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Published online by Cambridge University Press: 05 June 2012
“I shot an arrow into the air,
It fell to earth, I know not where.”
H.W. Longfellow (1807 - 1882)The Basic Equations
The air resistance acting on a projectile can be separated into four categories – forebody drag, base drag, skin friction and protuberance drag. Forebody drag arises because some of the energy of the projectile is used to compress the air in front of the projectile and in some cases to form shock waves. Base drag is due to the turbulent wake behind the projectile and is more pronounced if the rear of the projectile is blunt. Skin friction is caused by air adhering to the surface of the projectile. It can be reduced by polishing the surface. The protuberance drag is really a combination of the forebody drag, base drag and skin friction on any protuberance attached to the main projectile body. For example the principal protuberance on a shell fired from a gun is the driving band.
When the projectile's speed (v) is divided by the local speed of sound in air (α) this nondimensional ratio is called the Mach number (M). Near M = 1 (the transonic region) the forebody drag increases dramatically, and therefore becomes effectively the total aerodynamic drag. Since a is proportional to the square root of the absolute temperature of the air, and the drag coefficient CD introduced at the beginning of Chapter 3 also depends on air temperature, it follows that CD is a function of the Mach number for a given projectile (see Figure 4.1).
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