Launch Dynamics

Mathematical Description of Projectile Shot Exit Dynamics (Set-Forward)

[+] Author and Article Information
D. E. Carlucci, J. A. Cordes

Building 94, 2nd Floor,
Picatinny, NJ 07806-5000

A. M. Frydman

Army Research Laboratory,
Building 4600, Room 1017,
Adelphi, MD 20783

1Corresponding author.

Manuscript received June 28, 2012; final manuscript received September 18, 2012; accepted manuscript posted January 9, 2013; published online April 19, 2013. Assoc. Editor: Bo S. G. Janzon.This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Appl. Mech 80(3), 031501 (Apr 19, 2013) (9 pages) Paper No: JAM-12-1276; doi: 10.1115/1.4023335 History: Received June 28, 2012; Revised September 18, 2012; Accepted January 09, 2013

The dynamics or “ringing” of a projectile structure at gun-muzzle exit has been observed to cause a large number of electronics failures in projectiles as well as possible safety concerns with respect to components impacting one another or structural components of the projectile coming apart. Current numerical tools allow accurate calculation of the muzzle exit event given that the engineer understands the forces acting on the projectile. Dynamic response of a structure is well understood by persons working in the field; however, engineers who do not regularly deal with dynamic analyses generally have difficulty interpreting results from both analyses and tests. This paper details the mathematics associated with this event so that the engineer confronted with a dynamics related issue can have a reference for understanding and interpretation. The results of a simple model show that accelerometer data should be used with caution and the support of a finite element analysis of the projectile structure with the proper pressure decay is usually necessary. Recommendations for use of measured acceleration data for modeling and simulation are provided.

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Fig. 1

Typical gun launch acceleration-time curve

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Fig. 2

Depiction of projectile during gun launch [13]

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Fig. 3

Simplified model of the projectile, assuming axial symmetry about the CG

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Fig. 4

Simple system model of the projectile

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Fig. 5

Pressure decay curve on the base of the projectile

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Fig. 6

Response of the projectile “ogive” to pressure decay and step function

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Fig. 7

Response of the projectile “ogive” to (1/2) pressure decay and step function

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Fig. 8

Acceleration of the projectile “ogive” to pressure decay

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Fig. 9

Simple model of the accelerometer

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Fig. 10

Projectile ogive and sensor displacement in response to muzzle exit transient

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Fig. 11

Projectile ogive and sensor velocity in response to muzzle exit transient

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Fig. 12

Projectile ogive and sensor acceleration in response to muzzle exit transient

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Fig. 13

Plot of relative motion between sensor mass and projectile ogive




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