For an aircraft to maintain altitude in a level turn, total lift has to be increased, because the vertical component of lift is only the cosine of total lift.
Load Factor is the ratio of total lift required to vertical lift. Therefore, it is the reciprocal of the cosine of the bank angle (also called the secant).
"Three times as heavy" corresponds to 70.5 degrees of bank angle!
"Four times as heavy" corresponds to 75.5 degrees of bank angle!
By changing the bank angle from 0 degrees to 60 degrees you are putting an additional 100% of gross weight on the wings (200%, 2 x gross weight). By changing the bank angle from 60 degrees to 70.5 degrees (just 10 degrees more!) you are putting another 100% of gross weight on the wings! (300%, 3 x gross weight) And by changing the bank angle from 70.5 degrees to 75.5 degrees (just 5 degrees more!) you are putting another 100% of gross weight on the wings! (400%, 4 x gross weight) Any bank angle larger than 60 degrees is definitely DANGER ZONE!
Load Factor = total lift / vertical component of lift (that's also 1 / cos(bank angle))
Centrifugal Force = sin(bank angle) x total lift (that's also tan(bank angle))
Note: Load Factor and Centrifugal Force are sometimes explained with Weight and Load. In a level turn weight equals vertical component of lift, and load always equals lift, as they are equal and opposing forces. With weight and load you have the vectors "under" the plane, with lift you have them "above" the plane. We have chosen the lift-based representation here, but you get the same behavior if you use the weight-based representation.
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