[lWiNdY]

In "Katz & Plotkin: Low speed aerodynamics" the idea of the equivalence between a constant doublet panel and a vortex ring panel is discussed and proved. This allows the evaluation of the effect of doublet by means of a closed vortex ring which is an easier expression if you ask me.

However, and I have seen it in multiple papers/books, on 356 of K&P it is stressed that , where is the entry of the doublet influence matrix. That is, the effect of a unit strength doublet of panel j on the normal velocity at collocation point of panel j is a half.

This does not make sense in my opinion. Suppose we have a square panel with it's collocation point at [0,0,0]. Then, if we double the size of each vertex, the distance from each vertex (or vortex line) is increased and its influence is reduced.

I have attached a very simple python (in .txt) code which basically mimics the VORRING subroutine (eq 10.117, K&P) and if you play with the numbers it is simply confirmed that the influence on its own collocation point is not 0.5. For sources however this seems to be the case.

To that extend, are there any basic sanity checks to see whether or not the source/doublet influence matrices are constructed correctly? And do you agree with my point?

[lWiNdY]

I was mistaken; The velocity POTENTIAL influence matrix has this property. Not the velocity influence matrix!! Therefore, the question is irrelevant and the thread can be considered closed.