Questions and remarks of readers

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Answers of the author

Q: At which angle of departure does a  bullet achieve its maximum range? To Questions
Q: Why is the rotation of the bullet, after leaving the muzzle, clockwise and why not counterclockwise? To Questions
Q: Is it true that if a bullet and its shell are released simultaneously, they
will both hit the ground at the same time? why? To Questions
Q:  If a bullet is fired horizontally from a barrel that is perfectly level, will
the bullet, at some point, rise? To Questions
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 same time?
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 m (range)
2. Dropped: fall time 1.432 s, terminal velocity 13.9 m/s
To Questions

Q: Centrifugal force is a ficticious force, it does not exist! There is only a force radially inward which is the centripetal force.

To Questions
Q:Can a conventional gun fire an ordinary bullet in the vacuum of space? To Questions
Q: Will a bullet stabilize in space (absense of atmosphere), or tumble? To Questions
Q: How fast does a bullet lose its spin velocity? To Questions
Q: How fast do bullets travel through the air?
A: The answer depends on the type of gun.
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.

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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, Froude 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.
To Questions
Q: Where might I find more information about estimating CM (overturning moment coefficient) for various shaped bullets, primarily boat tail and flat base match bullets.
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.
To Questions
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.
To Questions
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 parameters
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.

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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 supermarket.
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