# How can we determine the maximum camber and thickness for airplane wings?

I want to know if there are any standard factors for determining maximum wing camber and thickness for heavy and light airplanes?

I'm using an optimization process to find the best wing shape to reach the best aerodynamics. E.g. in cruise mode to find the maximum lift-over-drag ratio, maybe choosing a thinner camber or thickness has a higher CL over CD ratio, but may lead to problems with structural limits.

Can anyone help me with some good references on the appropriate limits of changes in both maximum thickness and camber?

• Chamber is good, but camber is not bed either. – mins May 3 '16 at 9:03
• @mins If you take the effort to make that comment, you might as well take the effort to click 'edit' and improve the post. It is a lot more helpful to a new user. – DeltaLima May 3 '16 at 12:27
• @DeltaLima: It was actually a joke (chamber/bed). Keep cool. – mins May 3 '16 at 17:32

Camber pushes the lift coefficient operating range up and increases the pitching moment of an airfoil. It is advised to use lots of camber if you need to create lots of lift at low speed and have no need to fly fast. Conversely, high speed aircraft use uncambered wings. Flaps add camber - this makes them so effective for lowering the minimum speed of heavy aircraft.

Comparison of the same baseline airfoil at different camber values (picture source). This is taken from NACA Report 824 which later was turned into one of the most important books for aerodynamicists.

Wing thickness helps to build a lighter wing but will increase friction drag due to higher supervelocities caused by the displacement effect of the thick wing and cause earlier flow separation because the boundary layer is more stressed. In the end, you need to find a compromise: A 15% - 16% thickness is quite normal for GA aircraft, and high aspect ratio wings like those of the B-24 and the B-29 had a root thickness of 22%, but tapered the thickness down towards the outer wing as soon as practical. The tip thickness of both was just 9%.

The maximum lift will peak around 12% to 15% relative thickness. Below I copied figure 85 from NACA Report 460 to illustrate the point:

Now this was all subsonic aerodynamics. Once you move closer to the speed of sound, the supervelocities can cause pockets of supersonic air which end in a local shock. Therefore, the optimum thickness is reduced as the cruise speed approaches Mach 1, and wing sweep is added to cheat a little and keep thickness higher. Modern airliners use airfoils of around 13% relative thickness, and supersonic wings rarely use more than 6% relative thickness at the root, tapering to 2% to 3% at the tip.