StreetDyno - Dyno your car from home. My own physics model

[jpnovak]

I have had an interest in obtaining the relative output of my motor. To do this measurement at home would be useful in both a time, planning and cost perspective. For example, having your own dyno would be great to measure changes in engine tune (fuel system), intake changes or exhaust changes. It would also allow one to baseline a motor before a rebuild or internal modification.

I realized that I had some information that would allow me to determine the output. From a simplistic point of view, if you know the mass of the car and the rate of acceleration you can determine the force on the car. This of course, can be converted to wheel torque and finally engine HP.

Let’s quickly discuss methods for obtaining the acceleration rate. There are plenty of dataloggers and hand held meters (Gtech) that use accelerometers to directly measure the rate of acceleration. The information I will share will allow this data to be processed in a similar manner. I would just need to adjust a few parameters.

There was a web based system available years ago called street dyno. This system used a computer microphone to “record” a voltage signal from the ignition (tach). This program has been available in the Pelican technical archives but the program author has not provided support in nearly 6 years. I could not get the system to work and considered an alternative method for making the same measurement.

I am running EFI in my car. Since installation, I have been trying to figure out how to use the datalogger function in my Megasquirt system to generate engine output curves. I finally worked out the physics model to determine torque and HP curves based upon some of the information available in the system. In this particular case I use an rpm vs time curve to determine output.

I start with a datalog making a pull in second gear from low rpm to redline. The pull is done on an empty flat road. Usually two pulls are taken each direction and averaged to reduce wind effects. The datalog image looks like this.



The rpm dataline is yellow. You can also see some of the other parameters (but not all) that can be logged. I can extract my datalog into MS Excel and then extract the particular data cells I need for the calculations.

The physics model can be complicated to some. Let me walk you all through this. I will not make it math intensive. First let me say that the only correct way to do this measurement is to correct the acceleration for aerodynamic and rolling resistance drag. I do not yet have the atmospheric corrections built in but this is planned. I do have the ability to correct for air density and can measure this as calculated from air pressure in my EFI system.

Background and model setup:

The key performance metric is Force, more specifically torque output from an engine. HP is just a rotational and time based adaptation to compute power. I will discuss this conversion later. The force output of the motor is directly related to the forward acceleration of the car. The force output of the motor is just one of the many forces that make up the total force. In our case we will consider that the total force is equal to the sum of the engine force, aerodynamic drag and wheel (tire drag). The drag forces are negative in our vector space. The force equation is:
F(total) = F(car) – [F(aerodrag) + F(tiredrag)]

Let’s look at the individual forces now.

The force on the car is the actual measurement provided by the rpm vs time curve. Since we are measuring the acceleration of the car it already includes the aerodynamic drag and rolling resistance. Here is how to calculate F(total).

Starting with our rpm versus time curve we must first do some data manipulations. I first use the gearing and tire size (circumference) to determine the vehicle speed. You must know your ring and pinion measurements and the actual ratio of the gear you are doing your pull. Using a taller gear will help slow down the rate of acceleration and provide more data points at the expense of high rates of speed and more distance covered during the pull. I found it hard to find a flat, empty road capable of allowing 3rd gear pulls. After the conversion the graph is now speed versus rpm.

Recall earlier that I mentioned that the Force = mass x acceleration. This is a fundamental Newtonian equation. We also know that the acceleration can be determined from the first derivative of the velocity curve. So, that’s what you must do. This means that F = m (dV/dt). Take the first derivative of your speed versus time curve. This curve will likely be very noisy so you must do a smoothing algorithm and fit to get usable data. I usually do a 4th order fit to the curve that usually takes care of the noise. The fit equation is shown on the graph. Once you have your fit curve you are ready to move forward. The speed and (dV/dt) acceleration curves along with the fit are shown below.



Using this curve we have an individual, instantaneous acceleration value for each rpm in the datalog. This means we can calculate the instantaneous force for each rpm. Is this starting to sound familiar? It should force versus rpm is the same as torque versus rpm that you would see in a dyno curve. Now back to the math.

Aerodynamic drag can be calculated using the equation:

F(aerodrag) = ˝ C A (rho) V^2;

where C is the drag coefficient of the car, A is the projected frontal area of the car, (rho) is the aire density (temperature corrected) and V is the velocity or speed of the car. Notice that the aerodynamic drag is proportional to the square of the vehicle speed. I looked up published values for the early 911 body and then calculated the projected frontal area using width and height measurements. If anyone has accurate numbers for this please let me know.

