According to the 4H BB Rifle Safety Guide, "Bullets can skip off of
the water similar to skipping a flat rock on water. Never shoot at
water."

Can bullets really skip off water? What is the relationship between
angle of entry, shape and mass of bullet, surface tension, and the
ability for a bullet to skip off water? Is there any research or
antedotal evidence that shows that bullet can actually skip off water?

Sure, bullets can skip off the surface of water. But the angle of
incidence (with respect to the water's surface) must become shallower
as the bullet's energy (mv^2/2) increases. This is because the higher
the projectile's energy, the more penetrating it is.

   It's much like with light radiation. Infrared (IR) can be reflected
off a telescope mirror at a much higher incidence angle than x-rays.
X-rays are of a much higher energy than IR, and so tend to penetrate
rather than reflect. An x-ray mirror must be arranged such that the
x-radiation will strike it at a very slight angle. And so it is with
bullets. The faster & more massive the bullet, the more that it'll
tend to break the water's surface, so the angle at which it strikes
the water must approach closer to parallelness.

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

...one more thing...

qed100's comment is not correct.  The critical angle does *not* depend
on the mass of the projectile, it depends on the density of the
projectile (relative to the material it is impacting, water in this
case).  Furthermore, for water, the higher the velocity of the
projectile, the *larger* the critical angle, up to an asymptotic limit
of the empirical relationship.  This is the opposite of what he
stated.

"qed100's comment is not correct"

   Yes, you're right. Thanks. But it seemed reasonable at the time
from a theoretical point of view. :)

There was a story in the reader's digests several years ago about this
New York City Police Officer (not sure if he was uniform of detective)
who was following a  car along one of the freeways when all of a
sudden the vehicle went off to the right and crashed.
The police officer went to assist and discovered that the female
occupant was deceased.
An autopsy revealed that she had been shot in the ear with a British
Le-Enfield .303 calibre rifle. This matter was handed over to the
homicide squad and who through a bit of luck discovered the owner of
this rifle.
He told the police that he was on New York Harbour in his boat and
that he fired a shot, with this rifle, at a can or bottle floating on
the water. The bullet skipped off the water and travelled 1500 yards
went through the back window, which was down, of the victims vehicle
killing her. It was believed that if the window had of been up she
would not have beren killed because the bullet would have lost most of
its power.
I cannot recalled exactly what happened to the owner of the rifle. I
know they tried to charged him with murded originally but I think the
charged was reduced to discharged a firearm within city limits.

Please bear in mind that I read this story between 20 & 30 years ago
so some of the above may not be exactly right.
(Please excuse any spelling errors)

Kind regards

Ross (Australia)

Ross --

It's interesting that you mention that story because I recall reading
the original (uncondensed version) in The New Yorker.  But because it
was 20-30 years ago, I didn't think that I had enough to chase it
down.  Still, we know that the story of the NY detective made an
impact on at least two of us!

Best regards,

Omnivorous-GA

Don't forget the bouncing bombs that destroyed a German dam in world
war II depicted in the film "the Dambusters".

If anyone questions the previous comment, it's a fact, not just a film
fantasy.  I think it was the British that went to some effort to
figure out how to skip bombs under defenses to breach dams in Germany 
- successfully.

"If anyone questions the previous comment, it's a fact, not just a film
fantasy."

   I concur. The wartime dam busting project was a work of genius.

As far as BB guns are concerned as well as my own personal experience,
I was at a lake with a few friends after a BB skirmish and only 2 of
us could 'skip' bullets.

The only difference between our guns were:
2 people had spring powered pistols without hop-up (could skip water)
Everyone else had battery or gas rifles/pistols with hop-up(could barely)

I think if you have no hop-up and you are using top-grade
high-polished BB's then it is easy, however if you are using another
type of gun with hop-up (usually between 270-450 >550fps) it will
normally be going too fast with too much backspin.
But... we did manage to make some gas pistols skip. I think this is
because of the combination of high-polished BB's and Silicone. The
Silicone in green gas (silicone propane) would make BB's pretty slick,
hence the possibility of skipping.

As for real bullets, I would imagine that they would have to hit the
water at a very small angle to ricochet. But I do imagine it entirely
possible. Especially with an old musket with thier round rounds.