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#### gsbaker

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i4 e40 msport 19" 859M Sunset Orange
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Thinking about drag, BMW has published not only the drag coefficient but the refernce area, so we can compute the drag force vs speed. (1/2 ρ V^2 CD A) Power is the force times the speed.

Rolling resistance in the wheels is an almost constant force until high speeds, and is in the order of 1.4% of the weight.

Power train losses are some percentage of the power used. So if the drive train is 80% efficient the energy drain on the battery is power needed to drive the car, divided by the efficiency.

Putting these factors together, the power used at a given travel speed is:

P = (k1*V + k2*V^3)

Where k1 is the rolling resistance divided by the efficiency, and k2 is 1/2 ρ CD A divided by the efficiency.

So I set up a calculation with the speeds and durations of the EPA test cycle to get the total energy drain for the cycle, then the range of the battery. I also put in a usage of 2 kW for the cooling and heating cycle of the test. Then I adjusted the parameters to get the estimated EPA range of 300 miles.

This gave me an efficiency of 85%, which is about what Tesla says for their cars, and a rolling resistance of 1.4%. With those numbers I can estimate the power used for each travel speed.

If you have a vehicle you can record the power usage for several fixed speeds and solve for the k values for your particular vehicle.

One burning question is the delay due to recharging. You can figure that out by knowing the rate of power usage at your intended speed during a trip, and the charging rate of the fast charges you will use along the way. Both values are given in kW and from the above you can the power for driving, call it R1.

The charging rate, R2, is the speed of your charger. The fraction of your travel time spent driving is

R2 / (R1 + R2)

Your effective travel speed is your actual speed times this fraction of time driving.

The graph below plots this effective speed for several driving speeds.

#### 460

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thx for these formulas and results!

#### gsbaker

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thx for these formulas and results!
Yes, a constant 150. However, we can put another value for R2, representing the average rate over the time you spend charging.

I forgot to mention that for the I4 CD times A is 0.5544 sq.meters. Pretty small drag area.

#### 460

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representing the average rate over the time you spend charging.
great idea here for a full charge, it's about -25% @ 150kW:

#### gsbaker

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Thank you, Mycroft!

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