momentum in arrows. Below is information about the formulas for calculating kinetic energy and momentum, their relationship, and the derivation of these formulas. There are only two basic
formulas: one for kinetic energy and one for momentum, although there are
probably many ways to write them. Each formula has several constants that are required to make them usable in a form where the values are expressed in terms we are familiar with. Conversion to grains for the arrows and from the British gravitational units of poundals to pounds-mass are a part of that.

Determining An Arrow’s
Kinetic Energy
The basic formula for kinetic energy is: To use the weight of the arrow in grains, Our usual unit of measurement, it is neccessary to convert from poundaIs to grains
in the formuIa, therefore: Note: The acceleration of gravity
(g) varies with latitude. As latitude increases, “g” also increases. 32.16 feet
per second per second corresponds to about 40 degrees latitude, which is a
reasonably good average for the United States. Gravitational pull is higher at the
poles.

Dimensionally masses are measured
in poundals and velocities in feet per second. A poundal is defined as the
force which, if applied to the standard pound body, would give that body an
acceleration of one foot per second per second. One poundal equals 1 /3 2. 1 740
pound-force (lbf). These dimensions are stated in the British “absolute system” in which the basic dimensional units are: one poundal, one foot, and one second. Therefore, the basic unit of
momentum is one poundal-second.

When momentum is expressed in the British gravitational system (the system in most common use in the United States), the basic unit is one pound-second. One pound-second is equivalent
to 32.1740 poundal-seconds. Work or energy is expressed in foot- pounds in the British “gravitational system,” or as foot-poundals in the British “absolute system.” Again, the acceleration of gravity enters the picture so that: one foot-pound = 32.1740 foot-poundals.

Unfortunately the term “pound” is used ambiguously to define both “force”
and “mass” in most instances. To distinguish between these two usages, the term “pound- force” was coined to apply to the pound when it is used to express force, and the term “pound-mass” was designated to apply to pound when it is used to indicate mass.
Simply stated:
“A load that produces a vertically downward force because of the influence of gravity acting on a mass may be expressed in ‘mass’ units. Any other load is expressed in ‘force’ units.”
The kinetic energy of an arrow in flight is a function of its mass and velocity squared, as shown in the formula outlined above. It has the dimension of foot-pounds. The momentum of the same arrow is also a function of its mass and the single power of its velocity. Momentum
has the dimensions of foot»seconds. The difference between kinetic energy and momentum is a function of the velocity divided by 2 and, of course, the change in dimensions from foot-pounds to
pound-seconds. lf kinetic energy of the arrow is divided by “v/2,” then the result
is the momentum of the arrow. For example: An arrow with a weight of 450 grains and a velocity of 230 feet per second will have a kinetic energy of 52.8718 foot-pounds.
Dividing 230 by 2 yields 115. Dividing
52.8718 by 115 gives a momentum of
0.4598 pound-seconds.

To calculate momentum directly the following formula can be used:
momentum = wav/225120 Ib.-secs. 1
wa is arrow weight in grains {
v is arrow velocity in feet per second. y
For example: An arrow with a weight Y
of 450 grains and a velocity of 230 feet per
y second will have momentum equal to:
450 x 250/225120 = 0.4598 pound-seconds.
To Calculate momentum directly the following formula can be used. Archived By
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