Terminal Arrow Performance: Sorting through the Confusion

Each year, thousands of hunters take to the woods with their chosen archery tackle, to pursue the elusive whitetail. The fall colors, warmer weather, and extended seasons all add to the allure of bowhunting. Modern compound bow technology has advanced to the point that just about any bow will provide consistent, accurate, and reliable performance. Beyond those considerations, however, there are some important choices that the hunter must make when purchasing a new bow. In general, the industry has done a poor job educating hunters in the critical areas that determine which bow setup is right for them. Hunting magazines provide little more than glossy ad print and subjective reviews concerning “look” and “feel”. Manufacturers carry on about “dual-cams” vs. “single cams” (or newer hybrid cams), “kinetic energy”, draw weight, and of course, the all important “speed” factor. This provides the hunter with little information to go on.

Often times, broadhead selection is based upon what a friend uses, or what “looks” good, when in reality – broadhead select might be the most important factor in archery. It is, of course, the broadhead that completes the transaction, so to speak.

Little has been published in regard to broadhead performance and its relationship to the arrow and bow. Enter Dr. Ed Ashby, an avid hunter and writer. In 1985, Dr. Ashby traveled to Africa and performed extensive testing on almost three dozen different broadhead designs, including fixed blade steel to replaceable multi-blade heads, and a few semi-custom heads. The project was conducted at Mkuzi Game Reserve in the Province of Natal, Republic of South Africa. Tony Tomkinson, Chief Ranger at Mkuzi, was the moving force behind the research. He has also been the person primarily responsible for the opening of Natal to legalized bowhunting. Test data was recorded from shots on live animals as well as shots on carcasses (Those shots on carcasses occurred immediately after death so that tissue degradation did not affect the outcome). Animals tested ranged from the impala and bush buck (106 – 143 lbs) to the zebra (700 – 1000 lbs).

The results of the study were impressive. According to Dr. Ashby, the three most important elements in an arrow are:

1. the efficiency of the arrow to utilize the energy it has (mechanical advantage of a simple machine)
2. the momentum of the arrow (not kinetic energy that is often cited)
3. the resistance of the target

As noted in the paper, we can do nothing about the resistance of the target. Other factors can be controlled.

To gain an understanding of this body of work, one must understand some of the principles of physics behind the study. Dr. Ashby does a good job explaining these principles in the following excerpts from his 1996 research paper entitled “Broadhead Performance”:

Simple enough, right? Mechanical advantage tells us that the more blades on a broadhead (ie: the more surface area), the more resistance that head will meet upon impact with the target. This makes sense. As an example, which object would be easier to penetrate a wall – a screwdriver or a baseball bat?

We must also consider the energy that the arrow carries. Again, from Dr. Ashby’s paper:

Now that we have a better understanding of mechanical advantage, and kinetic energy vs. momentum, we can begin to understand their relationship towards a hunting arrow. I must stress again, at this point, that the “magic” number of .57 lb-seconds of momentum was established for large African game. Such a momentum is not necessary for the whitetail hunter, but the principles behind the calculation remain. The next logical question, for the whitetail hunter, becomes ‘what should my momentum be’, and ‘how to I relate mechanical advantage to momentum?’. Those questions will be answered shortly. There’s one more factor to discuss. Remember those three main factors determining arrow performance? Ability to do work, energy, and resistance? Well, its true that we can’t factor the resistance of the target. But we can factor the resistance of the arrow shaft as it passes through the animal.

To determine shaft drag through testing, Dr. Ashby used the same broadhead on arrow shafts that were

1) smaller diameter than the ferrule of the broadhead

2) same diameter than the ferrule of the broadhead

3) larger diameter than the ferrule of the broadhead

The results of his testing gave him the respective multipliers of 1.0, .9, and .6.

Dr. Ashby uses his own calculation, which throughout the data demonstrates a strong correlation to the arrow’s penetration ability. This is how he ties momentum to mechanical advantage, as well as shaft drag. He refers to the measurement as Tissue Penetration Index, or TPI.

