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Something I´ve been wondering for a long time:

At what point during a flight is the stress on an airplane the highest? Is it during take-off, landing or during (light/moderate/severe) turbulence?

With "stress" I mean the load applied to the aircraft structure.

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Landing - stress is highest on the pilot, because he/she can't afford to be too fast/too slow, or too high/too low.

Takeoff - stress is highest on the engines. They are at full power and have to hoist a heavy aircraft as high as possible in as short a time as possible.

Cruise - stress is highest on the airframe when encountering up/down drafts at cruising speed (bumpy air). Look at it this way, every plane in level flight, for a specific weight and configuration (flaps, etc.) has a stall speed. That is the slowest speed at which it can support its own weight. If it is going twice that speed, it can support four times its own weight (and the passengers will feel 4G, and it can go negative as well). If it is going three times that speed, in principal its wings could support nine times its own weight if they were strong enough. Typically they are not strong enough, and they will break instead, if they encounter a strong enough updraft or downdraft. That is why every aircraft has a particular speed, a fairly low speed, called "maneuvering speed", that they slow down to if they stupidly stumble into a storm cell. At that speed, there is no amount of up or down draft that can cause structural damage. Technically, it's the speed at which maximum control deflections cannot cause structural damage. Remember the accident in Far Rockaway NY? The pilot tore off the tail fin by stomping the rudder pedals too hard from one side to the other.

By contrast, military fighters and aerobatic stunt planes are built for high-G turns (12G is possible). You can see, since available lift is proportional to velocity squared, it is not at all difficult to go fast enough to get that kind of lift.

Also, don't forget a jetliner is a pressurized air bottle, for high-altitude flight with passenger comfort. It cycles from un-pressurized to pressurized every time it climbs to cruise altitude and back. This has been known to cause metal fatigue cracks, resulting in some accidents.

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Short answer: when there is severe turbulence since the wing carry-through structure has to support the plane weight plus high amount of acceleration/deceleration torsional forces.
Long answer: It depends on the aircraft and what it is doing.
A military aircraft and UAV will need to support heavy forces during high speed maneuvers. At high speeds, also you need to consider shock waves and high temperature differences too.

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The highest stress on the crankshaft is during takeoff. The highest stress on the reciprocating parts is in a low power situation aerodynamic load on the propeller is turning it faster than the power setting would. Or to state it another way: where the aircraft is pushing the prop. Since reciprocating parts failures are more common that crankshaft failures, it's fast glides, and quick power reductions that put engine output below what is needed for the airspeed your at.

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