Cole, J. D. (1955) Acceleration of Slender Bodies of Revolution through Sonic Velocity. Journal of Applied Physics, 26 (3). pp. 322327. ISSN 00218979. http://resolver.caltech.edu/CaltechAUTHORS:20140807142832610

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Abstract
The linearized theory of slender bodies in arbitrary motion at zero angle of attack has been worked out. The results have been applied to a smooth body accelerating uniformly through sonic velocity. The results theory can be used to estimate the nonlinear or transonic effects. For an accelerating body, the parameter (bl/c^2)^½ is important where 2b = acceleration, 2l = length of body, c = sound speed at infinity. For sufficiently high (bl/c^2)^½, transonic effects can be neglected. Using linearized theory to estimate the ratio of nonlinear terms in the differential equation gives λ= (nonlinear terms/significant linear terms) = 3/4 (γ+1) δ^2/(bl/c^2)^(1/2) {log2/δ^2 (c^2/bl)^(1/2) − 9/4} , where δ = thickness ratio of body. The result above is evaluated at the maximum thickness of a symmetric parabolic arc body at the instant it passes through sonic velocity. For λ<1 transonic effects can be neglected while for λ>1 they begin to dominate. For practical applications the result shows that there is a possibility of a sufficiently long and slender missile accelerating fast enough to avoid transonic effects (e.g., 50 feet long, 5 percent thick, 3g acceleration). For conventional aircraft, transonic effects will dominate. An interesting side result is that when the acceleration is sufficiently large so that transonic effects do not matter the drag coefficient near sonic speed is independent of the acceleration (C_D≐3δ^2 for parabolic arc body).
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Additional Information:  © 1955 American Institute of Physics. Received 11 January 1954. This paper was presented at a meeting of the American Physical Society in Albuquerque, New Mexico, September 3 1953. The research was carried out under ARDC Contract AF18(600)383. As a concluding remark, the author wishes to thank Dr. George Solomon for his able assistance.  
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Record Number:  CaltechAUTHORS:20140807142832610  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20140807142832610  
Official Citation:  Acceleration of Slender Bodies of Revolution through Sonic Velocity Cole, J. D., Journal of Applied Physics, 26, 322327 (1955), DOI:http://dx.doi.org/10.1063/1.1721986  
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ID Code:  48195  
Collection:  CaltechAUTHORS  
Deposited By:  George Porter  
Deposited On:  07 Aug 2014 21:47  
Last Modified:  13 Feb 2019 18:03 
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