forms between the supersonic airflow (above Mach 1.0) and the subsonic airflow (below Mach 1.0). This area is always accompanied by a shock wave. The boundary layer on the side of a pro- jectile can be said to be sticky. The air molecules stick to the surface, creating a layer near the surface — the bound- ary layer — that, in effect, changes the shape of the projectile. To make it more confusing, the boundary layer may lift off or separate from the bullet and cre- ate an effective shape much different from the physical shape of the bullet. And to add more to the confusion, the flow conditions in and near the projec- tile’s boundary layer are often unsteady (changing in time). As you can imagine, the boundary layer is very important in determining drag and projectile performance. There will be a static pressure in-
crease behind the wave that the bound- ary layer may not have sufficient kinetic energy to withstand. As the speed in- creases in the transonic range, the shock wave moves farther back and at Mach 1.0 and above, a bow wave will form. For long-range rifle work, ve-
locities in the transonic range should be avoided. Remember that for long- range work, the bullet’s velocity can drop into that range even if it started much higher. Now we should move on to some details on what influences this speed. It is well known that the speed
of sound changes with altitude. Most people believe the thinner air, which increases the velocity at the higher altitudes, causes it. Less air to hold it back, so to speak. This is a quote from the Aero-
dynamics Training Manual for Naval Aviators, NAVWEPS 00-80T-80. “The speed of sound is the rate at which small pressure disturbances will be propagated through the air and this propagation speed is solely a function of air temperature.” I generally recommend a formula
that is easy to use and works very well. To find the velocity of sound
with the air temperature in centigrade, multiply by 1,088 the square root of one plus the temperature divided by 273. The answer will be what we want in ballistics: feet per second. Remember to use centigrade. The National Aeronautics and
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Space Administration’s Glenn Research Center declares that the speed of sound depends on the type of medium (air in our case) and the temperature of the medium. They say that the speed of sound depends on the state of the gas — more specifically, the square root of the temperature of the gas. They use the formula: a = sqrt (g R T) Where: g = ratio of specific heats (1.4 for air at standard temperature) R = gas constant (286 m²/s²/K°
for air) T = absolute temperature
(273.15 + °C) Notice that the temperature must
be specified on an absolute scale (Kelvin or Rankin).
Another formula that is used for
air, solids, liquids, and gases is: v = the square root of B/p where v is the speed of sound, B is the bulk modulus of elasticity of the medium, and p is the density of the medium. The speed of the sound waves cre-
ated in a substance travel with a certain speed. The speed with which the sound wave travels depends on the interac- tion between neighboring molecules
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of the substance. The speed of sound decreases as the mass of the molecules increases because the mass of the mol- ecules is related to the force per accel- eration of the molecule. However, the speed of sound increases as the strength of the interaction between the molecules increases. Put in simple terms, the closer packed are the molecules, the faster the sound waves move through it. In this theme, there are three for-
mulas frequently given for air, solids, and water. The one for air is V = sqrt (bulk modulus/mass density). The bulk modulus is how easy it is to compress a volume of air. Frequently another formula is given that uses the adiabatic constant which is ~7/5 for air. There are so many formulas for
the speed of sound that researching it becomes ridiculous. (I have located about two dozen different formulas for the speed of sound, and perhaps another four dozen for related informa- tion. Don’t worry because I won’t bore you with any more.) Density, in simple terms, is the
mass of anything divided by the volume it occupies. The air’s density depends on its temperature, its pressure, and
Now booking for
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