Downwind Car Explanation: https://docs.google.com/View?docID=0AdR ... test&hgd=1

*"The downwind car is designed with a propeller that pushes it along like an aircraft's propeller does, it is not a windmill or a turbine. Instead of an engine to turn the propeller, the propeller is geared to the wheels of the car, so that as the car moves forward, the propeller spins in such a way that the car will speed up if there is energy available from a tailwind. The following explanation will show how this works by analyzing the forces acting on the vehicle and the energy flow through the system.*

In order for the car to travel directly downwind faster than the wind using only the wind for power, the total resistive force on the vehicle must be less than or equal to the thrust provided by the propeller (force balance) and the power provided at the wheels must be greater than or equal to the power consumed by the propeller (power balance). (Note: In this explanation we are describing the power balance as seen by an observer riding with the car, so the power for the propeller appears to come from the wheels. A similar analysis can be done from the ground-based reference frame, but it is more complicated.) The force equation tells us that the sum of the wheel resistance equals the propeller thrust when traveling at maximum speed (we are ignoring vehicle drag for simplicity in this explanation). The power balance tells us that the wheel force times the car speed (power input) must be equal to or greater than the propeller thrust times the relative velocity of the air (Vcar-Vwind) divided by the propeller efficiency (power output). Note: we are also neglecting drive train losses in this simplified analysis.

Figure 1: Force and power balance for a downwind car.

Understanding the power balance assumes that the reader knows that power is equal to speed times force. For the propeller, the speed we must use is the airspeed relative to the propeller, not the speed of the car, because the propeller is working against the air instead of the road surface. The power available from the wheels is proportional to the speed of the car ( Pinput = R*Vcar) where R is the wheel resistance force and Vcar is the car speed. The propeller power consumed is (Poutput = T*(Vcar-Vwind)/etap) where T is the propeller thrust, Vwind is the wind speed, and etap is the propeller efficiency which is related to the "slip" and viscous drag of the propeller in the air. If we combine the force and power equations and simplify the expression, the result is a simple equation that states that if the propeller exceeds a minimum level of efficiency, the car can travel faster than the wind downwind (figure 2).

Figure 2: Minimum required propeller efficiency for the car to work.

This equation defines the minimum propeller efficiency for the vehicle to work at a given ratio of wind speed. In reality, the required propeller efficiency will be higher since we neglected vehicle drag and drive train losses in this analysis. Figure 3 shows that even at very low propeller efficiency the car can run faster than the wind downwind and as the efficiency approaches 1.0 the speed ratio goes to infinity (assuming no other losses).

Figure 3: Variation of carÃ¢â‚¬â„¢s speed ratio as a function of propeller efficiency.

The reason the car works is that the propeller is pushing on air that is moving slower than the speed of the car because there is a tailwind. This allows energy to flow into the system for propulsion, something that would be impossible if there were no wind. Another way of looking at this is the tailwind allows the propeller to make more thrust for the same power than if there were no tailwind. The propeller must be geared to the wheels for this to work or else there is no way to keep it turning and accepting power from the wind."

In order for the car to travel directly downwind faster than the wind using only the wind for power, the total resistive force on the vehicle must be less than or equal to the thrust provided by the propeller (force balance) and the power provided at the wheels must be greater than or equal to the power consumed by the propeller (power balance). (Note: In this explanation we are describing the power balance as seen by an observer riding with the car, so the power for the propeller appears to come from the wheels. A similar analysis can be done from the ground-based reference frame, but it is more complicated.) The force equation tells us that the sum of the wheel resistance equals the propeller thrust when traveling at maximum speed (we are ignoring vehicle drag for simplicity in this explanation). The power balance tells us that the wheel force times the car speed (power input) must be equal to or greater than the propeller thrust times the relative velocity of the air (Vcar-Vwind) divided by the propeller efficiency (power output). Note: we are also neglecting drive train losses in this simplified analysis.

Figure 1: Force and power balance for a downwind car.

Understanding the power balance assumes that the reader knows that power is equal to speed times force. For the propeller, the speed we must use is the airspeed relative to the propeller, not the speed of the car, because the propeller is working against the air instead of the road surface. The power available from the wheels is proportional to the speed of the car ( Pinput = R*Vcar) where R is the wheel resistance force and Vcar is the car speed. The propeller power consumed is (Poutput = T*(Vcar-Vwind)/etap) where T is the propeller thrust, Vwind is the wind speed, and etap is the propeller efficiency which is related to the "slip" and viscous drag of the propeller in the air. If we combine the force and power equations and simplify the expression, the result is a simple equation that states that if the propeller exceeds a minimum level of efficiency, the car can travel faster than the wind downwind (figure 2).

Figure 2: Minimum required propeller efficiency for the car to work.

This equation defines the minimum propeller efficiency for the vehicle to work at a given ratio of wind speed. In reality, the required propeller efficiency will be higher since we neglected vehicle drag and drive train losses in this analysis. Figure 3 shows that even at very low propeller efficiency the car can run faster than the wind downwind and as the efficiency approaches 1.0 the speed ratio goes to infinity (assuming no other losses).

Figure 3: Variation of carÃ¢â‚¬â„¢s speed ratio as a function of propeller efficiency.

The reason the car works is that the propeller is pushing on air that is moving slower than the speed of the car because there is a tailwind. This allows energy to flow into the system for propulsion, something that would be impossible if there were no wind. Another way of looking at this is the tailwind allows the propeller to make more thrust for the same power than if there were no tailwind. The propeller must be geared to the wheels for this to work or else there is no way to keep it turning and accepting power from the wind."