How the question is different from asking a ppl during the training to accelerate from 60kts to 90kts while in the air?
Of course if you have a car style engine driving the wheel it will not fly…
Ps: Wolfgang Langewiesche has written a book that explains how airplanes fly if the student is lazy to write Newton laws of motion, fluid dynamics…
Peter wrote:
The belt is irrelevant. You could replace the landing gear with magnetic levitation, etc.I have seen some Turbs on skis
I think the biggest thing is that most people don’t realise that the landing gear (and thus the conveyor belt, and the entire discussion around that) are irrelevant – because the engine thrust acts purely on the airframe mass, so is bound to accelerate the airframe forwards. The wheel bearings will ensure the wheels rotate freely and don’t hold things up.
So the plane will get airborne just fine.
The bad wording of the problem (around the way the conveyor belt moves relative to the wheels) is just an irrelevance, probably designed to throw people off the scent, way back when this puzzle was originally posed
What I find interesting is that the majority of pilots and probably a majority of instructors don’t realise the irrelevance of the landing gear.
There is confusing wording and spooky set-up, this problem is designed to have both 
Unless the set-up is clear, you can’t draw and analogy, when you say “engine thrust acts purely on the air-frame mass” (which 100% true*), then you counter argument “why I don’t accelerate with foot on breaks (true on dry tarmac set-up)?” and then you counter counter argument “why you still accelerate with foot on breaks (true on wet muddy grass set-up)?”…
I found the same confusion sits during flying instruction: what the instructor means by “lift”? what is the role of the trim wheel? why talking cross-wind when the ball is centred?…
Even with technical background, you “get intuition” using approximate analogies (e.g. driving cars, sailing boats…) but you only “get it” by flying something different (e.g. gliders, balloons, slower/faster aircraft…)
For (*), it seems obvious in the air but on the ground? full-power and stick fully forward: the nose/propeller will hit the ground irrespective of what sits bellow or how she sits…
why I don’t accelerate with foot on breaks
Because the brakes lock the wheel bearings. This whole thing hangs on the wheel bearings being able to rotate, otherwise it becomes absurd
Peter wrote:
What I find interesting is that the majority of pilots and probably a majority of instructors don’t realise the irrelevance of the landing gear.
If there is friction in the landing gear — and it always is — it is not irrelevant.
Landing gear friction is minuscule compared to the thrust generated by the engine/propeller (or fan in the case of a jet). Last weekend I put new mainwheel tyres on my aircraft, and as part of the process, cleaned the wheel halves including cleaning and regreasing the bearings. With the wheel on but the plane still jacked up, I spin the wheel with my hand to make sure it will rotate freely, and if with a small low-effort hand movement I can make the wheel spin for several revolutions (maybe my hand spin had a power of a couple of watts max), then under anything resembling normal conditions, 120kW of power from the engine isn’t going to notice the few watts taken by tyre flex, the drag of the wheel bearings etc. Even at twice normal takeoff wheel rotation speed, landing gear friction will be minuscule to the extent it would be difficult to measure.
It’s only in the xkcd #3 scenario where any acceleration makes the conveyor belt want to accelerate to infinite speed that landing gear friction will have any import, and even then not in retarding the aircraft by friction – the tyres will probably have exploded from excessive forces long before the friction can set them on fire.
Why would a pilot want to take off a conveyor belt?
alioth wrote:
Landing gear friction is minuscule compared to the thrust generated by the engine/propeller (or fan in the case of a jet)
At normal speeds, of course. But here we are making a thought experiment with a conveyor which does not seem to have any physical limitations.
AfricanEagle wrote:
Why would a pilot want to take off a conveyor belt?
Don’t spoil the fun by making serious questions.
Stickandrudderman wrote:
Wheel ROTATION speed will be zero because every time it attempts to rotate the conveyor will counteract the rotation.
If engine thrust is sufficient tyre friction will be overcome and if enough conveyor belt length is available then flying speed may be achieved before fire consumes the undercarriage.
I don’t expect the conveyer belt to be required to be much longer either. The only difference is the tyre rotating at a higher speed, and whilst that adds a little rolling resistance and bearing drag, the surface type and hardness will make a much greater impact. I.e. soft field versus paved runway.
In other words, the question is designed to trick the reader into thinking that the plane will be stationary because the conveyer belt moves the opposite way at exact the same speed. However because the plane is not driven by the wheels, nor is it affected much whichever way the wheels rotate on their bearing, it will take-off almost like normal.
