Transformation is exactly what Brian M's cart does: it transforms a force of Fc over a distance x into a force of Fc/2 over a distance of 2x. Nothing unusual there.
A transformer cannot give power gain! Only change the ratio of V to F.
You are confusing the apparent acceleration of the vehicle, with power gain.
What do you mean by that? Of course all the power is coming from one source. Indeed, most machines only have one source of energy. That doesn't stop them working.
Can you point out this error and explain it? I don't see it in Brian's calculations.
That is not what I meant. You do have the same, single power source but for the cart to do what you expect, you would need twice as much, or another source to make up the difference.
This is your reasoning, I think.
Follow the force through from the circumference of the top wheel. The ratio between the wheel and gear is 2, so the force is doubled. The bottom wheel has a ratio of 4:1 dividing it by 4, so in total, it is halved. Fc = F/2, but Vc = 2V, so it goes twice as fast for the same input. Yes?
The relative velocity of the vehicles is first derived. The force "gain" is derived. The 'mistake' is to equate the two so directly.
Apply 10N, to a 1kg cart for 1s. Note the final velocity of the vehicle. However, in reality, there are retarding forces. Without this consideration, you have simply provided another example of a vehicle that can be accelerated to any velocity, if you apply a force for long enough!.
Sorry, I failed to point that out earlier F= Fc, when V = Vc. No difference in force, or velocity because of the gears. I did include a drawing in my reply to Brain-M, where parachutes provide the force.
There are the retarding forces of friction and drag. The final velocity is reached when there is no more force available to accelerate the vehicle any further. The incremental acceleration is zero.
What is being done here is to modify the way that the vehicle gets to that terminal velocity.
There is only enough power to drive it to the same velocity as an equivalent vehicle without gears. You can trade distance or velocity for force, but power keeps the accounts.
In the case of a very long board (or track) where the board velocity is to V, but force is not limited, you are indeed trading distance to V. If the board is very long, the cart need not reach the puller, but stop when there has been sufficient time for it to reach V.
"What! It would still be going at 2V!" Sorry, but no.
The speed 'gain' becomes divided, as those -Vs and +Vs shift there reference to be symmetrical around V, resulting in V.
Alarm bells should ring!. The speed gain is the
differential radial velocity of the two gears. What you are considering are only the initial conditions, where you can arbitrarily ascribe V to be the reference velocity to which you add the gain.
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The principles of physics, tested and verified over centuries, show that Spork's cart, Brian M's cart and all the other engines presented here can work. Once more: if you really don't think Brian's cart can work, why not make one yourself and test your theory?
A general comment, Michael_C. It does not apply to
all followers.
I don't need to test it, nor should you, unless you can find very good reason to doubt those very centuries tell you that it will not work.
If you
do believe in the rules of physics, it is not within those rules to manipulate the ratios of V to F, while ignoring the work that must be done.
" It is human nature to be optimistic about systems that beg us to be pessimistic".
Henry Petroski, on the cause of NASA's shuttle disasters.
Perhaps more like that, than deception.
