# Archery Physics Calculator - Draw Curve, Arrow Speed, Sight Marks, Archer’s Paradox

> Bow physics: draw-force curve to stored energy and arrow speed for longbow, recurve and compound bows, KE, momentum, trajectory, sight marks, drift, spine.

- URL: https://qilingtools.com/en/physics/archery
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Start from the draw-force curve: the area under it is the energy the bow stores, and a virtual-mass model turns that into arrow speed, kinetic energy and momentum for any arrow weight. Drag the points to reshape the curve and compare a longbow, a recurve and a compound with adjustable let-off. The trajectory tab integrates quadratic drag to give the aiming angle, drop, pin gaps and wind drift at each distance, and the paradox tab animates the shaft flexing around the riser and suggests a rough spine.

## How to use

1. Pick a preset bow or set the type, draw weight, draw length, brace height and arrow weight
2. Drag the dots on the draw-force curve and watch stored energy, speed and efficiency change
3. Open Trajectory & sight marks, set fletching, crosswind and zero distance, and read drop and pin gaps per distance
4. In Archer’s paradox & spine, choose spine, arrow length and point weight and play the slow-motion release

## Features

- Typical draw-force curves for longbow, recurve and compound (with let-off), editable by dragging
- Stored energy as the area under the curve; arrow speed in fps and m/s from a virtual-mass model
- Speed, kinetic energy and momentum vs arrow weight, with a grains-per-pound check
- Quadratic-drag trajectory: angle, time, speed, level-shot drop, height vs line of sight, pin gap, Didion wind drift
- Slow-motion archer’s paradox animation with the first bending frequency
- Rough spine suggestion from draw weight, arrow length and point weight

## FAQ

### Why does a compound shoot faster than a recurve of the same peak weight?

Arrow speed depends on stored energy, the area under the draw-force curve. A longbow or recurve builds force roughly linearly from zero, so the area is about half of peak × power stroke. A compound’s cams raise the force quickly to peak and hold it, filling 75–80% of that rectangle, so it stores much more energy. At full draw it lets off, so you only hold 20–30% of the peak while aiming.

### Heavier arrows are slower, so why use them?

On release, part of the energy goes to the arrow and part stays in the moving limbs and string. A heavier arrow leaves a smaller share behind, so the bow is more efficient: the arrow is slower but carries more kinetic energy and momentum, penetrates better and the bow is quieter. Light arrows fly flatter and suit target shooting. Very light arrows approach a dry fire and can damage the bow, which is why makers set a minimum grains per pound.

### How are the pin gaps calculated?

For each distance the tool finds, by bisection on the drag trajectory, the launch angle that hits the target. The line of sight runs from the eye through the pin to the target, and the eye sits above the arrow (the peep-to-arrow height), so the sight line is tilted down from the arrow by the launch angle plus atan(eye height / distance). The eye-to-pin distance times the tangent of that angle gives the pin position, listed relative to the shortest distance. Real marks still need to be confirmed by shooting.

### What is the archer’s paradox?

On a traditional bow without a centre-shot cut-out, the arrow rests beside the riser and seems to point off target, yet it flies straight. With a finger release the string rolls off the fingertips and pushes the nock sideways, so the shaft flexes from side to side and bends around the riser before straightening. Only an arrow whose spine matches the bow flexes with the right timing to clear it cleanly; too stiff and it veers to the riser side, too weak and it veers the other way.

### How accurate is the spine suggestion?

It is only an empirical approximation: effective weight ≈ draw weight (times 1.15 for compounds) plus corrections for arrow length over 28 inches and point weight over 100 grains, and spine ≈ 26000 ÷ effective weight. Real arrow selection also depends on bow efficiency, release style, point type and string material, so use the shaft maker’s chart and fine-tune with paper or bare-shaft tuning.

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