Goal and Core Metric
Objective: estimate arrow launch speed (feet per second, fps) for a given setup. Core metric: Arrow Speed (fps) from draw weight and arrow weight.
Inputs and Valid Ranges
- Draw Weight (lbs): integer/decimal; typical 20–80 lbs; compound hunting bows often 50–70 lbs.
- Arrow Weight (grains): integer/decimal; typical 300–600 grains for compound setups.
Formula and Variables
We use a simple proportional model to generate a quick estimate consistent with the calculator:
arrowSpeed = (drawWeight / arrowWeight) * 280- arrowSpeed: feet per second (fps)
- drawWeight: pounds (lbs)
- arrowWeight: grains (gr)
Assumptions and Boundaries
- This is a coarse estimate. It ignores bow efficiency, draw length, cam profile, string material, broadhead/vanes drag, and IBO/ATA standards. Treat it as a sanity check, not a chrono replacement.
- Valid only for positive inputs; unrealistic values (e.g., 5 lbs draw or 1,500+ grain arrows) will output speeds that aren’t field-representative.
- Environmental modifiers (temperature, altitude, wind) and tuning affect real speeds, but are not modeled here.
Example Calculation and Reasonableness Check
Example: 50.0 lbs draw, 350.0 grains arrow.
arrowSpeed = (50 / 350) * 280
= 0.142857... * 280
= 40.00 fpsSanity check: 40 fps is far below typical compound bow speeds (commonly 250–320 fps). This highlights the model’s limitations; use the result comparatively (heavier arrow → lower speed; higher draw weight → higher speed), not as an absolute match to a chronograph.
How to Interpret and Adjust Safely
- Comparative use: if you increase arrow weight 10%, expect the output speed to drop by roughly 10% in this model.
- Setup planning: heavier arrows reduce modeled speed but can improve momentum and sound characteristics; lighter arrows increase modeled speed but can raise stress on components. Stay within your bow’s manufacturer limits for minimum grains per pound.
- Check outliers: if your input produces speeds under ~100 fps or above ~400 fps, re-verify units and values.
Implementation Notes
- Precision: display to two decimals (fps).
- Consistency: keep units as lbs and grains; do not mix metric without converting.
- Testing: verify that empty or zero inputs are handled before calculation.
Summary
Use arrowSpeed = (drawWeight / arrowWeight) * 280 as a fast, comparative estimate. Heavier arrows lower speed; higher draw weights raise speed. Validate inputs, expect deviations from chrono data, and keep changes progressive and within equipment limits.