quote:
Originally posted by Stickywulf:
It is impossible to go faster than the true wind when heading directly downwind at least on a sailboard (or iceboat by association).
This is true for a sailcraft. A sailcraft needs a forwards and/or crosswind component to move forwards. The apparent crosswind is equal to the speed of the wind times sin(angle between wind direction and sailcraft direction), and since it's perpendicular to the sailcraft direction, it's independent of the sailcraft's forward speed, so the sailcrafts maximum speed is limited by it's effective lift to drag ratio for a given apparent crosswind.
Ignoring the analogy of the prop blades moving in a spiral path, the DDWFTTW carts work because the power input comes from the wheels which interact with faster moving ground, while the power output comes from the prop which interacts with slower moving air. This allows the force from the wheels to effectively be geared down to multiply the force and divide the speed, and even though there are losses, the resultant force from the prop is greater than the driving force from the wheels, it just occurs at a slower speed.
Power equals force times speed, so the wheel force times wheel speed can be "geared" so that prop force is greater while prop speed is less.
In a no wind situation, this doesn't help. But if there is a tailwind, then the reduction of speed at the prop is compensated for by the tailwind.
From my post at physics forums:
Note the speed factors here are relative to the medium the wheel and prop interact with. The wheels interact with the faster moving ground and the prop interacts with the slower (relative to cart) moving air.
If the cart is moving at the same speed of the air, then the only speed at the prop is due to it's own induced wash, which is 1/2 the sum of the entry and exit (when air pressure returns back to ambient downwash of the prop) speeds, while at the wheels, the relative gound speed is equal and opposite to the wind speed (if the cart is going the same speed as the wind).
The power input is the force the ground applies to the wheels time the forwards speed of the cart. The power output is the force the prop applies to the air times the backwards speed of the air flow through the prop.
Vw = speed of wind
Vc = speed of cart
Vp = speed of induced wash from prop
Fp = force from prop
Fc = force from cart wheels
Fd = overall losses (drag) related to forward speed of cart
The net force on the cart = Fp - (Fc + Fd)
The power input = Fc x Vc
The power output = Fp x (Vp + Vc - Vw)
The power loss = Fd x Vc
The point here is that Vc can be > Vw, Fp can be > Fc, with power output still well below power input as long as Vw is greater than zero (a tailwind), because the cart uses effective gearing to multiply the force and divide the speed from the ground to the prop, which works because the prop interacts with the air (wind), as long as the reduction of speed by the gearing is less than the difference than the speed between the air (wind) and the ground, and the force is mutliplied enough to overcome any loss factors.
quote:
The air forced through the propeller is moving in relation to the ground. The air is the driving force of the vessel therefore velocity also needs to be measured in relation to the ground.
Yes, and with a tailwind, the air is moving at 10mph forwards without any prop interaction. If the prop generates 5mph of thrust, then that 5mph of thrust is in addition to the 10mph of tailwind, for an effective thrust rate of 15mph. The induced wash required to generate the thrust is subtracted from this 15mph. If the required induced wash is 3mph, then the cart goes DDWFTTW at 12mph, 2mph faster than the tailwind.