Quasilinearization Method and Summation of the WKB Series

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the $p$-th QLM iterate in powers of $\hbar$ reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first $2^p$ terms reproduced exactly. The QLM quantization condition leads to exact energies for the P\"{o}schl-Teller, Hulthen, Hylleraas, Morse, Eckart potentials etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb Dirac equation has an accuracy of 20 significant figures

Effects of Nacelle configuration/position on performance of subsonic transport

An experimental study was conducted to explore possible reductions in installed propulsion system drag due to underwing aft nacelle locations. Both circular (C) and D inlet cross section nacelles were tested. The primary objectives were: to determine the relative installed drag of the C and D nacelle installations; and, to compare the drag of each aft nacelle installation with that of a conventional underwing forward, drag of each aft nacelle installation with that of a conventional underwing forward, pylon mounted (UTW) nacelle installation. The tests were performed in the NASA-Langley Research Center 16-Foot Transonic Wind Tunnel at Mach numbers from 0.70 to 0.85, airplane angles of attack from -2.5 to 4.1 degrees, and Reynolds numbers per foot from 3.4 to 4.0 million. The nacelles were installed on the NASA USB full span transonic transport model with horizontal tail on. The D nacelle installation had the smallest drag of those tested. The UTW nacelle installation had the largest drag, at 6.8 percent larger than the D at Mach number 0.80 and lift coefficient (C sub L) 0.45. Each tested configuration still had some interference drag, however. The effect of the aft nacelles on airplane lift was to increase C sub L at a fixed angle of attack relative to the wing body. There was higher lift on the inboard wing sections because of higher pressures on the wing lower surface. The effects of the UTW installation on lift were opposite to those of the aft nacelles