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(picture from ii.metu.edu) Trajectory of a body that is launched at x0=y0=0, with an initial velocity v0 at an angle of departure q0. The distance R is the horizontal range, and h is the maximum height. |
Author: Isaac Rowland
(Web Project for Physics 212, Fall 2001, UAF)
PROJECTILE MOTION
No discussion on ballistics can be understood without at least a basic knowledge of projectile motion.
A projectile is any body that is given an initial velocity and then follows a path determined by the effect of the gravitational acceleration and by air resistance. A thrown football, an object dropped from an airplane, and a bullet shot from a gun are all examples of projectiles. The path followed by a projectile is called its trajectory.
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(picture from ii.metu.edu) Trajectory of a body that is launched at x0=y0=0, with an initial velocity v0 at an angle of departure q0. The distance R is the horizontal range, and h is the maximum height. |
Figure above shows the path followed by a projectile under ideal conditions (i.e., air has no effect on the motion). The initial velocity v0 can be written as
v0 = v0xi + v0yj.
The components v0x and v0y can be found if the angle q0 is known:
v0x = v0 cos q0 and v0y = v0 sin q0.
The horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. The total drop is thus affected only by the total flight time. In the real world, knowing the drop of the projectile can be of utmost inportance.
The Problem
The problem with the above picture is that the real world is not ideal. Air drag acts as a force against the direction of motion of the projectile and causes it to take a longer time to get to the target. Thus making for a larger drop. The more drag, the more the bullet drops. For a far more detailed account of how a bullet flies, click here.
To accuratly predict where a bullet will land, it becomes nessary to know something about the amount of drag on the bullet. This is where the the calculation of Ballistic Coefficient comes in. Ballistic Coefficient is simply a number that can be used in trajectory calculations to accuratly predict drop.
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