# Cd Calculations

This will explain how to measure and calculate the coefficient of drag (Cd) for your car. This is useful information when your designing your electric vehicle because it will allow for more accurate estimates of your performance (range).

For the full description of how to calculate your car's Cd go hereWell, actually the site link listed above tells you the full story. It is done so well I didn't think it was worth adding anything. Below is part of the article that gives you an idea of how this works, but in order for you to try this yourself you'll have to visit the above site.

# BackGround (*Taken from the above site*)

## First, let’s define some quantities:

Fd is the force on the vehicle due to air resistance (drag) in Newtons

Frr is the force on the vehicle due to rolling resistance in Newtons

F is the total force on the vehicle in Newtons

V is the vehicle’s velocity in m/s

a is the vehicle’s acceleration in m/s^{2}

A is vehicle frontal area in m^{2}

M is vehicle mass including occupants in kg

rho is the density of air which is 1.22 kg/m^{3} at sea level

g is the gravitational acceleration constant which is 9.81 m/s^{2}

Cd is the vehicle’s drag coefficient we want to determine

Crr is the vehicle’s coefficient of rolling resistance we want to determine

Now for some formulas:

Fd = -Cd*A*0.5*rho*V^{2} (formula for force due to air resistance or drag)

Frr = -Crr*M*g (formula for force due to rolling resistance)

F = Fd + Frr (total force is the sum of Fd and Frr)

F = M*a (Newton’s second law)

Note that both Fd and Frr are negative indicating that these forces act opposite to the direction of the velocity. Note also that Fd is increases as the square of velocity. This is why driving at high speeds is much less efficient than driving at low speeds. Combining these formulas with a bit of algebra gives us the acceleration due to air and wind resistance as a function of velocity:

a = -(Cd*A*0.5*rho*V^{2})/M – Crr*g

Note that the acceleration is negative indicating that air and wind resistance will cause the velocity to decrease.

I found the above explanation very helpful and to the point. As shown in the full article, the final equation can be tuned to fit your deceleration data very well. While it is nice to know the Cd and Crr for your car, the real benefit here is that we can now accurately predict the total drag force on our car for any speed. Knowing the drag force allows us to calculate the work required to overcome the drag force. Work is force x distance, and our GPS logging system gives us distance information, every second in my case. This “work” is one of 3 work components that happen while driving, the other 2 are acceleration and elevation change (hills).