Technical Article:

How our Inertial RC Engine Dynamometer Works




This report displays the legitimacy of the MWD & Associates inertial dynamometer by demonstrating the basic physical processes and basic equations governing the measurements. If successful, this report will convince a skeptical reader that the inertial dynamometer is a simple device with simple physical relationships between the measurements and the calculated results. It will demonstrate that all measurements are accurate and precise enough to cite at worst +-0.05 HP.

The device measures time using the National Instruments Lab PC1200AI time base, accurate to .01%. Frequency is measured to within +-.05% with a National Instruments 5B45-04 frequency input module. Frequency and time were verified with a Tektronix 465 oscilloscope, and a Tower Hobbies Mini-Tach. Lengths of the geometry are accurately measured to within .001" with a Mitutoyo model CD-6"BS and to within .0001" with a Brown & Sharpe 0-1 micrometer caliper. Mass is measured to within 1g with an Acculab model 1200 Digital Electronic Scale. Voltage is measured to within +-2% with the 1200AI board, and was verified with a Fluke 78 multimeter.


Background and Introduction:


The recently completed inertial dynamometer at JFA Custom Engines has proven a valuable tool for measuring engine torque and power versus rpm. With this tool, the engine shop personnel can quickly decide if a modification has indeed improved performance, and if so, by how much.


In one season, MWD & Associates at JFA Custom Enginesí shop has improved the performance of all four of the popular model boat engine sizes including .21s, .45s, .67s, and .91s by a minimum of 41% increase in power versus our best engines last Fall. For example, Marty Davisí modified Nova Rossi 21s made 1.9 HP as configured for his 1st place finish at the 1997 IMPBA Internats. After 400+ dyno runs and improvements in combustion chamber geometry, compression ratio, inlet tract geometry, exhaust, intake, and transfer port timing, choice of carburetor, choice of tuned pipe, pipe length, pipe stinger work, engine cooling, and fuel chemistry, the newly modified Nova Rossi 21s produced over 3 HP.


Other people worldwide have achieved power levels from the 21s in the low 2 HP range, up to 2.8HP as quoted by CMB for their stock 21. Our proclamation of 3+ HP was met with much skepticism.


It is the purpose of this report to prove, without a doubt, that our dynamometer accurately and precisely measures engine torque and horsepower. This report will describe, in detail, the physics behind our inertial dynamometer in a way that the layman can understand. It will also describe an example of a real life torque measurement.


In the supplement, the report will answer seven proposed questions about some effects that were thought to throw off the results and also cover some other details of the power measuring business.


If, after reading this report, there are ANY questions or criticisms of our method for measuring engine power, please forward them to Marty or me, and I will field them individually. If enough interesting questions arise, I will publish the questions and answers in a future technical article.




a = linear acceleration

Do = outside diameter of inertia wheel

Di = inside diameter of inertia wheel

I = rotational inertia

F = force

L = length (i.e. thickness) of inertia wheel

m = mass

P = power

Pref = reference barometric pressure

Pactual = barometric pressure during dyno run

r = radius

RPM = engine speed, measured in revolutions per minute

t = time

T = torque

tempref = reference ambient temperature

tempactual = temperature during dyno run

V = volume

a = angular acceleration

P = ratio between the circumference of a circle and its diameter, roughly 3.14159

r = density

w = angular velocity, or engine speed


Governing Physics:


An Inertial Dynamometer, like ours, measures how quickly a given engine can accelerate a known rotational inertia from one rpm to another. This is enough information to know the average Torque the engine produced during that time, and, since we already know the rpm, the average Power the engine produced during that time. With enough small steps in rpm, say several dozen, this produces a smooth curve of Torque versus rpm and Power versus rpm.


So, first of all, what is happening physically that lets us know the engine torque?


Consider a cube of steel on slippery ice, with a model rocket engine attached to it, together weighing 1 pound. Ignore air drag. Say that the rocket engine produces 1 pound of thrust. That block of steel will accelerate at 1g, which is 22 MPH every second. After 1 second it will be going 22 MPH faster, 2 seconds, 22 more MPH faster, etcÖ, until the force stops being 1 pound or the ice stops being friction-free. This is a basic relationship in physics, called Newtonís Second Law (ref 1 pg 82, ref 2, pg 76):


F = m * a


Force equals mass times acceleration.


