INFLUENCE OF COMPRESSIBILITY UPON LATERAL CONTROL

After dealing with all the details of control effectiveness and hinge moments, there is one influence left to be discussed, namely compressibility and/or Mach number.

Prandtl Glauert Factor. The lift-curve slope of foil sec­tions (not that of wings having finite aspect ratios) grows in proportion to the Prandtl Glauert factor

PG = 1/11 – M*~ (25)

Experimental evidence as in (22) proves that due-to-flap lift-curve slopes dCL /doc, also tend to increase in propor­tion to PG, although the boundary layer can have an influence reducing this effect.

Hinge Moments. Usually, hinge moments due to flap de­flection are proportional to dCL /dcf. Hinge moments may, therefore, be expected also to grow in proportion to or possibly at a lesser rate than PG.

Spoilers. The effectiveness of suction-side spoiler devices usually increases with the lift coefficient. As a conse­quence, effectiveness may be expected to grow in propor­tion to PG. Experimental results listed in (9,p) confirm the prediction, although tunnel blocking (choking) seems to exaggerate the influence.

Critical Mach Number. The Prandtl-Glauert rule cited above ceases to apply as soon as at any point of the foil-and-flap section the velocity of sound is first reached. The maximum local velocities are a function of thickness ratio, lift coefficient and section shape. Considering a deflected and lifting control flap, a critical point is found at the suction side of the flap near its nose where the contour makes a bend. Particularly critical conditions (high local velocities) must be expected at the exposed side of an overhanging nose balance. The balancing quali­ties of such noses may thus be limited by compressibility, and the flap effectiveness may be expected to be reduced at the same time.

(22) Influence of compressibility upon flap characteristics:

(a) Stevenson, 9% Foil Sections, NACA TN 1406 & 1417 (1947).

(b) Hammond, Flaps and Spoilers, NACA RM L53D29a; also RM L56F20.

(c) Lindsey, 9% Foil with 30% Flap, NACA RM L56L11.

(d) Lowry, Rectangular Wings, NACA RM L56E18.

(e) Whitcomb, Transonic on Swept Wing, NASA TN D-620 (1961).

(f) MacLeod, Bump Tests, NACA RM L50G03.

(g) Using free-flight rockets, NACA RM L48A07 & L48I23.

(23) In a low-speed water tunnel, the time scale is considerably larger than in a wind tunnel (at one and the same Reynolds number).