vanesch
Staff Emeritus
Science Advisor
Gold Member
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zoobyshoe said:In order to understand the non-stored forces at work on the cart at wind=0 we have to imagine a "virgin" situation where the propeller is not in motion at all. Not rotating.
Wind speed = 0
Ground speed = say, 10mph but contrary to the direction we want the cart to accelerate into
Prop rotation speed = 0
Is there a total force on the cart here in the right direction that will cause acceleration in the right direction?
I think in the crude model I pointed to before (the 3 forces: prop force, air drag and wheel resistance), you can put K = 0 (gearing ratio 0) and then what remains is simply the drag term.
F_tot = rho_air x S x K x v_cart x ((K-1) x v_cart + v_wind) + W x (v_wind - v_cart)^3 - ...
... rho_air x S x K x ( (K^2-1) x v_cart^2 + 2 x v_cart x v_wind - v_wind^2)
So fill in K = 0 (gearing ratio 0, the propeller doesn't turn, no matter the wheel turning):
F_tot = W x (v_wind - v_cart)^3
Don't forget that the velocities here were originally expressed in the "floor" frame. However, as this is a difference of velocities, it is simply the air speed wrt the cart, and it doesn't matter where you calculate it.
