# When using the Source Panel method and dealing only with sources and sinks, why do lift and drag equal zero?

I am trying to deal with the airfoil with the "Source Panel method", and when I try to calculate the lift and drag, they always equal to zero. And I have found an explanation in some articles, that sources and sinks don’t create any drag/lift. But I don't understand the reason. Could someone give me some explanation?

• Welcome to Aviation! Your question is collecting close votes because it's not really clear what you're asking. Please edit you question to include more details. Perhaps include the formula(s) you're using and the numbers that you are plugging into it. Someone might spot some errors there and be able to guide you to correcting them. As it stands, you haven't really given anyone much of anything to go on. If you'll take the tour and read the help center, especially on "how to ask", you'll get a better idea of what to provide to get a good answer to your question. – FreeMan Jul 20 at 17:18
• @FreeMan Seems pretty clear to me what he's asking – JZYL Jul 20 at 17:39
• You should add links to the articles you don't understand so that it is easier to point out unclear passages. – Manu H Jul 21 at 13:36

A single source, or a source sheet comprised of infinitesimal sources (sinks are just sources with negative strength), produces a velocity field that contains no circulation. Without circulation, it can't possibly generate any lift. The Source Panel Method is just a discretized computational method for source sheet. It, therefore, only produces non-lifting flow.

Drag, in the context of incompressible potential flow, only arises through induced drag. Without lift, induced drag would also be nil.

To predict lifting flow, vortex sheet modeling is typically used that, by construction, produces non-zero circulation (unless the integral of sheet strength is zero by prescription). An additional prescription of the Kutta condition is required to guarantee a unique physically correct lifting flow.

Image collated from: http://web.mit.edu/16.unified/www/SPRING/fluids/Lecture_Notes/f18.pdf

A mathematically equivalent methodology is to use doublet sheet modeling, using the following tranform:

$$\vec{\gamma}=\hat{n} \times \tilde{\nabla}\mu$$

where $$\vec{\gamma}$$ is the vortex sheet strength, $$\hat{n}$$ is the sheet normal, $$\mu$$ is the doublet strength, and $$\tilde{\nabla}$$ is the surface-gradient operator.

Somewhat confusingly, a doublet is a combination of a source and sink that are separated by an infinitely small distance. A single doublet is non-lifting. However, a lifting flow can be generated if the doublet sheet varies in strength. This video based on Drela, Flight Vehicle Aerodynamics provides an extremely good intuitive explanation.

• It's great! Thanks for the explanation! It helped me a lot – ZMM Jul 20 at 20:51