Archery Ballistics

Recently, I invited you, my readers, to ask me any questions you have about archery and you responded. Over the next couple of blogs, I will try answer all of these questions to the best of my ability. I decided to answer the one I know the least about first. Although I am not into hunting, I am not against the practice if you are going to use the entire animal. Also, in my opinion, an animal deserves a quick humane kill and not left just wounded walking around in pain. David Roberts asked…

I’d be interested in seeing your take on ballistic; specifically focusing on achieving maximum momentum (e.g. A lightning fast arrow with the weight of a feather vs. a slow moving heavy clunker). Are there any equations for calculating the “perfect” arrow for inflicting the most damage on its target? It would have to involve the power of the bow, the weight of the arrow and the relation between the two. Is a 400 grain arrow traveling at 300 fps more damaging than a 700 grain arrow at 235 fps? Less?

For target shooting faster shots means less drop & better accuracy, but for us archery hunting folks a “perfect” arrow is one that is has the exact weight that will provide the most possible momentum of that arrow. You go into a sporting goods store and you see all the arrows advertising super light weight and giving performance metrics in the amount of energy that they transfer when they strike. That metric is the wrong one to use when looking for a damaging arrow. A damaging arrow doesn’t want to put x amount of kinetic energy into a target over the course of 2 inches, it wants to put x amount of kinetic energy into a target over 3 feet. Momentum calculations would pr

ovide that. I understand that you’re not really into the hunting with archery (I think?) and that this topic isn’t really beneficial to competition shooting at all, but for real world applications of archery it’s one of the most important topics around.

My understanding is hunting is about the kill and understanding arrow flight will help you make the most of the opportunities that are presented while in the bush.  There are two planes of accuracy that you need to be aware of; Horizontal (left – right) axis and Vertical (up – down) axis.

The horizontal arrow flight is managed through good proper form and the understanding about the effects of nature elements such as weather conditions. Check out my earlier blogs about the various effects.

The vertical arrow flight is tougher since all arrows fly on a parabolic course. Frequently misses are high and low since it is hard to judge the arc of your arrow flight for unmarked distances.

Parabola in mathematics, a parabola is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Another way to generate a parabola is to examine a point (the focus) and a line (the directrix). The locus of points in that plane that are equidistant from both the line and point is a parabola. – Wikipedia

Example. If you kick a soccer ball (or shoot an arrow, fire a missile or throw a stone) it will arc up into the air and come down again …… following the path of a parabola! (Except for how the air affects it.) – Math is Fun

Some bow hunters choose to use a 3-pin sight so they can guess better. By pre-sighting distances of 20, 40 and 60 yards as examples, it allows them to better judge the best impact for the kill zone between these sight marks.

Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles – Wikipedia.

Since the question is specifically about ballistics, understanding all components of a hunting arrow will help you select your “perfect” arrow configuration. There are a lot of variables to consider, here is a list of things to consider, I found on the following website

  • Shaft size (diameter and wall thickness)
  • Shaft length (+/- 3⁄4 to one-inch can significantly change shaft stiffness)
  • Weight of the broadhead to be shot (+/- 25 grains can significantly change shaft stiffness)
  • Draw weight of the bow (+/- 2.5 to five pounds can significantly change shaft stiffness)
  • Archer’s draw length (certain shafts become significantly weaker when cut past 28 inches)
  • String material (Dacron strings are slower and require a slightly softer arrow, for example)
  • Type of bow (recurve or compound with a wheel, soft-cam or speed-cam)
  • Finger or mechanical release (finger shooters require a slightly stiffer arrow)
  • Bow length (bows less than 40 inches in length require a slightly stiffer shaft)
  • Overdraw length, if used (three-inch-plus overdraws require a slightly stiffer arrow)

You can review my Arrows – The Series for details about most of these.

Faster shots means less drop & better accuracy” is true for all archers. Since, for example, at 150 fps, there is an 8” drop in trajectory at just 10 yards versus only 5 inch drop at 200 fps, there are benefits to maintaining a higher velocity. This allows you to shoot from farther away and better judge the curve; giving you more opportunities.

To continue, assuming all things are perfect, longer draw length or heavier draw weight should produce higher kinetic energy, momentum, and velocity that will result in deeper penetration. It also offers more choices in selecting your broadhead. My understanding is for small game, where penetration is not the issue you can use field tips. However for larger game and for a quick kill you need the proper broadhead choice as well as the proper arrow selection. Since, the weight of broadhead is the ballast of the arrow, and when we are talking about hunting you may need to start here.

