. That is just the opposite of a brushless inner runner. The outrunner provides more torque than an inner runner and the outrunner can turn prop sizes that the brushless inner runner would need a gear reducer to turn.

     Outrunners are generally less efficient than inner runner types with a gear reducer, but they are still efficient enough for general use. There are hundreds of different sizes of outrunners from very tiny to massively huge.

     Outrunner nomenclature is not standardized. Comparing one company's outrunner to another's is often difficult. Some companies use the outside measurements to describe their motors.

     Hobby King has a motor that it calls the TR 35-48-C 800kv weighing 163g. Hobby King uses outside dimensions to designate its motors. The C dimension is about 35mm and B dimension about 48mm. The stator dimensions are 28mm x 26mm. Dimension A is 4mm. Maximum current is rated at 55 amps. Price $14.95

     Scorpion has a motor that it calls the Scorpion SII-3020-780weighing 166g. Scorpion uses the stator dimensions to designate its motor numbers. It has a Kv of 780 (about the same as the Hobby King motor). The C dimension is 37.5mm and B dimension is 45.7mm. The stator dimensions are 30mm x 20mm. Dimension A is 5mm. Scorpion does not give the useless maximum current but does rate this motor at a continuous 40 amps with a continuous power level of 800 watts in. Price $65.95

     Hobby King would call the Scorpion motor a Turnigy 38-46 780Kv (they tend to put a dash between the external dimensions, but not always) and Scorpion would describe the Hobby King motor as a Scorpion 2826-800.

     Hobby King does not note that the magnets are of the ceramic ferrite type. Scorpion does note that its motors use the N-50EH type of rare-earth neodymium magnets.

     The two motors are not the same, but with a similar weight and Kv, they might be expected to perform close to the same level with the same battery, ESC and prop.

     The Cermark NEO 25-780 has a similar 780Kv, but it only weighs 149g. Using its outside measurements it would be called a 42-40 780Kv. It has a 5mm shaft. It is rated for a maximum of 460 watts in and 55 amps. While it does use neodymium magnets, it would require a larger diameter prop with more pitch to achieve the same watts in as the other two motors. It is not similar to either of the other two motors, and its performance will be quite different.

     Motor weights do NOT include the weight of the prop adapters, motor mounts and their related screws and usually not the connectors either.

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Kv or RPM/v

     Kv is a motor constant and is directly related to Kt, the motor torque constant. The specific motor's design and construction determine this constant. The Kv motor constant has nothing to do with the applied voltage. It is part of the motor's physical makeup. There are electrical and mechanical losses in all motors. The voltage in RPM/v is the VOLTAGE OUT not the voltage in. 

     The only time the input voltage and output voltage are about the same is when there is no load applied to the motor.

     The higher the voltage drop through the motor, the lower the RPM will be. The higher the current is, the greater the voltage drop will be. The less efficient a motor is, the higher the voltage drop will be.

More on Kv and how to measure it

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Timing and Apparent Kv

     Timing affects the apparent Kv. Advancing the timing on a brushless motor using the ESC increases the RPM by forcing the motor to turn at a rate higher than the native or raw Kv. It also increases the current draw and decreases the efficiency.

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Power In versus Power Out

     The power meter measures the power IN at the ESC. There are electrical losses in the ESC, and there are electrical and mechanical losses in the motor. The majority of the losses are turned into heat. The power out is considerably less than the power in.      If a power meter is showing 10.7v, 27.9 amps and 298.5 watts in, those numbers are input measurements. The motor is not 'making' 298.5 watts! It is not MAKING anything! It is using electrical energy and converting it to mechanical energy.      A useful drive system, using typical outrunners, will be somewhere between 70% and 80% efficient. That means about 209 watts out (70%) to 239 watts out (80%) for the noted system showing 298.5 watts in on the power meter.

     How do you know the power out? You don't! There are ways to measure the output, but they are too complicated for most modelers. Motor/prop/battery computer programs like Drive Calculator can estimate the power out. Drive Calculator is a FREE program and runs on Mac, Linux and Windows.      Power out may also be estimated using something known as prop constants and the measured RPM.      It is not really necessary to know the watts out. When electric fliers and authors use the term watts, they are referencing watts in.

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Prop Shaft Rotation

     It is easy to change the prop shaft rotation of a brushless motor. Switch the connection of any two leads between the motor and the ESC. The color coatings on the leads from the motor to the

ESC mean nothing. Different brands use different colors on the motor leads to the ESC and also different colors on the ESC to motor leads.

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Props

     The APC props, slow fly (SF), thin electric (E), sport and pattern have RPM limits. The limits are listed on their Web site. They all have applications that work well with electric motors.

     Master Airscrew standard wood props and G/F 3 series work well with electric motors. The Master Airscrew electric props are not very efficient and should be avoided.

     Zinger props are not useful for most electric applications, but make excellent prop blanks, according to Keith Shaw, if you want to create your own props.

     GWS has basically two lines of props, RS and DD/HD. The RS (reduction series) are used in applications similar to the APC SF type props. The DD/HD (direct drive/hyper drive) props are used in applications similar to the APC E, but have lower RPM limits than the APC E props.

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Selecting the CORRECT Supplier Recommended Props

     Many times a supplier will recommend props for a motor and battery combination. It can be confusing.

     The graphic was captured from the specifications for the E-flite Power 25 870Kv BL Outrunner at Horizon Hobby. The props and battery packs (Cells) are listed from 'smallest' to 'largest'. What is NOT apparent is that the largest prop (14x7) is only the largest prop for the 3S pack and the smallest prop (11x8) is the largest prop recommended for the 4S pack. It is not a range at all, but a recommendation for each type of pack with this motor.

A much better way to list them would be 3S up to 14x7 4S up to 11x8

     Not all props are created equal. That is another reason for having a power meter! One manufacturer's 14x7 will not be placing the same load on the motor as another manufacturer's 14x7. It is entirely possible that one company's 14x7 will fall within the safe operating limits for the power system while another company's will be outside the safe operating zone. Only flying will prove which prop is best in a given application.

Power Levels for Various Types of Aircraft

     This is Common Sense RC's table suggesting power levels based on Watts (watts in) per pound for ready to fly aircraft weight. It is a reasonable guide.

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Tips for Being Successful with Electrically Powered Flight

1.) Start out slowly and take the time to learn what you need to know 2.) Avoid impulse purchases - have a specific goal in mind 3.) Glow or gas conversions should be put off until you have acquired the knowledge to do so 4.) When choosing power systems, at first, follow the recommendations of the designers of plans and kits and the recommendations of airframe manufacturers and suppliers 5.) Get the proper equipment to do it right the first time 

6.) Ask reliable sources for input and guidance with a project, especially before an equipment purchase - it is best and cheaper not to try to 'go it alone'

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Safety Precautions

1.) Store Li-Poly batteries safely and away from combustibles. 2.) Remove the propeller or blades from the motor when working on the radio system and the power battery must be plugged in. 3.) Plug in the power battery just prior to a flight. 4.) Unplug the power battery immediately after landing and returning the aircraft to the pit area. 5.) Be aware that once the power battery is plugged in, the motor may run. 6.) Arming switches and ESCs may or may not keep the motor from running once the power battery is plugged in. 7.) Make or break arming switches, like those sold by Maxx Products International, LLC., are an excellent type of safety "switch", especially for large scale aircraft.

 Maxx Products Arming Switch

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Other Resources:

Online forums: RC Groups, Watt Flyer,   RC Universe  and more - be aware that some of the experts on the forums started flying electric RC last week. Most forums contain about 98% 'noise' and about 2% decent advice. There is useful advice to be found, but finding it can be quite time consuming.

An excellent independent site is RC Model Reviews. The author has excellent knowledge and is the most unbiased reviewer I've ever read. The reviews and information provided on the site are not just for electric fliers.

Books: The majority of books about electric flight are 'old' and contain a lot of outdated information. Two books that are not outdated are RCadvisor Model Airplane Design Made Easy and RCadvisor ModiFly. Both are by Carlos Reyes. He also has an excellent Web site. Both books are available on the Web site.

The EFO Web site and monthly Ampeer electric flight newsletter have a lot of reliable information regarding electric flight topics.