What that means is, if you know the mass, say by weighing the steel block, and you measure the acceleration (Iíll get to that in a minute), you know the force that the rocket engine was producing during your measurement.


How do you measure acceleration?


There are several ways, but by far the simplest and most accurate is to measure the position of the block at different times. If you know how far the block traveled in a certain time, that is Velocity. Like in your car, for instance, you can describe your velocity by knowing how many miles you travel in an hour. Once you know the velocity at each time, the next thing to do is figure out how quickly the velocity is changing. This is acceleration. In a powerful sports car, you can go from 0 to 60 MPH in say 6.0 seconds. That means the car accelerated at an average of (60MPH / 6sec =) 10 MPH per second. That describes the magnitude of the acceleration. Notice that there are many different units for acceleration. But, all of them have the same form: length/time*time. e.g. Miles (length) per hour (time) per second (time). Another one: 1 "g" equals 32 feet (length) per second (time) per second (time).


Now comes the next step.


The above relationship was for straight-line motion. A very similar relationship holds for rotational motion.


T = I * a


Torque (T) equals Rotational Inertia (I) times Angular Acceleration (a) (ref 1 pg 242, ref 2 pg 280).


Torque is familiar to anyone that knows about engines or torque wrenches. It is a force crossed with a length. If you tighten a bolt by pulling a certain force on a wrench with your hand out 6" from the center, that is a certain torque. If you pull with twice the force at the same distance, that is twice the torque.


Rotational Inertia (I) is probably a new concept for many people. Just like Torque is to Force, Rotational Inertia is to Mass. It is mass, but combined with the geometry of the rotating part.


Consider a figure skater spinning with her arms out. She spins along at a good clip. She has a certain mass, and with her arms out, a certain rotational inertia. When she pulls her arms in, she spins faster. Why? Nobody was out there spinning her up, and for the sake of argument weíll assume sheís not pushing with her skates.


The difference is, her rotational inertia changed. Rotational inertia depends on both mass and mass distribution. She didnít go on a quick diet, so her mass didnít change, but rather she changed her geometry by distributing the mass of her arms closer her axis of revolution. To know the rotational inertia, you must know the mass, plus how the mass is distributed about axis of rotation.


Calculating rotational inertia comes from considering your rotating part as the sum of a bunch of little tiny masses, each contributing their part to the whole. Those particles close to the radius of rotation donít contribute much, since their moment arm isnít very long, but the ones farther out contribute much more, since they have a longer "arm". Through methods of calculus you can find the rotational inertia for any arbitrary geometry and distributed mass. But, it is much easier to stick to a simple geometry, for example a cylinder, and then look up the relationship in a book (i.e. someone else has gone through the calculus for you!) The rotational inertia of a solid cylinder made of uniform material is (ref 1 pg 238, ref 2 pg 283, ref 3 pg 72):


I = m/2 * r2


Rotational Inertia of a solid cylinder equals one half the mass of the cylinder times Radius of the cylinder squared (i.e. radius * radius)


Whatís the mass of a cylinder? Well,


m = P r2 * L * r


Mass of a cylinder is its volume times its density. Volume is Pr2*L, which is the area of its face times its thickness. Density (r) is the density of steel, since thatís what our cylinder is made of, which is about 0.28 pounds per cubic inch.


One other way to determine mass of the cylinder is stick it on a scale!


By the way, notice how much the radius of the cylinder affects its rotational inertia. First of all, the mass depends on the radius squared. A cylinder twice the width of another has four times the mass. Then, the rotational inertia is that times radius squared AGAIN. This comes from the particle distribution like we talked about a few paragraphs up. Two cylinders with the same mass, but one with twice the radius of the other (i.e. not so thick, but wider), has four times the rotational inertia. This is why our disks are wide but relatively thin, by the way.


