The Naval Postgraduate School Online Panel Code is based on the approach of Hess and Smith. A brief summary of the method follows. The flow is assumed to be incompressible, inviscid and irrotational, and is referred to as a potential flow. Potential systems are governed by the Laplace equation, and adhere to the principle of superposition. This means that complicated flowfields can be described merely by summing the influence of a number of simple flowfields. In the present approach, the airfoil surface is represented by a finite number of flat panels spanning adjacent airfoil surface points, as shown in the figure below.

Each panel has a distributed source strength, q(j), and a distributed vortex strength, gamma, as shown in the picture below. The goal is to determine the pressure on each of the these panels that approximate the airfoil surface, and to do this we must choose the source strengths and vorticity strength that will deflect the ambient flow around the airfoil, that is, we want the flow to be tangent to the airfoil surface. If we have N panels, then we have N unknown source strengths. By forcing the flow to be tangent to the foil surface at the N panel midpoints, Vn(j)=0, we obtain N boundary conditions.

There is one further condition that must be satisfied, the Kutta condition. The Kutta condition states that the pressure on the upper and lower surface at the trailing edge must be equal. Essentially this guarantees that the flow will separate at the trailing edge. This is the N+1th boundary condition, and the N+1th unknown is the vorticity strength. Thus, we have a system of N+1 linear, coupled, algebraic equations with N+1 unknowns, and the system is solvable using any of a number of common matrix solution schemes.

As with any numerical approximation of real-world physics, there are limitations to the application of the panel code. The most obvious limitations are due to the approximations of incompressibility and lack of fluid viscosity. The assumption of incompressibility means that these are low-speed solutions (i.e., Mach numbers up to around 0.3). The assumption of inviscid flow does not strongly influence predictions of lift and moment substantially if we limit ourselves to low angles of attack (typically 5-10 degrees, depending on the airfoil shape) where flow separation would be minimal. At high angles of attack the flow typically separates from the suction side of the airfoil, and this phenomenon is not captured by potential-flow theory, in fact, it is precluded by potential-flow theory. Clearly, this is unrealistic in many cases. If you specify a NACA 0012 at 90 degrees angle of attack the panel code will predict a lift coefficient of around 7, a value you will never approach experimentally. Lift coefficient values above 2 should be questioned, and above 3 should not be believed.

The panel code is about 400 lines of Fortran code (less a hundred or so lines of comments). You can take a look at and/or download the Fortran source code here.

The graphics are produced using the PGPlot graphics package driven by a script file created in the Fortran code. The Fortran code, and several image translation/modification tools are executed by a Perl CGI-script that is called by your form submission. All of this is executed on an NPS Aero Department Linux Pentium II 400 webserver.