Esk8 aerodynamics

To maintain steady velocity your thrust has to equal your drag. The drag equation is:

Drag = Cd * 0.5 * rho * V^2 * A

Cd is your drag coefficient. The coefficient of drag for a skydiver is 1.0 when horizontal and 0.7 feet first. Your tuck can’t improve your coefficient of drag by a lot. Assume it is a constant 0.8. V is your velocity. Your velocity was constant at 27 mph which is ~40 ft/s. Rho is the density of air. The correct English units for density of air are slug/ft^3 and the value is .002378.

With the torque constant of your motor(s) and the amps you were drawing you can calculate the torque you were producing. Multiply it by the wheel radius to get thrust. From that you can back calculate the area when you were standing and the area in your tuck.

To(rque) = Kt * amps
Th(rust) = R * To

R is the wheel radius. Kt is your torque constant.

Thrust = Drag

R * Kt * amps = 0.8 * 0.5 * .002378 slugs/ft^3 * (40 ft/s)^2 * A

A = 0.66 ft-s-s/slugs * R * Kt * amps

keep your units consistent feet and seconds

I went through that quick. I can’t vouch for perfect math but that is how you do it.

Edit: You probably want an efficiency factor on the torque depending on your power train. Divide the right side of the equation by your efficiency, E.

A = 0.66 ft-s-s/slugs * R * Kt * amps / E

Edit: Corrected to add gear ratio (GR)

A = 0.66 ft-s-s/slugs * R * Kt * amps * GR / E

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