The von Karman Rule for Transonic Flow

The potential Equation (9.49), for the present case of two-dimensional transonic flow, reduces to:

Equation (9.97) results in a form due to Sprieter (see also Liepmann and Roshko, 1963 [4]) for ML & 1, as:

2/3

[(Y + i)m!]1/3

(9.97b)

and Cp is the similarity pressure coefficient. It follows from Equation (9.97a) that the lift and drag coefficients are given by:

Equations (9.97a), (9.97c) and (9.97d) are valid for local as well as for total values. Sometimes, instead of thickness ratio t/c, ‘fineness ratio’ defined as in Figure 9.12 is used.

For the wedge shown in Figure 9.12:

1 t t

= tan во, – = 2 tan в0

2 c c

The ratio t/c is called the fineness ratio (at angle of attack = 0).

tan(eo±a) =tan [2C J1 ± t/c] ] .

where the ‘plus’ sign is for the upper surface and the ‘minus’ sign is for the lower surface. For finding the local values of Cp, CL and CD, we must use fineness ratio defined by these equations.