Now, let’s finally take a look at a real world hunting setup, using Dr. Ashby’s TPI as a predictor of the penetrating ability of the arrow. We’ll also compare this to one of the many examples that Dr. Ashby cites in his paper. First off, to calculate your TPI, use the following:

(momentum*MA*shaft drag factor)

For our example, we’ll use my hunting rig, which is:

2004 Martin Prowler, Tru-arc hybrid cam system, 62 lb, 29” draw, with a 450 grain carbon arrow (Beman ICS shaft), tipped with a Magnus Stinger, 100 grain, 2 blade broadhead having a cutting surface of 2 1/8” and a cutting diameter of 1 1/16”.

First, lets calculate the momentum of my arrow:

momentum= (weight*speed)/(acceleration of gravity), with weight it pounds and speed in feet per second, therefore:

m=(450/7000)*(230) / 32 feet per second per second, which roughly equals 0.462 lbs-sec.

Now consider the mechanical advantage of my broadhead:

MA=2.125/((1.0625*.5)*2)= 2

Lastly, my arrow shaft is slightly smaller than the ferrule of my broadhead, so when considering shaft drag, I can use a multiplier of 1.0.

Based on this information, I can determine the TPI of my arrow to be:

(momentum*MA*shaft drag factor) or in my case:

.462*2*1 = 0.924 TPI

Great, you might say, but how does that relate to whitetails? Consider two examples from Dr. Ashby’s paper:

From longbow:

Consider a 60 pound longbow firing a 788 grain compressed cedar arrow, with a 190 grain Grizzly two blade broadhead, at 148 fps has only 38.34 ft. lbs of K.E., .52 lb.-sec. of momentum, but has a TPI of 1.50. T hat combination was used to repeatedly shoot through the scapula of a large zebra stallion and through the thorax to the off side, often breaking off-side ribs (never failing to penetrate the scapula and completely through the thorax).

Additionally, he tested a modern compound bow:

This combination was also compared to a high energy compound firing a 450 grain carbon arrow tipped with a three blade head, with cut width of 1 1/8" and a cutting blade length of 2", at a velocity of 259+ fps. This combination yields 76.56 ft. lbs. of K.E., .52 lb.-sec. of momentum, but a TPI of only 0.62. It was unable to penetrate the zebra scapula.

Note that in both examples, the momentum was the same – the only thing that changed were two constants – arrow weight, and mechanical advantage of the broadhead. Performance could be matched with the compound bow if only different arrows and broadheads were selected. Now, you don't need to be able to penetrate the scapula of a zebra to hunt whitetails - I'm not claiming that AT ALL. but notice the difference in my bow setup compared to the one tested, and the TPI difference of .924 compared to .62 .

Based on this information, I'm very comfortable with my setup. its one man's research, I know, but he is very educated, has done years of testing, and considering the lack of any other real testing data, what else do we have to go on?

I realize this was long winded, but hopefully its clear enough to allow some people to get a picture of the real dynamics involved in killing with a bow and arrow, not just the often quoted draw weight, kinetic energy, and speed that are quoted by the manufacturers. I’d recommend to anyone interested to read Dr. Ashby’s works – it’s the most extensive testing I’ve come across. I’ll conclude with Dr. Ashby’s summary recommendations for today’s bowhunters:

1) Maximize your bow’s efficiency: 12 to 14 grains of arrow mass per pound of draw weight is peak efficiency for most compound bows.

2) Use broadheads of high mechanical advantage.

3) Use broadheads with a cut on impact tip

4) Accept nothing less than perfect arrow flight. A tuned bow with proper arrow spine will ensure that minimal energy is lost due to flexing in flight.

5) Do not use mechanical broadheads. In Dr. Ashby’s testing, mechanicals were the most prone to breaking, which stops penetration cold. They have a poor mechanical advantage as well, and require additional energy to deploy.

6) Use an arrow shaft smaller in diameter than the ferrule of the broadhead.

7) Shaft finish – basically, the smoother, the better – there is less resistance.