How to determine individual wing loading of a triplane for stress analysis?

Question

How to determine individual wing loading of a triplane for stress analysis?

I understand that a monoplane must be able to withstand the weight of a plane x a load factor, say n=4, for a standard flight envelope, and also asymetrical loading.

What about triplanes?

Should each wing carry 1/3 the load?

Assuming 1 deg decalage each for the 2nd and 3rd top wings, they will stall before the bottom wing.

But.... you could have a situation where the top wing is stalled and the bottom 2 wings see the full load of the plane

And... you could have a situation where the top 2 wings are stalled, and the bottom wing is subjected to the entire weight of the plane.

So.... how strong do you have to make each wing of a triplane? Of course, if the plane has struts, all 3 wings would be part of the equation.

My gut feeling is that the top wing should be 33% loading, middle wing 50% loading, and bottom wing 100% loading, and then model the wings as 3 joined cantilevered beams.

Is this correct?

Answer 1

A stalled wing will still produce considerable lift, so it is not on - off. That said, the best you can do is to model the lift distribution at least in a vortex lattice code which correctly computes the mutual interference. This will give you very good results for attached flow and unstalled wings.

But triplanes have successfully been designed before the availability of computers, so for a first approximation distribute the load according to the wing incidence. Lift will be proportional to the angle of attack of each wing, calculated from the airfoil's zero-lift angle. Stagger will increase the local angle of attack of the forward wing and vice versa. How much depends on the ratio between stagger and vertical wing distance. The first solid theory of lift distribution was developed by Ludwig Prandtl and his pupil Max Munk, whose tabulations can be found in NACA Report 458 which is for biplanes but can be extended for triplanes.

If you like more recent literature: Even a publication from 2009 refers to Munk's tables, so they should still be relevant today. However, it finds a lift difference between positive and negative stagger that – according to Munk – should not exist.

Note that with struts and inter-wing bracing the whole triplane is your bending beam and will collectively carry the lift loads. Only with cantilevered wings will you need to worry about the root bending moment on individual wings. Bending between struts needs still to be carried by the single wing but will be small compared to the root bending of a cantilevered wing.