#1: i don't believe this works, due to my point that the apparent wind will be from directly ahead, not behind.
Not on the bottom half of the spokes. When the wagon travels at wind speed the point half way down the bottom spoke is going in the same direction as the cart, but at half the wind speed. So pushing on this point at wind speed will still accelerate the wagon - well past true wind speed.
#2 first, i can't really visually how the yo yo gets pulled up the string, i think the string would just unroll.
You don't have to visualize it. Do you have a yo-yo?
gdorfman wrote:as the yo yo goes downwind and catches up to wind speed, the parachute falls out of the sky b/c the lines are tethered to it. again, you have reached 0 wind, or a headwind.
Again, when the yo-yo has reached wind speed the parachute has reached only half wind speed since it exits the yo-yo below the axle midway between the axle and the ground. Again, you can easily try this with a yo-yo. You'll see that when you pull the string with your fingers the yo-yo will be going twice as fast as your fingers. This will keep tension in the line until the parachute is going true wind-speed - and the yo-yo is going 2X true wind speed.
#3 actually i like this one! as long as you can get get downwind VMG greater that windspeed (my 3rd question) then you can create a box to have that vmg turned into direction by having the boats tack inside it. cool.
#4 i believe this is similar to #1. again, you're using gearing, and you're also using prop rotation (kind of like kite looping) to create greater windspeed over the foil than the vessel is actually travelling. however, again, once the vessel reaches a greater downwind speed than windspeed, you will have a headwind. okay, your props can still turn in the head wind (if they are rotated) but they are creating drag, not lift. an airplane on a runway doesn't magically move forward if a headwind blows on it and the prop is already turning (with no power source).
This one is actually far more like #3 than it is like #1. I'm simply taking my boat that tacks downwind and constraining it to follow a continuously spiraling 45-degree downwind path (one long continuous tack). It's true that a plane won't move forward on the runway when it encounters a headwind. But it will if it encounters a sufficient tail-wind - which is how this craft works. Of course the plane won't exceed the wind speed when blown downwind on the runway, but that's because we haven't geared the prop to the wheels properly, sized things appropriately, and reduced drag sufficiently.
#5 i agree with your point here, but don't see the connection to going downwind faster than wind.
This one isn't obvious. If a boat can tack into a purely relative wind when being pushed by the current (thus outrunning the current that pushes it), then it can similarly be "pushed" downwind faster than the wind. Because of the relative L/D of keels and sails we rarely see a boat that can achieve this feat (Steve Fosset's PLayStation is said to have polars that would make it possible). However, both the keel and the sail are simply wings acting in their own fluid. So there's no theoretical difference between the two. Any boat tacking into the wind in still water is exactly the same as a boat being pushed down-current by the water, but beating the water that pushes it. You just have to look at it from the inertial reference frame of the wind.
but i don't think you could ever head directly downwind, which is the point we're getting at.
Yes, you're right. I mis-spoke here. This one simply demonstrates that the boat can absolutely make a VMG downwind (or downcurrent as the case may be) faster than the wind (or current). We still have to stick it in a frame to meet the original constraints of the problem.
actually, the more i think about it, i think the feasibility of 3 and 4 should be equivalent, because 3 seems similar to the idea of a prop where it's private apparent wind overpowers the fact that the vessel feels a headwind.
DOH! You're ahead of me. That's what I am getting at above.
hmm. i don't like 4 being true.
I don't like taxes. But that doesn't change the fact that they exist and I pay 'em
maybe this leads to a proof that a vessel actually can't have a downwind vmg greater than windspeed. i don't know.
Well, my $100K is still available. Please get back to me sooner rather than later - because my day job is cutting into my kiting time.