# How can I calculate the effect of winglets on aircraft performance?

For a project at university I am having to produce a SIMULINK model of a Nimrod MR2 aircraft. The next step is to increase the endurance of aircraft and a possible route for this is adding winglets to the tips of the wing to increase the efficiency of the wing. However I am struggling to calculate the effect this will have on the performance of the aircraft.

Could anyone offer some help on this topic please?

• You should be specific about what you need help with. Remember that StackExchange is not a forum, it's a question/answer site. Please let us know what you are stuck on. Commented Feb 21, 2017 at 15:57
• you can start by having a look here: aviation.stackexchange.com/questions/8556 Commented Feb 21, 2017 at 15:57
• I need to know how a winglet device will affect the lift and drag produced by the aerofoil? Is there a formula to calculate this? Commented Feb 21, 2017 at 16:11
• the airfoil is a section of the wing, its characteristics do not change. what matters is the vehicle in its ensemble. Commented Feb 21, 2017 at 18:31
• I think Peter Kämpf's answer on the question Federico linked probably answers your question. Peter's not a big fan of winglets and he makes a good case as to how wing extensions are more effective. But all the math is there Commented Feb 21, 2017 at 18:58

## 1 Answer

Basically, there are two ways. One is easy but imprecise, and the other is hard but more precise.

First the easy one: Look at other aircraft and estimate how much winglets affect lift and drag. Make sure to do this at several lift coefficients; winglets help much more at high lift coefficients. Don't forget to account for the added mass of the winglets and their added friction over their surface area. Bonus points for estimating losses due to sideslip.

The hard way is to do a numerical simulation of the wing. Since you want to know what difference the winglets make, you can focus on a comparison between a regular and a winglet-equipped wing and transfer the effect to the full airplane. For the lift and induced drag effects, you will at least need to divide the wing into panels and simultaneously solve the Biot-Savart equations for bound vortices at the quarter chord of each panel plus the trailing free vortices with control points at the three-quarter point where local flow must be parallel with local wing inclination. Make sure you use a method which does better than to assume that all panels lie in one plane!

I have no experience with Simulink - I guess there are libraries around for vortex lattice or even Euler codes, but if you are free to choose your tools, maybe it is worth to take a look at XFLR5. This should work out of the box for your project, and all you need to add is a proper input file.