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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Carlucci, D., and Vega, J., 2007, “Empirical Relationship for Muzzle Exit Pressure in a 155mm Gun Tube,” Computational Ballistics III, C. A.Brebbia, ed., WIT Press, Ashurst, UK.
Cordes, J. A., Carlucci, D., and Jafar, J., 2004, “Dynamics of a Simplified Gun Launched Projectile,” Proceedings of the 21st International Symposium on Ballistics, Adelaide, South Australia, April 19–23.
Cordes, J. A., Vega, J., Carlucci, D., Chaplin, R., and Peterson, W.S., 2005, “Structural Loading Statistics of Live Gun Firings for the Army's Excalibur Projectile,” Tech. Report No. ARAET-TR-05005.
Carlucci, D., Vega, J., and Cordes, J. A., 2004, “Effect of a Bore Evacuator on Projectile In-Bore Dynamics,” U.S. Army Armament Research Development and Engineering Center, Dover, NJ, Tech. Report No. ARAET-TR-04017.
Yorke, G., and Carlucci, D., 2008, “Collection and Modeling of 155 mm Artillery Projectile In-Bore Ballistic Data,” Ballistics 2008: 24th International Symposium on Ballistics, S.Bless and J.Walker, eds, Destech Publications, Inc., Lancaster, PA, pp. 336–343.
Walter, P., 2008, “Selecting Accelerometers For and Assessing Data From Mechanical Shock Measurements,” PCB Electronics, Depew, NY, PCB Electronics Technical Note No. TN-24.
Sterne, T. E., 1944, “On Jump Due to Bore Clearance,” Ballistic Research Laboratories, Aberdeen Proving Ground, MD, BRL Report No. 491.
Gay, H. P., 1961, “On the Motion of a Projectile as it Leaves the Muzzle,” Army Ballistic Research Lab, Aberdeen Proving Ground, MD, Report No. AD801974.
Friedman, E. M., and Hudgins, H. E., Jr., 1976, “Throw-off of Projectile at Muzzle,” Picatinny Arsenal, Dover, NJ, Report No. TM 2195.
Carlucci, D., Cordes, J., Morris, S., and Gast, R., 2006, “Muzzle Exit (Set Forward) Effects on Projectile Dynamics,” U.S. Army Armament Research Development and Engineering Center, Dover, NJ, Tech. Report No. ARAET-TR-06003.
Thompson, W. T., and Dahleh, M. D., 1998, Theory of Vibration with Applications, 5th ed., Prentice-Hall, Upper Saddle River, NJ.
Harris, C. M., and Piersol, A. G., 2002, Harris' Shock and Vibration Handbook, 5th ed., McGraw-Hill, New York.
Tongue, B. H., 2002, Principles of Vibration, 2nd ed., Oxford University Press, New York.
Groessler, P., and Nissl, N., 1984, “High Shock Recorder for Penetrators,” Proceedings of 8th International Symposium on Ballistics, Orlando, FL, October 23–25, American Defense Preparedness Association, Arlington, VA, pp. 632–637.
Pomeroy, S., and Niemeyer, R. T., 1991, “5”/54 Gun Environment Study,” Naval Surface Warfare Center, Tech. Report No. NAVSWC TR 91-604.
Cordes, J. A., Lee, J., Myers, T. L., Hader, G., Reinhardt, L., Kessler, C., Gray, N., and Guevara, M.A., 2010, “Statistical Comparisons Between Qualification Tests For Gun-Fired Projectiles,” ASME J. Appl. Mech., 77(5), p. 051602. [CrossRef]
Myers, T., Carlucci, D., and Cordes, J., 2005, “Rail Gun Test Projectile for Improved Developmental Testing of Precision Munition Electronics,” Proceedings of the 22nd International Symposium on Ballistics, Vancouver, Canada, November 14–18, pp 427–434.
Whitcraft, J. S., 1976, “Development Test (DT 11) of Howitzer, Medium, Towed 155-mm, XM198 First Partial Report,”, U.S. Army Test and Evaluation Command, Report No. APG-Mt-4765.
Lee, J., Groeschler, S., Hollis, M., and Cordes, J., 2010, “Means of Improving the Inertial Measurement Unit Reliability for Cannon Launching Applications,” US Army Armament Research, Development and Engineering Center, Picatinny Arsenal, NJ, Tech. Report No. ARMET-TR-09056.


Grahic Jump Location
Fig. 4

Simple system model of the projectile

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 2

Depiction of projectile during gun launch [13]

Grahic Jump Location
Fig. 1

Typical gun launch acceleration-time curve

Grahic Jump Location
Fig. 5

Pressure decay curve on the base of the projectile

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

Acceleration of the projectile “ogive” to pressure decay

Grahic Jump Location
Fig. 9

Simple model of the accelerometer

Grahic Jump Location
Fig. 10

Projectile ogive and sensor displacement in response to muzzle exit transient

Grahic Jump Location
Fig. 11

Projectile ogive and sensor velocity in response to muzzle exit transient

Grahic Jump Location
Fig. 12

Projectile ogive and sensor acceleration in response to muzzle exit transient

Grahic Jump Location
Fig. 13

Plot of relative motion between sensor mass and projectile ogive



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In