If the plane is stationary, then according to the questions rules, the conveyor belt must also be stationary.
So you can not have the conveyor moving at a speed which keeps the plane in a static position or the rule is broken. That means the plane must move forward so that the conveyor belt can move at the same speed as the plane. But it is impossible for the conveyor to be moving at the same speed as the plane without the plane stopping which means the conveyor would also have to stop. Therefore the questions premise that the conveyor would accelerate at the same speed as the aircraft would be impossible to achieve under the rules of the question. It’s a dumb question.
Ok the question is kind of flawed. First of fit says that the speed of the aircraft is measured. I assume this is measured in relationship to the entire earth and not to the conveyor belt.
If that is true then if the plane needs X speed to get airborne then the conveyor belt would be moving at the same speed. The only thing that would change is the rotational speed of the wheels. The wheels would effectively spin twice as fast as they originally would. I assume the conveyor would be the length of a typical take off distance. That being said it might take a slightly longer time to get airborne and slightly more energy to spin the wheels at twice the speed. We know that the added resistance from the wheels wouldn’t really be significant compared to the air resistance of take off. I believe the wheels to be over engineered for take off and would handle the extra time and twice the rotational speed. This is really the only question. Would the wheel function at twice the normal rotational speed at take off. This is an important question and it would depend on the tire. For example a 747 landing gear is has a 148" landing gear, I have no idea if this is properly inflated or the diameter as it spins at twice take off speed. Lets assume it expands to 150" and the take off speed of 180 miles per hour, which means the conveyor and the outside of the wheel would spin at 360 miles per hour.
180 miles * 5280 = 950400 FT per hr / 60 = 15840 ft per min / 39 = 406 rpm, which is pretty fast for a an inflated rubber tire.
thus 360 miles would be 812 RPM.
but really it comes down to the rubber and reinforcement at the outer diameter can resist the desire to fly off at 360 miles per hour. Seeing that we know there are car wheels that can resist it we know they could make a wheel for a jet liner that could do it as well. The RPMs really don’t matter, I was just bored and wanted to waste your time and show off that I know pie to the 26th place. Of course I could of looked it up, but sadly I didn’t.
In any case I think the tires must withstand the intense force of landing an suddenly accelerating to 160 mph. So I believe that stock tires would be strong enough, but even if they weren’t,the good people at Bridgestone could make a pair of tires that could easily handle 360 mph. They make the tires for the 7e7 when they are first delivered.
I will e-mail them, I don’t expect a response.
In any case it comes down to the extra energy to spin wheels to 360mph and if they can handle it.
I’m sure that I’m going to regret jumping into this train wreck but I have a related question. Is a seaplane taking off upstream against a river a comparable situation?
Not really, as there is much more drag between a float plane’s pontoons/fuselage and the water than there is with the wheels of a conventional aircraft.
Hydrodynamic drag is a bit complex. Seaplane floats are designed to go from displacement (rowboat) to hydroplaning (water skier) mode. Taking off upstream allows them to plane at lower airspeed, which lowers drag. In still water, the seaplane spends a fair bit of it’s takeoff run getting the floats onto plane. Once the floats get “on the step” the seaplane accelerates much faster.
If the current were such that the seaplane were able to plane when stationary to the bank, then the takeoff would be possible in only the after-hydroplane distance.
Thus the river current helps shorten the hydraulic part of the takeoff run in the same way that a headwind shortens the aerodynamic part.
If the current were really, really fast, then there might be a problem that the hydraulic drag would be so high that the aircraft wouldn’t have enough power to reach flying speed.
It’s not much more “in Seine” than a giant conveyor belt IMHO. Just imagine that the river is below a dam that is letting out more and more water. And somehow, they’re not just releasing it but also pumping it faster and faster to increase the flow rate. Makes perfect sense.
Technically, the first post on this is correct, however I think everyone understands that the jist of the questions was that if thrust. which would tend to move a plane forward at a given speed. was matched in the opposite direction with a conveyor moving the same speed…, etc etc.
It is not really a stupid question, but actually would make a good mind bender question for some people.
The reality is that no matter what speed the conveyor the plane is sitting on, the plane will be capable of taking off. If the plane were deriving it’s thrust from the wheels, and you sent the wheels spinning in a manner that would propel the plane, say 60mph, and the conveyor under it were travelling 60mph in the opposite direction, then yes, it would remain stationary. However, the plane does not derive it’s thrust from the wheels, which are pretty much free spinning (ignoring the friction of bearings). The plane derives it’s thrust from the engine thrust, pushing through the air, not against the ground.
One thing many people are not aware of is an airplanes ability to hover. When flying a plane which is capable of flying at a slower speed… say 60 knots, and that plane is meeting a headwind of 60 knots. then relative to the ground, the plane will be stationary. If under these conditions the plane is on the ground, it can take off, fly, and land without moving relative to the ground. I once saw a pilot, faced with landing in a 70 knot crosswind, turn the plane into the wind, match the air speed, and landed straight down perpendicular to the runway. If a plane is capable of flying at 60 knots, and is in a headwind of say, 70 knots… then relative to the ground a plane is actually flying BACKWARDS at a speed of 10 knots.
In the end, the speed of the ground is irrelevant. All that is required is enough thrust to make the air flow over the wings at a speed above stall speed.
Pretty much if you ignore the fact if the increased drag resulting from hydrodynamics. You can think of it as using the conveyor scenario with the wheel brakes on.
