The sketches at right show the horizontal forces at some point during the acceleration towards take-off: the propellor provides forward thrust to the plane. In this case, with these approximations, the question and answer are both simple. So the plane accelerates at its normal acceleration and, after a normal period, achieves its take-off velocity and then, with the usual values of flaps etc, takes off. Because we've assumed that the conveyor belt doesn't affect the air, these horizontal forces have their normal values. So, subject to our approximations, the horizontal forces on the plane are only the thrust of the engines and the drag exerted by the air. The moving conveyor belt starts to rotate the wheels but, according to our initial approximation of freely rotating, massless wheels and no rolling resistance, this requires negligible horizontal force from the ground. Let's start the plane's engines and the conveyor belt simultaneously. ( On the other hand, i f we make the conveyor belt the size of a planet, we end up with Question 3.) In principle, however, we could imagine this to be very small: there could be one very narrow belt for each wheel: these would not affect the air much, though it might require precise steering. In practice, the conveyor has to be very long and probably very wide and so will move air to some extent. Second, we assume that the conveyor belt does not create a wind with respect to the ground. We might even use hovercraft or maglev instead of wheels. In principle, however, we could imagine making this effect very small. This is obviously approximate: because of their mass and thus their moment of inertia, the wheels do require a force (and thus a torque) to make them rotate because of friction in bearings they require a force (and thus a torque) to keep them rotating because of the deformation of the tires there is a rolling resistance and this requires a force as well. First we assume that there is no rolling resistance, that the wheels roll completely freely and that they have negligible mass: therefore it takes no force to turn the wheels, even at high speed. We'll start by making two approximations, and then consider the effects of these effects more closely. Question 1: belt speed = normal take-off speed ( One could do this one experimentally with existing technologies.) Question 3: plane assumed stationary with respect to centre of the Earth.This requires looking at some of the same effects, but under very different – and difficult – circumstances.
( This one may not be technologically possible.) Question 2: plane assumed stationary with respect to ground.( Technologically, this could be done using an aircraft carrier instead of the conveyor belt, and a plane with a very low take-off speed, such as the Gossamer Condor.) Let's answer this first by making two approximations, and then deal with the approximations. Question 1: belt speed = normal take-off speed.We also assume that there is no wind (except later when we consider the wind that may be generated by the conveyor belt itself). The plane has wings (and other surfaces that we shan't mention further) that generate lift as air passes over them. The plane has either propellor or jet engines which push against the air, with negligible effect on the ground. Much of the confusion of the students who have asked this question, and the disagreements among them, can be traced to confusion over which (if either) of these conditions has been specified.Ī few assumptions first: Let's assume that the plane has wheels that roll on the ground, but that there is no engine to drive these wheels. Can the plane take off?Īs we shall see, these two sets of conditions are very different. The belt speed is controlled and it can move sufficiently fast that, with respect to the ground, the plane never moves forwards. A plane is on a conveyor belt which, when turned on, moves the plane backwards. If the pilot uses the normal amount of throttle and other controls, can the plane take off? A plane is on a conveyor belt which, when turned on, moves the plane backwards at a speed equal to the normal take-off speed of the plane. The question was asked with two very different conditions: It was written to answer an odd question put to me by several students. This page is an appendix to the Physclips page Vectors and relative motion. A plane is on a conveyor belt which moves in the opposite direction.
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