Optimum configurations for bangless sonic booms
Authors:
Wallace D. Hayes and Jr. Weiskopf
Journal:
Quart. Appl. Math. 30 (1972), 311-328
DOI:
https://doi.org/10.1090/qam/99725
MathSciNet review:
QAM99725
Full-text PDF Free Access
Abstract |
References |
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Abstract: A number of optimization problems are posed and solved for supersonic aircraft flight subject to the condition that a shock wave appears only incipiently in the sonic boom signal at a given point. The principal result is one giving the maximum effective gross weight of an aircraft of given effective length under given flight conditions. The calculus of variations with inequality constraints is used, with the novel features of a non-local isoperimetric relation and of only an upper bound on a control variable.
W. D. Hayes, Sonic boom, Annual Review of Fluid Mechanics 3, 209–290 (1971)
F. E. McLean, Some nonasymptotic effects of the sonic boom of large airplanes, NASA Tech. Note TN D-2877 (1965)
W. D. Hayes, R. C. Haefeli, and H. E. Kulsrud, Sonic boom propagation in a stratified atmosphere, with computer program, NASA Contr. Rep CR-1299 (1969)
- G. Leitmann, Variational problems with bounded control variables, Optimization techniques, Academic Press, New York, 1962, pp. 171–204. MR 0162670
- Angelo Miele, The calculus of variations in applied aerodynamics and flight mechanics, Optimization techniques, Academic Press, New York, 1962, pp. 99–170. MR 0162669
F. B. Weiskopf, Jr., The optimization of certain aerodynamic parameters with the constraint of a bangless sonic boom, M.S.E. Thesis, Department of Aerospace and Mechanical Sciences, Princeton University (1971)
L. B. Jones, Lower bounds for sonic bangs in the far field, Aeron. Quart. 18, 1–21 (1967); see also J. Roy. Aeron. Soc. 65, 433–436 (1961)
W. D. Hayes, J. H. Gardner, D. A. Caughey, and F. B. Weiskopf, Jr., Theoretical problems related to sonic boom, in Third conference on sonic boom research, NASA SP-255, 27–31 (1971)
R. Seebass, Minimum sonic boom shock strengths and overpressures, Nature 221, 651–653 (1969)
A. R. George, Lower bounds for sonic booms in the midfield, A.I.A.A. J. 7, 1542–1545 (1969)
L. B. Jones, Lower bounds for the pressure jump of the bow shock of a supersonic transport, Aeron. Quart. 21, 1–17 (1970)
R. Seebass and A. R. George, Sonic boom minimization, Proc. Second Sonic Boom Symp., 1970, J. Acoust. Soc. Amer. 44, (1971)
A. R. George and R. Seebass, Sonic boom minimization including both front and rear shocks, AIAA J. (1971)
W. D. Hayes, Sonic boom, Annual Review of Fluid Mechanics 3, 209–290 (1971)
F. E. McLean, Some nonasymptotic effects of the sonic boom of large airplanes, NASA Tech. Note TN D-2877 (1965)
W. D. Hayes, R. C. Haefeli, and H. E. Kulsrud, Sonic boom propagation in a stratified atmosphere, with computer program, NASA Contr. Rep CR-1299 (1969)
G. Leitmann, Variational problems with bounded control variables, in Optimization techniques with applications to aerospace systems (G. Leitmann, ed.), Academic Press, New York, 171–204 (1962)
A. Miele, Calculus of variations in applied aerodynamics and flight mechanics, in Optimization techniques with applications to aerospace systems (G. Leitmann, ed.), Academic Press, New York, 99–170 (1962)
F. B. Weiskopf, Jr., The optimization of certain aerodynamic parameters with the constraint of a bangless sonic boom, M.S.E. Thesis, Department of Aerospace and Mechanical Sciences, Princeton University (1971)
L. B. Jones, Lower bounds for sonic bangs in the far field, Aeron. Quart. 18, 1–21 (1967); see also J. Roy. Aeron. Soc. 65, 433–436 (1961)
W. D. Hayes, J. H. Gardner, D. A. Caughey, and F. B. Weiskopf, Jr., Theoretical problems related to sonic boom, in Third conference on sonic boom research, NASA SP-255, 27–31 (1971)
R. Seebass, Minimum sonic boom shock strengths and overpressures, Nature 221, 651–653 (1969)
A. R. George, Lower bounds for sonic booms in the midfield, A.I.A.A. J. 7, 1542–1545 (1969)
L. B. Jones, Lower bounds for the pressure jump of the bow shock of a supersonic transport, Aeron. Quart. 21, 1–17 (1970)
R. Seebass and A. R. George, Sonic boom minimization, Proc. Second Sonic Boom Symp., 1970, J. Acoust. Soc. Amer. 44, (1971)
A. R. George and R. Seebass, Sonic boom minimization including both front and rear shocks, AIAA J. (1971)
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Article copyright:
© Copyright 1972
American Mathematical Society
