# The Panel Method

A Panel method is used to calculate the velocity distribution along the surface of the airfoil. Panel methods have been developed to analyze the flow field around arbitrary bodies in two and three dimensions.

The geometry of the airfoil is divided into straight, individual panels. Mathematically, each panel induces a (yet unknown) velocity on itself and also on the remaining panels. This velocity can be expressed by relatively simple equations, which contain geometric relations like distances and angles between the panels only. All these influences are collected in a matrix and, additionally, a flow condition is defined on the surface, which must be satisfied by the induced velocities. This boundary condition is the requirement, that the flow does not pass through the airfoil, but flows tangential along the surface. Together with the onset flow direction, a system of linear equations can be composed and solved for the unknown panel velocities.

Various panel methods have been developed over the last 30 years, ranging from simple 0th order to complex higher order methods. The module behind this web page uses a 2nd order panel method with a linear varying vortex distribution, like the XFOIL code does, whereas the well known Eppler analysis method contains a 3rd order panel method, which will yield better results with less panels, but is more sensitive to wavy surfaces. Other codes still use 1st order methods, for simplicity and speed.

The panel method can theoretically calculate the flow around any airfoil, using exactly the given coordinates, but some problems may occur. To resolve the flow properties in curved regions, enough panels must be used. You should use between 50 and 100 coordinate points, distributed more dense in the leading and trailing edge regions, where the velocity changes rapidly. Very thin airfoils or pointed trailing edges can create numerical difficulties and, the method has no implicit smoothing property. This means, that a small deviation of a coordinate from the smooth airfoil shape will result in a wiggle in the resulting velocity distribution. While this is good for smoothing airfoils, it is bad for the subsequent boundary layer analysis. As in real life, wiggles cause premature transition and increased drag. Thus it does not make sense to use the panel method for the analysis of an airfoil with a very wavy surface. You can use the inverse design module to smooth airfoil coordinates. For an elaborate description of panel methods see [26].

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