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.

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.

Arrows Series – Part 3: Draw Weight

Obviously, force is required to move the arrow forward off the bow and it is generated from the tension of the limbs through the bowstring. Therefore, when purchasing arrows you need to know your draw weight so you can purchase the correct corresponding spine size for best performance. Limbs stiffness is determined by the amount of force, measured in pounds, required to draw the bow to a 28” draw length as outlined in the following Archery Trade Association (ATA) standard.

AMO BOW WEIGHT STANDARD

For Conventional Bows

Bow weight is the force required to draw the nocking point of the bow string a given distance from the pivot point of the bow grip (or the theoretical vertical projection of a tangency line to the pivot point parallel to the string). Draw length from pivot point shall be designated as DLPP and shall be referred to as TRUE

DRAW LENGTH.

For the purpose of uniform bow weight designation, bow weight is the force required to draw the bow string 26 1/4” from the pivot point. This weight will be marked on bow as being taken at 28” draw (26 1/4” plus 1 3/4” = 28”) See DRAW LENGTH STANDARD.

EXAMPLE: Weight Adjustment Range: 45/55 lbs. Weight Set At: 50 lbs.; Hold 32 lbs. Draw Length Range: 29” – 30”

EXPLANATION: The pivot point is a more realistic measuring point (when compared to the variations of profile of the back of bows at the handle section) for establishing bow weight since the pivot point is a constant in all bows as well as the contact point of the bow hand from which the true draw length is generated.

The 26 1/4” DLPP is the approximate equivalent of the 28” draw used previously on the more massive wooden handle bows.

Therefore, your draw weight is a combination of your draw length (See Arrow Series – Part 2 Measurements) and the combination of your riser (23” or 25”) and your limb stiffness (15#-50#).

For example, a 25” riser with a 34# long limb produces a 70” bow with a draw weight of 34 pounds at a 28” draw length.  If these same limbs were used on a 23” riser, the combination would produce a 68” bow with a draw weight of 36 pounds at a 28” draw length.

However, not everyone has 28” draw length, especially young archers whose draw length will change progressively with growth. So as a rule of thumb you can add or subtract approximately two pounds for each inch your draw length is over or under the 28” standard.

Using the previous example, if an archer has a 26” draw length and uses a 25” riser with 34# long limbs it will produce 30# of force at full draw OR uses the 23” riser with 34# long limbs it will produce 32#.

This is very important to select limbs that enable you to develop and compete however do not cause long-term physical damage. When purchasing limbs you need to determine if the limbs are too heavy, you can try this simple 7-second challenge.

7-second challenge

1. Draw the bow to the anchor
2. Hold seven seconds
3. Let down without lowering your hands, stay in set-up position to take a 2 sec brake,
4. Repeat several times.

If you cannot do it properly then the limbs are too heavy for you. If you find this challenge extremely easy, you can look at heavier poundage limbs, if you choose.

Now you understand draw weight and used in combination with your draw length you can see the arrows that match your equipment using a manufacturers arrow selection chart. In the up coming blogs we will try to examine the arrow spine, flex and stiffness.

Arrows – The Series (This time, it’s personal)

Since arrows are extremely important for an archer, I thought I would do a couple of blogs about arrows starting with the various components. I will be focusing on arrows for recurve target archers, since there are a lot of articles about arrows for both compound and traditional archery already. Selecting the correct arrows for your best performance is not simple task. There are tons of things to know and understand and it may require some trial and error. In this first blog we will start with the basic components.

An arrow is comprised of four major components the shaft, the point, the nock and the fletching.

Shaft : The shaft is primary structural component of the arrow and all other components are attached to it. Originally arrows shafts were made from wood however new shafts are made from aluminum, carbon fibre or both.  It is very important to properly match the arrow stiffness (or spine) to the archer for the best groups. Spine, or stiffness of the arrow, references how much or little the shaft bends when compressed through the shot and it typically matched by using the archer’s draw length and the bow poundage.

Fletching : Glued towards the back of the arrow, fletching are the airfoils for the arrows designed to stabilize the arrow in flight. Traditionally made from real feathers, target arrow fletching are now typically either plastic feathers or plastic vanes. Most target arrows have three fletches that are attached with a slight twist to help the arrow spin and stabilize faster in the air.  The quicker and more stabile the arrows is, the more consistent your groups will be.

Point : The point, or arrowhead, is the functional part of the arrow that is inserted and glued to the front end. It provides the weight and is typically made of various types of metal include tungsten.  Target points are usually bullet-shaped and designed to penetrate target butts easily without large amounts of damage.

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Nock : Found at the rear end of the arrow, target nocks are typically made of plastic. They are inserted, capped over or combined with separate medal pins inserts and held in place by friction. Target nocks are designed to gently pinch the bowstring to hold it in place when the bow string is drawn.

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Over the next few blogs we will dive deeper about these components, various discussion concepts like center shot, arrow indexing and numbering your arrows in upcoming posts and help understanding things like spine and Archer’s Paradox.

Remember, this blog is not meant cover everything about arrows. I am still learning and visit my coach regularly to help me develop my understanding about everything archery. I encourage you to share your knowledge and experiences so we can all develop together.

Remember Cartel Doosung offer a wide variety of arrow lines including aluminum and carbon fiber including their new line of Arista arrows for young archers. If you are in the market for some new arrows check my earlier blog about selecting and purchasing arrows.