1. What is an Arrow Speed Calculator?

Definition: This calculator determines the actual speed of an arrow, along with its momentum and kinetic energy, based on the bow's IBO speed, draw length, additional weight on the bowstring, arrow weight, and draw weight.

Purpose: It is used by archers to estimate arrow speed, momentum, and kinetic energy for better accuracy and performance in hunting, target shooting, or competitive archery.

2. How Does the Calculator Work?

The calculator performs the following calculations:

Arrow Speed: \[ v = \text{IBO} + (L - 30) \times 10 - \frac{W}{3} + \min(0, -(A - 5D)/3) \] Momentum: \[ \text{momentum} = \frac{A}{225218} \times v \quad (\text{in slug-ft/s}) \] Kinetic Energy: \[ \text{kinetic energy} = \frac{A \times v^2}{450240} \quad (\text{in ft-lb}) \] Where:

• \(v\): Actual arrow speed (ft/s)
• \(\text{IBO}\): IBO speed (ft/s)
• \(L\): Draw length (inches)
• \(W\): Additional weight on the bowstring (grains)
• \(A\): Arrow weight (grains)
• \(D\): Draw weight (pounds)

Unit Conversions:

• Speed Units: m/s, km/h, ft/s, mph, kn, ft/min
• Momentum Units: N·s, kN·s, kg·m/s, slug-ft/s
• Kinetic Energy Units: J, kJ, MJ, Wh, kWh, ft-lb

Steps:

• Enter the IBO speed of the bow, selecting the unit (m/s, km/h, ft/s, mph, kn, ft/min)
• Enter the draw length, selecting the unit (mm, cm, m, in, ft)
• Enter the additional weight on the bowstring, selecting the unit (g, kg, gr, oz, lb, st)
• Enter the arrow weight, selecting the unit (g, kg, gr, oz, lb, st)
• Enter the draw weight, selecting the unit (g, kg, gr, oz, lb, st)
• Convert all inputs to the required units (ft/s, inches, grains, pounds)
• Calculate the arrow speed, momentum, and kinetic energy
• Select the desired units for the results and view the converted values

3. Importance of Arrow Speed, Momentum, and Kinetic Energy

Knowing the arrow speed, momentum, and kinetic energy is crucial for archers:

• Arrow Speed: Affects the trajectory and accuracy of the arrow.
• Momentum: Indicates the arrow's ability to penetrate a target, important for hunting.
• Kinetic Energy: Measures the energy delivered to the target, critical for ensuring effective impact in hunting or competition.

4. Using the Calculator

Examples:

• Example 1: For \(\text{IBO} = 300 \, \text{ft/s}\), \(L = 32 \, \text{in}\), \(W = 5 \, \text{gr}\), \(A = 400 \, \text{gr}\), \(D = 70 \, \text{lb}\):
  • Draw length adjustment = \((32 - 30) \times 10 = 20\)
  • Weight penalty = \(5 / 3 = 1.67\)

  • Arrow weight adjustment =

    \(\min(0, -(400 - 5 \times 70) / 3) = \min(0, -(400 - 350) / 3) = \min(0, -16.67) = -16.67\)
  • Arrow speed = \(300 + 20 - 1.67 - 16.67 = 301.67 \, \text{ft/s}\)
  • Momentum = \(\frac{400}{225218} \times 301.67 = 0.5360 \, \text{slug-ft/s}\)
  • Kinetic energy = \(\frac{400 \times (301.67)^2}{450240} = 80.82 \, \text{ft-lb}\)
• Example 2: For \(\text{IBO} = 320 \, \text{ft/s}\), \(L = 30 \, \text{in}\), \(W = 0 \, \text{gr}\), \(A = 400 \, \text{gr}\), \(D = 70 \, \text{lb}\):
  • Draw length adjustment = \((30 - 30) \times 10 = 0\)
  • Weight penalty = \(0 / 3 = 0\)

  • Arrow weight adjustment =

    \(\min(0, -(400 - 5 \times 70) / 3) = \min(0, -(400 - 350) / 3) = \min(0, -16.67) = -16.67\)
  • Arrow speed = \(320 + 0 - 0 + (-16.67) = 303.33 \, \text{ft/s}\)
  • Momentum = \(\frac{400}{225218} \times 303.33 = 0.5388 \, \text{slug-ft/s}\)
  • Kinetic energy = \(\frac{400 \times (303.33)^2}{450240} = 81.77 \, \text{ft-lb}\)

5. Frequently Asked Questions (FAQ)

Q: What is IBO speed?
A: IBO speed is a standard measure of a bow's arrow speed, typically measured at a draw length of 30 inches, a draw weight of 70 pounds, and an arrow weight of 350 grains.

Q: Why does the draw length affect arrow speed?
A: A longer draw length allows the bow to store more energy, increasing the arrow speed. The formula adjusts the speed by 10 ft/s for each inch deviation from 30 inches.

Q: What is the arrow weight adjustment?
A: The arrow weight adjustment accounts for the difference between the actual arrow weight and the ideal weight (5 grains per pound of draw weight). Heavier arrows reduce speed.

Q: Why are momentum and kinetic energy important?
A: Momentum indicates the arrow's penetration ability, while kinetic energy measures the energy delivered to the target, both of which are critical for effective hunting and target shooting.