L=1/2 ρv2 Sref CL where: L denotes lift force. V defines the velocity of aircraft expressed in m/s. ρ is air density, affected by altitude. Sref is the reference area or the wing area of an aircraft measured in square metres. CL is the coefficient of lift, depending on the angle of attack and the type of aerofoil. Velocity is measured as the air moving over the wing (ie, possibly by a pitot tube)
Well, its been months (years) since I chimed in but apparently it's still confusing to some. Imagine you are standing next to the conveyor (not on it) and holding a stick with a wheel on it like the ones contractors push along the ground to measure distances. Stick that wheel on the conveyor while holding the stick firmly. The wheel will spin like crazy according to how fast the conveyor is moving. If you don't believe you can hold the wheel stationary while it spins like crazy and the conveyor moves rearward under it, then don't bother reading further as there is no hope for you. Now imagine that instead of standing next to the conveyor you're in a car with your arm out the window and the wheel on the conveyor. I guarantee that as the car moves forward the wheel will also move forward albeit now spinning even faster (forward movement plus rearward movement of the conveyor). If your arm is enough to hold the wheel stationary, then your arm and a car's engine is enough to move it forward. And now instead of sitting in a car, imagine a 2000 hp radial engine strapped to the front of your body while you're holding the wheel on the conveyor. Got to get it through your mind that there is very very little friction between the wheels and the conveyor and hence very little effort is required to overcome that friction and let the planes wheels move forward under power. Yes the conveyor will speed up as the plane moves forward but the plane doesn't care as it has no problem overcoming the friction. It will reach take-off speed in essential the same distance as it would on a concrete runway. The propellors pull the plane forward, not the wheels. They only keep the belly from rubbing on the ground (now that would be a mess of friction).
So..why not install treadmills on aircraft carriers..rather than the classified operations of the steam catapult? Think of the money that could be saved..set that f16 on the mill..and let her go!! I get they have to land..but the arrestor cables still do their job.. The plane can't move forward..as the question is worded. It will not fly as it cannot produce lift. If you took a car on a treadmill..put your arm out the window. The treadmill exactly cancels the wheels forward movements..car is stationary..does your hand get pushed back like it would if you were traveling at 60mph on a regular road?
You guys just don't get it. An airplane, unlike a car, does not move because of its wheels. They are free-wheeling. An airplane moves because of the thrust produced by its engine/propellor. An airplane can take off from any nominally smooth surface, be it water (with pontoons), dirt, pavement, conveyor, ice, etc, because its engine/propellor accelerates it forward eventually producing enough air speed (not ground speed) to generate sufficient lift to fly. A seaplane can take off from a river flowing in the opposite direction of its intended take off direction. Actually a plane can and will lift off if a strong enough wind is blowing head on at the plane. The only obstacles a plane needs to overcome is the drag produced by atmosphere and the drag produced by the friction between its wheels (pontoons) and whatever surface it is on, and have sufficient lift to counteract the effects of gravity (i.e., its weight). Both sources of drag (atmospheric and surface) are grossly negligible compared to the thrust produced by its engine.
A car uses it's wheels and the friction between them and whatever surface it is on to create forward momentum, a plane does not use it's wheels for anything other than keeping the rest of the airplane off whatever surface it is on. A catapult is attached to the airframe and propels that airframe, a conveyor is not attached to the airframe. Airspeed is airspeed edit: hopeful beat me to it...
Umm..the catapult..pushes on the wheels or gear. To move forward..you need a stationary object to push against. The conveyor is not stationary.
the catapult does not propel the wheels, but they do come along for the ride. what would a conveyor do to an object (could be a plane) with wheels but the hubs had zero friction? Everything would also be level. i think you are pulling our legs here? the conveyor is most definitely stationary, the conveyor belt is not. A reverse of this is a piece of equipment with tracks. What is the ground speed of a bulldozer track if the dozer is moving at 5 mph?
Ok..the conveyer matches the speed of the plane. The wheels are attached to the plane. No matter how hard the engines push the plane forward..the plane does not move because it gets canceled. It can't lift off..it has zero ground speed. I understand..if the plane had zero wheels and the thrust pushed the plane along the runways on its belly..it would indeed eventually take off. That is clear. The aircraft doesn't really need the wheels to take off..but it's so much nicer.. But because the plane is attached to the wheels..any forward movement by thrust..is canceled by the conveyer..because the plane hasn't left the ground yet. The only way the plane flys.. is if it moves faster than the conveyer so it can create lift. Other than that..it's stationary.
This has been repeated a billion times and I agree. It seems some are just incapable of understanding this.
The way the question is written, the tire and conveyor speed both have to go to infinity the moment thrust is applied.
I've offered alternative explanations that meet the criteria of the question. End of the day it doesn't matter how it is worded, a conveyor is incapable of holding an aircraft stationary. People however believe that isn't the case because both an airplane and a car have wheels.
Would the plane take off if it had all wheel drive? A propeller plane would do it if you put tire chains on the propeller. More traction, you see.
Still that would require the wheels to move faster than the conveyor. The limitation is not placed by the inability of a plane to take off on a conveyor belt but by the question imposing an impossible restraint of the conveyor matching the wheel speed.
It's not impossible. Plane applies thrust. Conveyor matches airframe speed. At the point the aircraft reaches takeoff speed, the aircraft, tires and conveyor are all going exactly the same speed. The conveyor is moving in the opposite direction of rotation. That cancels any wheel rotation of the aircraft, all speeds/criteria match.
That’s a different situation and not interesting. If the conveyor belt is matching the speed of the wheels, as specified in the original post, the aircraft is not moving relative to the air.
I'm sorry but you have zero understanding of this. The plane would require the same take off distance.
It exactly matches the question and meets all criteria. Conveyor exactly matches the speed of the wheels and is moving in the opposite direction of rotation in order to do so.
No if the conveyor belt is matching the speed of the aircraft in the opposite direction, the wheels are going twice as fast.
Wrong. The question states the conveyor is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of -Rotation- .....NOT moving in the opposite direction of the aircraft, there's a difference. The conveyor moving in the opposite direction of wheel rotation cancels wheel rotation as it exactly matches it's speed. So, aircraft gaining airspeed? Check Conveyor matching speed of the wheels at any given time? Check Conveyor moving in the opposite direction of rotation? Check If the conveyor was accelerating the wheels it would be moving the same direction of rotation and the speeds could never match. -Fails to meet criteria.
I see how you’re interpreting it, but in your interpretation the wheels are not rotating at all because the conveyor belt is traveling at the same speed as the aircraft, in the same direction. Rotation has an axis not a direction, so it’s just ambiguous as to which they intended it to be interpreted as.
