Arrow Kinetic Energy & Momentum

  • Here it is! The basic calculator, preset with the Rule of 400 installed!
    • Kinetic Energy (ft-lb)
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    Momentum (slug·ft/s)
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    Formulas: KE = (grains × fps²) / 450240; Momentum = (grains × fps) / 225218.

    Arrow Weight Change Calculator

    Assumes the bow delivers roughly the same kinetic energy when you change arrow weight, then solves for the new speed. (Real-world results can vary.)
    Predicted New Speed (fps)
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    Speed Change (fps)
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    Current KE (ft-lb)
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    Crossbow Efficiency Calculator

  • This is a fun one! Crossbows are very inefficient weapons.
  • There's no way to get exact results without measuring the entire draw, but this still gives a decent measurement to compare one crossbow to another, and one arrow setup to another.
    • Kinetic Energy (ft-lb)
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    Stored Energy (ft-lb)
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    Efficiency (%)
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    Notes
    Stored energy model assumes roughly linear draw force (avg force ≈ DW/2).
    Formulas: KE = (gr × fps²) / 450240; Stored = (DW × PS) / 24; Efficiency = (KE / Stored) × 100.

    Efficient Arrow Weight (Estimate)

    This estimates an “efficient” total arrow weight by assuming a linear speed change: k grains of arrow weight ≈ 1 fps change (as used in DBB/OGH’s Arrow Weight Change tool). :contentReference[oaicite:3]{index=3}
    Common guesses: 2–4 gr/fps
    KE peak gives a finite “best” weight under the linear model. Momentum in this model increases as you add weight until speed approaches zero, so we constrain it to a practical range.
    Estimated Efficient Weight (gr)
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    Predicted Speed at that Weight (fps)
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    Kinetic Energy (ft-lb)
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    Momentum (slug·ft/s)
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    Model: V(W)=V0−(W−W0)/k. KE=(W·V²)/450240. Momentum=(W·V)/225218.

    FOC (Front of Center) Calculator

    Measure from the throat of the nock:
    • Arrow Length (L): to the back of the point / end of shaft, not including broadhead
    • Balance Point (B): to the spot where the finished arrow balances with broadhead installed

    Crossbow Minimum Arrow Weight Calculator

    Calculates a recommended minimum finished arrow weight using:
    • GPP method: Draw Weight × Grains-Per-Pound
    • Manufacturer minimum (optional): uses whichever is higher
    Common “minimum” starting point is often 5.0 GPP.
    Example: some TenPoint/Wicked Ridge models specify minimum finished arrow weights (varies by model/year). :contentReference[oaicite:4]{index=4}
    Minimum by GPP (gr)
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    Manufacturer Min (gr)
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    Recommended Minimum (grains)
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    Recommended Minimum (grams)
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    Recommended Minimum (ounces)
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    Conversions: 1 grain = 0.06479891 g :contentReference[oaicite:5]{index=5}; 1 lb = 7000 grains :contentReference[oaicite:6]{index=6}.