# What methods are used to calculate the geometry needed to obtain a bell-shaped lift distribution?

In aerodynamics, what methods do people use to calculate the geometry of a wing (and body) needed to obtain a bell shaped lift distribution? Please go into as much detail as possible for a stack exchange answer. Also, when feasible, please provide resources to back up claims.

• – user14897
Commented May 16, 2022 at 2:43
• @ymb1 I appreciate the references. Commented May 16, 2022 at 3:38
• To whoever disliked this question: Could you please comment why you disliked it and give suggestions on improvements Commented May 16, 2022 at 3:40

For an unswept wing of an at least moderate aspect ratio in subsonic flow you can use the Multhopp panel tabulation. This divides the wing into an odd number of sections and is easily implemented on a computer.

Over the years, extensions have been published which allow to include wing sweep and the influence of fuselages. In general, any method based on potential flow theory will do.

The way to achieve a bell distribution is to start with an arbitrary wing design and then to iterate chord and twist in order to achieve the desired distribution for the desired angle of attack.

• Thank you this is very helpful! Commented May 17, 2022 at 6:09

I think you are referring to a bell-shaped lift distribution for the entire aircraft.

If you take a look at the SU-27 fight jet, you can see that the wings aren't distinct from the center body of the jet. You see that wings merge together with the central body, creating one single lift body of the aircraft, as opposed to the traditional design where wings and the center of the aircraft.

This design has been proven to be extremely aerodynamic, and this aerodynamic configuration is still being used today on many fighter jets, examples include the Chinese J-11 and the Russian SU-35, which are all very good jets.

Moreover, if you are looking to reduce drag overall, you can also try to have winglets for your aircraft. They can reduce the amount of vortex drag created by your wings. But just be careful because winglets will reduce the maneuverability of your aircraft and will negatively impact supersonic flight performance.

Hopefully this is the answer you were looking for. If not, have a nice day :)

• Thank you for the answer. Although it is not exactly what I am looking for (due to ambiguity in the question which I will fix shortly), you did bring up a good point about including the body into my design. I will keep this in mind. Have a nice day as well! :) Commented May 16, 2022 at 0:25
• No problem. And let me just add something to my answer. The reason why I mentioned the design of merging wings into the body is because this would allow the body to contribute to the lift as well. And thus, it would create a U-shaped lift distribution as the middle of the aircraft (body) would have the largest amount of lift, and the sides (wings) would have less. Commented May 16, 2022 at 3:42