So, all you have to do is accurately machine a cylinder (we ground ours to within .0005 inches on the radius and thickness), and then measure it with a good set of calipers (we measured ours with a Mitutoyo model CD-6"BS and a Brown & Sharpe 0-1 micrometer caliper), and look up the density of steel, and you know the rotational inertia. Just in case the value for density you look up is not the same as the actual steel alloy you used, you can double check by weighing the disk on an accurate scale (we weighed ours on an Acculab model 1200 Digital Electronic Scale), and substitute the mass directly into the equation instead of calculating it based on the density. Here is an example:


The disk we use for testing our 45 engines is 3.7495" diameter, and .750" thick. It has a hole cut out of the center, diameter .503". It is made from 4140 steel, which has a density of 7900 kg/m^3 (ref 3, pg 171).


V= (P * 1/4*Do2 *L )- (P*1/4* Di2 * L)


This is the same as the volume for a cylinder from above, except one with a hole cut out of it. What you do is calculate the volume of a cylinder of diameter Do (outer diameter), then subtract the volume of the hole, which is the volume of a cylinder of diameter Di (inner diameter).


plug in the numbers:


V = (3.14159 * .25* 3.74952 * .750) Ė (3.14159 * .25 * .5032 * .750)

= 8.1322 cubic inches


convert that to metric, so that it will jive with the units of density from the book,


= .00013326 cubic meters (since 1 cubic meter = 61024 cubic inches)


Now that we know the volume, look up the density from the book, and calculate the mass:


m = r * V = 7900 * .00013326 = 1.0527 kg = 1053 grams


On the scale, it weighed 1047g. Thatís pretty close to the calculation based on the density from the book, within 0.6%.


Now, on to actually calculating the rotational inertia


To calculate the rotational inertia of the disk, we go ahead and assume it is a solid cylinder of diameter 3.4795", .750" thick with no hole, since there is a shaft that goes through the hole which is also made of steel.


Combine the equations for rotational inertia and mass from before,


I = [m/2] * [r]2


I = [1/2 * r* (P * (Do/2)2 * t)] * [Do/2]2


(first convert Do and t to meters to keep the units consistent. 3.7495" = .095237 m and .750" = .0191 m)


I = [1/2 * 7900 * (3.14159 * (.095237/2) 2 * .0191 * (.095237/2) 2]


= .001216 kg m2.


The rotational inertia of the 45 wheel is .001216 kilogram meters squared. Whew!


You must also do this for all components "downstream" of the flex cable, and add their inertia, too. On our system, this includes the trigger wheel, the support shaft, the retaining nut, two washers, pin retaining sleeve, and other sundry stuff. The total rotational inertia for the shafting only comes out to be 0.66% of the inertia of our smallest wheel (which is .0006173 kg m2). This makes sense, since rotational inertia is such a big function of the diameter, and all the shafting is relatively low diameter compared to the wheel.



Angular Acceleration is analogous to straight line acceleration, except it talks about rate of increase in rotational velocity rather than straight line velocity.


a = dw/dt


Angular acceleration (a) equals change in angular velocity (w) per change in time.


Angular velocity (w) is simply how quickly something turns, like RPM, or Revolutions per Minute. To keep the units consistent, you want to use radians per second (1 revolution = 6.28 radians) before you plug it into any calculation, but itís easier to think of RPM. If you go from say, 20,000 rpm to 30,000 rpm in one second, the Angular Acceleration is 10,000 rpm per second. Notice the units are very similar to straight line acceleration. Change in angle per time, per time.



Back to the basic equation:


T = I * a


Torque, which is what weíre trying to measure, equals rotational inertia, which is a function of the disk youíre accelerating, times angular acceleration, which you calculate from how quickly the RPM is changing.


This is the basic physics behind our dynamometer. If you know the rotational inertia of the steel disk, and you know that it goes from one rpm to another in a certain time, thatís enough to know the torque it took to accelerate it at that rate. Itís as simple as that!




