Kinetic Energy, Momentum, Bows and Arrows
There has been some debate-- and misconceptions-- on the use and application of Kinetic Energy (KE) and Momentum (M) in the bowhunting world. Which is better? Which is more accurate? Why are they important?
Answers to these questions lie more in the application of KE and Momentum, not whether or not one is better than the other. KE and Momentum are both real and accurate formulas, quantifying real physics that stretch far beyond just bows and arrows. The secret to using these formulas is knowing how they apply to you as a bowhunter. To explain let's jump into physics mode for a few, then I'll explain how this affects our ability to judge of our hunting arrow penetration potential.
Physics Explanation
This says the kinetic energy equals one-half the arrow’s mass (measured in grains), multiplied by the arrow’s velocity (expressed in feet-per-second), then multiplied by the arrow’s velocity again, and all of that is then divided by 225218. The answer will be expressed in foot-pounds.
Momentum equals the arrow’s mass (measured in grains), multiplied by the arrow’s velocity, expressed in feet per second and then divided by 225218. The resultant answer will be expressed in slug-feet per second.
The denominator in the above equations, 225218, converts the arrow’s physical weight, measured in grains, into pounds, and also factors in the gravitational constant (gc).
There are 7000 grains per pound. The gravitational constant is 32.174 feet per second, per second. Thus, 7000 x 32.174 = 225218.
Kinetic Energy (ft./lbs.)= ½ Mass x Velocity2
225218
Momentum (slug ft./sec.) = Mass x Velocity
225218
The Bottom Line
Notice in the Kinetic Energy (KE) formula the mass factor is cut in half and the velocity factor is doubled. This makes this formula good for measuring the shock an object hits with (such as a bullet), but not so much in regards to the actual penetration potential of an arrow which is much slower.
The momentum formula is much more accurate for estimating the penetration potential of an arrow because the shock it hits with is irrelevant. For arrows the factor that matters most is how hard the arrow is to stop.
Ready to find out more?
To learn how these formulas to apply to arrow performance, get a copy of the book “Can’t Lose Bowhunting” by Jeremy Johnson
