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**1. The POWER requirements of your car to maintain a particular speed is:**

Power = (power to overcome rolling drag) + (power to overcome aerodynamic drag)

so

Power in Watts = ((Mass in kg) (9.8m/s²) (Velocity in m/s) (Rolling Resistance)) + (0.5)(1.293 kg/m³) (Coefficient of Drag) (Area in m²) (Velocity^3))

The 9.8m/s is acceleration due to gravity, 0.5 is a constant from the derivation of the formula, the 0.6465 is the density of air in kg/m^3 (a different air density could be substituted if desired for different conditions). The first velocity is the speed that the vehicle is moving on the road; the second velocity is the relative speed of airflow over the vehicle, which is equal to the road speed of the vehicle in the absence of wind. If you enter the required numbers it will give you your power consumption in watts. Once you have worked that out you can use it to work out the following...

**2. The ENERGY required to maintain the speed in Step 1. for a certain period of time is given by:**

Energy in Watt-Hours = (Power in Watts)(Time in Hours)

For example the power required to travel 60 mph (converted to m/s) might be 20kW, driving for ninety minutes would mean you use (20 000)(1.5) = 30 kWh of energy. Assuming no efficiency losses (in the drive train or batteries) you would get 90 miles of range with a 30kwh pack. You could use this value for Sizing your Battery Pack, since the energy stored in your battery pack will be its voltage times its amp-hour rating but please allow for your drive train inefficiency and the characteristics of your batteries.

**3. The EFFICIENCY of you vehicle at the speed from Step 1. is given by:**

Efficiency in Wh/mile = ((Power in Watts)(1 hour))/(velocity in mph)*

So if it takes 20 kW to travel 60 mph then you will get (20 000 W)(1hr)/(60 miles/hr) = 333 Wh/mile. Please note that is the efficiency after the wheel, please take into account the energy losses of the electrical and mechanical drive train in order to better reflect your real world efficiency.

A great read on automotive power: http://wps.aw.com/wps/media/objects/877/898586/topics/topic02.pdf

* This equation is incorrect. "Efficiency in Wh/mile = ((Power in Watts)(1 hour))/(velocity in mph)" It should read " Efficiency in Wh/mile = (Power in Watts)/(speed in mph)". Of course the Power in Watts is that which is required for that particular speed. The term "speed" should be used because velocity typically infers a vector quantity.