A broadhead weight can range from 85 grain and can be more than 140 grains and the number of blades is important since more blades increase the wind resistance causing greater dive. I am not an expert about broadheads however I know you can select from various types including fixed blades and mechanical blades. You can also check out this video I found about types of broadheads and this website for the pros and cons of each. I also ran across these two websites about penetration of various different broadheads. (Wibowhunters and Bowonlyoutdoors). Once you have selected your style of broadhead, you can properly select the arrow to match your bow to maximize your velocity and penetration.

If you really want to understand the technical details of an arrow ballistics, arrow parabolic course and the calculations; check out this website. However I am not a math major and If you are like me that is far too technical. So for specific arrows and bow configurations including total momentum, there are several options available including online ballistics calculators such as Outdoorsden OR Peteward. You can also purchase highly rated archery applications such as The Archery Program Pro by Tony Virnoche and OnTarget!2 Software for Archers by Pinwheel Software that provide more than just ballistics information. Lastly if you are mobile user there is a phone/android application called Archery Ballistics that you can carry around with you to the sporting goods store to help you make your selections.

Remember every setup is different and changing even one thing can effect everything else. You will need to spend time with the calculators and trying various combinations until you find the right one for you and your bow.

Although, I am not into hunting I hope that I have been able to answer your question and provide some high-level direction.

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Arrows Series – Part 4: Spine, Flex and Stiffness

Before we discuss the topic of arrow spine, for proper safety and best performance, arrows need to match your entire bow setup. If you change draw weight, draw length, limbs, riser size, etc. this will affect you arrows. You may need to adjust the arrow length or require different arrows.

Arrow Myth:  An arrow is always straight.

Arrows SHOULD be perfectly straight when not in motion. However, when an arrow is released the force applied from the string causes the arrow shaft to be compressed against the resistant static weight of the arrow point and therefore bends.

Newton’s First Law of Motion: Every object in a state of uniform motion (rest) tends to remain in that state of motion (rest) unless an external force is applied to it.

Since the force applied is greater than the  resistance (weight of the tip), the arrow is propelled forward, and the shaft continues to flex and oscillate as it straightens itself. Arrow shafts that are either too stiff or too flexible will not fly well and will impact the accuracy of your shots or fail causing damage and/or injury. Therefore, we need to manage the flex properly so the arrow does not make any contact with the bow, or your arrow flight will be affected.

Important Tip: Arrow spine refers to the arrow shaft’s degree of stiffness (how much the arrow resists being bent) and is called spine deflection.

Basic Rule 1:  Shorter arrows act stiffer and longer arrows act more flexible.

Basic Rule 2: Powerful bows require stiffer arrows and less powerful bows require shafts that are more flexible.

Basic Rule 3: The heavier the tip equals greater the resistance, therefore the greater amount of compression.  So, a heavier tip causes the arrow to flex more and a lighter tip increase the stiffness.

According to the American Society for Testing and Materials (ASTM) the modern standards (ASTM F2031-05) an arrow’s official spine deflection is measured by hanging a 1.94 lb. weight in the center of a 28″ suspended section of the arrow shaft and is used for aluminum and carbon fiber arrows. (I believe original AMO standard has a basic guide to use for wood arrows spine determination and uses of 2 lb. and 26” section for standard measurement.) The actual distance the 1.94 lb. weight causes the shaft to sag down is the arrow’s actual spine deflection

For example, if a 1.94 lb. weight causes the center of a 28″ arrow to bend down 1/2 inch (.500″) the spine deflection would be .500″.  Stiffer arrows will bend less and more flexible arrows with bend more.

Almost every arrow manufacturer has its own numbering system and there are no universally agreed spine sizes among the various arrow manufacturers. Simply, the lower the deflection measurement equates to a stiffer arrow and higher the deflection measurement the more flexible the arrow. Manufacturers can number, size, and market their arrows anyway they want, as long as they provide the deflection data and test using the industry standard method.

Fortunately for us the engineers have already done the math for us and manufacturers provide spine selection charts. You are able to select an arrow based on your draw length and draw weight.

So when selecting arrows a good rule of thumb is that lighter draw weight, shorter draw length and/or lighter tip weight equals LESS arrow spine OR heavier draw weight, longer draw length and/or heavier tip weight equals MORE arrow spine.