I'm willing to answer, or try to find answers, for questions regarding electric flight at kmyersefo@theampeer.org

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Ken Myers' Modeling Background: 1958 Started CL (mostly Cox 0.49) & rubber powered free flight (Guillows, Sterling, Comet) 1960 Started RC with ground based Tx and escapements, small displacement glow & diesel engines 1969 Started using Citizenship handheld TX with pulser and Rand actuators 1972 First proportional 2-ch Cox-Sanwa used with Cox 0.49/0.51, followed by Cox-Sanwa 4-channel and Enya RC engines, then switched to Futaba as Cox-Sanwa (later marketed as Airtronics) became harder to get 1980 Started AMA pattern flying and traveling to meets; Flew Novice, Sportsman then Advanced 1982 First electric, Midwest Sweet Stik 40 with Astro Flight Ferrite 25 and 12 and 14 NiCads 1982 Met Keith Shaw (Mr. Electric) at IMAC meet, both flying glow aerobatic biplanes at time 1984 First 4-stroke, Enya .36 used on small pattern plane 1985 Started Mid-America Electric Flies as CD with Keith Shaw of the Ann Arbor Falcons 1987 Stopped flying glow engines (except when training at Midwest) 1988 Started Electric Flyers Only and Ampeer electric flight newsletter 1995 & 1996 CD of electric events at the Nats in Muncie & chairman of National Electric Aircraft Council (NEAC) 1982 - 2005 used mostly Astro Flight cobalt brushed motors in most planes 1996 EFO site started online and the Ampeer goes online as well 2003 First brushless outrunner, AXI 2820/10, Castle Creations Phoenix 45 2006 First Li-Poly battery, 4S1P True RC 4000mAh used in Sportsman Aviation Sport Stik - First Li-Poly charger Astro Flight 109 2006 First used E-moli and "A123" 2300mAh cells 2009 First scratch built Foamboard plane, Modifly from Rcadvisor's Modifly by Carlos Reyes - last Li-Poly purchased, only one left in use, rest were given away 2009 Mid-Am celebrates its 25th year

     Over the years Ken Myers has authored articles for "Model Airplanes News", "Sailplane and Electric Modeler", "Electric Flight UK" and other magazines.

Ken Myers, President Electric Flyers Only (decades), Editor Ampeerelectric flight newsletter (decades), Vice-president Midwest RC Society (decades), Editor Midwest Monitor newsletter, President and founder of the Union Lake Flying Organization (now United Flying Organization in Heartland, MI), Contest director (UFO pattern meets 1980-1986, electric meet Mid-Am since 1985), AMA NEAC (National Electric Aircraft Council) SIG chairman 1995 & 1996, Head flight instructor Midwest since 2008, AMA Leader Member (decades)

Major accomplishment in electric flight, learning from and reporting on Keith Shaw's phenomenal Scale electrics.

Main interest - sport and sport scale electrically powered fixed wing aircraft.

The First Bit

Hello all, we are back again for another exciting installment of (cue drum roll) The Inside Story. I want to start by thanking everyone for their encouragement and support for the column. Many of you who emailed me wanted to know more about actuators, in particular how to drive them, so this article contains a mini-article on just that. It is hard to write articles covering such a large field without feeling that you will frustrate the reader by not telling the whole story all at once. Please bear with us as we will try to cover plenty of the basics as quickly as possible but in the mean time always feel welcome to log on to the EZone's excellent discussion forums. Also in this issue is an excellent feature article by Joachim Bergmeyer. It covers the theory of how to work out what that mystery motor is good for. It contains a little mathematics but is set out in such a way that you can know as much as you want to know, from using the ready to fill in form to reading the derivations. After reading this article, I feel a personal cloud of ignorance had been lifted and I hope you will too. On a lighter note (pun intended) Gordon Johnson has written two mini-articles (gold star for that man!), one covering the lightening of normal micro servos and receivers and the other on the need to keep a close eye on your volts when using the new Lithium Polymer cells. I have also managed to squeeze out a second mini on making a simple circuit board to allow two multimeters to be used simultaneously and conveniently. Just to prove the microwave is good for something more than cooking ready meals we have a tip from Peter Frostick a free flight and micro RC guru on his unusual method of fast prototyping balsa props. You should probably be working while reading this so let's get started.

Feature Article - Motor Constants, How To Find Them And Use Themby Joachim Bergmeyer

Introduction

Have you ever bought a tiny DC motor from a surplus store and asked yourself at which current and voltage it might work best? Do you believe that the well-known KP00 motor is an "amp hog" and eats up the current more quickly than it should? Then read on; you might find some help and a new point of view.

Abstract

This article describes how to measure and calculate the motor constants of small, brushed, DC motors at home with common and relatively cheap tools and instruments. Furthermore, it describes how to make use of them to choose a good point of operation for an unknown (or known) DC motor i.e. the working voltage and current. It also gives some insight to the physical basics. For this purpose, some high school level mathematics will be used.

What Is A Brushed DC Motor?

The motors we are referring to consist of very few parts.

The Stator: In most cases, it is the outer housing of the motor. It is made of a soft (does not remain magnetized) magnetic material, most commonly iron and contains magnets that are arranged to have one north and one south pole. There are also two bearings, either plain plastic or porous brass bushes or (in more expensive motors) ball bearings.

The Rotor: This either consists of an iron core carrying sets of windings (called poles) or is coreless. In the latter case, the windings are wound by a machine and then fixed by resin such that they stand alone without the iron core. The number of poles is most commonly three, and sometimes (in better motors) five. More poles tend to be used only with bigger motors that are too large for small indoor models.

The Commutator: This consists of two halves; one-half fixed to the rotor, the other to the stator. Its purpose is to route the current from the motor terminals to the rotor windings and switch the current in such a way that the windings of the poles generate magnetic forces that cause the rotor to turn indefinitely. This is the part of the brushed DC motor that makes it brushed. It is the brushes that connect the rotating rotor to the stationary stator.

How do voltage, current, torque and rpm relate?

A DC motor converts current into torque and voltage into rpm. Unfortunately, there are losses. Friction in the bearings must be overcome by an idle current I0. The resistance Ri of the rotor and alternator cause voltage losses, and there are also so-called "iron losses" caused by current in the core iron which is generated by the changing magnetic field in the rotor. In this article, the iron losses are ignored because they are also represented by the idle current (and because they are not calculated as easily as the other losses). Besides that, the often-used coreless motors do not have a core and therefore have much less iron losses, which make them more efficient than cored motors.

Here Are The Fundamental Motor Equations.

The generated voltage of a motor and the rpm have a fixed ratio. It is called the rpm constant  :

(1) 

The input power of a DC motor is the terminal voltage times the current:

(2) 

The output power from a mechanical point of view is rotor torque times rotating speed (in radians per second):

(3) 

Here arises a problem, as is difficult to measure the torque. You have to build some sort of test fixture and you need a good balance to measure the counteracting forces. Even if you do the former and already have or are willing to buy the latter, it is difficult to get exact readings. However, there is another possibility. We will not measure the torque, but calculate the output power as the input power minus the losses.

 is the voltage that we can measure at the motor terminals.   is the motor current. However, not all the voltage counts for the output power, only the voltage generated in the rotor windings according to

formula (1) does. a part of the voltage is lost at the inner resistance   when   flows through it.

therefore, we have to subtract the voltage loss across the motor resistance  , (which is, according to

Ohm's law,  ) from the battery voltage:

(5) 

The motor torque caused by the idle current   is needed to compensate for the friction of the bearings and the alternator; we do not see any torque outside the motor from this part of the current so we subtract it from the battery current:

(6) 

Now we multiply the effective voltage by the effective current and get the output power:

(4) 

We can now find the output power without measuring torque!

The efficiency is the ratio between input and output power:

(7) 

The rpm can be calculated using equation (1) and (5):

(8) 

Now we have shown that with the help of the motor constants  ,   and  , we can calculate all these

values including the  . We just need the motor current and motor terminal voltage, both of which are easy to measure. We need a voltmeter and an ammeter. The cheapest and easiest way is to use two multimeters at the same time. These multimeters do not have to be very expensive, but those with digital display are easier to read, and of course, multimeters that are more exact are more expensive than simpler ones. There are also combined instruments available that show voltage, current and input power at the same time; these are a taste of luxury.

There are even more interesting values!

The most important questions when trying out a new motor are...

How much power can I expect? At which current will I get maximum power? Which efficiency can I expect? At which current will I get maximum efficiency? Which current should I use? How fast will the motor turn?

All these questions can be answered by help of the motor constants. First, we should decide about the power source, because that will tell us how much voltage we can use. In general, more voltage leads to more efficiency, more power, more current and, worst, more weight. The latter is because we micro-flyers tend to use the smallest available batteries that provide us with the necessary power. Since energy to weight ratio is worse with smaller cells, we always should try to use less cells first, not smaller cells. The only reason to use smaller cells is when we are down to one LiPoly cell only and this one cell is too heavy!

The new star under the power sources is the Kokam Li-Poly cell with 145mAh, giving us about 3.6V under load and up to 1A. About the same can be expected from three Sanyo 50mAh NiCad cells (for a shorter time, of course) or from three GP 120mAh NiMH cells. One of these power sources is generally used in the "1oz-class" (models with an all-up weight of up to ~30g). More voltage needs a DC/DC booster which adds complexity, costs and weight, or more cells, which also adds weight and therefore is used more in the "2oz-class" (all-up weight up to ~60g). (Apart for some pager motor powered models that require a DC-DC and weigh <1oz, Graham) Therefore, depending on the class to which our model belongs, we assume that we have 3.6V or 7.2V and up to 1A.

