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Out of turns, stalls and climbs, which of the basic maneuvers increases the load factor on an airplane as compared to straight and level flight?

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The load factor of an aircraft is given as the ratio of lift to weight.

i.e. $n = \frac{L}{W}$

So, an maneuver that changes any of these two forces acting on the aircraft causes a change in the load factor. Usually, it is the lift which is considered the variable.

Consider an aircraft in a level turn. In addition to the lift and weight, the aircraft experiences centrifugal force, which is counteracted b the horizontal component of the lift.

enter image description here Courtesy: www.rainierflightservice.com

For a bank angle of $\theta$, it can be shown that the load factor can be given as,

$n = \frac{1}{cos\theta}$

So, as the bank becomes 'tighter', the load factor increases. A load factor greater than one will cause the stall speed to increase by the square of the load factor.

Basically, as the load factor is increased, the aircraft minimum speed should be increased to prevent stall.

For aircrafts in steady climb, the principle is essentially the same.

enter image description here Picture Source: classicairshows.com

Here, the weight is less than the lift and as such, the load factor is (slightly) less than one.

As the aircraft stalls in level flight or unaccelerated straight climb, the lift becomes zeros and the load factor also becomes zero.

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I'm assuming you mean structural loading, not things like passenger loading. If you think about it generally, ANY maneuver or change of configuration changes the loads on an aircraft. I would also contend that any change in loading "increases" the load on at least some of the components of an aircraft. As an example, "reducing" the G-loading on an aircraft that is in straight-and-level flight by pushing the nose down will increase the load on other parts of the airframe even though the "net" loading on the aircraft has decreased.

As to which maneuvers generate more loading, it's completely dependent on the design and behavior of the airplane, as well as how aggressively the pilot has provided control input. I think many people would think that a stall provides more loading than a climb, but I've stalled a piper cub so gently that you could barely feel it - but if you pull a high performance airplane into a steep climb you can easily exceed 5g or more.

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