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# Acceleration of Slender Bodies of Revolution through Sonic Velocity

Cole, J. D. (1955) Acceleration of Slender Bodies of Revolution through Sonic Velocity. Journal of Applied Physics, 26 (3). pp. 322-327. ISSN 0021-8979. doi:10.1063/1.1721986. https://resolver.caltech.edu/CaltechAUTHORS:20140807-142832610

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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).

Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1721986DOIArticle
http://scitation.aip.org/content/aip/journal/jap/26/3/10.1063/1.1721986PublisherArticle
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 AF-18(600)-383. As a concluding remark, the author wishes to thank Dr. George Solomon for his able assistance.
Funders:
Funding AgencyGrant Number
Air Force Research and Development Center (ARDC)AF-18(600)-383
Issue or Number:3
DOI:10.1063/1.1721986
Record Number:CaltechAUTHORS:20140807-142832610
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140807-142832610
Official Citation:Acceleration of Slender Bodies of Revolution through Sonic Velocity Cole, J. D., Journal of Applied Physics, 26, 322-327 (1955), DOI:http://dx.doi.org/10.1063/1.1721986
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48195
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Aug 2014 21:47