How much power and how far do it go

So i made a chart to show how much power it takes to drive versus speed, and then added a fat curve to estimate how many miles per fuel gauge bar (1 bar ~1kWh) you might expect versus speed also.  It could be tweaked to dial it in better, but this will get you in the ball park and be fairly close to Real Life… Due to storage limits on this free blog site,  i had to remove the charts

aero_rolling_powerpower_vs_speed+range

 

Power Calculation Methods

1.  Calculate the power required to maintain a constant speed on a flat and level road considering only the aerodynamic drag and rolling resistance forces where power equals force times speed.

Fa(V) = aerodynamic drag force at V = 0.5 * D(air) * V^2 * Cd * A

Frr = rolling resistance force = Crr * Weight

where D(air) is the density of air
V is the speed
Cd is the coefficient of drag
A is the frontal area
Crr is the coefficient of rolling resistance

Total force at speed Ft(V) = Frr + Fa(V)

Power(V) = Ft(V) * V  .  This is what is plotted in the first graph above.

2.  Calculate the power required to accelerate a massive object up to speed in t seconds.

i like to use is the kinetic energy approach
Kinetic Energy = 1/2 * mass * V^2 , and Power = KE/t

some folks like to use acceleration and P=F*V, where the Force = mass*accel, but this requires more math steps and gives the same answer.

This is a theoretical estimate, the real power is slightly higher due to the drag forces, but it will give you some idea of how much power you burn in jack rabbit starts off the line.

3.  Calculate the power required to pull up a hill at a constant speed.

So you are traveling flat and level at a speed V, then want to climb a steep hill with grade of  slope%.  The slope is rise/run so the angle is tan-1(slope%/100).

The slope adds an additional force that gets added to the aero and rr drag.

Fslope = Weight * sine(angle)

New force total  Ft(V) = Fslope + Frr + Fa(V)

Power(V) = Ft(V) * V

4.  Calculate the terminal velocity when coasting down a hill with grade slope%.

Coasting in N, balance the drag forces with the force of gravity pulling downhill.

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