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A Slender Cone Starting Impulsively


Jensen, Arnold Axtell (1951) A Slender Cone Starting Impulsively. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19KD-1M64.


The problem of a semi-infinite slender cone which starts impulsively from rest so that it suddenly has a constant supersonic velocity is considered. It is treated by using the acoustic wave equation for the air at rest at infinity. The problem is reduced to that of dealing with the radial velocity in two conical variables in space-time. It is shown that there are three fundamental regions from the physical or mathematical standpoint. The boundary conditions and equations for each of these regions are developed so that a numerical solution of the problem may be obtained for a given Mach number and cone angle. From the solution of the radial velocity the potential and thence the pressure on the cone are obtained. An approximation to the pressure far back on the cone where the curvature is small is obtained as an improvement on the piston value for zero curvature. This is done by suppressing variations in the axial direction and solving the resulting equation by Riemann's integration method. An attempt to solve the problem by distributing sources on the axis with resulting difficulties is discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lagerstrom, Paco A.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1951
Record Number:CaltechETD:etd-03102009-074636
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:921
Deposited By: Imported from ETD-db
Deposited On:10 Mar 2009
Last Modified:03 May 2023 19:23

Thesis Files

PDF (Jensen_aa_1951.pdf) - Final Version
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