Units

Most XFOIL operations are performed on the airfoil’s cartesian coordinates x,y , which do not necessarily have a unit chord c. Since the chord is ambiguous for odd shapes, the XFOIL force coefficients CL, CD, CM are obtained by normalizing the forces and moment with only the freestream dynamic pressure (the reference chord is assumed to be unity). Likewise, the XFOIL Reynolds number RE is defined with the freestream velocity and viscosity, and an implied unit chord:

CL = L / q	V = freestream speed
CD = D / q	v = freestream kinematic viscosity
CM = M / q	r = freestream density
RE = V / v	q = 0.5 r V^2

The conventional definitions are

Cl = L / q c

Cd = D / q c

Cm = M / q c^2

Rc = V c / v

so that the conventional and XFOIL definitions differ only by the chord factor c or c^2.

For example, a NACA 4412 airfoil is operated in the OPER menu at

 RE   = 500000
 ALFA = 3

first with chord=1.0, and then with chord=0.5 (changed with SCAL command in the GDES menu, say). The results produced by XFOIL are:

 c = 1.0 :    CL = 0.80    CD = 0.0082    (RE = 500000, Rc = 500000)
 c = 0.5 :    CL = 0.40    CD = 0.0053    (RE = 500000, Rc = 250000)

Since CL is not normalized with the chord, it is nearly proportional to the airfoil size. It is not exactly proportional, since the true chord Reynolds number Rc is different, and there is always a weak Reynolds number effect on lift. In contrast, the CD for the smaller airfoil is significantly greater than 1/2 times the larger-airfoil CD, since chord Reynolds number has a significant impact on profile drag.

Repeating the c = 0.5 case at RE = 1000000, produces the expected result that CL and CD are exactly 1/2 times their c = 1.0 values.

c = 0.5 : CL = 0.40 CD = 0.0041 (RE = 1000000, Rc = 500000)

Although XFOIL performs its operations with no regard to the size of the airfoil, some quantities are nevertheless defined in terms of the chord length. Examples are the camber line shape and BL trip locations, which are specified in terms of the relative x/c,y/c along and normal to the airfoil chord line. This is done only for the user’s convenience. In the input and output labeling, “x,y” always refer to the cartesian coordinates, while “x/c,y/c” refer to the chord- based coordinates which are shifted, rotated, and scaled so that the airfoil’s leading edge is at (x/c,y/c) = (0,0), and the airfoil’s trailing edge is at (x/c,y/c) = (1,0). The two systems cooincide only if the airfoil is normalized.