How to Calculate Bow Efficiency

Your bow's efficiency is a measure of how much of the potential energy you put into it at its full draw length gets transferred to the arrow you shoot. To calculate your bow's efficiency, you need to find the potential energy stored in your bow when it is drawn and the kinetic energy of an arrow leaving your bow from a full draw length. Then, with some calculation, you can find your bow's efficiency by dividing your bow's potential energy by the kinetic energy of a drawn arrow.

Things You'll Need

  • Note paper
  • Graph paper
  • Pen or pencil
  • Ruler or tape measure
  • Handheld digital scale
  • Analog scale
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Instructions

  1. Finding Your Bow's Potential Energy

    • 1

      Hold your arms naturally outward with your palms facing forward, and have a friend measure the distance from one middle finger's tip to the other. Divide this distance by 2.5 to find your full draw length, and write down this number.

    • 2

      Notch an arrow to your bow, and get the digital scale into your drawing hand.

    • 3

      Pull your bow string back one inch.

    • 4

      Get a friend to measure your draw length with a measuring tape and write it down. Also have the friend write down the digital scale's weight reading for this draw length. Repeat this process for every inch up to your full draw length.

    • 5

      Draw an x-y axis on a piece of graph paper. Label this graph "Draw-Force Curve."

    • 6

      Label the x-axis "Draw Length," and mark each square of this axis in increments of one (from zero to your full draw length). Label the y-axis "Draw Weight," and mark each square of this axis with a scale in increments of five (from zero to the nearest five over your highest draw weight).

      For example, along the squares of the x-axis, you could write 1, then 2, then 3, etc. Along the squares of the y-axis, you could write 5, 10, 15, etc.

    • 7

      Put your finger on the "1" on the x-axis, and then trace straight upward to the weight that you found for your draw of 1 inch. Make an "x" there. Repeat this process for every number along the x-axis.

    • 8

      Connect all the "x" marks on your graph to make your "Draw Force Curve."

    • 9

      Count all the squares (including half squares) between the line connecting your x's and the line that is your x-axis to find this space's area.

    • 10

      Multiply the area by five (to account for your y-axis' scale) to find your bow's potential energy. For example, if you counted 204 squares, multiply 204 by 5 to find that your bow's potential energy is 1,020.

    Finding an Arrow's Kinetic Energy

    • 11

      Weigh your arrow using an analog scale. Use an online weight converter to change this weight from pounds to grains. Write down this weight in grains.

    • 12

      Shoot two test shots at an archery range. Make a note of the distance of both these shots. Also note the sight mark setting (the notch that you adjust to match your sight to the distance of your shot) for these shots, and the distance from your eye to the sight pin (what you look over or through to see where your shot is going) for each shot.

    • 13

      Use an online conversion tool to convert your measurements from feet and inches to meters and centimeters.

    • 14

      Go to the online "Arrow Speed Calculator."

    • 15

      Type the distance of your two test shots, the difference between the sight mark settings for both of these shots and the distance from your eye to the sight pin into the online "Arrow Speed Calculator."

    • 16

      Click the "Show Me!" button in the online "Arrow Speed Calculator" to get your arrow's speed in feet per seconds, or fps. Write down this speed.

    • 17

      Write down the formula KE = 450,800*m*v^2.

    • 18

      Change the formula's "m" to the weight of your arrow in grains and the formula's "v" to the speed of your arrow.

    • 19

      Multiply the speed of your arrow by itself (square it), and then multiply this number by your arrow's mass. Divide this number by 450,800 to find the kinetic energy of your arrow. Make a note of the resulting number.

      For example, if your speed is 200 fps, multiply 200 by 200 to get 40,000. And if your arrow's mass is 350 grains, multiply 40,000 by 350 to get 14,000,000. Finally, divide 14,000,000 by 450,800 to find 31.06.

    Calculating Bow Efficiency

    • 20

      Write down the equation Bow Efficiency = Potential Energy/Kinetic Energy.

    • 21

      Change the "Potential Energy" and "Kinetic Energy" in the equation to the numbers you found for those variables.

    • 22

      Divide your bow's potential energy by the kinetic energy of your arrow to solve the equation and find your bow's efficiency.

      For example, if your bow's potential energy is 1,020, and your arrow's kinetic energy is 31.06, then you would divide 1,020 by 31.06 to find that your bow's efficiency is 32.28%.