Calculating load factor for airplane

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Hello!

When calculating the load factor in a loop the formula is n=V^2/(g*R)+cos(teta) during pull-up of a loop and another formula is n=1/cos(phi) during a level-flight banked turn. How does one combine these to calculate the load factor during a twisted loop?
 

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.Scott
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When calculating the load factor in a loop the formula is n=V^2/(g*R)+cos(teta) during pull-up of a loop and another formula is n=1/cos(phi) during a level-flight banked turn. How does one combine these to calculate the load factor during a twisted loop?
The problem is that you need to be more specific on what this "twisted loop" is. The load that you are calculating for the bank is not the load going into the bank, but the load you have once the bank is established. At that point you are not gaining (or losing) altitude. It is not obvious how that would combine with a loop.

There are several aerobatic maneuvers that are like a loop. The first is a barrel roll. That would have approximately the same loading as the inside loop.

The second would be an Imellmann where the loop is interrupted by a roll. Note that fully rolling while following the path of a loop is not possible because once the wings are pointed directly towards the center of the loop, the plane can no longer significantly accelerate towards the loops center.

The third is a snap roll. In that case, one wing has essentially no loading, the other has quite high loading. If done a maneuvering speed (as it should), that wing will be close to maximum loading.
 
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You can find resultant acceleration using vector addition.
 
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Given a flight path, you can determine accelerations and the associated load factor (remember that a rolling airplane will have different forces on each wing). But only very simple, idealistic maneuvers are calculated as you are trying to do. Calculations for general maneuvers are done the other way around. The aerodynamics gives you forces from which the accelerations and load factor can be calculated. Then the flight path is calculated. There is no point doing calculations for maneuvers that the airplane aerodynamics can not do.
 
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...a rolling airplane will have different forces on each wing
Roll, yaw or pitch rotations per se don't affect load factor. You are only concerned with the acceleration of the airplane's center of gravity.
 
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Roll, yaw or pitch rotations per se don't affect load factor. You are only concerned with the acceleration of the airplane's center of gravity.
I stand corrected. I was thinking of normal load.
 

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