Maximum Power

A formula for the current at the point of maximum power for a given motor can be derived from formula (4).

(10) 

Here I just show the formula, if you are interested in the derivations then you can find it here.

Power, efficiency, and rpm can be calculated using formulae (4), (7), and (8). Just put in the motor

constants, the chosen motor terminal voltage and use   for  .

We should never use more than   in any case with any motor because if you pull more than   then the efficiency goes down more quickly than the power consumption rises, so we will get less (not more) power. The motor will become very hot, since all the electrical power that is not converted into mechanical power will be converted into heat instead.

Of course, this tells nothing about how long the motor will stay alive at this power level. Formula (10) only tells us at which current this particular motor will have the most output power when used with the

assumed voltage. Electrical motors generally have no fixed maximum working voltage, so this has to be answered by experience. As stated above, the motor could quit by overheating, by burning the brushes or by destroying the rotor.

The coreless motors are more sensitive because their rotor has little mass and thus will heat up very quickly, and since it has no iron core, if the resin that fixes the windings melts then the rotor will expand and rub to the outer housing of the motor, generating a lot of friction. In this way, I myself damaged some tiny coreless pager motors.

Maximum Efficiency

The motor current at the point of maximum efficiency is:

(11) 

The derivation can again be seen here. We also have a nice formula to calculate the maximum efficiency

directly (we could also put   into formula (7) for the same result):

(12) 

The motor current at full throttle should never be less than   because the output power would be very low and the efficiency would be bad. So, we have some nice guidelines on what we can expect from a motor and which current we should try to reach by choosing prop and gear ratio.

The Rules

Use at least   . If this is already too much power for your model, use a smaller motor.

Never use more than   . Otherwise, your motor will burn and the output power will be low.

It is a good rule of thumb to use about 70-90% of   for static current at full throttle for the small motors we normally use.

The output power, rpm and of course the efficiency can again be calculated using equations (4), (7) and (8) in any point of operation, so we will know anything that we need.

But how do we get the constants?

We get the constants by measuring values that are relatively easy to get, and then use some special formulas.

Firstly, we measure the idle current  . This is dependent on the motor terminal voltage, so we measure it at about 2/3 of the operating voltage (means: battery voltage) that we want to use later. This is because it will more or less be the rpm level at which the motor will run later with the best compromise of efficiency and power. Measure the idle current without having a gearbox attached to the motor.

Then we choose two different loads that we believe to be near the upper and lower border of the operating range of the motor. In the simplest case, these are the two props that we think are ok but which we do not know which fits better. It does not matter whether the props are directly driven or geared, but in the geared case, of course we have to multiply the measured rpm with the chosen gear ratio.

We take two sets of data.   ,   and   with the first prop,  ,  , and   with the second prop. We should take the voltage directly at the motor terminals to avoid a measuring error. All

values should be taken at the same moment, or it might be easier to use a battery with big capacity because the voltage will then not drop quickly during the measurements.

If we find later that the measured currents are about 30-60% of   for the lighter load and about 80-

100% of   for the heavier load then we guessed right about the two different test loads. If the readings are much different from that then we should choose some other loads (means: props) and redo all our measurements and calculations. Otherwise, our results might be less precise than they could be.

The motor resistance   can be calculated as:

(9-6) 

...and the speed constant   will be:

(8-4) 

These formulas are also derived here.

Examples

1). The Kp00 Motor

I have measured the following data at this little workhorse and got the following results.

Measurement with load 1 (bigger prop):U1 2.10 VI1 0.66 An1 13900 rpm

Measurement with load 2 (smaller prop):U2 2.08 VI2 0.62 An2 14450 rpm

Measured idle current at 2.1V: I0 0.10 A

We put our values into the formulas and get the following motor constants:

(9-6) Ri = 1.559 Ohm

(8-4) kv = 12980 rpm/V

Assuming an average discharge voltage of 3.3V for one Kokam 145mAh Li-Poly cell, we get the following predicted data:

(10) 

 = 1,108 A

This fits well to the maximum current of the Li-Poly cell. We don't want to go all the way up to the maximum power anyway. (Very Good!)

(4) 

= 1.59 W

This is quite a lot of power. A rule of thumb says that the INPUT power of a sports plane should be 50W/kg, So we could expect to be able to power models up to 3.3V*1.1A/50W*kg = 72g. This isn't a micro flyer anymore, right? Right! I would recommend this motor for models in the 1oz-class (around 30g maximum). (good again)

(7) 

 = 43%

This is a quite high efficiency at the maximum power point of a so small motor (50% is the theoretical maximum value here!), also very good.

(8) 

 = 20405 rpm

We can only use small props or have to use big gear ratios, since this motor turns fast! The micro scale builders will enjoy this, as most micro scale flyers will be able to use a prop of about scale diameter! If you are searching for efficiency of the prop then you will have to use a big gear ratio. We have all the possibilities, good again.

(11) 

 = 0.46 A

(12) 

 = 61%

(4) 

 = 0,93 W

(8) 

 = 33524 rpm

Now comes the excellent part. The point of maximum efficiency for this motor at this voltage is still within the area of useable power! Yes, this motor likes amps, but it gives us a lot of torque back for it also! Lighter models (around 20-25g) will be able to stay in the air with this power, and a motor this small performing with an efficiency of more than 60% is outstanding! Yes, we will have to use a high gear ratio to make use of this high rpm.

My conclusion is that the KP00 motor is a very efficient and powerful one if you use a light load (=small prop or high gearing) and let him turn as fast as he wants to. The useable current range reaches from

0.5A to 1A at 3.3V, which is exactly what we want for micro scale models around 1 ounce total weight. My Guided Mite did loops! Yes, I love this little powerhouse! :-)

2) The N-20 Lv Motor

It is available from many surplus sources; mine are from Allelectronics.

I've measured the following data with this motor and got the following results:

Measurement with load 1 (bigger prop):U1 3.19 VI1 0.84 An1 7900 rpm

Measurement with load 2 (smaller prop):U2 3.36 VI2 0.52 An2 15700 rpm

Measured idle current: I0 0.12 A

We get the following motor constants:

(9-6) Ri = 2.592 Ohm

(8-4) kv = 7803 rpm/V

I've used this motor with a DC/DC booster that happened to deliver 5.2V. We get the following predicted data:

(10) 

 = 1,063 A

This fits well to the maximum current that my DC/DC booster can deliver. (good)

(4) 

 = 2.3 W

This is more power than from the KP00. The rule of thumb (for bigger models) says 5.2V*1.06A/50W*kg = 110g. I would doubt that this motor would carry around a model that heavy, but it works at least for up to 60g. (good again)

(7) 

 = 42%

The efficiency of this motor is slightly lower, but still good.

(8) 

 = 19075 rpm

We still have all the possibilities. (good again)

(11) 

 = 0.491 A

(12) 

 = 57%

(4) 

 = 1,456 W

(8) 

 = 30653 rpm

As said above, at 5.2V this motor is not as efficient as the KP00 at 3.3V, but is still good. It is heavier, but it will carry around models that are heavier also.

The N-20 LV performs well at a minimum voltage of 5V. It works notably less efficiently from one Li-Poly cell without booster. It is therefore probably not ideal for the very small models. However, it works well in my models around 2oz. In addition, it is cheap! So, if one ever quits (no one did yet for me), take the next one! It will probably quit sooner if working from two Li-Poly cells, but this should be a quite efficient drive system if you keep the current low enough (say at about 1A maximum).

3) Your Own Motor:

You can download a blank form that can be printed out and filled in with your measured values here. You will need Adobe Acrobat Viewer to read it.

Conclusion

I wanted to show that these calculations are no black magic and that you don't have to grope in the dark when you ask yourself how to make the best use of the tiny motor that you have recently found somewhere. Some predictions are calculated easily, and it is even possible to develop the mathematics yourself.

Bibliography

The following books helped me to understand the theory of DC motors.

K. Gieck, Technische Formelsammlung, Gieck Verlag 1981, Heilbronn, Germany Dipl.-Ing. L. Retzbach, Ratgeber Elektroflug, Neckar-Verlag 1999, Villingen-

Schwenningen, Germany

Mini Article - Lightening Rotary Servos and the R4P ReceiverBy Gordon Johnson

One of the keys to building a successful micro plane is an accurate estimate of the final AUW (All Up Weight). A major part of the AUW for any of our planes will be the receiver, speed control, servos, motor, and battery. A good estimate of what these will weigh allows us to determine in advance whether we will

achieve a low enough wing loading for the type of flying we are interested in, indoor or outdoor. This in turn allows us to either (1) scale the plane up to achieve the target wing loading, or (2) select different, and usually more expensive, equipment. One problem we face is that the weights listed by the manufacturers for servos are not the effective weight including wires, plugs, and servo arms. Moreover, the manufacturers don't tell us how much weight we can save by lightening their products.

