I'm going to come over all sarcastic, I think, but I'm wondering if you aren't coming up with the right (FCVO "right") answer for totally erroneous reasons. Let's break it down/
If I remember this correctly, the engine is independent from the wheels, therefore the power comes solely from the props/jets;
This
is how planes work. Your memory does you great honour, sir.
with that in mind, the treadmill also works as a compressed runway, matching the speed of the aircraft as it speeds up;
I
think you're imagining the runway as moving in the
same direction as the plane. Such that less (moving) belt is being used because it's "keeping up" with the plane. (c.f. the comment about "I don't know why they developed catapults" comment from that web-site, that I quoted a while ago... Sounds like you have the wrong end of the wrong stick, here...) Of course the amount of conveyor belt infrastructure (i.e. the fixed (but, of course rotating) rollers that guide the belt one way
or another) is going to be at
least as long as the standard static airstrip it is replacing.
(As an airstrip is normally not going to be
exactly as long as needed for a standard plane to take off from static ground. I'm going to say that a similar length of conveyor-top ('replenished' at the fixed front end as it moves backwards, of course) is probably going to be long enough even to deal with a slightly-more frictional take-off situation with an extra percentage point or two of friction through the wheels, so it would still be a safe take-off situation, albeit with slightly lower margins than before.)
overall, reducing the amount of takeoff (since the engine only moves faster, and any friction from the treadmill and the wheels drags it back more;
...except here you're ascribing to it some sort of air-moving ability? To provide an assisting headwind? Personally, I would assume unless there was mention of beltside-mounted baffles, or somesuch, that (except for a very close-to-ground(/belt) zone), that air (insofar as that which the airscrews/jets works against, and that the wings and other bits of fuselage move through) is not moving at all, w.r.t. stationary ground.
To that end, I still subscribe to it being a normal(ish) ground-length. But maybe a little longer (for the given friction factors) but no
shorter at all.
but only limited to the maximum friction relative to the weight of the aircraft itself (heavier craft yielding more friction, naturally)), and maybe even landing required for the plane on the strip.
I'm lost on this one. I'm assuming a same-weight aircraft under both standard and belt-borne take-offs. And landings aren't discussed.
That's at least as far as my understanding goes;
..and yet I don't understand your understanding, I think. Please correct me where I've gotten it wrong.
and the Mythbusters did do a pretty good job at tackling this myth, even illustrating the explanation above.
Can't see this (national limitations, on the Youtube link, cited), but as I understand it they dealt with it how
I see the problem, and succeeded, ICBW on the first count, though it does appear they succeeded at least.
(This interposting quotes thing is getting sillier than I might imagine, let's try it freestyle...)
And... no, no boost. And I'm assuming no wind (more
or less than over a stationary runway, at least). Airflow over the wings is proportional to absolute speed (forward), which is significantly unaffected by the equal (but opposite) absolute speed (backward) of the surface the plane is rolling over during take-off.
The treadmill cannot keep the plane still
at all, and you're falling into the trap some of the nay-sayers seem to have done. It (the conveyor) only travels backwards when the plane goes forwards. If the plane isn't travelling forwards then the treadmill isn't travelling backwards, thus even if it were a
car in the conveyor it wouldn't stop the car from moving. It would go as fast backwards (based on absolute stationariness) as the car is going forwards (based on absolute stationariness,
not based upon relative speed to the conveyor) and so at all times the attempted speed of the car would result in half this speed by 'absolute' measurement, the difference being the other half of the matched speed being that of the retrograde conveyor movement. Here, V
car wheels is equated to V
car absolute-V
conveyor absolute (which is
negative, thus it's just the sum of the two |V|s, thus the car wheels are going twice as fast as either the absolute car speed or the (equal) conveyor retrograde speed). But in a plane then you have |V
plane engines| equalling |V
conveyor|, only oppositely signed, with the plane's landing gear passing over the belt at V
plane engines-V
conveyor absolute, thus V
plane wheels == V
plane absolute-V
conveyor absolute == V
plane absolute+V
conveyor retrograde which is just another V
wheels=2*(|either V
absolute|). IYSWIM.
Friction to hold the plane down? No, sorry, I'm lost. Friction to make the plane
slower, I would understand. And consider either absent (in a simplified example) or sufficiently inconsequential (in a true-to-life example) to mean there's still no practical problem with take-off (maybe uses 10% more runway or something, plucking an arbitrary figure out of the air which is probably an exaggeration anyway).
...so, I'm probably looking very rude, but I wanted to make sure that there were no misunderstandings left.
To the continued nay-sayers, the possibility that the problem is "the conveyor moves backwards as fast as is needed to counteract (via exponential friction on the plane wheels) all forward force by the plane given by the engines" is a totally
different problem, I'll allow and would (assuming this does not also drag enough air across the wings at near-ground level to effect lift). But that isn't even the problem as quoted on page 1 of this thread, and I'm afraid you've got no chance of convincing me that it is. You're welcome to your answer to
your problem, but I'm (as you might be able to detect) quite agitated that anyone would think that this other scenario (or any
part of this scenario) is a part of the originally posited question.
Rant over? Maybe. (It wasn't
supposed to be a rant, but may end up looking like one, I'll allow.) Having gotten it (whatever 'it' is) out of my system I shall now do my best to stay quiet except for any direct challenge. But the mathematical adrenaline is still coursing through my veins, so I may not be accountable for any immediate reactions I might make.
(Still, I regret any perceived abrasiveness. Not my intention, but a possible interpretation nonetheless. [note=to self]Shut up about it![/note])