Consider a good 45 engine bolted to the 45 wheel for which we just calculated the rotational inertia (ignore the shafting for the sake of argument). The engine is spinning along at a comfortable idle, about 14,000 rpm. We start the data acquisition, go to full throttle, and the computer measures that it took 0.12 seconds to go from 20,000 to 21,000 rpm. What torque did it take to do this, and what power did the engine make in this rpm range?


(Side note: time between measurements is measured by our National Instruments Lab PC 1200AI data acquisition board in continuous scan mode, which uses an 8MHz source frequency, and is guaranteed accurate to within 0.01%. Trigger wheel frequency is measured by our Omron H21A1 optical interrupter, which reads the 6 holes in our trigger wheel, then feeds the frequency into a National Instruments 5B45-04 frequency input module, guaranteed accurate to within +-.05%. This voltage is fed into the 1200AI board, which is guaranteed accurate to within +-2%).


(Another side note: To double check the time, frequency, and voltage calibration that are used to calculate rpm, we spun a Kavan propeller and verified the rpm reading vs. a Tower Hobbies Mini-Tach. Readings were within 100 rpm, which is the accuracy of the Mini-Tach. As a third check, verified the calculated rpm readings by measuring frequency from the trigger wheel with a Tektronix 465 oscilloscope).


To increase 1000 rpm in 0.12 seconds is 8,330 rpm/sec. So, a= 872.7 radians/sec/sec. (remember I told you weíd have to whip the units into shape before calculating, and that there are 6.28 radians per revolution and 60 seconds in a minute).


from before,

T = I * a


I = .00121614 kg m2 and a = 827.7 rad/sec/sec


so, T = 1.06 kg m2/sec/sec, or 1.06 N m (because 1 Newton = 1 kg m/s2. F=ma, remember?!).


Or, if you prefer, thatís 150 oz in. (since 1 newton = .2248 lb, 1pound = 16 ounces, and 1 inch = .0254 meters)


To accelerate that wheel at that rate, the engine had to produce an average of 150 oz in from 20,000 to 21,000 rpm.


How about power?


P = T * w


Power = Torque * engine speed (ref 6, pg 46). For engine speed, we use the midpoint between the two measured points: 20,500 RPM. (In reality, the dyno uses much smaller rpm steps, about 10 or 20 rpm, which makes the approximation valid).


P = 150 * 20,500

= 3079000 oz in * rev / min


Those are strange units, so work them into something familiar:


= 1680 ft lb / sec (since 1 ft = 12 in, 1 lb = 16 oz, and 1 rev = 6.28 radians)

= 3.1 HP (since 1HP = 550 ft lb/sec)


The engine had to develop 3.1 HP to accelerate that inertia wheel, at that rate, at 20,500 rpm.


Now, just record RPM at little time steps during the whole run, say every 500th of a second, and do this same calculation between each step. Since I canít write that many numbers that fast, I have the computer record rpm vs. time at 500 Hz for the whole run and store the numbers in an array. Then, to get rid of the high frequency noise that is inherent in a finite bit digitized signal, we pass the data through a low-pass simulated Butterworth filter set at 10 Hz, which leaves just the data weíre interested in. Then the software steps through the data, and calculates Angular Acceleration at each point, and plugs that into the Torque equation. That gives a Torque at each rpm.


Temperature and Barometric Pressure Normalization:


Before the torque values go to the power calculation, they go through an algorithm that normalizes them to what the engine would have done if the air was actually at some reference density. Any engine will make more power if the air is cool and high pressure, but you donít have control over the atmosphere on race day. So, we normalize all results.

Tnormalized = Tmeasured * Pref/Pactual * sqrt(Tempactual/Tempref)


The normalized torque equals the measured torque times the ratio of the reference pressure to the pressure during the run, and then times the square root of the ratio of the ambient temperature during the run to the reference temperature (ref 3, pg 331). Notice that the units must be consistent for this to make sense, and your only choice for temperature units are Kelvin or Rankine.


What are the reference temperature and barometric pressure? We chose the National Hot Rod Association standard of 60 degrees F, and 29.92 inches of mercury on the barometer. After normalization, the program reports the power the engine would have made had it been 60 degrees F at 29.92" Hg in the shop.