The aerodynamic drag can be calculated from the speed versus time curve above. This will give you an array of drag force vs rpm (time)

Tire drag can also be called rolling resistance. Tire drag can be calculated using the equation:

F(tiredrag) = Cf m g;

Where Cf is the friction coefficient of the tires, m is the mass of the car and g is the gravitational acceleration constant. You must use the mg product if weighing the mass of your car in kg or you will have unit issues. If imperial units are used, you can use the weight of the car in pounds. The coefficient of friction for the tire was taken as 0.015. I found this number in a publication on tire technology. I have seen numbers as high as 0.05 in other sources. I took the rolling resistance as constant versus speed although it can increase or decrease depending on tire contact patch and aerodynamic down force considerations of the car. I assumed these to be negligible since I want a comparison model compared with a full analytical, numerical solution. Calculate the rolling resistance drag as an array just like the aerodynamic drag.

We now have this array that contains rpm, speed, acceleration, smoothed acceleration, aerodynamic drag and rolling resistance drag versus time. We now solve for the total force using the following equation.

F(total) = m a;

Where m is the weight of the car and a is the acceleration that we just calculated. This means multiply each acceleration point by the mass (weight) of the car. The resulting product adds another column to our array as the total force of the car as a function of time and rpm. Next we use the first equation to solve for the force of the engine.

F(car) = F(total) + [F(aerodrag) + F(tiredrag)]

First we sum all the forces according to the above equation. The issue here is what force are we actually calculating. I have labeled the force as the force put out by the car. This is actually the Force at the wheel. Ahh, now we are getting somewhere.

Once you have summed the forces into yet another column of the array you can start to convert this to torque. First we must define that:

F(car) = F(wheel)

Torque is the force applied to a lever arm. In our case the lever arm is the wheel. It does not matter that the wheel is considered a cylinder; the force is still applied at a tangential direction to the circumference. Torque can be calculated by the following equation:

Torque(wheel) = F(wheel) x r(wheel)

This means that the wheel torque is the product of the wheel force and the wheel radius. We can easily measure the wheel radius and have already calculated the force at the wheel. Next we need to convert through the torque multiplication supplied by the ring and pinion and selected gear in the transmission.

T(engine) = T(wheel)/[R(R&P) x R(gear)]

Next we convert T (engine) to HP

HP = [T(engine) x rpm] / 5252

Now we have a full output curve that contains HP and Tq values vs rpm. I have already corrected for the drivetrain loss (15%) so this curve represents an actual output from the motor. Here is an example of my 3.2SS that runs ITB EFI with Dc40 cams and a 10:1 CR. The output matches well with what one would expect from the motor. The peak rpm and TQ values occur where one might expect. I also see that the SSI based exhaust starts to limit output above 6500 as one can see the torque curve start to drop off rapidly due to flow choking. I also plotted the AFR as a function of rpm. There are a few blips to take care of and the system goes rich above 6500 exasperating the problem of torque drop-off.

[jpnovak]

This was just a test case. I wanted to complete this model before installing my headers such that I can make an accurate comparison. I expect that my actual numbers are close but may have some error. I welcome any input on improving my model and calculations.

Hope you enjoyed today’s lecture.

[ianc]

ianc

[bourgeois911]

I was told that there would be no math involved.

[jcge]

Jamie - some input on "drivetrain loss"

Rotational inertia
All rotating parts (wheels, tyres, rotors, shafts, gears etc) must be accelerated both linearly (with the vehicle) and rotationally (to increase in the components rotational speed). Thus, the gear you select for your dyno run, will have an impact on your output. For example, in second gear, you will be (rotationally) accelerating the rotating assemblies at a greater rate (requiring more torque and power at a given rpm), than if you did your dyno run in 4th gear.

To build these into your model, you would need to calculate or measure the rotational inertia of each rotating assembly.

Transmission efficiency
Consider that the transmission (at any given, steady speed) will absorb some level of power (due to mechanical efficiency, friction etc).

Your "drivetrain loss" is the addition of these, and potentially other components (given your seperate treatment of the tyre's effects)

Page 13, 14 & 15 of the below reference has some detail on HP measurement (and definitions like SAE HP vs DIN HP) and losses.

http://www.automotive-tradition.de/BDA/Typ90A.pdf ** Large file 5.3MB **

Also, if you're measuring the ignition signal, don't forget that any clutch slip or wheel slip would register as speed increase (a front wheel speed sensor may be a better indicator)

I'm not being critical, and applaud your creativity - your dyno will certainly be useful in registering any changes that you make to your car.

