There would be no force gained, yes. But that's not the point of the machine. Any machine will trade speed with force: in a low gear, a bicycle produces a lot of force bit not much speed, enabling you to climb a hill slowly, or in a fast gear it produces less force and more speed, enabling you to go fast on a flat road.
Yes, that is transformation.
Spork's cart, Brian-M's cart and all the other devices presented here do not propose to give an advantage in force: they will all need a greater force to push them than the force with which they could push something. They propose to give an increase in speed, at the cost of a decrease in force.
That is the problem. You need more power from
exactly the same source. Brian-M's device indicates you DO need more force.
There is an error that leads to the conclusion that F = Fc/2. (#925)
The ratio of the gray gears demands that F = Fc, meaning twice the force of a standard cart, for twice the velocity. The second ground wheel can be made idle, just somewhere for the belt to go, so think of how much power the remaining ground wheel consumes, and how much the upper wheel must supply. That ground wheel is greedy!
The "speed of the wind" is not itself a force. It is the kinetic energy of the wind that provides the motive force for the cart. Kinetic energy is proportional to mass. The force gained from the wind comes from the mass of air hitting the propeller. You can gain more force from the same wind by increasing the size of the propeller.
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Agreed, though you can find posts where the two are equated.
Gathering momentum from the wind is largely what sailing boats do. They extract more power, so that it may be transformed by various means. They are sophisticated machines that have been developed to do just that, and use lift to reduce the drag of the hull, for example.
Direct comparison with the cart is unfounded, because as you note, it can only gather what impinges upon the propeller, imaginary sliding booms or not. A bigger propeller may mean more power, but the forces generated will be opposed. More power is more speed, but that only extends the terminal velocity as expected, which will still be below windspeed.
Just a note. Supporters are invariably upset when claims of deception are made. Sometimes the deception is deliberate, and sometimes it is the designer fooling himself. One of science's attributes, is that it helps control those errors. An 'honest' video would have at least shown the forces involved; a cheap spring force-gauge would have been sufficient, a simple grid behind the cart could show the relative velocities. Evidence need to be more than "look, it works".