In the tables below, I give effective weights for common servos and receivers to aid in planning a model. I also give weights after relatively easy to perform lightening techniques. There are more aggressive lightening techniques that I do not cover here. For example, you can lighten a R4P receiver even more by removing the plugs and part of the circuit board and then soldering the wires from the servos directly to it. People have also lightened servos by taking apart the cases and drilling many small holes. If you do a search in the EZone micro forum, you will find examples of aggressive lightening of servos and receivers. My emphasis here is on less aggressive techniques, and I will give a breakdown of the amount of weight saved from each technique.

Now let's look at the table. First, even the very light Westechnik servos weigh almost half a gram more than their stated weights once the wires and plug are included. Similarly, a HS50 is listed by the manufacturer as weighing 5.8g, but is 6.24g with the wire and plug and a servo arm, and a GWS Pico listed at 5.4g weighs 6.20g for the version with a JST plug.

Where do we get the greatest reduction in weight for the least effort? The picture below shows the wires and plugs for (top to bottom) the HS50/Futaba, the GWS/JST, and very thin JST wires/plug from Dave Lewis. Their wire diameters including insulation are 0.7mm, 0.5mm, and 0.4mm, respectively. The "Potential Weight Reduction Breakdown" section of the table confirms that the biggest bang for the effort

for the HS50's is replacing the wire/plug for a saving of 0.84g. The wire/plug substitution yields only a 0.35g savings for the GWS.

The next picture shows both servos (the HS50 on the right) after the external wires have been replaced. But, the wires inside the servo are also quite large. However, the HS50 uses very thin wires to the motor while the GWS uses the thick wires for all internal connections. I measured the wire inside the servos and estimated what the savings would be if thin wire were substituted. The savings would only be .07g for the HS50 and 0.12g for the GWS. Ralph Bradley has performed this substitution on the HS50's, and he says the resulting weight savings are generally not worth the effort.

The last two simple weight reduction techniques are to cut off the mounting tabs and leave off the bottom part of the case. Removing the mounting tabs save 0.08g and 0.13g for the HS50 and GWS respectively. This doesn't save much weight, but if the servos are going to be mounted with double-sided cellophane tape, it's easy to remove the tabs. Removing the bottom part of the case is also easy and saves roughly a third of a gram, but will leave the servo open to the elements and the circuit board floating free. This is a matter of choice, and it might depend on whether the servos are going to be mounted internally or externally.

What this shows is that with only a little work a conventional rotary micro servo like the HS50 can get to within 1.54g of the effective weight of the Westechnik "3.0" servo, and possibly closer if the servo arm is shortened on one side and cut off on the other. In addition, one does not have to resort to replacing the internal wires to achieve this. Given that micro planes are clearly moving to using LiPoly cells, many planes could now afford a three-gram increase in weight for using lightened, but less expensive, rotary servos.

Here are a final few notes on replacing wires and the GWS and Hitec servos. Sketch out the circuit board and color of the wires you are going to replace. For both the Hitec and GWS the wire colors correspond to the JST wire colors from Dave Lewis as follows. Red=Red, Yellow=White, and Black=Grey, where the second color is the JST color. When replacing the external wires I shortened the length to three inches since I've found that to be plenty for most applications. The HS50 seems to come with two lengths of wires. I recently purchased four of these from the same mail order house and one of them came with wires that were 6-inches long instead of 4-inches, and the weight was 0.3g higher for that one. The GWS Pico servos with the JST connector, but thicker wires, are available from Dave Lewis and are the standard version, not the ball bearing version. The motor used in the GWS is 7.8mm diameter while the one in the HS50 is 5.8mm diameter. I don't know the weights of the two motors, but this could be one reason the HS50 ultimately maintains a slim weight advantage over the somewhat less expensive GWS servo. Finally, the GWS Pico servos with regular Futaba plugs can be found for lower prices than the

ones with the JST plugs. If you know you are going to replace the wires anyway, it may worth shopping around for the best price on the Futaba version.

Receiver Lightening

One of the most common receivers for micro planes is the GWS R4P, because of its low price and relatively low weight. Like servos, it can easily be lightened. The three major types of R4P receiver are shown in the picture below. They are (left to right) the JST plugs, Futaba side plugs, and Futaba end-plugs.

The table below shows the weights and some other receivers for comparison. Most people know they can save some weight by removing the case. However, weight can be saved by choosing the right version of this receiver. The JST plug version is the lightest, which also means the servos will use the lighter JST plugs. Even more weight can be saved by replacing the antenna. Again, different versions of this receiver can have different diameter antenna wires. It is worth checking yours. Better yet, replace it entirely with either a 1/2 length of fine wire or the Azarr antenna. The bottom line is that by choosing the GWS receiver with JST plugs, and then going with a litz wire antenna and no case, you can save about 3.3g over the heaviest version.

Mini Article - Actuator basics part II (Driving the actuator)By Graham Stabler

I have brought this part of the planned (yeah right) series on actuators forward to the second issue as I have received several emails and have seen just as many messages appear on the boards asking if it possible to use these devices with standard receivers and if so, how? Therefore in this mini-article, I will attempt to explain how we can use actuators in practice and a little of the theory behind how they are driven for those who are interested. I will cover only proportional control, as it is likely that when bang-bang (on/off) control is used it will be with a system made just for that purpose.

A Recap

Let us look back at what we learned last month. If you place a magnet in a coil, and current flows through the coil, torque is applied to the magnet. This torque is proportional to the current. That means as the current increases so does the torque. This in turn means that in order to control the torque generated by an actuator we must be able to control the average current flowing through it.

The most common way to produce this controlled current is to use PWM (Pulse Width Modulation) this is what is used in most speed controllers. The way it works is quite simple; imagine standing on the edge of a dam with your hand on the outlet valve while listening to the ticking of a clock (as one often does). On each tick, you open the valve and wait until some percentage of the time between ticks before closing it again. If the percentage is 100% then the valve stays open and if 0%, it stays closed. Between 0 and

100%, the flow pulsates. Now if someone had built a flourmill downstream of the dam, they would be much happier as the percentage of the time the valve opened increased, as this would mean the average flow of water would be larger.

Obviously, there is no room for dams and clocks in our models but the system works in the same way. The valve is a mosfet, a transistor, or similar electronic switch and the poor guy with the timer is a microprocessor or similar piece of electronics. For those who are interested, the fraction/percentage of "on time" is known as the duty cycle in electronic circles.

The added complication of an actuator drive over a speed control is that it must be bi-directional, i.e. the current must be controllable in both directions so we can go left AND right. So just to recap, with the stick in the middle the PWM duty cycle is 0, if we then move the stick to the left and the duty cycle increases, as this happens, more torque is applied to the magnet/control surface. Moreover, the same thing happens if we move the stick to the right, except in this case the current flows in the opposite direction.

Variations

Some systems drive the coils straight from the microprocessor without the mosfet/transistors; other people flip the current back and forth. The PWM is a little different in this case, because the current is flowing one way or the other, rather than being off or on in a particular direction. This means that with left stick, it is mainly pulsing left and with right stick, it is mainly pulsing right. At neutral, it spends half the time between "ticks" left and half-right. You would think that this would cause the rudder to oscillate but the high frequency of the clock and mechanical damping of the rudder mean that it cannot be seen. The main advantage of this drive system is ease of building drive circuitry; the disadvantage is the constant current flow even with no rudder/elevator deflection.

Another more subtle variation is to smooth the PWM before it is amplified and fed to the actuators. This results in a constant current being applied to the coil and makes the operation silent. The only disadvantage it could be argued is the higher component count and the inherent lower efficiency of linear amplification. This however is not a problem in practice.

Very nice, but what do I buy, beg, borrow, or steal?

To actually use actuators, there are essentially two routes to go down.

1. A dedicated receiver2. A piece of hardware between a standard micro receiver and actuator coil

In the case of a dedicated receiver, you have a couple of choices presently, the RFFS-100 by Dynamics Unlimited, the Micromag, to be made by FMA direct in near future, the Ztron system now out of production effectively but still around (www.aeronutz.flyer.co.uk), the new infrared system by Didel and Nick Leichty's ultralight system.

In terms of add on boards often know as DPCs (digital pulse converters), there are also a few options, such as Cloud9 for single coil drivers and Bob Selman for single and dual coil drivers. If there are others out there, drop me a line for a mention.

I'm Too Poor.

There are also options for the experimenter. You could look at Andy Birkett's website, there you can download info on building a programmer for PIC microprocessors as well as the software required to drive two actuators and a mosfet for speed control. This chip can then be connected to a standard but lightened micro receiver. In this case, the microprocessor is not used to drive mosfets / transistors but rather the coil is driven directly from its outputs. The current available is small (~25mA) so it is worth mentioning that as it will only drive coils of around 200Ohms (not less) but these are fine for sub ounce models. Actually, Andy has used 130-ohm coils without ill effect, but be cautious.

