
10-26-2009, 11:30 AM
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Join Date: Mar 2008
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A (very) quick google came up with this:
LINK
If it isn't useful, the references will be. I suspect THIS one may be the most useful.
The below calculations give out typical results of 1-2 degrees for all bullet types.
Quote:
The fact that projectiles can "skip" or ricochet off water has been
know since at least the 16th century. "The Art of Shooting in Great
Ordnaunce" by William Bourne, which was published around 1578, clearly
describes and diagrams the conditions necessary for the ricochet of
cannon shot. This technique was used to increase the range of
cannons, as well as increase the damage inflicted on the target
(hitting near the water line is more damaging than being hit by a
decending shot).
Empirically, it has been found that for non-spinning spherical
projectiles, the critical angle (measured in degrees from the surface
of the water) for ricochet is approximately given by:
18/D^(1/2)
where D is the specific gravity (the density relative to water) of the
projectile. Non-spinning projectiles encountering the water surface
at angles greater than the critical angle will simply enter the water;
projectiles encountering the water surface at lower angles will
ricochet. A theoretical, but still approximate, treatment (IM
Hutchings, 1976) gives the result:
17.3/D^(1/2)
which is reasonably close to the empirical relationship. The
analogous result for a non-spinning cylindrical projectile is:
18.7/D^(1/2)
so spherical and cylindrical projectiles behave pretty close to the
same if they are not spinning.
If the projectile is spinning, the problem becomes much more complex.
Spinning spheres can actually penetrate into the water a distance many
times their diameter, and still reexit, sometimes back in the same
direction they came from! (This has been shown experimentally in the
paper by Shlien listed below). A discussion of the effects of spin is
given in the paper by Hutchings.
Note that the relationships above do not include a dependence on the
velocity of the projectile. The velocity only becomes important at
low speeds (less than ~300 ft/sec). Experimental results on the
effect of velocity on the critical angle (see paper by Soliman and
others) show that the critical angle is lower for slower speed
projectiles, and approaches the theoretical/empirical relationship of
~18/D^1/2 as the speed increases.
In the case of a BB gun, typical projectile velocities are between 250
and 1000 ft/sec, so the dependence of the critical angle on velocity
will be small.
References. (Those with digital object identifier (doi) numbers are
available electronically on the Web, though you may need to have a
subscription to the journal to see the full text. You can use doi
"resolver" at the bottom of the page at <http://www.doi.org/> to try
to retrieve these articles.)
Johnson W; Reid SR (1975) Ricochet of spheres off water. J Mech Eng
Science 17: 71?81.
IM Hutchings, 1976, The ricochet of spheres and cylinders from the
surface of water. Intl. J. of Mechanical Sci. 18 pp 243-47.
doi:10.1016/0020-7403(76)90006-0
AS Soliman, SR Reid and W Johnson, 1976, The effect of spherical
projectile speed in ricochet off water and sand. Intl. J. of
Mechanical Sci. 18 pp 279-84. doi:10.1016/0020-7403(76)90029-1
T Miloh and Y Shukron (1991) Ricochet off water of spherical
projectiles. J. Ship Research 35, pp. 91?100
DJ Shlien, 1994, Unexpected ricochet of spheres off water.
Experiments in Fluids 17, pp 267-71. doi:10.1007/BF00203046
W. Johnson, 1998, Ricochet of non-spinning projectiles, mainly from
water Part I: Some historical contributions. Intl. J. of Impact
Engineering v21, 1-2, pp 15-24. doi:10.1016/S0734-743X(97)00032-8
W. Johnson, 1998, The ricochet of spinning and non-spinning spherical
projectiles, mainly from water. Part II: An outline of theory and
warlike applications. Intl. J. of Impact Engineering v21, 1-2, pp
25-34. doi:10.1016/S0734-743X(97)00033-X
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Last edited by Letum; 10-26-2009 at 11:59 AM.
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