# Is there an equation to solve for bank angle using load factor and wing loading as variables? If so, what is it?

The problem is that I'm looking for both wing loading and load factor as variables to solve for bank angle and cannot find any equation that represents this. After searching various websites and not coming across the right equation, I asked an A.I. chatbot. It gave me the following equation:

$$\theta ≈ \arctan \frac{1}{N​⋅\frac{W}{S}}$$ $$\theta$$ = Bank Angle

$$N$$ = Load Factor

$$\frac{W}{S}$$ = Wing load, Total Weight of Aircraft ($$W$$) divided by wing area ($$S$$),

However, when the load factor input increases, the denominator increases, making the bank angle smaller. Wouldn't a higher load factor equate to a greater bank angle? What would the correct equation be?

• I don't think your formula is correct, see this question Nov 3, 2023 at 13:48
• "I asked an A.I. chatbot..." Well, there's the first problem. The current state of AI "chat" is an answer that sounds right, and actual veracity is an occasional byproduct of that, nothing more.
– Ralph J
Nov 3, 2023 at 13:56
• Does this answer your question? How can I compute the minimum possible bank angle for a turn with a given radius? Nov 3, 2023 at 14:00
• Consider that load factor is a multiplier for the weight of the aircraft, and as such it doesn't care what that weight happens to be. A heavy and a light aircraft flying the same path (i.e. maintaining the same bank angle and speed) will have the same load factor, regardless of weight (or wing area).
– Ralph J
Nov 3, 2023 at 14:01
• Wing loading would have nothing to do with it. You can put it as a term in your equation if you want, as long as you make sure to multiply be zero! Now if if you are trying to solve for turn radius, and airspeed isn't a variable but lift coefficient is -- then the wing loading would make a difference. Nov 5, 2023 at 2:46