MadSci Network: Physics

Re: Can a bullet mortally wound when coming down from being fire

Date: Thu Dec 17 12:24:20 1998
Posted By: Tye Morancy, Grad student/Teaching Asst. Physics and Radiology, UMASS Lowell/Radiation Tech. Harvard Univ. EH&S
Area of science: Physics
ID: 912487958.Ph


    Yes, a bullet could mortally wound for such a case...I'll explain why:

    If you were to aim a gun straight up in the air and fire it, the 
physics that follows is actually pretty simple.  The bullet leaves the gun 
with some initial velocity which is called the muzzle velocity of the 
projectile.  This velocity will vary with the caliber and the shells 
used.  On average I would say that a good number for a muzzle velocity 
would be something on the order of 500 to 900 m/s.  For example, a 30 
caliber bullet sizzles along at 900 m/s when leaving the barrel.  Just to 
give you an idea of how fast that is, the speed of sound is about 330 m/s, 
so the bullet in our example is moving at supersonic speed.
    Ok, back to the situation, the bullet leaves the muzzle and travels 
straight upward.  Just like any projectile, the bullet slows down as the 
pull of gravity causes it to deccelerate.  The bullet reaches its peak 
height and stops for an instant.  If we neglect wind and friction of air, 
the bullet will start to fall and accelerate towards the earth along the 
same path it took to get there.  The bullet will then reach a high 
velocity and actually return to its point of origin (the gun or with any 
bad luck...the shooter) with the same speed that it left.
    On the other hand, if we want to include the consideration of air 
friction to make this situation have a realistic outcome we have to 
consider such factors as resistive forces such as drag and also to see 
whether or not we have to consider something called terminal velocity.  
Terminal velocity is the idea that a falling object in a resistive medium 
like our atmosphere will reach a peak velocity.  The resistance of the 
medium prevents the object from moving any faster and provides an opposing 
force to slow the falling object down. 
    This is something that is considered all the time in skydiving since 
skydivers will plummet towards the earth and will reach a maximum 
velocity.  Now, terminal velocity here depends on the surface area of the 
object which is facing the earth (A), the density of the air(p), the mass 
of the object(m), the acceleration due to gravity(g), and a 
proportionality constant called the drag coefficient(C).  The terminal 
velocity is calculated as follows :

                      V(term) = (2mg/CpA)^1/2

    The coefficient C is 0.5 for a spherical object and the number can go 
up to 2 for irregular objects; I have assumed 1 for the bullet.  I have 
also assumed a mass of about 20 grams for the bullet.  The area, A, was 
calculated to be 4.56x10^-5 m^2 taking into account that the diameter of 
the bullet is about 7.62 mm for a 30 caliber shell.  After doing this 
calculation with these factors, I determined the terminal velocity to be :

                      40.79 m/s  or  91.24 mph

    So, instead of the bullet returning to the shooter at 900 m/s, the 
velocity is significantly less, but still pretty damaging for such a 
speed. Of course, it would be fatal if it struck in a vital area of the 
body like the head or chest.  I have assumed that since the bullet was 
fired upwards, the impact coming back down would most likely be to the 
    To summarize, the unfortunate result of this story is that the bullet 
leaves the muzzle at 900 m/s  travels upwards, stops, and comes back 
towards the shooter and impacts at 40.79 m/s.  Definitely a bad thing if 
you ask me.
    Just think about this when you see those festive celebrations around 
the world when they fire their guns into the air blindly to celebrate ...

Tye Morancy

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