Calculating the Math Behind Archery

Archery is known to have attracted a lot of sports enthusiasts since the immemorial time. The sport of shooting at the bull’s eye of a target has prompted the same people to master and hone their skills. However, choosing the right size of the bow is very important because a bow that is too large or too small for the shooter can lead to failure once he starts shooting. He can only become truly satisfied with his artistry if and when he considers the math behind the sport. In this case, three things are to be considered vital; the draw length, the bow size and the draw weight.

In determining the proper bow size, the proper draw length should first be taken into consideration. This can be done by using either of the two methods:

  1. Calculated Draw Length
  2. ATA Draw Length Standard

The Calculated Draw Length is fast and easy to do. It is sufficient and reliable, especially in purchasing your  first bow. Also, it has been tested and proven over the years. To determine the draw length, these steps should be followed:

  1. Measure your arm span. Stand against a wall and make a letter “T” by stretching your arms with palms open, facing forward.
  2. Have someone measure from the tip of your right middle finger to the tip of your left middle finger by using a tape measure.
  3. Put marks of arm span on the wall by using a pen or marker.
  4. Measure the distance between both marks.
  5. Record as “arm span”.
  6. Divide the “arm span” by 2.5
  7. The answer is the calculated draw length.
  8. Record the calculated draw length.
  9. Round up to the nearest ½ inch.
  10. The bow size can now be determined using the calculated draw length.

The ATA Draw Length Standard is another method used in obtaining the precise draw length. This is highly recommended if access to a suitable bow is at hand.

compound bow precision calculations

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Once the calculated draw length is recorded, selection of the appropriate bow size follows. Also, two types of bow are available for choosing: the recurved bow and the compound bow. With recurved bows, the bow has to be drawn further more while more of the recurved shape has to be drawn out of the limbs. To ascertain that the bow remains its efficiency, a certain degree of recurve should stay in the limb. This is to determine how the ideal limb size complements the archer’s body. On the other hand, Compound bows make use of a wheel to extremely boost the energy stashed in the limbs. A standard compound bow has a release of about 50% which explains why the force needed to hold the bow in fully drawn position should be doubled when exerted in the middle of undrawn and fully drawn situation. This just goes to show that with the best compound bow, more than twice as much energy can be stored in the limbs.


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Furthermore, the proper draw weight should not be taken for granted. If the weight is too heavy or too light, it will hamper the archer’s shooting skills. In reality, however, there is no ideal weight to begin with. Each individual is unique, has his own needs and has different capabilities. So, the best thing to do is to talk to the instructor first to see what he can suggest and start from there.

Having taken into account the draw length, the best compound bow size and the draw weight, it is not surprising for an archer to hit the target. In archery, there is a phenomenon known as “Archer’s Paradox” where upon the release of the arrow to the left or right and even if it is calculated to be off target, still it will rectify and aim at the target. This is the physics behind archery.

The math or physics behind archery, by and large, proves to have helped a number of archers in becoming successful and professional in their field. Whether they rely on empirical or analytical data, the accuracy in aiming at the target and hitting it bull’s eye still depends on the archer’s abilities, skills and commitment to get to the top.

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