. Effect of Sweep Angle

The significance of sweep for a wing comes into the picture for compressible flows in achieving high critical Mach numbers. Here, for the sake of completeness we are going to briefly analyze the effect of sweep for incompressible flows.

As we did for the steady flow, let us define the sweep angle K as the angle between the quarter chord line of the wing and the line normal to the free stream. It is, on the other hand, possible to find the aerodynamic coefficients via chordwise strip theory for the wings with the constant spanwise twist and downwash distri­bution. Multiplying Eq. 3.36a, b in Chap. 3 with cosK gives us the aerody­namic coefficients for the swept wings. For this case only, for the nonorthogonal coordinate system having its axis as the free stream direction and the half chord line, we can write downwash expression along the chord as follows

Inverting Eq. 4.61 and substituting it into the lifting pressure coefficient helps us to find the sectional lift coefficient with chordwise integral of the lifting pressure. At each section, assuming that the strip theory is valid, spanwise inte­gration of the sectional values of lift will give us the total lift (BAH 1996).

Another approach here is redefining the coordinate system as у in spanwise direction and x to the normal to spanwise direction. If we now denote the vertical
displacement by r and torsion by s, we can find the aerodynamic forces as functions of r and s (BAH 1996).

Both of the approaches are not quiet sufficient from the aerodynamical angle. Therefore, in practice a semi-numerical method called ‘doublet lattice’ is used extensively. We will be studying the doublet lattice method in next chapter.