Ya I thought I might have TAS and ground speed mixed up…
so in the 50 kts headwind at takeoff the IAS would be 100 kts and the ground speed would be 50 kts…so what is the TAS?
Found it.
Basically, the speed at which air molecules are zipping past the airplane.
IAS is just a bit trickier, since it depends on air density (at a given true airspeed, lower density implies a lower IAS). Basically, IAS has to do with the air’s ability to exert force on an aircraft.
Aeroplanes propulsion is from moving air. This has been mentioned a million times. A plane propelled forward on top of a countermoving belt is not the same as a boat propelled forward on top of a countermoving water current.
You can completely stall a boat by throwing at it a water current of equal velocity to the boat’s maximum attainable velocity in still water. To stall an aircraft, you would have to throw a headwind at it at the aircraft’s maximum attainable velocity in air. Obviously a conveyor belt cannot create such a headwind, unless we are talking viscous flow inside a tube, which really isn’t in the spirit of this thought experiment.
I am not discounting the effect of the conveyor belt on the forward movement of the plane. Meanwhile we should not overcount it. There seems to be a wrong perception that an increased belt velocity would require an increased engine output to overcome. This is not the case, as friction caused by the belt is a function of the plane’s weight, not the belt velocity. You can increase the belt velocity infinitely but since the friction is not a function of this velocity, the backwards acceleration of the plane is always the same. Guess what? The magnitude of this negative acceleration is exactly the same as the one you would encounter if the plane was on flat ground. After all, the belt is made of the same material as a flat runway, as per the spirit of this thought experiment.
If the aerospace engineers gave the plane an engine that could overcome ground resistance, then the plane can overcome the belt resistance.
I am going to pre-empt a question: “What if the belt is moving at 999,999mph? After awhile, wouldn’t the aeroplane be moving backward at say 100,000mph?”
Eventually it would reach 999,999mph, if we disregard alot of real-world physics. This is because the plane is being accelerated backwards by friction at the belt/wheel interface. Yes, the wheels would always be running close to 999,999mph, but the plane would start slow and accelerate slow, and the engine will always manage to overcome this negative velocity and propel the plane forward at take off velocity eventually. This negative acceleration is a constant, like I said, and it is the same if the belt were moving at 50 or 50,000mph. It is also a small value because that’s what wheels are supposed to do: keep kinetic friction low. This small value is the exact same value you would encounter if the plane were rolling on a flat runway. This same value was considered by the aerospace engineers who built the plane. ie, If the plane can take off on a runway, it can take off on a countermoving belt moving at any velocity.
This is a good point. If an airplane had skids like a helicopter, it would probably have a lot of difficulty overcoming the drag on the runway to begin takeoff, and if it was on a conveyor belt, it would be much harder to reach the airspeed necessary to provide enough lift for take-off. Because it has wheels, that drag is minimized, and forward motion is possible. Any drag from a conveyor belt is likewise minimized.
“Stall” isn’t the best word to use here, as it has a specific meaning in connection with winged aircraft that isn’t related to retarding motion across the ground.
You can think of IAS as the rate at which air *mass *is flowing over the wings. That’s really what’s holding the airplane up, and why IAS at stall is independent of altitude. Lower TAS and higher density can give the same IAS as higher TAS and lower density, if those give you the same mass air flow.
Only if you assume that the tires and the bearings don’t give out, which they damn well will at 999,999 mph.
If we are operating in a universe with a conveyor belt that can go 999,999 mph, I am sure they also have wheels and bearings capable of withstanding such speeds.
DanBlather said:
It’s a bit of a competition between inertia and friction. If the speed transition is slow, the friction can possibly overcome the inertia and the plane start moving. If the speed transition is quick, inertia wins and the wheels just roll.
Kinda like the old magician’s trick of removing a table cloth but leaving the place settings in place. How? Give a quick, solid yank on the table cloth. Inertia keeps the dishes from moving and overcomes the friction with the cloth.
If an airplane is sitting on a conveyor belt with the engine off, and the conveyor belt starts to move, and it accelerates slowly, the plane will probably start moving with the belt. Then start up the plane engine.
