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If the aircraft runway were like a teaspoon (by this I mean, flat in the beginning, then curving downwards and finally upwards), would it not work in favor of the propulsion of the aircraft? In spite of this, why are the runways flat?

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The primary factor that determines the ability of an aircraft to takeoff is having a speed exceeding that of the liftoff speed: that is the minimum (air) speed of the aircraft to generate sufficient lift by its wings to counteract the gravitational pull from the earth.

Large passenger planes at takeoff often change the wing configuration (lowers flaps etc) to reduce the required speed: else you would need airplanes traveling at several hundred km/h before takeoff is possible.

The reason that prior to takeoff aircrafts often lift their noses is not to change the direction of travel! Indeed, since the aircraft is still on the ground, it is only traveling horizontally. The lifting of the noses is to increase the angle of attack of the wings relative to the direction of travel, thus further lowering the speed required for takeoff.

A runway designed like a spoon would not significantly affect the aerodynamics, if all else being equal. By having the plane go up an incline you are not increasing its speed nor decreasing the require liftoff speed. Hence it would not significantly improve the takeoff of an aircraft.

In fact, for the purpose of increasing the aircraft speed, it is usually better to have the aircraft going downhill instead for take-off: that is how many gliders are launched!

(There are, of course, exceptions. For example if the runway is built somewhere there is always a predominant wind, then pitching the runway to accomodate the wind direction may change the aerodynamics.)

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+1 Good explanation. The object is not to get lofted into the air. The object is to reach a speed and angle of attack at which the wings can carry the weight. –  Mike Dunlavey Jul 12 '12 at 21:42
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A problem I can see with this layout is that it generates a point (at the last upward curvature) for the plane to lift off. In general planes need different runway lengths depending on weight and type of the plane, as well as on external influences like wind.

I therefore assume(!) that a typical flat layout is suited for a wider range of aircraft, and also safer, as it is more forgiving to errors.

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If you are particularly short on space, and you have a consistent type (so speed and weight) of aircraft - you can add a ski-jump to help convert the forward speed into vertical lift.

enter image description here

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I'm not completely sure, but I'm pretty sure that this image is of an Harrier (en.wikipedia.org/wiki/Harrier_Jump_Jet), an aircraft that can takeoff vertically... –  J. C. Leitão Jul 12 '12 at 21:36
    
@J.C.Leitão: Right. Its weight is supported on its downward-thrusting jets (as you can see from the severely downturned flaps and tail), which is assisted by some upward acceleration from the ramp. Check the 2nd sentence here. –  Mike Dunlavey Jul 12 '12 at 21:57
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@J.C.Leitão - it can take off vertically but it costs a lot of fuel and limits the payload you can carry and these carriers don't have catapults so the ramp gives you more lift at the relatively low take-off speed. –  Martin Beckett Jul 12 '12 at 23:37
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@Martin Beckett I'm not invalidating your argument, but this factor is relevant for the discussion, mainly because the lift of this aircraft is completely different from standard. –  J. C. Leitão Jul 13 '12 at 3:17
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Not "vertical lift" (at least in the case of non "jump" jets); it should be "vertical momentum". In the PDF document @Martin linked to, on p.4: "When the Navy first considered using inclined ramps, the objective was to reduce or eliminate the aircraft sinking below the carrier flight deck ... The aircraft leaves the ramp with a vertical velocity ... The speed, however, is below the minimum level flight speed, so the aircraft is not able to maintain its upward velocity. The vertical velocity decreases as the aircraft accelerates and at some point the degradation is stopped." –  Willie Wong Jul 13 '12 at 6:50
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