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 Force, Distance, and Energy

 Force x Distance = Energy

The simple looking force x distance equation contains a powerful subtlety which is perhaps a little more visible if the equation is rewritten as

    Distance = ------   
To go farther you can increase the stored energy in the car or reduce the forces. If you add energy say, by doubling the number of batteries, the force will have to increase to drive the extra weight - so doubling the batteries doesn't double the distance.

The second option is to reduce the forces which tug at the vehicle.

It says, if you have to apply power at a certain rate to push the car, there is NO WAY to go farther than the energy stored in your batteries. Yes, you can get out and push your exhausted vehicle but that's now adding in your body energy for producing the new pushing force; be sure to eat a good breakfast!

We can do a little thought experiment. Let's say we have 0 aerodynamic drag and the only thing holding us back is the "rolling resistance". The 'energy' in the equation is the stored electric energy in the batteries. The farthest we can go is:

    Distance = Energy / Fr , where Fr is the rolling resistance (force)  
Since we're ignoring aerodynamic drag, the calculated distance is unrealistically optimistic but gives you a quick idea of how far you could possibly go. It also makes you consider reducing the rolling resistance with techniques mentioned elsewhere (hard, large, narrow tires; less total weight overall, etc).

For one of the cars I studied, the aerodynamic drag became equal in magnitude to the rolling resistance at 50mph. Thus the force had doubled. Thus the range was now half of what you could get if you drove the car so slowly that was no effectively no aerodynamic drag.