Cheers Chuck.
It's fun though, and ever since school and my degree physics has been a kind of hobby with me, so it is interesting to go through the processes SN3's misunderstandings of basic physics force upon me.
SN3
Still no actual, relevant examples?
If you move more air (say by using a larger prop) with the same power then it moves more slowly than moving a small amount of air with the same power. However because there is more mass flow the thrust is actually higher. Thus the size of prop is critical in understanding the issue we are talking about (note that I never mentioned propellor speed at all. I am not sure where you got that from).
That is why the helicopter rotor is relevant. It is nothing to do with the forward component of lift causing the forward motion of as helicopter, that really is irrelevant and I have no idea why you brought it in. It is to do with how a large prop compares with a small prop in terms of producing thrust from a given power. A helicopter rotor moves a larger amount of air than an aircraft prop, at a lower speed given the same power. The helicopter is straight-forward proof of this. An R44 rotor can produce thrust greater than its own max all-up weight in order to hover using only 205 hp. An Arrow with only 5 hp less could not hover on its prop even with only a pilot on board and a small amount of fuel, when it would be lighter than the R44.
Just because you say it ain't so doesn't mean it isn't, or a lot of 777s with their nice high-bypass turbofans would have started crashing just as you said it!
I can prove it with a few equations if necessary, but it is rather irrelevant if you are unable to understand those equations. If you could understand them they should be irrelevant, if I give the following description.
Energy is 1/2mv^2 and momentum is mv. Power is rate of change of energy, and force is rate of change of momentum (thrust is a force). So take m to be the mass of air passing in a second, v its change of velocity, mv is then momentum change in a second, i.e thrust and 1/2mv^2 is energy conversion in a second, i.e. power.
So increasing the mass flow by a factor of x at the same power reduces the velocity by a factor √x. The thrust is proportional to the mass flow and velocity, so is multiplied by a factor of x/√x. This is √x. So at the same power, reducing the speed of the airflow increases the thrust, as I said in the first place! Double the mass flow you have 41% more static thrust.
Power does not achieve lift. In the case of a helicopter, you're confused between the relative motion of the rotor...which will turn with or without power (visit autorotation)
How does a rotor achieve relative motion without power?
Autorotation requires power. The rotors require power to start moving and to overcome drag and friction in all its various forms. The power in autorotation is the conversion of potential to kinetic energy. It's still power, even if it doesn't involve chemical energy!
You really don't understand what power is, do you? I say again: power is the rate of conversion or transfer of energy. Nothing more, nothing less. It does not require machinery. It can come from the burning of fossil fuel, the falling of a weight or the differential heating of the Earth's surface. It's still power!
An autogyro is not a better example. I wanted a more direct example of motive, mechanical power (i.e. what you already accepted as power, as I didn't at the time feel the need to teach you basic physics) producing lift than a fixed-wing aircraft, which does it by producing thrust, which moves the aircraft, which causes airflow across the wing which then produces lift. The helicopter just uses power to movement of a wing that produces lift. You then come up with an autogyro, which does use power to produce lift but in an even more roundabout way than a fixed-wing aircraft!
Of course, you seem to have trouble understanding how the introduction of a light single engine piston powered general aviation airplane relates to a conversation involving light single engine piston powered general aviation airplanes...so it's no surprise that you're confused.
Have you ever actually read the title of the forum? Do you know what "Private Flying" is? Have you noticed that there is a separate forum for "Biz Jets, Ag planes GA etc." flying, in which an answer including an ag plane might indeed have been relevant?
The matching number of engines and the power plant type are beside the point, as is the fact that it is a GA aircraft. The fact that it is not used for "Private Flying", the entire purpose of this forum, means it is irrelevant to the discussion.