Another option is to cannibalize a micro servo. Take the servo and remove the small circuit board from inside. Then disconnect the motor and connect your coil where the motor had been connected. Then de-solder the potentiometer; this is a circular device with three pins and a shaft that rotates with the output

arm of the servo. In its place, either solder two 2.5kOhm fixed resisters or a 5kOhm surface mount potentiometer. This will control an actuator proportionally because a servo drive without the feedback works like a bi-directional speed control. Replacing the original feedback with fixed or surface mounted resisters just makes it lighter and allows the current flowing through the coil to be set to zero when the stick is centered (will require tweaking if a pot is used). Unfortunately, most servos will draw about 100mA even when the coil is disconnected so they are hungry little things. That said they would work well with a rudder only model in the sub 2oz range especially with the new Lithium Polymer cells available. Here is a diagram showing the wiring, the important thing to know is that the potentiometer has a middle pin. This is the slider, it is important to make sure that you connect this wire to the slider of your replacement potentiometer or in-between the two fixed resisters.

Conclusion

There is more than one way to skin a cat but all the methods of driving a coil will help to produce a light model that keeps a smile on your face.

Mini Article - Super Cheap WattmeterBy Graham Stabler

I first built one of these about a year ago when testing some DC-DC converters. In that instance, I wanted to know input power and output power to gauge efficiency. To do this I needed to measure current and voltage at the same time because power = current x voltage. I already had a couple of meters lying around and so I used them. Then after an hour of grappling with wires and clips, I yearned for one of those lovely devices that many use to measure power into their electric drive trains. There are several available, including the AstroFlight wattmeter. They are in no doubt highly useful but I really needed two of them and I had other things to spend my cash on at the time. So I bought some super cheap multimeters (5GBP/8USD for a pair on special offer) and set about making them a more convenient proposition for measuring current and voltage simultaneously. What I did was to make a simple circuit board with 4mm banana plugs attached that could be plugged into both meters at once. This made the simple circuit of one meter in parallel with the load and the other in series, the former measuring voltage, and the latter current, while also getting rid of several leads, and turning the two meters into a single "super" unit. Here are the steps.

1. Procure some copper clad PCB material (fiberglass board with copper on one side), the normal FR4 1.6mm stuff is ok, it is not that critical for micro applications. You only need a small bit so scrounge some like me.

Here is what you need.2. Work out which hole is which on your meters and draw out your "circuit" on the copper clad using a pencil or pen. Also, mark out the holes for the banana sockets.

Here is the circuit that needs to be made. (Diagrammatic only!)3. Drill the holes and remove the copper from the surface of the board where the lines were drawn.

Here is the copper clad after it has been engraved using my Dremel drill, you can of course etch it, scratch it or even use a different make of drill but the main thing is that the copper is removed between the islands that make

the circuit.

Now the holes have been drilled, make them a little oversize unless you are

very accurate.4. Put the sockets in the board and insert into the meters, then solder them in place, be gentle, as you do not want to damage the meters.

Here you can see the board in place and soldered. Notice I have left a few holes blank. The top left hole is redundant but I thought it might make it

more durable and hold the meters together, in the end I did not bother. Top right is the output from the meter for the low current range, if used as the

positive output you can do sensitive measurements, as yet I haven't needed to.

5. Have a cup of tea.

To hook your battery/motor/dc-dc/electronic gubbins to the meter you have a few options. You can solder the wires direct for experimentation, Add flying leads with crock clips or even use special banana plugs that also include a socket in the top allowing a selection of leads.

Conclusion

Takes 5 min to make, saves clutter, costs pence/cents/groats. Add a web cam and you have a data capture system BUT the downside is you have to do the multiplication yourself to get the power.

Micro Tip - Rapid Prototyping in the MicrowaveCourtesy of Peter Frostick

This little tip comes from Peter Frostick and describes his method of making small propeller blades FAST. I'll let the picture do the talking but it basically allows you to test lots of options quickly. Anything you can carve into a block you can mould. Balsa blades are ideal for floaters (slow flying models) and free flight models as well as the smaller electrics, guess that's most things then. You will need to make a hub of some sort from balsa or bamboo and glue the blades into that. More to come on prop making including hub manufacture and we have a few articles on carbon fiber lined up as well for the high-tech inclined.

Mini Article - LiPoly Voltage MonitorBy Gordon Johnson

When we first started flying models with single LiPoly cells, we all wondered how we would know if we were discharging the cell below its 3-volt limit. Discharging below 3 volts should be avoided and the cells should definitely not be discharged below 2.7 volts, which could cause permanent damage. In both cases, these are volts under load. At first people thought the plane would "land itself" because of insufficient power to keep it airborne and that it wouldn't be a problem. However, a number of people have been developing airborne systems to monitor voltage and signal when it drops below 3 volts via a LED. Bob Selman and Dynamic Web enterprises are both selling voltage monitors made by the same source. Bob also has a two-cell monitor that signals when the volts drop to 6v. Dave Lewis has recently introduced a single-cell monitor and will soon introduce one for two cells. And, Abbott Lahti has developed one that blinks when volts drop below 3 volts, and blinks faster when they drop below 2.7 volts. (This one will probably be available from Cloud 9 RC.) The monitor sold by DWE and Bob Selmanis shown in the picture below.

I installed the Dave Lewis voltage monitor (shown in the picture below) on a small Depron plane; I built to use the RFFS-100 and a geared M20-LV motor. I knew that this motor would pull about 0.75 amps out of the single Kokum 145 cell, so I thought this would be a good model to test the voltage monitor. I removed two unisex pins from their plastic housing. These plugged perfectly into the power lead pins on the RFFS-100. Then, I soldered the leads from the voltage monitor crosswise on the outside of the pins. This allows the pins to be plugged into the RFFS-100, and then the leads from the battery to be plugged into these pins. I mounted it on the LE of the wing pylon, where it would be easy to see, with a piece of foam sticky tape. An alternate position would have been to let it dangle a short distance below the fuselage.

Using the Dave Lewis voltage monitor I found that when my plane was flying noticeably slower, but still very flyable, the red light on the voltage monitor would go out indicating I had dropped below 3 volts. Most of the time if I throttled back to just barely cruise speed, the light would come back on as the load decreased, indicating in an increase in volts. Other times the light would not come back on until I landed the plane and taxied it back across the floor at low throttle.

What this tells me is that for my planes that have higher current draw propulsion set-ups I may want to consider a voltage monitor if I intend to fly them as long as possible. An exception is my planes with a Sky Hooks and Rigging hybrid receiver that can be set for a soft 1/4 throttle cut-off at six volts when using a two-cell pack. In any case, micro fliers may want to consider the amp draw of their propulsion system and their flying style and decide if a voltage monitor makes sense for them.

The Last Bit

This is the end of this month's installment. Keep the suggestions coming in and lets have some photos of what you lot are up to, the wackier the better. It struck me while sticking this issue together that one thing we are lacking is models. In fact, I don't think we have had a single picture of a complete model. I would like to do some plan features so any budding designers out there get drawing. You know who you are! Also, you will have noticed how simple my second mini-article and Peter's microtip was, so why not have a go if you have something useful to share.

Happy flying, Graham

Quadrotor Physics 101

OK, it's finally time to make good on the promises I made in the first post and describe quadrotor physics. I will start off pretty slow, just so we're all on the same page. 

Quadrotors (and many other objects of engineering interest, flying or otherwise) can be modeled via Newton's Laws (unless your quad is sub-atomic or can fly close to the speed of light). The overall governing equation is F = m a (hopefully this sounds familiar to you), where:F is the net force in pounds, ounces, or Newtonsm is the mass in slugs (yes, slugs!), grams or kilogramsa is the acceleration in feet/second/second, or meters/s/s or centimeters/s^2 (all of these units are just common examples; there are others)

In words, net forces cause masses to accelerate. This is why larger vehicles tend to be more stable - it takes larger forces to move them. Similarly, smaller craft tend to be more agile. Stability vs agility is a frequent design engineering trade off - at least before feedback augmentation was available.

A certain amount of force has to be generated just to maintain a steady condition. For example, for the quad to hover it must provide sufficient force to overcome gravity. For it to maintain forward flight, the quad must overcome both gravity and air resistance (also known as aerodynamic drag). When aircraft are in this steady condition, they are said to be "trimmed" or "in trim". Only forces that are in excess of the forces required to trim the quad will cause it to accelerate.

Acceleration is, by definition, the rate of change of velocity.Velocity has typical units of feet/sec, meters/sec, miles per hour or kilometers/hour. If you're familiar with calculus, acceleration is the derivative of velocity: a = dv / dt. So, for the quad to change its velocity, it must:1) apply forces over and above the trim forces to accelerate2) wait until the desired velocity is attained, then remove the additional forces, 3) then finally supply the trim forces to maintain steady flight at the new condition. 

