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Determining power loss in drive train

Hello,


I'm trying to find out what is the power loss in drive train for my vehicle, ie. what is the power delivered by the wheels vs the power output from the engine (I assume that it can be calculated by multiplying the engine shaft RPM with torque). In real world this could be done with a dynamometer, but what would be a proper way to achieve this in Vortex?


Best Answer

The approach you are describing is correct but, in this way, the result will be an average over the time spent.

My colleague Michel provided me with a technique that is close to your approach. Then we'll look at the difference between the two methods. 

A kinetic energy approach


Let's start with some math:

Pin = Pout + Plost
      = dK/dt + Plost  ( where K is the kinetic energy and dK/dt is the rate of change of the kinetic energy which is the instantaneous power)
      = 1/2 * m * d(V^2)/dt + Plost
      = m * V * dV/dt + Plost
      = m * V * a + Plost  (where dV/dt = a is the acceleration)

This shows that, at stady state, a=0 and therefore,

Pin = Plost  (at steady state)

The math suggests a simple way to measure the power lost at any desired vehicle speed. Just run the vehicle on horizontal flat ground, bring the vehicle to a constant speed, and look at the engine power. Do this for a set of speeds between 0 and maximum vehicle speed, and you get the data to plot the power lost vs. the vehicle speed. 


The "dynamo-meter" approach

To answer your question above: at full throttle, the brake has to be applied until the engine shaft gets a steady speed. Perform the operation for different speeds in order to capture the power lost vs engine speeds (remember to run this test on a frictionless surface). 


Comparisons between the two


The two techniques are valid, but they don't measure the same thing. In the Kinetic approach, you are capturing the power loss due to all forces that exist in the environment (likely the ground reaction force, rolling resistance and/or tire model compaction resistance force, etc). In the dynamo-meter approach, you are getting the power loss of the drive train of the vehicle only. 



Here's one way to do it (and many thanks to Daniel and Michel from our Dynamic team for their help!):

 

Let's define:

  1. Pin as the Power Input 
  2. Pout_i as the power output at wheel i 
  3. Ploss as the power loss in the drive train 

 

Let's define the total power output as:

 

Pout = Pout_1 + Pout_2 + ... Pout_n where n is the number of powered wheels

 

Now, Vortex Studio's Vehicle Systems contains all the data that is needed. To more easily find it, all following world written in Bold can be easily located in the Vehicle Systems extension by pasting them in the search box at the top of the Vehicle Dynamics Component's Properties panel. 

 

Pin = Shaft RPM * Shaft Torque * 0.104719755 (where the constant converts RPM to rd/sec)

 

Now comes the tricky part. We can deduce the power output at a wheel by applying some input brakes. This mimic the dynamometer mentioned in the question. 


Pout_i = Input Brake * Maximum Brake Torque * Angular Speed (here we assume that the Brake Scale is 1 for all wheels)

 

Finally the power loss is given:

 

Ploss = Pin - Pout ( or efficiency = Ploss / Pin )

 

In general, the efficiency is measured at different speeds of the wheel. You can adjust the Maximum Brake Torque in order to have different wheel speeds. Don't forget that during such measurement of efficiency, the wheel of the vehicle must be free from any other external forces. So the vehicle must be on a frictionless plane, or the chassis held statically above the ground.


Thanks for the reply. However, the described process is a bit unclear to me. How much does the brakes have to be applied to achieve sensible results and does the throttle have to be fully applied at the same time?

My initial approach was to determine the total power output by calculating the kinetic energy of the vehicle (0.5*m*v*v) and dividing it by time (from the moment the vehicle started accelerating from static position), then I solved the power efficiency by comparing it to the Pin mentioned in the post above. Since I'm not a physicist, I'm not sure if this is a sensible way to calculate the total power output, since it seems so simple.
Answer

The approach you are describing is correct but, in this way, the result will be an average over the time spent.

My colleague Michel provided me with a technique that is close to your approach. Then we'll look at the difference between the two methods. 

A kinetic energy approach


Let's start with some math:

Pin = Pout + Plost
      = dK/dt + Plost  ( where K is the kinetic energy and dK/dt is the rate of change of the kinetic energy which is the instantaneous power)
      = 1/2 * m * d(V^2)/dt + Plost
      = m * V * dV/dt + Plost
      = m * V * a + Plost  (where dV/dt = a is the acceleration)

This shows that, at stady state, a=0 and therefore,

Pin = Plost  (at steady state)

The math suggests a simple way to measure the power lost at any desired vehicle speed. Just run the vehicle on horizontal flat ground, bring the vehicle to a constant speed, and look at the engine power. Do this for a set of speeds between 0 and maximum vehicle speed, and you get the data to plot the power lost vs. the vehicle speed. 


The "dynamo-meter" approach

To answer your question above: at full throttle, the brake has to be applied until the engine shaft gets a steady speed. Perform the operation for different speeds in order to capture the power lost vs engine speeds (remember to run this test on a frictionless surface). 


Comparisons between the two


The two techniques are valid, but they don't measure the same thing. In the Kinetic approach, you are capturing the power loss due to all forces that exist in the environment (likely the ground reaction force, rolling resistance and/or tire model compaction resistance force, etc). In the dynamo-meter approach, you are getting the power loss of the drive train of the vehicle only. 



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