Speed kills! Right?

Traditional archers generally shoot heavier arrows than compound archers. Traditionalists tend to not speak about arrow speeds, and may have never chronographed their projectiles. However, the average compound bow commercial boast about the feet-per-second that can be achieved. Apparently arrow speed is important; or is it?

From the perspective of a relative beginner the amount of information that can be unearthed with a simple internet search is staggering. Unfortunately any click on an online forum or Facebook group yields the all-too-common contradicting statements. And while getting it right is important for competitive endeavours on the archery or 3D range, getting it right for hunting can be the difference between life and death, or worse.

As always, when the problem looks overwhelmingly complicated, breaking it down into smaller questions can help. Let’s ‘break it down’.

Accuracy

“A heavy arrow/faster bow/insert-any-discussion-topic-here doesn’t mean a hill of beans if you can’t hit them where it counts!” is a very popular, and true, one-liner that pops up in most discussions. That statement hides two aspects: performance of the bow-arrow combination and ability of the shooter. Since obviously we can all challenge Robin Hood to a shooting match and win, let’s focus on the equipment. Given a certain bow and a certain distance, and Howard-Hill-like abilities, is a lighter, faster arrow inherently more accurate than a slower, heavier arrow?

The consensus seems to be “no”; overall weight doesn’t seem to have an influence on accuracy in ideal conditions. Some say that heavier arrows are “more forgiving”, which supposedly means it responds less frantically to shooter error. I am not experienced enough to judge that claim. However, two factors enter the equation in hunting conditions. One is wind. The heavier arrow is accredited with better wind-bucking characteristics, more prone to stay close to the intended path. Where I live and hunt (bald-ass prairies, and high mountain ridges), that could become a major factor.

Trajectory

The second factor is trajectory, not an issue if we have flawless ranging and aiming abilities, but important for those mortals who may occasionally have trouble calling it 22, 26, or 31 steps to a deer. The lighter, faster arrow has a flatter trajectory in the near to medium ranges, our hunting ranges, and therefore is less likely to punish the shooter for ranging errors. With heavier arrows, and draw weights at the lighter end of the spectrum, estimating the range correctly becomes critical especially on longer shots.

Penetration

So why would you consider a heavier arrow, if you lose out on a flatter flight? Here is where the fun starts, and the topics of contention is arrow penetration. In the blue corner we have those that feel the need for speed. “Speed kills” says a compound bow commercial. In the red corner we have those that live by big brass inserts, and point weights in the hundreds of grains. Traditional archers don’t care about arrow speed, right? Let the bout commence.

Round 1: Kinetic Energy

At the risk of boring you to death, here is the formula for calculating kinetic energy once more, you have probably seen it a hundred times:

Kinetic Energy = 1/2 x m x v2

The weight* of the arrow is in there (m) multiplied by the square of the arrow speed (v). Speed makes the biggest contribution. The faster you can push the arrow, the more energy you have flying through the air. Since from a bow of a given draw weight the heavier arrow will go slower than the lighter arrow, this round goes to the lighter arrow.

* If you want to get really particular, the formula asks for the mass of the arrow. For this purpose the weight is an acceptable substitute. Check here for some very basic explanations about the difference: http://www.physlink.com/education/askexperts/ae321.cfm

Round 2: Momentum

More formulas:

M = m x v

Momentum equals the product of arrow weight and speed. So from a bow with a given draw weight, the heavy arrow goes slower, and the light arrow faster, but which has the advantage? Using 3Rivers Archery’s spine calculator (http://www.3riversarchery.com/dynamic-spine-arrow-calculator-from-3rivers-archery.html), which also estimates arrow speed, we can plunk in some numbers to see who wins.

Using a generic 50# recurve at 28″ draw weight as our weapon, how do the following two properly-spined set-ups perform (theoretically)?

Carbon Express Heritage 90 – 29″ – 125 grs tip – 10 grs insert

Total arrow weight 420 grs: calculated arrow speed is 200 fps

Carbon Express Heritage 350 – 29.25″ – 200 grs tip – 100 grs insert

Total arrow weight 663 grs: calculated arrow speed is 160 fps.