If the conveyor belt is moving the plane forward, it is providing forward speed, which translates into airspeed over the wings, so the airplane requires less thrust to get to the takeoff point. However, as soon as it leaves the belt, the engine will need to ramp quickly to proper thrust, or the plane will not maintain airspeed and will drop back onto the belt, have some skidding until the wheels grip and bearings spin in sync, then when proper thrust is achieved the airplane will take off again. So if one doesn’t want a bouncy take off, one should get the engine to proper thrust before lifting up rather than going early.
If the conveyor belt is moving the plane backward, it is providing backwards speed, but as soon as the engines start pushing air, the wheels will start spinning and the engine will overcome the belt drag. Then the plane will proceed to take off as normal with the wheels spinning extra fast.
It all comes down to assumptions. If you have a magic treadmill, but a real world plane, you can keep it down. Actually, if you created a treadmill that could apply enough force through the wheels to keep the plane from moving it would not be stationary, it would flip (picture what would happen if you tied a chain to the wheels and hit full throttle). So to keep the plane stationary you need a magic treadmill (impossible speeds and accelerations with no air dragged back over the plane) and a partially magic plane (wheels that don’t break down but aren’t frictionless, and a profile that puts the wheels in line with the propeller).
New here. Reading this whole thread and came to a conclusion. I love science but I wouldn’t say I’m an expert. I’m barely a novice. I’m seeing a pattern though.
Originally the point was that if you could make a conveyor belt that exactly matched the plane speed or something. (honestly the math was a bit above me but I got the gist.) That the plane wouldn’t move and therefore no airflow therefore no lift therefore no liftoff. Ok fine.
Here’s my thing. I think the answers right. I think the question is wrong. It’s like Hitchhiker’s Guide. The answer to the meaning of life the universe and everything IS 42. The question however is wrong.
Most people seem to be answering the question “would a plane on a treadmill take off.” Answer: yes.
The second set of people seem to be answering a different question. Here’s the question I think they are answering. “If you nailed a plane to the F****ing ground could the plane take off?” They just seem to be complicating the way in which you manage to nail a plane to the ground. I would use nails. Heck even chains would work. Where they use a really complicated system involving really complicated math and really complicated physics when a simple nail would do.
So basically to me realistically a plane on a treadmill can take off. A plane nailed to the ground(motionless) can’t. Whatever method you use to keep it motionless
I think the problem description is sufficiently precise that only one answer is possible: “This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).” So if the plane is going forward at 30 miles per hour, the conveyer is going backwards at 30 miles per hour. The sole effect of such a conveyer would be a tiny bit of extra friction and extra wear on the wheels.
The trap people fall into is assuming the conveyer’s speed will match the linear speed of the wheels. That is not what the problem says. (And if it did, you would truly need a magic conveyer.)
unbelievable! mythbusters proved the plane will take off. the wheels of an airplane are free spinning in bearings. there is friction in the bearings, but it is minimal, not considerable. the scenario is no different than a plane with some worn bearings in the wheels. as long as the planes propellor produces enough thrust to overcome the friction in the bearings, it will take off. a plane can take off without wheels if there is a strong enough headwind, or if the plane is on the back of a truck moving fast enough. the only purpose of the wheels is to reduce friction on the ground during the take off. early aircraft used skids instead of wheels, with considerably more friction to overcome, but they flew. i guess people keep forgetting that the free-spinning wheels isolate the plane from the ground.
Was that in response to any particular post, or just stream-of-consciousness?
just tired of hearing about this inane supposition from many sources.
Alan Molumby comments over at chicagoreader.com:
… and suggests that Cecil ignores the point of version 1.
But, as we’ve established, the answer to version 1 is trivial to anyone who understands aerodynamics.
Powers &8^]
… and, I should point out, nothing in the original question suggests that the plane must be kept stationary! So I see no reason to even consider “version 1”, since it’s clearly not what the question is asking.
Powers &8^]
As we have beaten to death, the original question is not clear. The part about the treadbelt matching the speed of the plane or the speed of the plane’s wheels is misleading/confusing.
If the question is 1, that is stupid. No, if the airplane is chained to the ground, bolted down, or put on a magic treadmill that prevents the fuselage from moving, then the airplane cannot take off.
If the question is 2, there is no treadmill that can prevent the airplane from taking off.