Just some input to this discussion
Hi There Fellow Nerds
I have some input to this discussion.
Consider the case of a horizontal axis wind turbine mounted on a car.
Look at the case where you want to go directly in the upwind direction.
A first shot at the mechanics here could be obtained by just looking at the effects of the wind turbine, that is neglect non-ideal stuff like car drag, rolling resistance and transmission losses. Apply simple 1D momentum theory for how the rotor behaves (The most simple rotor aerodynamic model. This assumes an ideal turbine: no viscous (fluid-friction) losses, no rotation of the flow in the wake of the turbine, etc etc)
The results from 1D momentum theory basically states, that the thrust force on the wind turbine is
T=0.5*rho*A*Vrel^2*CT where CT=4*a*(1-a)
(rho=density of fluid; A=Area of wind turbine; Vrel=relative free stream velocity of the fluid, as seen by the turbine; CT=Non-dimensional Thrust coefficient; a=axial induction coefficient, a nondimensional factor saying how much the axial flow velocity is reduced in the rotor plane relative to the far stream value)
Analogousy, the power output from the turbine is
P=0.5*rho*A*Vrel^3*CP where CP=4*a*(1-a)^2
(CP=Non-dimensional Power coefficient)
Under the above ideal assumptions the maximum velocity of such a vehicle is determined from the equilibrium of the forces at top speed (obs: no inertial at this maximum, top speed). Remember, that since power equals force times velocity, the propulsive force obtainable from the power production on the rotor (at the velocity V of the vehicle) is P=Fprop*V => Fprop=P/V
Noting that the relative velocity seen from the turbine is Vrel=Vwind+V, so the equation for determining the top speed reads
P/V=T
Putting in Vrel=Vwind+V into the equations for P and T, and feeding all into P/V=T and reducing, we end with this result (after some slight manipulation)
V/Vwind=(1-a)/a
This expression actually goes toward infinity for a tending to zero. This is clearly unphysical, and is due to the assumption of negigible car drag, and the other ideal asumptions. However, it is clearly shown that if we have a free stream velocity that is not zero, we can make a car move straight into the wind. And if we design the car good enough, we can even make it go faster than the free stream velocty. Agains the wind!
Neat, right.
If you do similar considerations, including car drag, transmission loss, and account for non-ideality of the rotor, you still actually end up with a wind car that could go faster than the free stream velocity in the upwind direction.
But I don't think such a car is built.
Yet.
Let's see how fast the cars at the Aeolus contes in Holland will go. Here's a link to the contest site:
www.windenergyevents.com
I hope this post was not too nerdy :)
-Mac G