Example: the program measures that the engine made 100 oz in of torque, but the ambient air is 68 degrees F, and the barometer read 30.22" Hg. What is the normalized torque?


First, get the units worked out: 68 F = 293 K, and 60 F = 289 K (since degrees Celsius = [degrees F Ė 32] * 5/9, and degrees Kelvin = degrees Celsius +273)


Tnormalized = 100 * [29.92/30.22] * sqrt [293/289] = 99.8 oz in


It was a little warmer than reference during the test, but quite a bit higher pressure. So, the engine would have made a touch less torque at the same rpm with the worse air density.



Next, the software takes each of the normalized Torque values, along with their corresponding RPM values, and calculates the Power at each rpm. Finally, it displays both the Torque and Power on pretty graphs!







Some Questions Raised about the Inertial Dynamometer


1. What about "Pulse Kinetic Energy"? Wonít that affect the accuracy of the dyno?


Here I will account for three possible meanings for this phrase, and answer them one at a time.


1a. If using a one-way clutch, wouldnít the power stroke of the engine accelerate the wheel, but on the upstroke NOT decelerate it?




Yes, but that still doesnít change the power.


When in operation, the engine not only pushes the piston down, but also must get the piston back to the top against the resistance of the air and fuel charge squeezing and sliding through the ports, compressing the charge, and friction. Even with a ratcheting device, like a one-way clutch, the energy to get the piston back to the top has to come from somewhere. In this case, it comes from the momentum in the engineís flywheel, crankshaft, and the other rotating parts. This is energy the engine must supply on the next stroke to get itself back up to speed. You canít get something for nothing.


As a side note, we have abandoned the concept of using a one-way clutch in our dynamometer. We could not get one to consistently stand the rpm we were using without runaway slippage. On the 21 and 45 engines, we have been simply locking the wheel to the cable, and have not been able to test the big engines. We recently tried switching to a solid shaft to the inertia wheel, but the pin couplers couldnít take the impact from starting the engine or engine stuttering. At the moment we are switching to a cable that can take torque in BOTH directions, and still eliminating the one-way clutch.


1b. If youíre measuring acceleration, it seems that on each power stroke youíll measure too high acceleration, and on each compression stroke, it will measure too low.




YES! It is important to average the measured acceleration with an appropriate time constant. Whatís appropriate? Well, the average should include several, if not dozens of crankshaft revolutions at a minimum. If too few, you will start to see the cyclical torque fluctuations that we notice as torsional vibration in the driveline. While this might be useful information, and in fact some people have used this effect to their advantage by pitching one blade of their prop higher than the other, it is not what we want to measure.


If you count too many, you canít tell precisely enough which rpm youíre talking about. Say you measured 375 engine revs to calculate your average, but the engine went from 20,000 to 25,000 rpm at 5000 rpm/sec. At what rpm can you say you made that torque? Best you can say is somewhere between 20k and 25k, which is a little coarse.


We use a 0.1 second time constant for smoothing our curve. This is long enough to ensure at least a few dozen revolutions at low rpm (20 @ 12,000 rpm), but quick enough to notice changes in the torque of the engine vs. rpm. Since the test takes 2 to 3 seconds, thatís 20 to 30 time constants, plenty to describe a curve.


On top of that, we make sure to oversample the actual rpm signal. We sample rpm 500 times per second (500 Hz). That ensures a minimum of 1 sample per revolution in the 30,000 rpm range, and more samples at lower rpm. This is more data than necessary, which allows the smoothing algorithm (low-pass, 1st order Butterworth filter VI in LabView set at 10Hz cutoff frequency) to ignore the quick, 100+Hz ripples in the rpm vs. time curve due to cycle-to-cycle variation, but pay attention to the data where we want to look, which is in the 10Hz and slower regime.


With proper choice of time constant for smoothing out the high frequency content of the rpm signal, this effect is avoided.


1c. If you have flexibility in your driveline, this will artificially help the piston on its up-stroke, and youíll only get the power strokes accelerating the wheel. This will end up not measuring the "true" horsepower.