Velocity is, by definition, the rate of change of position. Or, v = dx/dt. Similarly, acceleration is the second derivative of position, a = d^2x/dt^2. Changing the position of the quad is therefore more complicated. One way it can be done is as follows:

1) - 3) are the same steps as above4) coast at this velocity for a certain period of time.5) apply a force in the opposite direction to decelerate the quad (or take advantage of existing forces, such as gravity or drag)6) time the deceleration in step 5) such that zero velocity is reached precisely at the new desired position7) adjust forces to maintain the new trim condition.

I have enclosed a cartoon showing the relationship between acceleration, velocity, and position for the above maneuver. I have simplified it by leaving out any considerations of trim forces. Also, in the real world, it would not be possible to change the acceleration as

abruptly as shown in the figure.

Its important to recognize that, since we live in a three dimensional world (or at least a world with 3 spatial dimensions, no matter what the string theorists would have you believe) acceleration, velocity, and position are all vectors in 3 dimensions. Each one has three components, which are usually referred to as X, Y, and Z; or lateral, longitudinal, and vertical; or left/right, back/forth, and up/down.

Bottom line: in order for the quad to follow a desired trajectory in space and time, its control system (and/or the human flying it) must determine the correct forces to apply and when to apply them according to the above equations, which are repeated here:

F = m aa = dv/dt = d^2x/dt^2v = dx/dt

The last two equations are often called kinematics. They describe motion without explaining how it happens. The first is called the dynamic equation, since forces are what cause motion to take place. Together, they are known as mechanics, or "classical" mechanics, to distinguish them from quantum or relativistic mechanics.

Are you with me so far? Did I lose anyone, or did I just bore you to death?

- Roy

Quadrotor Dynamics 102: Simple Rotations

The kinematics and dynamics of rotational motion are much more complicated than that of translational motion, which I discussed last time. For now, I'll just confine myself to simple rotation, where the axis of rotation always points in the same direction for the duration of the rotation. We'll get to see at least some more of the complexity when I explain the sensing of orientation in a future post.

The governing equation for rotational dynamics is similar to the translational equation we encountered last time (F = m a). It is T = I alpha, where:

T = torque, which is twisting force, or force times a moment arm. Typical units include foot-

pounds, ounce-inches, Newton-meters, etc.I = moment of inertia, which depends on not just the amount of mass, but the distribution of mass in the body. Units are kilogram-meters^2, or slug-feet^2, and so onalpha (this is supposed to be a Greek letter) = angular acceleration, in degrees per second per second, or radians/s/s (read on to find out what a radian is)

You may be familiar with torque since many motors (electric and otherwise) are often rated by the maximum torque they can output. Our quadrotor motors and props also put out a varying torque due to the electrical power we supply, the aerodynamic forces on the propellers, friction in the motor, and other factors. The torque output depends in general on the speed of the motors. The steady torque that results from the props spinning at a constant RPM is not the torque of T = I alpha, since there is no angular acceleration in a steady rotation. The steady torque is a "trim" torque. But, as the props change RPM, then they must accelerate or decelerate and the T = I alpha formula tells us how much additional torque is required. Another familiar use of torque is the wrench we might find in our toolbox. If we can't unscrew a stubborn bolt with a particular wrench, we can use one with a longer handle that allows us to apply more torque to the bolt. Hence, torque is proportional to the applied force times the moment arm.

I hope you'll recognize the formula for the circumference of a circle based on its radius r. It is, of course 2 pi r. This suggests a more natural unit to express the angle subtended by a circular arc, which is called the radian. There are 2 pi radians in a complete circle (we only use 360 degrees to describe the complete circle because the ancients once thought there were only 360 days in a year. Also, it a convenient since 360 can be divided evenly by many numbers). So, if we rotate our quad by a particular angle theta (another Greek letter) measured in radians, then any point along the quad will travel a distance of r theta, where r is the distance from the center of rotation to the point in question. Similarly, if the quad is rotating with an angular velocity of omega (yet another Greek letter) radians/sec, then that point would be traveling with a velocity of r omega. If r is in meters, then the angular velocity would be in meters/s (since a radian is a ratio of the arc length and the radius, it is unitless). Finally, if the quad were accelerating angularly at alpha rad/s/s, then that same point would be accelerating along its circular arc at r alpha.

Let's put it all together. The torque is the force F times the moment arm r, T = F r. But since F = m a, T = m a r. And, since a = r alpha, we have T = m r^2 alpha. If we set I = m r ^2, we have the equation we started with: T = I alpha. From I = m r^2, we see that the further the mass is away from the center of rotation, the more torque will be required to change the angular velocity. And the closer the mass is to the center of rotation, the easier it is to change the speed of rotation.

So, if we want to change the rotation rate or angular position of a quad, we need to follow the same steps as in the previous post, just substituting "torque" for "force" and putting "angular" in front of "acceleration", "velocity", and "position". For completeness, here are the steps written out:

1) apply torques over and above the trim torque to accelerate angularly2) wait until the desired angular velocity is attained, then remove the additional torque3) then finally supply the trim torque to maintain steady rotation at the new condition.

If we just want to change the angular velocity, we'd stop there. To change the angular position, follow the rest of these steps:

4) coast at this angular velocity for a certain period of time.5) apply a torque in the opposite direction to decelerate the quad (or take advantage of existing torques, such as drag)6) time the deceleration in step 5) such that zero angular velocity is reached precisely at the new desired angular position7) adjust torque to maintain the new trim orientation.

And here are the formulas:

T = I alphaI = m r^2alpha = d omega / dtomega = d theta / dta = r alphav = r omegax = r theta

- Roy

Quadrotor Dynamics 103: Applying the Principles to the Quadrotor

Most of what we've said thus far could apply to just about any physical object. Let's focus in on the specifics of the quadrotor. As wikipedia will tell you, a quadrotor is just a cross with a propeller (and probably a motor) at end of each of the four arms. Each propeller produces a force, which we call thrust, and a torque, both of which increase as the speed of rotation increases (we'll get into more details about thrust and torque generation in future posts). 

There's another Law of Newton that we haven't covered yet, which is "If a force (or torque) acts upon a body, then an equal and opposite force (or torque) must act upon another body". This is how the props work: they apply a force to the air to accelerate it downward, and the air applies an equal and opposite force on the prop to accelerate it upward. Similarly, the motors provide a torque to the propellers and the propellers supply an equal an opposite torque to the motor - and anything the motor is connected to, like the frame of the quadrotor. So, the frame will tend to spin in the opposite direction as the props. The inertia of the props is smaller than that of the frame, so the props will accelerate more than the frame (recall the equation T = I alpha? The torques (T) are the same, but since the moments of inertia (I) are different, so are the accelerations (alpha)). 

In a typical quad, adjacent props will spin in opposite directions, so that the prop on the other end of the axis will spin in the same direction (see picture). In other words, two of the props will spin in a clockwise direction and the other two will spin counter-clockwise. In a stationary trimmed hover condition, the torques from the clockwise spinning motors balance

out the torques from the counter-clockwise ones and the net yawing moment is zero ("moment" is another way of saying "torque"). In other words, there is no tendency for the quad to spin about its vertical axis when it is trimmed. All the thrust forces are balanced as well, so there are no pitching or rolling moments. That is, the quad does not rotate about either of the two axes that are represented by the arms that connect two motors. It is this symmetry and balance of the forces and torques that allow the quadrotor to work.

But what if we want the quad to rotate? Referring to the lower left corner of the picture, we can increase the thrust on one prop - lets call it the left one - and decrease the thrust on the opposite (right) prop by the same amount. The yaw torques are still balanced: the sum of the axial torque of the left and right propellers is exactly the same as it was during the trimmed hover. Hence, it is still balanced by the torque of the other propellers (the front and rear ones). Similarly, the net thrust is exactly the same as it was during the hover. The only difference, relative to trim, is that the props have applied a rolling moment to the airframe, which will cause it to accelerate angularly about the roll axis. Due to the symmetry of the quad, the "pitch" axis behaves exactly the same as the roll axis. 

How about if we want to yaw the quad? As you can see in the lower right figure in the picture, we can, for example, increase the RPM of the two clockwise rotating motors and decrease the speed of the two counter-clockwise propellers. Once again, the net thrust is the same as for the hover case, and the net roll and pitch moments are also balanced. Since the yaw moment is unbalanced, the quad will yaw counter-clockwise (opposite to the direction of the net propeller yawing moment). To yaw the quad clockwise, we just reverse the situation.

To increase (or decrease) the altitude of the quadrotor, all we have to do is increase (or decrease) the speed of all 4 props equally, as shown in the upper right corner of the picture. As before, pitch, roll, and yaw torques are all balanced, so the quad will climb (or descend) but remain at a level, flat attitude without yawing.

The longer the arms of the quadrotor are and the heavier the motors are, the larger the moments of inertia will be and the less maneuverable the quad will be. This is especially true for the yaw axis. The propellers we typically use are designed to produce lots of thrust but not very much torque. After all, the more torque the props require, the more torque the motors must supply and the shorter the flight times will be.

