And you are saying that the amount of air displaced (downwash) is irrelevant if the aircraft is not moving relative to the earth. So in the helicopter example, although the blades are moving a whole lot of air and holding the helicopter up against gravity, that the Trust HorsePower is still zero, because we haven't gone anywhere? A force is being applied, but no distance travelled, therefore no work completed?
Yup! You got it. Thrust is a force. It's the same as me pushing really hard against the side of a big box. If the box doesn't move, I haven't done any work. I have sure used a lot of energy though! Exactly same with the airplane and the helicopter. The engine is using a ton of energy (fuel) to create that force (thrust)... but since the thrust isn't moving the aircraft, the thrust isn't doing any work. Therefore, there is zero Thrust Horsepower.
If that is the case, again I say that the helicopter example is a bad one. Because measuring THP for a helicopter is useless. Again helicopter POH's have very clear performance graphs that display hover in/out of ground effect charts to prove this. (Yes I know that these are a chart to provide a guide as to the helicopter performance based on expected SHP vs weight given certain Dalt)
How is the helicopter a bad example? I think it's more your 'feeling' that since the engine is producing thrust to keep the aircraft hovering in the air, it must be doing work on the aircraft. I can see how people can think that way - but it isn't correct.
I think in a scientific calculation you would say that although an engine is producing SHP there is no THP because we haven't gone anywhere, but in reality (a practical sense) you would simply describe that there is insufficient SHP being applied to create enough Trust to provide movement.
This is exactly how things get screwed up and taught wrong in the first place! Science IS reality and a theory isn't just some made up thing that a scientist came up with late at night! What happens is someone who doesn't have a physics/engineering background decides that it makes way more sense to explain something their way and so they do. Two problems with that: 1) Have you ever played telephone? If you have, you'd realize that after a few people, the message isn't the same anymore. 2) There is only so much that can be done to simplify something before you actually start 'lying'. And that person doesn't have the physics/engineering background to be able to know which parts could be simplified and which ones can't. The Hydraulic-electric analogy is an example of this:
Hydraulic analogy - Wikipedia, the free encyclopedia. It works well for explaining the basics to someone because most people are familiar with water, etc. But there is a point when teaching electricity that there aren't any analogies that accurately describe what is going on. You enter an area where all the concepts are new and different in ways you wouldn't imagine. This is a video I think is quite funny... because it's true!
Armstrong & Miller Physics Special - YouTube
Another example is the forces in a turn. There is a book currently published by Transport Canada that depicts the forces in a turn incorrectly. It shows that all the forces are balanced. A little bit of physics will tell you that in a turn you're constantly accelerating since acceleration is related to velocity and velocity has two components: speed and direction. If you're changing speed, you're accelerating (either positively or negatively). The same goes for direction. In a turn, you're constantly changing direction and, therefore, you're constantly accelerating. Looking at Newton's laws you can see that F=ma. If a mass is accelerating, there must be a net force acting on it. A net force means that the forces CAN NOT be balanced! I had a Class 1 Flight Instructor tell me that we should be teaching it that way because it's "easier to understand", after I explained that it was completely wrong. I never did teach it their way and never had a problem. This Class 1 FI didn't have a good understanding on a number of other topics as well.