Static stability and aperiodic divergence

Abstract

equivalent area, AL, at the equivalent length, L, is proportional to W/q, where W is the cruise weight and q, the dynamic pressure. At constant Mach number and with a pressure scale height of 25,000 ft, the approximation for q yields equivalent area distributions that are too low to reflect the cruise weight requirements at the given altitude and Mach number in the real atmosphere (Fig. 3). Within the isothermal approximation, A L may be corrected in one of two ways: using the correct value for q at the given altitude or selecting the scale height which gives the proper pressure at altitude. For the given conditions at M=3, the correct q yields the correct area distribution to within 3% but Ap was overpredicted by 20%. Alternatively, changing the scale height corrects the area distribution to within 1.5% of the real distribution but overpredicts Ap by 8%. Thus, it appears that the most accurate prediction of Ap occurs when using a scale height of 25,000 ft in the isothermal atmosphere. The resulting area distribution may be improved by the factor ^L,Reai^L,isoF° a scale height of 25,000 ft, values of this ratio as a function of altitude are shown in Fig. 4. After correction, the isothermal distribution differs by less than 8% from the real atmosphere distribution (Fig. 5). This corrected area distribution overpredicts Ap by 5% after propogation through the real atmosphere. Thus, for sonic boom minimization studies in mid-range supersonic Mach numbers, use of the isothermal atmosphere with a scale height of 25,000 ft provides reliable estimates of overpressures, and a simple adjustment to the isothermal equivalent areas provides a good approximation to the correct area distribution. However, for design studies, propagation of a known F function or minimization studies at low supersonic Mach numbers, the isothermal approximation to the real atmosphere becomes unsatisfactory.