We now know how to rotate the quad about all three axes (pitch, roll, and, yaw) and how to climb or descend, that is how to move or translate in the z axis. How do we get the quad to move in the other two axes (x and y)? We'll find out next time.

- Roy

Quadrotor Dynamics 104 - Moving right along.

I feel confident that someone reading this thread has thought, "Why can't I just connect the receiver directly to the motors? Why do I need sensors and a microprocessor and PID and all that stuff?" I won't come out and say that this is impossible to fly - I work with test pilots, so I know just how adaptable human beings can be. However, most people who tried this for themselves probably found out just how difficult it is to control an unaugmented quadrotor. Let's see why this is so.

Imagine we have our quad perfectly trimmed in hover over a particular spot of ground, and we want it to hover at the same altitude, but several yards from where it is now. What do the propellers have to do to achieve this objective? Recall in what follows, that it does not matter how the rotors were commanded - either from a sophisticated feedback control algorithm, or via direct commands from the r/c receiver. The rotors have to do something similar to what I'm describing. 

We already know what has to happen: we need to accelerate the quad in the direction we want to go, coast at a particular velocity, then decelerate so the quad comes to a stop

exactly at the desired final hover spot. In order to accelerate, we need to tilt (pitch or roll) the quad so some of the thrust of the rotors is pointing in the direction we want it to go. As it rolls (or pitches), we have to increase the overall thrust to balance gravity, otherwise it will accelerate into the ground. Of course, every time we adjust the attitude, we'll also have to adjust the overall thrust to maintain altitude.

Next, we'll have to roll the quad back to level to stop its acceleration over the ground and have it coast at a constant velocity. But, as its coasting along, there will be air resistance (drag) slowing it down. Depending on how fast and how far we want the quad to travel, we may have to tilt the quad slightly into the direction of motion to provide sufficient force to overcome the drag. As it nears the destination, we have to roll the quad back toward the direction it came to decelerate it. Once the the quad comes to a halt we have to roll it back to level to keep it there.

And how to we get it to roll to a particular angle? Again, we already know. We have to apply a rolling moment (spin up the rotors on one side and spin them down on the opposite side), remove the moment (let it coast), then apply a rolling moment in the opposite direction to halt the angular motion when it arrives at the desired angular position. This three step process has to happen every time we want to alter the angular position. Does this sound like a lot of work for a simple re-positioning maneuver? There's more.

If the quad is flying outside it (or you, the "pilot") will have to cope with wind gusts. Even indoors, the propeller wakes will interact with the arms and other structures (and the floor and walls if you get too close). The quad components and/or each prop/motor are probably not perfectly balanced either, which may result in a requirement for offset trim. Finally, even if you have all these factors completely solved, the quadrotor is dynamically unstable. The situation is analogous to balancing a broomstick on the palm of your hand. This means that if you (or the electronics) aren't actively controlling it, the quad will tend to deviate from its hovering position and eventually spiral out of control and crash.

To summarize:- Since the quad only has four motors, it can only directly control 4 degrees of freedom: pitch, roll, yaw, and thrust. That is, it is underactuated.- To control the other two degrees (longitudinal and lateral translation), we must tilt the quadrotor. In other words, the translational and rotational dynamics arecoupled. To control the position of the quad over the ground, we have to control its orientation or attitude.There's not too much we can do about these (unless we want to add additional propellers or control surfaces). 

However, there are some undesirable aspects of the dynamics that we can correct:- Mother Nature (or Newton, if you prefer), only provides us with forces and torques to control the quad - meaning we can directly control accelerations. But, we'd rather have control over velocities and positions.- The quad is susceptible to unwanted disturbances, both external (wind) and internal (mass balance)- The quad is unstable and requires constant attention to hover.

These are the very items that control theory can address, as we'll discuss next time.Control Theory 100 – Some Introductory Remarks

Finally - the topic you've all been waiting for - Control Theory! An auspicious topic for the 100th post of this thread! (it sure took me long enough to get here)

Before we begin, I hope that no one reading this thinks they can become an expert controls engineer by reading a few blog posts. After all, it takes a one-semester sophomore level course in a typical engineering undergraduate program just to understand the language of control systems. 

Why is it so difficult to study Control Systems?

- You need to have a solid understanding of the physics of the systems you are trying to control.

- The theory is based on a lot of mathematics: differential equations, difference equations, complex analysis (in the sense of imaginary numbers), linear algebra, probability, information theory, optimization, transforms, and more. It is not necessary to master all these subjects, but a solid knowledge of the requisite components of these topics is required.

- There is a considerable amount of “art” involved. Despite the overwhelming amount of mathematics and the existence of sophisticated computer aided engineering packages, it is still not really possible to press a button and have the computer design a practical control system. There are so many tools in the controls toolbox that it requires some experience and knowledge to know exactly which one is the best to use for the problem at hand. And there is almost always some tweaking that must be done to ensure that every condition is covered. As many of you have found out, it is entirely possible to ignore all the math and just wrap a PID loop around the problem and continually tweak it until it basically works – which is an art unto itself.

Why is it so difficult to teach Control Theory? (in case you care)

- There is no obvious hierarchy of the mathematical concepts; they’re all just needed at once. This makes it difficult to determine an order or sequence to properly teach the subject, and I think many professors and textbook authors choose the wrong path. My intended audience is, of course, not control engineers. But if you are an undergraduate suffering through a controls program, let me know. I might be convinced to write some supplemental posts.

Why is control theory so useful?

- The theory is pretty much the same no matter what the system is that you are trying to control. Essentially the same theory that works for flying quadrotors also applies to: robots, the cruise control of your car (and the engine controls, too), temperature control of your living room (or of a bio-reactor), or even the economy. - Much of the theory overlaps with other subjects, such as Digital Signal Processing. In fact, a control algorithm running on a microcontroller can be viewed as a specialized digital signal processor.

- I would claim that it is difficult to get very far in the study of other sciences, such as biology, without a firm grasp of the concept of feedback, which plays a central role in control theory. 

So, presuming I haven’t scared you off, let’s get started!Control Theory 101 – The Joy of Feedback

As we indicated in post 99, the objectives of control systems include the following:

1) Make the system (a quadrotor in our case) follow a desired trajectory – that is, an evolving sequence of velocities and/or positions over time. It does not matter if the trajectory is predetermined (like a sequence of waypoints) or generated in real-time (from r/c joystick commands, for example)2) Reject any disturbances, such as might be caused by wind gusts or an imbalanced configuration3) Stabilize the system – that is, alter the tendency for the system to diverge from trim

Practically, we have to figure out how to adjust the 4 propeller thrusts (which are the only means we have to influence the quad’s behavior) to achieve these objectives. How can we accomplish this?

To find the answer, we have to go back to the physics fundamentals that we discussed earlier. Forces cause masses to accelerate (and the angular equivalent: torques cause inertias to accelerate angularly). Acceleration, by definition, is the time rate of change of velocity: a = dv/dt for those of you who have had some calculus. Velocity is, in turn, the time rate of change of position: v= dx/dt (remember all that?). The last part of the puzzle is that the inherent forces (that is, the forces other than the ones coming from the control system itself) are themselves functions of velocity and position. For example, we said earlier that the drag force on the quad is a function of its velocity through the air. Similarly, the direction of the propeller thrust vector depends on the angular position of the quad. So, to sum up, forces cause acceleration, which cause velocity to change, which in turn cause position to change. These new velocities and positions result in new forces being generated, and the loop repeats itself endlessly. Computer programmers out there may recognize this concept as “recursion”. Control engineers call it “feedback”, and it is the key to control theory.

Besides “recursion” and “feedback”, this structure is also known as a differential equation, because it defines relationships between variables and their rates of change. Recall

F = m a

The total force F comes from the control, which we’ll call “u” (the prop-motor thrusts in our case), plus a function of velocity plus a function of position. 

F_total = u + F_velocity + F_position

For simplicity, we’ll represent the force due to velocity as just a constant (b) times the velocity v. 

F_velocity = -b v

In general, this function may be more complicated than this. In fact, the actual aerodynamic drag force is proportional to velocity squared. We will discuss later when this type of simplification can be justified. The minus sign indicates that the force opposes the direction of motion, similar to the way the drag force opposes the velocity (assuming b is positive).

We’ll also write the position-based force equation as just a constant (k) times the position

F_position = - k x

As with the velocity case, reality may be more complicated. The negative sign indicates the force is acting to bring the mass back to zero displacement, like a spring, if k is positive. However, if k is negative, the force will tend to pull the mass away from zero displacement, like an inverted pendulum (which is a fancy way of describing balancing a broomstick on your hand).