Now that we understand that it takes a certain amount of power to accelerate a known inertia from one rpm to another in a certain time, we agree that something delivered that power to the wheel.


The First Law of Thermodynamics (ref 4, pg 83) states that energy in a closed system can neither be created nor destroyed. The only thing available for delivering that power to the wheel is the engine. Therefore, if we know the power it took to accelerate that wheel, we know it came from the engine.



2. Shouldnít a Steady-State test method dynamometer read the same as an Acceleration test method dyno?






There are several reasons:


  1. With the inertial dynamometer, the optimum fuel mixture setting will be different. During our test, the carburetor metering system is in a transient condition, with the flow changing with time. During a steady state test, the flow settles to a constant. This could make more or less power, depending on how optimized the mixture is for each rpm in each test.
  2. The powertrainís rotating components themselves have rotational inertia. The engine must accelerate its own flywheel, crankshaft, part of the rod, and part of the bearings, the coupler, and the flexshaft just the same as it has to accelerate the inertia wheel. By the way, we intentionally ignore this because thatís YOUR problem! We care about the power delivered TO THE PROP. If your engine has a heavy flywheel, for instance, that simply represents extra power your engine must impart to deliver the same net power to the prop at a given acceleration rate.
  3. The gas temperatures inside the pipe will be different. With our short test, the temperatures probably wonít be the same as steady state, since it takes a finite amount of time to warm or cool the walls of the pipe. The difference in gas temperatures inside the pipe affects the speed of the scavenging and supercharging waves that let the pipe do its job, and therefore synchronizes them with the exhaust opened event differently. Best thing to do is try to match the acceleration rate you see ON THE WATER as best you can. Neither the steady-state nor the acceleration test method is perfect in simulating this.


3. How much differently will they read?




Nobody can say for sure, since we have not yet done a comparison test with our dyno. However, in their SAE paper, (ref 5), Drs. Kee and Blair measured that the engine made roughly 10% more power on their inertial dyno vs. their steady state dyno.


We hope to do a fair comparison some day, with identical engines, pipes, fuel system, etcÖ However, it will never be completely the same, for the reasons described in Answer #2.



4. Which one is "correct"?






An ideal dynamometer simulates the engine exactly as it operates in the vehicle. That would mean using the same fuel tank as the actual boat, blowing 70 MPH air over the head and pipe, spraying a roostertail at it every so often, side loading the engine and fuel system at 2+ gís every few seconds, bouncing it up and down like going over waves, having it mounted in an enclosure that vibrates just like the actual hull, loading and unloading the engine like the prop does going in and out of each wave, and on and on! Neither dyno simulates actual operation exactly, and it would be foolish to try. Personally, I wouldnít even want to be in the room with all that going on!


One big point of the inertial dynamometer concept is to simulate the engine accelerating just like it does when you come off the turn, which is the slowest speed on the course, and accelerate down the straightaway. However, the hydrodynamic and aerodynamic drag are not linear with boat speed, and in fact increase at least as the square of the speed. The dyno, on the other hand, simulates a constant load, as if the drag didnít change with speed. This might be a decent approximation for a low speed car (<150 MPH) or a boat with the prop pitched for good acceleration instead of good top speed, but for boats that spend more than say 5 seconds on the straightaway, maybe itís not so good.


With a steady state dyno, youíre totally ignoring the engine changing speed. This might not be so bad for a boat on the straightaway after itís done accelerating, or maybe a boat going for a speed record after itís already up to speed, but itís not so good for simulating whatís going on right off the corner.


Basically, the inertial dyno is good at simulating the acceleration part of the operation, and the steady state dyno is good at simulating the steady part.


5. What about SAE J1349?

Doesnít SAE prescribe a steady state test?




Yes, but that does not cover model boats!


That is a standard test prescribed by the Society of Automotive Engineers for passenger cars, trucks, stationary power units, and some hand-held power units. If you think about it, for most applications it makes sense to specify steady power, since thatís what you care about for your lawn mower, your car, or your tractor trailer. Everything happens over several minutes or hours. In the racing world, especially drag racing or sprint events, like ours, this steady state test becomes less and less meaningful.


