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Questions and remarks
Answers of the author
Q: At which angle of departure
does a bullet achieve its maximum range?
A: 1. If one neglects the atmosphere and
considers bullet motion in vacuum, the
maximum range will be reached for a 45°
2. For bullets fired from handguns through
the atmosphere, the maximum range (typically in the range of a few kilometres
or less) is usually reached for a 30°- 35° departure angle. This
is a consequence of bullet retardation
by the drag force.
3. Artillery shells may reach maximum ranges
of a few dozens of kilometres. When fired at higher departure angles, theseprojectiles
are capable to reach much higher altitudes than handgun bullets.However
in those altitudes the air density is considerably smaller than the ground
air density. Lower air density goes
along with lower drag and this is the reason why artillery shells reach
their maximum range for higher angles of departure (typically at 45°).
Q: Why is the rotation
of the bullet, after leaving the muzzle, clockwise and why not counterclockwise?
A: Of course - in the real world - there
exists clockwise (right handed) as well
as counterclockwise (left handed) twist. For unknown reasons, atleast for
handguns, the majority of barrels have clockwise twist. Just for the purpose
of simplification this article restricts
only to clockwise twist. In fact, for counterclockwise twist, some forces
(e.g. Magnus) change their orientation.
it true that if a bullet and its shell are released simultaneously, they
will both hit the ground at the same
A: It would be exactly true if there was
no drag - or with other words if those objects
were dropped in vacuum. In vacuum the only active force is gravity
m=mass g= gravitational constant.
As a consequence the fall time t is independent
of the mass (s = falling distance):
If both objects are dropped in air, their
fall times to reach the ground will not
be exactly the same, because they experience different retardations, depending
on their shape, the way they tumble while they fall, and other factors.
However, while falling, the drag of both
objects will be very small, and they
will "approximately" hit the ground at the same time.
If a bullet is fired horizontally from a barrel that is perfectly level,
the bullet, at some point, rise?
A: There is no way a bullet can rise over
the axis of bore of the gun, because there
is no "upward" directed force:
1. The drag acts opposite to the direction
of movement and simply retards the
2. the force of gravity is directed downward.
Some kind of confusion may arise, because
the bullet normally rises over
the line of sight of a gun. The line of sight however is usually inclined
with respect to the axis of bore.
Q: If a bullet is
fired horizontally from a barrel and another bullet is dropped from the
same altitude at the same instant, will they both hit the ground at the
A: This is an interesting question
and the answer is not trivial.
It is true that the horizontally fired
bullet and the dropped bullet would hit the surface at the same moment,
if the experiment happens in vacuum. In vacuum there is only the force
of gravity which affects both objects in the same way.
However if the shooting occurs in air
there is the additional force of drag.
Both objects - let us assume spheres -
experience drag. The difference however is, that the horizontally fired
bullet has a much higher velocity. Only the "downward" velocity components
vy at t=0 are the same (vy=0) for both bullets.
The force of drag is (roughly) proportional
to the square of the velocity v (v = sqrt(vx2 + vy2))
and not only to the vy component! Thus, the drag experienced
by the fired bullet is much higher than the drag experienced by the dropped
bullet. As a consequence the fired bullet will reach the surface later.
Example: Sphere of 10 mm diameter, 10
g mass, fired at 500 m/s from 10 m height
1. Horizontally fired: flight time 1.649
s; terminal velocity 160.2 m/s; point of impact at approx. X = 400
2. Dropped: fall time 1.432 s, terminal
velocity 13.9 m/s
force is a ficticious force, it does not exist! There is only a force radially
inward which is the centripetal force.
A: For a discussion of that subject please
see this source
Q:Can a conventional
gun fire an ordinary bullet in the vacuum of space?
A: There is no reason why a conventional
gun shouldn´t fire in vacuum.
First, the primer in the cartridge (which
contains explosive material) is mechanically ignited. Hot particles are
produced which ignite the powder charge.
The powder however already contains the
oxygen which is needed for "burning".
If this wouldn´t be the case (if
e.g. the powder had to take oxygen from the surrounding atmosphere), the
burning process would be too slow.
It would be interesting to ask NASA for
Please also read that Internet
source! It seems that the Soviets already thought about using guns
in outer space!
Q: Will a bullet stabilize
in space (absense of atmosphere), or tumble?
Q: How fast does a
bullet lose its spin velocity?
A:This question cannot be answered in
general. As a rule, spin is much less reduced than velocity: An estimate
for the M80 bullet (7.62 x 51 Nato) fired vertically up gives
the following values:
all of the velocity has been lost at the summit
only approx. 36% of the angular velocity has
been lost at the summit.
Q: How fast do bullets
travel through the air?
A: The answer depends on the type
Typically bullets fired from pistols and
revolvers travel at 300 - 500 m/s.
Hunting or miltary bullets are faster
(approx. 800 - 1000 m/s).
Air rifles are in the 100 - 200 m/s range.
Q: What is the unit
of the drag coefficient cD and what is the connection between
cD and the projectile caliber?
A:The drag coefficient is a dimensionless
number (in the area of 0.1 - 1) and
depends on Mach number, Reynolds Number,
The drag coefficient is usually measured
by Doppler Radar or other velocity
loss measurements. There is no simple
relationship between bullet geometry (length, diameter,
shape) and cD.
Q: Where might I
find more information about estimating CM (overturning moment
coefficient) for various shaped bullets, primarily boat tail and flat base
A: All the aerodynamic coefficients
are usually hard to obtain. Military research institutes measure them but
only for military bullets. Almost no data is available for bullets from
the civilian market. There is some (expensive) software available which
estimates the aerodynamic coefficients from bullet geometry.
Q: If a bullet is
fired vertically from a rifle, what will its terminal velocity be if it
strikes the top of someones head on its way back down?
A: This question is hard to answer
in general. The best I can give is a "worst-case" estimation.
When a gun is fired vertically, the bullet
after some time reaches a summit where the velocity is zero, and
then falls back. The bullet will fall back base first which is hard
to calculate. I can estimate the velocity if it would fall nose first,
that is the normal flying position for which drag is well known - so the
real terminal velocity will actually be smaller than the following prediction.
For a .22 lr bullet (m=40 grain, v0 = 1150
the summit will be at 1164 ft, the total flight time 30 seconds and the
terminal velocity 270 ft/s
For a SS109 military bullet (m= 55 grain,
the summit will be at 2650 ft, the total flight time 44 seconds and the
terminal velocity 404 ft/s.
For this bullet are indications that it will become unstable. This will
further reduce summit height and terminal velocity considerably.
Q: How can bullet
drift can be calculated from spin?
A: This is not an easy task and
can only be done with some accuracy by applying exterior ballistics software.
There is a simple formula for estimation purposes.
z = k1*T2
T is the total flight time in seconds
k1 is a factor in the area of 0,1 ...
0,12 m/s2 which depends on spin, muzzle velocity and bullet
z is the side deviation in meters
Generally bullet drift at short distances
(100 - 300 yd) is by far smaller than the normal scatter.
Drift is only of some practical importance
for artillery shells, at ranges of several miles.
Q; I would like to
photograph a bullet in flight with the shadowgraph technique. What equipment
do I need?
A: The most important (and expensive
part) of the equipment will be a light source -
a spark flash of very small flash time
(in the area of 1 millionth of a second).
This is something you do not get in the
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