For the calculus savvy, we’ve said earlier that acceleration is the derivative of velocity. This means that velocity is the integral of acceleration. Similarly, since velocity itself is the derivative of position, position is therefore the integral of velocity. If these terms don’t mean anything to you, don’t worry. We will be getting to a place soon where we can simplify some of the details of calculus. For now, you can just think of it this way: forces cause acceleration, which causes velocity to change, which causes position to change.

Putting it all together:

(-k x - b v + u) /m = av = (integral of) ax = (integral of) v

If we put this into a diagram form, as in Figure 1, the feedback loops become apparent. I’ve included the integral signs, for those of you who understand such things. If you think of this as a computer simulation program, all you have to do is give it an initial velocity and position and supply it with the control input at each instant in time and let the computer crank through the program to determine the system behavior for all future time. This is how flight simulators and other physics based sims work. Its recursive because the current position and velocity depends on the earlier position and velocity, which depends in turn on the v and x before that, and so on - all using the same function at each time step (but with potentially different inputs each time).

The behavior of the system is characterized by the parameters k, b, and m. If our quad is very streamlined, for example, then the b term will be smaller, since aerodynamic drag won’t affect us as much as it would for a less streamlined configuration. If we don’t like how the system behaves, we have to change these parameters somehow. For example, as we discussed earlier, if the sign of k is negative, the system will diverge, like the broomstick balanced in our hand. In the past, such changes had to be accomplished entirely in the physical domain. For example, this is why fixed wing airplanes, like passenger jet liners, have tails (vertical and horizontal stabilizers). Without them, wind gusts would blow them completely off course. The tail provides a restoring force to keep the plane pointing in the

right direction, like a weathervane. In other words, tails make the negative k of the fuselage and wings into an overall positive k of the airplane as a whole.

Today, we can alter the system parameters using computers. Figure 2 shows us the basic premise. If we can sense the position and velocity, the control system (which is essentially just a computer) can simply multiply them by whatever numbers we want, and use these values to provide additional forces via the control inputs (up to the limits of our control actuators, of course). If the k of the physical system is negative, we can use this electronic or digital feedback to make the overall k value positive. This is how the F117A Stealth Fighter can get away with such a relatively small tail: it employs a sophisticated digital “fly by wire” feedback control system. We refer to the combination of the system itself plus the control system as a “closed loop system”, for obvious reasons.

We have discussed how feedback control can stabilize an unstable system (objective # 3 above). What about the first two objectives, trajectory tracking and disturbance rejection? Once again, feedback comes to the rescue. If we alter our feedback loops from Figure 2 to compare the sensed position and velocity with desired position and velocity, we can drive the control system with the errors. The control system (if properly designed) can cause the errors to converge to zero, or at least be minimized. In this manner, the quadrotor will follow the desired trajectory (to a greater or lesser extent) See Figure 3. Note that if the desired trajectory is zero, the system is identical to the one in figure 2. As in the earlier figures, the blocks labeled Kv and Kp may be more complicated in practice than just constant values. This diagram is meant as a notional illustration of the feedback concept, and shouldn’t necessarily be taken as a practical design solution.

Summary:

- Physical systems are feedback systems, and can be modeled via differential equations. - The behavior of the system depends on its parameters (the coefficients of the differential equations)- Feedback control systems can be used to manipulate the inherent parameters, thus altering the behavior of the physical system.- Feedback control systems can also be used to compel the system to track a desired trajectory and reject unwanted disturbances.

Next time, we will go into more detail on the physics and mathematics of the all-important feedback loop

Right Said Fred - Modeling 101

Yes, I’m back – has it really been that long? Hopefully some of you are still with me. As a reminder of where we left off, I’m responding to gke’s request to create a model of the angular response of the quad from the data provided (from post 169 http://www.rcgroups.com/forums/showp...&postcount=169).

As I mentioned earlier, this is getting ahead of my initial "lesson plan". So, if you're confused, don't worry - I will backtrack and fill in the missing details later.

Every control design has 4 steps 1) understanding the dynamics of the object you are trying to control; 2) understanding the desired behavior 3) choosing a controller architecture (based on the first two steps); and 4) tuning the gains. You may find that you just can’t obtain the desired performance in step 4, so you have to choose another controller. Or that you have to go back and revise your ideas about the desired behavior, if you just can’t get there. You may even have to go back and learn more about the dynamics. Very little is completely easy or straightforward when it comes to control design. 

I suspect that, for most people reading this, the architecture used is PID because that is the only option they know. The other three steps are conducted simultaneously under the guise

of tuning the gains. Clearly this is not the optimal approach. A more analytical approach is to first derive a mathematical computer model of the quadrotor based on physics and experiments (that’s step 1 above). Having a model won’t preclude iteration and experimentation, but it is a lot safer and cheaper to experiment on a model than on a real quad. The model will also help guide the real-world experiments. Finally, there are many advanced control methods that require a model.

Let’s take a look at the data that gke provided. First, a quick sanity check – does it make sense? Is the rate the derivative of the angle? Yes, it checks out. In half a second, the quad rolled about 0.6 radians = 34 deg, which is feasible. At that time it’s rolling at 2.5 radians/sec = 143 degrees/second, which is certainly possible. The rate trace exhibits what I’d call “higher order dynamics” (all that wiggling), but let’s ignore that at least for now. We should strive for the simplest model we can that adequately captures the important characteristics. 

Note that the average angular rate is a fairly straight line, as gke's excel plot shows (ignoring the wiggles). There’s no evidence of rate damping, at least as of the 0.5 second mark . Damping is a negative function of velocity. The faster the rotation, the more damping would resist the motion and the curve would start to flatten out. That does not happen in the 0.5 seconds worth of data we have.

Recall from post 75 (http://www.rcgroups.com/forums/showp...9&postcount=75) that the physics for this case is simply torque = inertia times angular acceleration. For convenience, let’s say the input is 5 PWM counts (gke said it was +5 to one motor and -5 to the opposite motor) This results in the ESCs changing the speed of the two opposed motors, which results in a changed thrust force in the two propellers. These (roughly) equal and opposite thrust forces (known as a “couple”) create a net torque when multiplied by the (unknown) motor-to-motor distance. This is then equal to angular acceleration multiplied by the (unknown) moment of inertia, per the physics. I’m leaving out a lot of non-linear dynamics and the algorithms inside the ESC. For reasons that I’ll explain later, what we often desire in the control world is a linear model. 

Sounds like too many unknowns, but it isn’t. What we are primarily concerned about is how the motor commands affect the rotation of the quad, and we have that. The angular acceleration (alpha) is just the slope of the angular velocity curve – in this case 5.2856 radians/second/second. And the quad achieved that alpha with a motor command of 5 PWM counts. All of those unknowns collapse into the 5.2856 number. 

If the dynamics were truly linear, we would expect that doubling the motor command to 10 PWM counts would produce double the acceleration, or 10.6 rad/s/s. But, since the response isn’t necessarily linear, this might not be the case. We’d have to get gke to perform more experiments to be sure. For now, we’ll ignore this inconvenient situation.

So, the relevant equation is 5 PWM counts = 5.2856 rad/s/s. Since we want to get this in the form of figure 1 of post 129 (http://www.rcgroups.com/forums/showp...&postcount=129), we have to solve for angular acceleration. Hence:

alpha = 1.05712 U

where alpha is the angular acceleration in rad/s/s and U is the motor command input in PWM counts.

All we have to do next is integrate alpha to determine the angular velocity (omega) and integrate again to find the angular position (theta). As we’ve already mentioned, there’s no apparent damping, so the “b” term from figure 1 of post 129 is zero. There’s obviously no spring trying to pull theta to zero, so the “k” term is also zero. Our model is almost complete. There are just two more items I’d like to include, at least for now: the delay in the response and disturbance modeling.

Although it isn’t shown on the graph, the input steps at time 0 (the input trace is in the excel file), but the quad doesn’t really start to respond until about 0.03 seconds later. This could be due to a pure delay. If the internal ESC control loop is only running at 50 Hz, it would take 0.02 sec for it to respond to a command. Or, the apparent lag in the response could be due to the fact that it takes time for the propeller to spool up to speed. Just like the quad itself, the motor supplies a torque, which results in angular acceleration of the prop, which means it takes time to change the prop speed. Which of these is the culprit behind the response delay? It is probably due to a combination of both effects. We may need more experimentation or details of the ESC to be certain. Thirty milliseconds may not seem like a lot of time, but either of these phenomena will have consequences for our controller design (as we shall see). So, they should be included in our model.

Our quadrotor has to contend with more than just the forces and moments due to the motors that our control system is deliberately commanding. For example, there are also wind gusts and other undesirable aerodynamic phenomena (like blade flapping). Or, there may be a center of mass offset due to the configuration. All of these can result in uncommanded torques. Our model should include these effects, so we can test how well our control algorithms can reject these disturbances.

Now we have enough information to create a model. As I mentioned earlier, I will implement it using the free ScicosLab tool in the next post. But, you can do it in MATLAB or other similar tool.