Plotting a Power Graph using Torque & RPM

[A Devlin]

Hi guys,

Sorry if this has been covered before but I have been searching the forum looking for the exact information and have been unable to find it. I am currently carrying out a project to make a Honda GX35 engine suitable for competing in the Shell Eco-Marathon where I will perform modifications to the engine to increase its fuel economy and power output.

I have carried out initial tests to the engine to find the power output and fuel consumption before any modifications are carried out but I am running into problems with calculating the power output;

The engine is hooked up to an Inertia Dynamometer (Flywheel) with a MOI of 0.073 Kg M^2.

So far I have;

- Found the Angular Acceleration [(Change in Engine Rad/Sec)/Time Taken]

This was done by revving the engine from idle (2520rpm) to the max rpm (8056rpm) in a time of 13.7 seconds giving a difference of 5536rpm which equates to 579.73 Rad/Sec. Thus Angular Acceleration is equal to 42.32

- Found the Torque of the Flywheel [(Angular Acceleration of engine)*(MOI of Flywheel)]
- Found the Torque of the engine (The output shaft of the engine has a gear with 7 teeth and the shaft of the flywheel has a gear with 21 teeth so I divided the flywheel Torque by 3 to find the Engine Torque)

Is dividing by 3 the correct procedure or have I made an error?

Using this method I have found the average torque of the engine to be 1.1Nm which sounds reasonable but this is an average torque figure for across the whole rev range?

How can I find the torque at any point throughout the rev range to then calculate the power at any point to then plot the graph?

Thank you for your help, its much appreciated!

 

[jrmichler]

The torque to accelerate the flywheel is the angular acceleration of the flywheel times the inertia of the flywheel. Then you can divide by the gear ratio to get torque at the engine. The angular acceleration of the flywheel IS NOT the angular acceleration of the engine. So, yes, you made an error.

Your method gets the average torque over the RPM range over which you ran the test. If you want a torque curve, you have a couple of possibilities:

1) A data acquisition system to capture RPM vs time, from which you calculate torque vs RPM from the slope of the RPM curve.
2) A larger flywheel, and a series of tests over smaller RPM ranges.

 

[A Devlin]

The torque to accelerate the flywheel is the angular acceleration of the flywheel times the inertia of the flywheel. Then you can divide by the gear ratio to get torque at the engine. The angular acceleration of the flywheel IS NOT the angular acceleration of the engine. So, yes, you made an error.

Your method gets the average torque over the RPM range over which you ran the test. If you want a torque curve, you have a couple of possibilities:

1) A data acquisition system to capture RPM vs time, from which you calculate torque vs RPM from the slope of the RPM curve.
2) A larger flywheel, and a series of tests over smaller RPM ranges.

Thank you for your reply jrmichler - A few more questions;

Can I easily calculate the Angular Acceleration of the flywheel if I know its dimensions and I know the Angular Acceleration of the engine?

Also, I have tried reading the torque values for RPM ranges of 1000rpm (Eg. 3500rpm to 4500rpm) but I am getting numbers much higher than I should be, however, this is probably because my procedure is incorrect. If the average torque between 3500rpm and 4500rpm is, for example, 2Nm, should I just use this value for the middle of the RPM range? So the engine produces approximately 2Nm at approximately 4000rpm?

Alternatively, I have a graph of RPM vs Time from a set of software which measured the engine during the acceleration, how do I calculate Torque from the slope?

 

[jrmichler]

The torque and horsepower curves for the Honda GX35 engine are posted online. Your measured values will be less than the posted values because you are not including the friction losses of the gears and the flywheel bearings.

The angular acceleration of the flywheel is the angular acceleration of the engine multiplied / divided by the gear ratio. It has nothing to do with the flywheel dimensions.

Acceleration is (change in RPM) / (change in time). If you have the data for the RPM vs time curve as a text file, you can do this with a spreadsheet. If you only have the printed curve, use a straightedge to measure the slope of the curve, and use hand calculations.

You reported RPM readings to four significant digits. That implies a digital tachometer. Digital tachs typically update the display at relatively large time intervals, on the order of 0.5 seconds. This is a significant source of error when the RPM is changing.

You can measure the friction of the flywheel bearings by a coastdown test. Disconnect the engine, spin up the flywheel, and measure the rate at which it decelerates. Note that the friction may be a function of speed, so you will need to generate a curve of friction vs RPM. One way to measure flywheel speed is to add an index mark (piece of tape, paint, etc) to the flywheel, then video it while it coasts down. Make sure you use a video frame rate that is at least two, and preferably three, frames per revolution at the highest speed. Counting frames in a video is tedious, but very accurate.