General range vs temperature curve

Range vs temperature?

  • Can we get a simpler version

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  • Just right

    Votes: 1 100.0%
  • Could we include tire temperature effects

    Votes: 0 0.0%
  • I'd rather have pie

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  • Total voters
    1

bwilson4web

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Some basic physics can help. If we keep the rolling drag constant by keeping the tires at a constant pressure, then aerodynamics defines the performance. Aerodynamic drag is driven by the air density so I copied this chart from Wiki and added details:

air_drag_020.webp


The modifications:
  • added a grid
  • added the (fahrenheit) to celsius values
  • used 20 C / 68 F as a Standard Day temperature (what I use for performance benchmarks instead of 15 C (59 F))
  • added the "drag %" and "power %"
So keeping the same tire pressure (add air when colder) and speed (62 mph is a good number), use that particular consumption in Wh/mi and multiply it by the "power %". For example:
  • 229 Wh/mi = 250 Wh/mi * 91.5% -- the warm weather, 86 F advantage
  • 250 Wh/mi = 250 Wh/mi * 100% -- Standard day, 68 F
  • 282 Wh/mi -- 50 F day
  • 311 Wh/mi -- 32 F day
  • 348 Wh/mi -- 14 F day
  • 389 Wh/mi -- -4 F day
This was a 'back of the envelope' analysis. Another, non-dimension number, Reynold Number, can modify the power so I've posted the cube. This was mostly to give a math model, the background, to estimate the range loss as a function of temperature at a given speed with tire pressure kept at a constant value.

In reality we need to air up the tires on a cold day and then run a series of round-trip, benchmarks recording the Wh/mi and temperature. Then wait for the temperature to increase, deflate the tires to the target pressure, and rerun the benchmark. With enough data points, we can derive the Wh/mi as a function of temperature.

Once the function is derived for one Tesla or EV model, other EV models can do a benchmark and scale the function. Sloppy but close enough for the GOM.

BENCHMARKS

The blue line shows the Wh/mi from earlier benchmarks. Reading up the 60-65 mph speed, we're seeing ~230-235 Wh/mi:
mph_miles.webp

NOTE: This chart was made using Tesla inflated tires, ~45 psi in part to match what an OEM Model 3 would achieve. Fully inflated, the blue curve is lower and range longer.

A math model needs to be validated. So I drove both directions on a 20 mi route with the tires at 50 psi before dawn at 34 F (1 C):
  • 276.6 Wh/mi measured / 124.2% ~= 223 Wh/mi @68 F (20 C)
Now I wait for a noon to 2 PM window with a temperature close to 50 F (10 C). Repeat the calculation and see how close we come to "223 Wh/mi".

Bob Wilson
 
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