oggers:
I’d like to give you the benefit of the doubt but I’m afraid the suggestion that you were sitting on this knowledge about induced power (just when the aircraft was still, obviously, the rest of the time you call it THP) doesn’t quite dovetail with a lot of what you have written:
I don't care what you think. I was not sitting on that information. 'Induced power' had not entered my mine ONCE while in this discussion. Would it have been easier to mention induced power, you ask? No, induced power is how efficient thrust is made. It is not about THP. I do believe it adds another perspective to everything and it's great you introduced it but to accuse me of 'holding out' info is a bunch of bullocks.
Yes. That navy reference you keep using states clearly at the top that it is predicated on the assumption of “equilibrium flight”. That doesn’t include sitting on the ground. For that you need the alternative method of calculating power output from the book and the essay I linked to.
They stated those at the beginning so that they wouldn't have to keep repeating all the different conditions for every specific thing they talk about. It does not affect THP actually. For THP, it doesn't matter and here's why. THP has to do with
thrust and
velocity. That is it. There is no lift equation in there, lift was not mentioned once, weight was not mentioned once, for all intents and purposes, that aircraft can be assumed to be no different in this condition than in "equilibrium flight". If the TAS of the aircraft is zero, there is zero THP.
And no, it's not just an alternative method of calculating power output. It's a
different way. They aren't the same, oggers! I've already proved that with the difference in words and, more importantly, with the difference in equations!
Forgive me for labouring the point as you do seem to rely on that equation, but it assumes equilibrium flight as stated clearly at the top of your reference document. An aircraft on the ground is not in equilibrium flight.
See above.
OTOH, a helicopter in the hover [where you insist there is no THP] is in equilibrium flight. The aircraft itself is not moving but there is a velocity which is the induced airflow. You have acknowledged that there is thrust. Therefore you can apply the formula – weight x [velocity of induced air flow]. The result is THP. It has to be because it’s the power associated with the thrust. Although you insist there is no THP for a helo in the hover.
As stated a number of times, THP = thrust x
flight velocity (which is TAS) and it is NOT induced velocity!! You're mixing up all the equations and calling them all the same.
I'd suggest the THP is exactly the same into wind as it would be downwind and the earth has nowt to do with it.
You found a legitimate error, finally, so I would congratulate you for it, but I find it hard to do that because you didn't even realize that it was an error!
In the quote you used, I said THP is relative to the distance the aircraft moves with reference to the earth. That's incorrect. It's TAS, which is flight velocity and explicitly states as so in the Aerodynamics for Naval Aviators text. I made a mistake.
I'd suggest the THP is exactly the same into wind as it would be downwind and the earth has nowt to do with it.
That's how I knew you didn't know it was an error. You just happened to think and suggest something that was actually turned out to be true but, again, with no proof. If you really did know I had made a mistake you'd jump over the opportunity to prove me wrong, something you've been trying really hard to do this whole thread! You could have posted this picture that I've used a few times:
http://i.imgur.com/NXLV3.png, and tell me that it's flight velocity and not relative to the ground!
But I really don't care if you knew or not. I'm glad that you did point my mistake out to me. I'm just mentioning this because of you consistently trying to prove me wrong and then accuse me of holding out info. It's just a way of keeping track of what is going on. It's also to prevent you in the end saying "I knew it was wrong...".
Regarding my two, seemingly, different comments separated by a few posts: 1) There is no need to complicate the THP with special or general relativity. That's why I said that! 2) We started getting into more complex examples actually dealing with relativity and not THP anymore, so that's why I said that second comment. Without the context I've provided here, it does seem I'm a bit off my rocker... but I think that's what you were trying to show! Nice try
Now, getting back to this induced power and induced velocity stuff. Reference this propulsive efficiency equation:
http://i.imgur.com/NXLV3.png
I just realized that the bottom part is actually the formula for the 'induced power' that you provided. In the AfNA document they call it input power. On top is the output power and in this case, it's THP. I think that blows your whole "induced power = THP" out of the water!... again!
Check this out:
http://i.imgur.com/1Ev3y.png
That's from the Wikipedia page on Disc loading. You'll notice that they're calculating the power required to hover - which is what you've been trying to figure out all this time. Just like we've been discussing, Power = thrust x velocity. However, in this case, the velocity part is "induced velocity". If you read the AfNA document I posted, immediately before the propulsive equation part they talk about induced velocity. It is 1/2 the total velocity change of the air, and it is measured at the propeller. Since the helicopter is in the hover, the flight velocity is zero so you can take that term out of the induced power equation and you are left with: Induced power = thrust x induced velocity. And that's exactly what the Wikipedia page shows.
I hope now you can see more clearly what THP is and that THP is not induced power.
Not being sarcastic at all, I have to say thanks for introducing the talk about induced power. It's added more clarity regarding all of this for me.