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Jul 27, 2003, 02:43 PM
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Justin Jackson's Avatar

Ideas? - Differential Equation for Stresses on the leading edge of a wing...

This ode doesn't have to be for a particular plane or a particular wing structure, I'm just looking for an equation that I can use to calculate the stresses involved in flying through calm day air from the edge of the wing nearest the fuse to the edge of the wing nearist the wing tip. Thanks for any help.

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Jul 27, 2003, 05:06 PM
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There are three kinds of stresses on the wing structure. There is the stress caused by the lift forces, the stress caused by the drag forces and the twisting stress caused by the pitching moment. All of these loads are distributed along the span. Solving for the stresses begins by finding the distribution of the forces and moment.

The lift forces on a wing, supported only at the wing root, are usually carried mainly by the wing spar and show up as tension stress in the bottom spar cap, compression stress in the top spar cap and shear stress in the web between them. There may also be buckling forces on the compression member that show up as additional stresses in the web between the spar caps.

A well designed wing often has a lift distribution that is a semiellipse between the wing tips. The shear is the integral of the load distribution. So an intregal not a differential equation applies. The bending moment is the integral of the shear. After the bending moment is found, it is divided by the distance between the spar caps to find the tension and compression forces in the spar caps. The stress in a spar cap is the force divided by the crossectional area of the spar cap.

So, you see, from this example, that stresses can not be determined independently of the specific dimensions of the spar. A deep spar will have lower stresses for the same lift distribution than a less deep spar. A spar with large cross section spar caps will have less stress than one with smaller crossectional area. Similar arguments would apply to the case of a sparless, stressed-skin wing structure but the calculations would be much more complicated because of the varying depth along the chord of the airfoil. The higher the aspect ratio of the wing the greater the bending moment and the resulatnt stresses near the wing root.

Similar arguments would apply to the stresses associated with drag but they are seldom calculated because thay are usually two or three orders of magnitude smaller than the stresses associated with lift.

The twisting loads on a wing are closely related to the mean camber line of the airfoil. The more camber the larger the pitching moment coefficient. The larger the pitching moment coefficient the greater the twisting moment. Also, the higher the aspect ratio of the wing the greater the torsional forces near the wing root.

All the aerodynamic forces and moments increase as the square of the airspeed.
Last edited by Ollie; Jul 27, 2003 at 07:26 PM.

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