Ever hear or read about someone claiming that a lightweight and fast arrow penetrates a target further than a heavier, slower arrow? What about the argument that slower and heavier arrows penetrate better on animals than their lighter, faster counterparts? Do these arguments contradict each other? The answer may be a surprise.
Let’s start at the beginning and understand why an arrow stops. There are three main phenomena that slow an arrow: resistance to material failure, friction and drag.
Material failure is an easy one to understand; in order to move past a solid object, the arrow must either move the material out of the way and/or break it. Shoot an arrow at paper, the paper is “broken” and the arrow moves past it and slows down a tiny bit because of the resistance. Shoot an arrow at 1/8″ plywood and the same occurs, but this time the arrow slows down more because more energy was used to cause failure in the wood. Shoot an arrow at a reinforced concrete wall and well…you get the idea. To cause material to fail the arrow expends some of it’s energy and the overall kinetic energy left in the arrow is less as well as its speed.
Friction is a much tougher animal to tackle because of the complexities of the phenomena. It comes in various forms, the one most familiar being solid to solid friction or dry friction. This friction is governed by the equation
Force = mu x N
where “mu” is the coefficient of friction, a value experimentally determined depending on the materials of the solids, and N is the normal (perpendicular) force between the objects. Basically this formula says that the harder you push two moving objects together, the greater the resistance force to move them. Energy from the moving objects is converted into heat in this case, which can readily be seen by rubbing your hands together and feeling them heat up.
When an arrow penetrates an animal full of fluids, there is some lubricated friction that occurs between the wetted parts of the animal and the solid arrow, and more importantly, skin friction. Skin friction is the friction between a solid and a fluid moving parallel to each other and is a large factor in the overall drag of an object moving through a fluid. If you put your hand under water and sweep it around you in a big arc has fast as possible, you will feel the skin on your hand that runs parallel to the path of your hand pushed back, this is skin friction (no pun intended!) The force you feel on the front of you hand that is perpendicular to the movement is the frontal drag force.
Drag is what occurs when an object moves through a fluid and the fluid pushes back on the object. We already discussed part of the drag as skin friction; the other part is the form drag. Form drag is the resistance to movement of the solid through the liquid because of the form or shape of the solid. An arrow head must push the fluid out of the way before it can pass through the fluid. Unlike breaking through a solid, the arrow head does not “break” the fluid, but rather moves it out of the way and the fluid collapses back upon itself after the solid has passed. A sleek, pointed arrow head is going to move fluid out of the way much easier and with less resistance to a blunt object.
So what does all this have to do with penetration of faster/slower and lighter/heavier arrows? I’m glad you asked! When an arrow enters a target, let’s say solid foam for simplicity sake, the foam directly in front of the arrow head is broken or pushed past it’s failure level by the arrow head. As the head passes and the initial shock diminishes, the material begins to collapse back onto itself and onto the arrow shaft; dry friction! The faster the arrow, the longer time that more of the shaft has to pass before the target foam collapses and exerts a normal force onto the shaft, increasing friction and creating heat, thereby robbing the arrow of energy and slowing it to a stop. Generally speaking with a target of perfectly homogeneous foam throughout, a faster, lighter arrow has a better chance to penetrate deeper than a slower, heavier arrow. This is a very tough test to carry out to any degree of accuracy because every section of a target, even ballistic gel, is different and will act accordingly; not to mention gravity adding another dimension to the problem. But that is beyond the discussion at hand.
Now back to penetration in an animal. Just like with a target, the arrow point must first break through the solids of the animal before the lubricated/skin friction and drag forces begin to take affect. However, once into an area of high fluid concentration, the arrow head begins to experience a phenomena completely different from a solid target. The resistance to the solid arrow passing through the fluid, the drag, is actually greatly increased with higher velocities. An extreme example of this would be gently entering a pool or doing a belly flop; care to try this experiment and share the results with us? In a simple way of explaining it, fluid particles have a harder time getting out of the way of a faster moving solid than a slower one and thus faster moving objects experience a higher drag.
To fully explain this subject could fill volumes, but hopefully this short post has shed some light onto why people that claim they get better penetration with fast, light arrows on their targets could be just as right as people that claim better penetration occurs on animals with slower, heavier arrows. Of course nothing is ever as simple as it seems and all sorts of issues and differences arise when arrows hit heavier bones or take a longer path through the guts of an animal rather than a perfect broadside shot that missed any ribs or other hard objects.
The other side of the issue has to do with the kinetic energy and momentum of an arrow and how they can be an indicator of penetration ability. For more on this subject, see the Kinetic Energy and Momentum Article.
Other posts you may enjoy:
- Heavy vs. Light Arrows: Downrange Speed and Power
- Kinetic Energy, Momentum and Arrows: a Simplified Approach
- Penetration Testing: Why You Should NOT Use Foam for Comparing Hunting Penetration
- Arrow Kinetic Energy and Momentum: what they mean to the archer
- Arrow Penetration Testing: Real Bows, Real Arrows, Real Results…Part II