Direct Downwind Faster Than The Wind #3 (DDWFTTW)

the fact that the cart is gaining ground on the treadmill proves nothing except the fact that the wind speed from the fan is faster than the treadmill speed. this allows the cart to have just a little positive traction that it wouldn't have on solid ground.

Wrong. There is no fan. Just a treadmill.

I get it now. My bad.

So, are you guys going to build a full sized ddwfttw land sailor and beat some land sailing speed records?

We're threatening to build a full-scale cart that we can ride in. We hope to definitively beat the wind on a direct downwind heading. I don't expect there are records for such.

Really this is as simple and as counter-intuitive (at first) as the yo-yo along a table & cotton reel examples.

Basically the cart is being _pushed_ by the wind, and uses the rotation of the wheels to turn a propeller which pushes against the wind even more and allows it to move a little faster than the wind which is pushing it.

Most people seem to assume that they see a windmill (turbine) which powers the wheels.

Well in an outside situation, the power would come from the wind pushing the vehicle along the ground. The propeller would rotate and generate extra thrust, which is pushing back on the already moving wind, slinging the craft forward.
The art is getting the optimum gear ratio to give the craft the maximum increase in speed relative to the tailwind, without the propeller overspinning and generating so much drag that the craft is slowed down.

The "outside" situation is no different from the "inside" situation. In either case you need a gearing that gives you an advance ratio of less than 1.0 (the distance the prop would advance in a single rotation divided by the distance the wheels would roll in one rotation of the prop). As you get closer to 1.0 the theoretical speed increases - but at the same time the allowable losses decrease.

That's a good idea, I never thought of it in terms of propeller pitch and development from one rotation

It's really not a "balancing act". There can be a great deal of excess energy which will accelerate the cart well beyond wind speed.