Estimation from Drawings

6.2.1 Early Methods

The elements of stability and control prediction from drawings started to be avail­able as early as aerodynamic theory itself. That is, aside from elements such as propellers and jet intakes and exhausts, airplane configurations are combinations of lifting surfaces and bodies. However, it took some time before the lift and moment of lifting surfaces and bodies were codified into a form useful for preliminary stability and control design. Simple correlations of lift and moment with geometrical characteristics such as wing aspect and taper ratios and the longitudinal distributions of body volume were needed.

6.2.2 Wing and Tail Methods

For stability and control calculations at the design stage, the variations of lift coefficient with angle of attack, or lift curve slope, are needed for airplane wings and tail surfaces. Wing and tail lift curve slopes are to first-order functions of aspect ratio and sweepback angle, and to a lesser extent of Mach number, section trailing-edge angle, and taper ratio. The primary aspect ratio effect is given by Ludwig Prandtl’s lifting line theory and can be found as charts of lift curve slope versus aspect ratio in early stability and control research reports. The sweepback effect was added by DeYoung and Harper (1948).

However, classical lifting line theory for wings and tails fails for large sweep angles and low aspect ratios, even at low Mach numbers. A 1925 theory of supersonic airfoils in two-dimensional flow due to Ackeret existed, and also in the 1920s Prandtl and Glauert showed how subsonic airfoil theory could be corrected for subsonic Mach number effects. Both the Ackeret theory and Prandtl-Glauert subsonic Mach number correction theory fail at Mach 1. R. T Jones (1946) developed a very low aspect-ratio wing theory, valid for all Mach numbers, which applies to highly swept wings, that is, wings whose leading edges are well inside the Mach cone formed at the vertex.

6.2.3 Bodies

A fundamental source for the effects of bodies on longitudinal and directional stability is the momentum or apparent mass analysis of Max M. Munk (1923). This models the flow around nonlifting bodies such as fuselages, nacelles, and external fuel tanks in terms of the growing or diminishing momentum imparted to segments of the air that the body passes through. Pitching and yawing moments as functions of angle of attack and sideslip are found by this method.