Efficient car tuning using a Tesla example

This article is a compare and contrast of using "roll-down" and "benchmark" testing of efficient cars like the Prius and Tesla. We are often dealing with small differences, less than 10%, that can easily be swamped by noise or peripheral effects.

Roll-Down Testing

Described by SAE J1263, this involves running 16 roll down tests where the car starts above 70 mph and then coasts down to 15 mph. But this requires a level track, low winds, 5 mph, limited temperature ranges, and turns out to be difficult for individuals. For example, my initial attempt to do roll-down tests with our Std Rng Plus Model 3.

Finding a sufficiently flat track, I used a road that runs along side the local airport:

Per the standard, the altitude variation of this track can be corrected provided the test data comes from the most level part. There is a mathematical way to compensate for these small variations but it requires close coupling of the exact car location and altitude variations. It can be done but for an individual, requires labor.

So here is the GPS logged data from four passes, two headed South and two headed North:

The GPS velocity and altitude data shows even a couple of feet change is enough to adulterate the velocity. It has to be mathematically removed, probably using kinetic and potential energy relationship, but this is not trivial. A program processing the raw GPS data (maybe a spreadsheet) becomes a one time task but to what end? Would anyone outside of the manufactures and EPA even care? One interesting paper is an engineering paper:
Experimental Studies in Ground Vehicle Coastdown Testingwww.asee.org › conferences › papers › download

The following graph shows the problem:


Down to 40 mph, aerodynamic effects are higher than rolling drag. This suppresses the altitude induced changes. But below 40 mph, altitude changes begin to over ride rolling drag yet this is an important area if one wants to compare rolling drag effects like tire resistance.

Happily, the EPA posts roll down coefficient which I use to compare different cars. Add informed opinions about drivetrain efficiency, the engine and transmission, we can compare the 'claims' against the actual performance. But these roll-down numbers are in the OEM configuration and don't help when replacing tires or advanced lubrication.

Three Point Benchmarks

Another approach is to perform at least three benchmarks, and then curve fit to a quadratic equation:

y = A(x**2) + B(x) + C

y - MPG or Wh/mi
x - velocity

A - drag force as a function of the velocity squared the aerodynamic drag.
B - drag force as a linear function of velocity the rolling drag.
C - vehicle overhead when turned on but not providing power to drive wheels.​

Each benchmark is at fixed speed over routes that neutralize altitude and wind effects. Temperature has to be recorded to compensate for aerodynamic drag.

Speeds

Low speed ranges, 10-15 mph, and 25-30 mph. This brackets the lowest drag region, a local minimum. Experience has shown the lowest drag, Prius speed, is 18 mph +/- 3 mph. By measuring below and above the likely, minimum drag speed, we can get two, accurate, low-speed points. These typically do not require temperature compensation provided the car is run for about 10 miles to warm-up the tires and lubricants.

Middle and high speed ranges, 35-45 mph, and 65-75 mph. At these speeds, aerodynamic effects predominate. This provides two, high-speed data points, the lower one for urban driving and the upper one for highway.

Using four data points allows cross checking to make sure the benchmarks were fair. For example:

In this case, I'd left the cabin heater at 70F for the 39 mph benchmark. The effect was to double the energy used which is shown in the graph. However, the EPA curve and my benchmark curve from three valid points shows close agreement with the issue of low speed accuracy of the traditional roll-down coefficients. This is the methodology:

• Route
  • Relatively flat, not perfect, but avoid large elevation changes.
  • Start=Stop location to minimize elevation changes and wind effects.
  • Minimum wind which between midnight and dawn tends to be the lowest wind conditions.
  • Temperatures between 50-80F, ideally at ~60F to approximate a Standard Day
  • Best to use a circular route but two, bi-directional runs can be combined for a data point.
    • If using bi-directional routes, convert each to gallons or Wh with distance each way. Add the two energy metrics and distance and then calculate the energy/mi value.
• Duration
  • The goal is to see minimum changes in MPG or Wh/mi values.
  • Empirical data shows ~10 mi, 16 km, is enough to achieve a steady state rate.
• Coefficients
  • Use any of the web pages that convert three points to the coefficients of a parabola:
    • "Three Point Parabola Calculator"
    • "Three Point Quadratic Calculator"

CONCLUSIONS

Although roll-down testing is the approved, 'gold standard', it is a pain for individuals. This is due to having to combine high resolution velocity and altitude changes to make a synthetic, flat track. Not impossible, it isn't clear there are open-sourced spreadsheet or software that converts the raw GPS data into a form usable for roll-down metrics.

An easier approach is to use three, vehicle MPG or Wh/mi metrics, across a slow, medium, and highway speed range. Use a quadratic formula conversion to get the derived roll-down coefficients.

Bob Wilson

 

I wasn't sure where to put it. It spans all makes and models of Prius so I thought about "Fred's House of Pancakes." Regardless, sometimes I miss where postings should go. I don't care where as long as not the 'bit bucket.' <grins>

I originally posted it in a Tesla technical group for obvious reasons. But it applies to the Prius IF there are any others like me hanging around.

Bob Wilson