John

[jpnovak]

John, you make some great points. I will go through the reference and see what I can build into the model. Thanks for the input.

I don't think my clutch is slipping but how would I actually know? With a wheel speed sensor I could easily compare wheel speed to engine speed (rpm). I might have to look at providing an input on the EFI.

[Quicksilver77]

Great write up! Takes me back to my school days!!!
Any more progress?

[jpnovak]

HMM updates? I have just finished coding a 3-axis accelerometer on a breadboard. The output logs to a micro-SD card. I can get almost 30Hz timing on it.

I am going to repeat the runs with both the accelerometer and the rpm log to see how they compare.

This will be an ongoing project and I will post any significant updates.

[RWebb]

I think you'll want to do a sensitivity analysis on the model & compare with the differences you are trying to detect.

Cf is one I'd like to see some variance est.s on...

[StayGold808]

There is also an iPhone application that just does this!... it utilises the phone's in built accelerometer to measure the g-forces.

It measures many things, such as 0-60, HP and torque curve etc. I haven't used it personally but have heard about it.

[DW SD]

Jamie,
This is very cool.

Can you also use empirical data to evaluate aero drag and maybe rolling resistance? Deceleration can be measured at different speeds as you slow down from say 100mph in neutral? Would this not be a good estimate of the aero forces?

You could then use a calculation to determine resistance to acceleartion of the wheels and tires.
I suppose for the purpose of comparing force from the engine, these will come close to cancelling out.

Nice job!

Doug

[joetiii]

Originally Posted by StayGold808

There is also an iPhone application that just does this!... it utilises the phone's in built accelerometer to measure the g-forces.

It measures many things, such as 0-60, HP and torque curve etc. I haven't used it personally but have heard about it.

The application for Blackberry is called DynoStorm. It asks you for weight of car including driver and % driveline loss. It then gives you various time to distance, max speed, max accel (in Gs), then it calculates peak power both at the crank and at the wheel. There is also a skid pad feature that shows you how many Gs the car pulls while stopping, turning, accelerating.


From the 4 passes with my blackberry, the results I got were mixed. A low HP reading of 169 rwhp up to 232rwhp was recorded. My car pulled 182 rwhp on a dynojet a few years back and I did one run showing 193 rwhp so it seems to be somewhere inbetween.

Like anything, it takes time to build accuracy in. I think the key is proper calibration, a steady cradle, and consistent launches. It's been some time since I drove my 68 Charger in the quarter and I've never launched my 911 like that car. TorqueFlites are a bit sturdier than a 901 box.

I've got to get out and do a few more passes soon. I'm changing to a dual out mffler and am curious if this program can measure the difference.

Keep up the good work Jamie, your model will be much more valuable to us tuners & tweakers once its complete.

Until Then.... can someone tell me what this dynostorm graph means.

[jpnovak]

Randy, You are correct. The reason I built the accelerometer setup is to compare the data. Same calculations I just don't have to convert rpm to speed to acceleration and eliminate some error.

Doug, The rolling resistance can be empirically measured. It would be a sum of tires, bearings, transmission loss, aerodynamics, gravity and atmospheric (wind). Since the losses all sum it would be a "loss factor" that could be subtracted. It might take a few runs to work out the kinks. It would be similar to the roll down measurements done on a dyno to measure parasitic loss (tires, bearings and transmission) within the car.

The problem is finding a flat enough road to get accurate data both on accel and decel.

Joe, Thanks for the compliment. Just doing my part to keep the enthusiasts level of interest high.

That graph is pretty simple. I assume your blackberry has a GPS unit that tracks speed. This is then converted to acceleration (gs) and then HP. same basic setup as my system. If you have an accelerometer (I don't think they do) then it will measure gs directly and then integrate between points to get speed. The issue is that most commercial units like this have very slow data collection (1Hz GPS is fast in a cell phone). There is just not enough resolution to get accurate measurements and lower the noise floor. As you can see, the spikes in the yellow line are due to the noise and this is the cause of our misleading numbers. I admit I do a high-order fit to my curve to smooth the noise.

[RWebb]

Originally Posted by jpnovak

... I admit I do a high-order fit to my curve to smooth the noise.

you are not the first!


PS - I think the iphones do have accelerometers - you can shake them and some software apps will pick that up.