However, we have the freedom to choose which test best measures what we're trying to improve, and that is the power available to achieve good oval times or record straightaway speeds. We are not stuck with J1349.


6. What about hysteresis losses in the driveline? Wonít that affect accuracy?




Yes, that is there, but probably small.


Hysteresis losses are energy losses due to working something back-and-forth, and not having it spring back 100% each time. A common example is the tires on your car heating up to a higher temperature than the road surface as you drive. Whatís happening is the rubber flexes back and forth as it presses on the road each revolution, but itís not a perfect spring, and so some of the energy that should have gone into flexing it actually went into heating it up, and so when it comes time to un-flex, itís not all there.


The same thing happens anywhere in our driveline there is a flexible member. Steel itself is really good at avoiding these losses, but youíll see measurable hysteresis losses in rubber couplings, loose pin couplings, basically anywhere there is not a piece of metal transmitting the power. A rough way to gage how much hysteresis energy losses youíre encountering is to see how warm each coupling component gets, or look for mashed metal.


We have no polymer coupling in our driveline, but where the shear pin interfaces the tail shaft supporting the inertia wheel, you can notice fretting and a little chowed steel where the pin has been beating on it. The pin is 1/8" diameter, and it bears on two walls roughly .060" thick, on both sides of the shaft. That means that it bears on roughly .030 in2 of material. It mushed it probably .020". Believe me, to move that little bit of steel around, spread out over several hundred dyno runs, is not much energy.


Hysteresis losses will make the dyno report that the engine produced LESS power than it actually did, since it only measures what made it to the wheel.


7. What about friction losses and aerodynamic drag on the inertial wheel?




Yes, that affects the accuracy of our dyno, and we hope to add a compensation algorithm for that in the future.


The bearings do get warm, and if you put your hand next to the wheel as it spins at high rpm, you can feel air blowing off of it. These both imply energy losses. These will skew our results such that the power we report is less than what the engine delivered to the tailshaft. To make the dyno more accurate, we intend to measure these frictional and aerodynamic losses in the near future by executing a "run-down" test.




Future Tests:


In the future, we plan to publish a benchmark test done on a common engine (weíre considering stock OS Max RZ-M 21 engines), complete with raw data, equations, and final results. It will then compare our results to those quoted by other people (OS Max themselves, for instance). The purpose of showing this is to provide the reader with enough detail and information so that if he desires to duplicate our test, exactly, he will satisfy himself that his measured power will be the same as ours. We will choose an engine such that anybody worldwide can acquire the same engine we used, and feel confident that it will perform the SAME on THEIR dynamometer, if tested EXACTLY as we tested. The report will give enough detail to enable anyone in the world to EXACTLY duplicate our benchmark test, and decide for themselves the legitimacy of any claim we make from our measurements.




Brian Callahan, Phd



  1. Halliday and Resnick, "Fundamentals of Physics, 3rd edition", John Wiley & Sons, New York, NY, 1988.
  2. Wolfson and Pasachoff, "Physics", Little, Brown & Company, Boston, MA, 1987.
  3. Robert Bosch GmbH, "Automotive Handbook, 2nd edition", 1986, SAE, Warrendale, PA.
  4. Wylen and Sonntag, "Fundamentals of Classical Thermodynamics, 3rd Edition", John Wiley & Sons, New York, NY, 1985.
  5. Kee and Blair, "Acceleration Test Method for a High Performance Two-Stroke Racing Engine", SAE 942478, Warrendale, PA, 1994.
  6. Heywood, "Internal Combustion Engine Fundamentals", McGraw-Hill, Inc., New York, NY, 1988.



by Brian Callahan


Previous contributions to tech articles for MWD & Associates:


"An Inertial Dynamometer and Radio Telemetry System for High Speed, Glow Ignition, Two-Stroke Racing Engines"


"Multiphase Flow on a Ventilated Marine Propeller and Rudder"



ENGINE Analysis Software for the Serious RC Competitor



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