Physics of the Compound Bow

Physics of the Compound Bow

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A Brief History of the Bow

* Arrowheads have been found in Africa that date back as far as 25,000 to 50,000 B.C.
* Throughout the next few tens of thousands of years, humans had PLENTY of time to refine their techniques. Fire-hardening arrow heads, fletching arrow shafts to improve their flight characteristics, "tillering" bows so that the upper and lower limbs had the same bend radius, etc. All of these improvements helped increase the efficiency and accuracy of the bow and arrow, and helped humans to survive and advance throughout the ages.

* One major advance was the creation of composite bows. Around 2,800 B.C. people began blending different materials together to create better bows. The Egyptians of these times had long composite bows capable of shooting an arrow up to 400 yards!
* As you can see, the bow has been around a long while. It wasn't until recently, however, that the actual design of the bow itself was changed. In fact, this ingenious modification happened about forty years ago...

The Compound Bow

* On December 30th, 1969, Holless Wilbur Allen was granted the patent that would change archery forever.

* The invention of the compound bow was just the beginning. As with the invention of the original bow and arrow, time and ingenuity would take the basic concept to new heights. However, the modern understanding of physics, coupled with advanced materials and construction techniques, has greatly increased the pace at which advances are made.
* Using cams on one or both limbs of a bow allowed for an increased draw weight in the middle of the draw and a reduced weight at full draw. Archers firing traditional recurve bows encounter the highest resistance and draw weight at full draw. This means less time sighting in on a target before fatigue sets in, due to the strain of holding the bow at full draw. Compound bows, on the other hand, use a cam system which places the most resistance about 2/3 of the way through the drawstroke. At full draw, the compound bow reduces the tension in the bowstring by as much as 75-80%, allowing an archer to remain in position and more carefully sight in on a target.

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* Different cam designs, along with different limb materials, can significantly increase the advantage of compound bows. Bow manufacturers boast arrow speeds in excess of 300 feet per second nowadays. That's over 205 miles per hour!

Understanding Compound Bows

* Basically, the energy stored in a compound bow at full draw is still stored in the limbs. Several factors control the "power" of the bow. Let's take a look at some of these factors:
* Draw Weight- Amount of force necessary to draw the bowstring.
* Draw Length- How far the bowstring pulls back from rest to full draw.
* Let-Off- The decrease in tension needed to hold a bow at full draw. Can be anywhere from 35% to over 75% less tension than required in the middle of the drawstroke.
* Cam Design- Basically, larger, more aggressive cams give more speed. They are also harder to draw, though, so there are benefits and drawbacks to any cam.
* Brace Height- This is the distance from the string to the grip of the bow. Longer brace heights can be a little more forgiving of form, since the arrow doesn't travel quite as far on the bowstring before it is released.
* The Force Draw Curve graph above shows the amount of energy stored in the bow at full draw (dark gray area). Increasing this area under the curve by increasing draw length increases the power stored in the bow. By increasing the draw weight, the height of the curve would increase, increasing the area. By increasing the draw length, obviously, the length of the curve would increase. Changing the brace height (distance from string at rest to the handle of the bow) would effectively increase the powerstroke, which means the curve would have a steeper slope initially. As you can see, making power in a compound bow is quite possible. The side-effects of these adjustments would make the bow more difficult to shoot, however. Changing the weight, length, or duration of the bowstring's travel changes the shooting characteristics of the bow, so any adjustments and potential benefits should be carefully weighed against the drawbacks.


The arrow used is another important factor in the performance of a compound bow. The higher the draw weight of a bow, the higher the required weight of the arrow. This rule holds because lighter arrows are not stiff enough, nor rugged enough, to withstand the acceleration a heavy bow produces. Another consideration to keep in mind is that heavier arrows dampen vibrations, and resist acceleration more due to their increased mass. This actually protects the bow from damage, since firing a light arrow in a heavy bow can have almost the same negative effect as dry firing it. There are minimum recommended arrow weights for different draw weights. In all actuality, setting the bow up properly and firing the correct minimum weight arrow actually levels the playing field quite a bit, speed wise. This is because lighter arrows are significantly faster, so being fired by a less powerful bow these arrows still perform very well.

"Knockdown" power is also a consideration to keep in mind. The impact between an arrow and it's target contains a certain amount of force. The amount of force is proportional to the amount of mass of the arrow, relative to the speed. An experiment conducted by showed the following results regarding arrow speed vs. arrow weight:

In Conclusion...

Physics has played an important role in archery for many years. Recent advances, however, are showing just how important a tool physics can be. Refining different manufacturing and design techniques to maximize the performance of a bow is directly related to physics, which really isn't much of a surprise.

Each of the different techniques discussed earlier to optimize the performance of a bow revolve around basic physics principles. Changing the mass of an arrow to increase penetration is a basic force concept. Increasing the draw weight of a bow, or increasing the draw length, or changing the brace height, all change the physical characteristics of the bow in some fundamental way, increasing the amount of potential energy the bow is capable of storing. In other words, understanding basic physics is pretty important for archers. Or anyone else interested in the world around them.
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