A quick session with the calculator shows that the momentum of the lighter arrow is about 21% lower than that of the heavier arrow (and coincidentally, the kinetic energy is roughly equal).

So why is momentum important again? One of the many online dictionaries says it nicely. Momentum is “the property or tendency of a moving object to continue moving”. And that is what we want from an arrow, keep moving into and preferably through the animal’s body. A heavier arrow, with the same kinetic energy, does that better than a light arrow.

Round 3: FOC

FOC stands for Forward Of Centre. Usually expressed as a percentage, it is a measure of how much weight of the arrow sits forward of the balancing point of the arrow. The formulas are getting more complicated:

%FOC = 100 x  (A – L/2) / L

A is the distance from the low-point on the nock to the balance point of the arrow (where it sits in equilibrium on a sharp-edged object) and L is the total arrow length from the nock to the edge of the insert. There are more than a few sites that explain this in detail and even provide a calculator, here is one: http://www.grizzlystik.com/Calculating-Forward-of-Center-FOC.aspx

FOC is worthy of consideration because it is one of the most important parameters that influences penetration, according to Dr. Ashby (http://www.alaskabowhunting.com/PR/ATA_Handout_Text_Web.pdf). This discussion can become way too technical quickly. An arrow is a pretty flexible projectile, and the more mass sits towards the back of the arrow, the more awkward the moment of impact becomes. Mass towards the back end can push the arrow out of its path of perfect flight, negatively influencing penetration. If you have a lot of time and interest, you should try reading some of Ashby’s findings that results from years of studying and field testing (http://www.grizzlystik.com/Dr.-Ed-Ashby-W26.aspx).

All of this is relevant to our discussion on arrow weight because a higher percentage FOC is easier to achieve with a heavier arrow; a heavier arrow that is achieved mostly by increasing the point weight. Heavy tips and brass inserts help putting together an arrow that is “tip heavy”, and therefore has a high FOC.

Round 3 goes to the heavier arrow as well.

Conclusion

We looked at three factors that presumably influence penetration. Kinetic energy, momentum, and FOC. There are other factors that were ignored for now (arrow integrity – it can’t break on impact, arrow flight – we assumed that your arrow was perfectly tuned to your bow, relative diameter of broadhead ferrule and shaft – if the shaft is narrow, there will be less drag on the arrow from body tissue, shape of the broadhead – length to width ratio and type of bevel, and more).

One of these has only an indirect influence on penetration, and that is kinetic energy. Momentum is what counts when it comes to resisting the slowing-down forces of the animal’s body. Arrow speed does increase momentum, so it definitely has an effect. But not as dramatic an effect as the mathematical number of kinetic energy seems to suggest. As indicated by the example, for two arrows with practically the same kinetic energy, the heavier one has significantly more momentum. By the way, it also has a significantly higher %FOC (21.8 vs. 14.8).

So why doesn’t everybody shoot 1000 grs arrows? Because of trajectory. A lighter arrow shoots flatter than a heavy one. And if your arrow gets so heavy and the flight so curvy that aiming becomes difficult, you may just have lost all advantage. You can make up for that by increasing your bow’s draw weight, but not everybody is physically equipped to handle that (including me).

In this treatise that already ran on too long, we haven’t even touched on what stands on the receiving end of our arrows. It makes a difference whether you are hunting rabbits, a turkey, a small Southern whitetail, a big Northern mule deer, elk, moose, or bigger. Or shooting 3D targets. As a totally unbiased TV show watcher, I get confused by the number of whitetail deer of medium size that I see running off with considerable lengths of arrow sticking out of them on the shooter side. These are shot predominantly by compound bows of recent manufacture. And they are not shoulder hits, where the arrow might encounter heavy bone. In my layman’s perspective that means that something is not right. If they can’t get an arrow through a broadside deer, with all the power of their compound, how am I going to kill one with a light longbow? Are they shooting ultra-light arrows, chasing the speed that the bow manufacturer claims kills? I don’t know. All I have figured out is that I am going to build the heaviest arrow I can shoot out of my bow with a trajectory that still makes sense for hunting. What exactly does that mean? Once I have it figured out I will report back.

Frans Diepstraten