Archery · Physics of Bows, Arrows & Aim

Store the energy. Release it clean. Let gravity do its part.

A bow is a spring, an arrow is a projectile, and the 10-ring at 70 m is a tenth of a degree wide. Take the challenge, learn the science with an Arrow Lab, then find coaching, competitions and academies in India at your level.

How well do you know the physics of archery?

15 questions on bow energy, arrow flight and gravity, spine and fletching, aiming and scoring, holding and breathing, and wind and range safety. No trick wording and no exam pressure. You'll get your score, a verdict, an explanation for every answer, and a link to the chapter for anything you missed.

02 · The science

Six chapters. Every number worked out.

Each chapter explains one idea in plain language, then works a real example. Try the Arrow Lab to see how draw weight, arrow mass and distance change the flight.

Interactive · Arrow Lab

Set the bow, the draw and the arrow, then pick a distance and see how far the arrow falls

A simple model: stored energy ≈ ½ × draw force × power stroke (draw length minus an 8.75-inch brace height), with 75% of it going into the arrow. Flight ignores air drag, so real arrows arrive a little slower and lower. These are illustrative values for learning, not tuning advice.

Draw weight40 lb

Draw length28 in

Arrow mass20 g

Distance

Energy stored in the limbs43.5 JCh 1 · ½ × force × stroke

Arrow speed57.1 m/sCh 1 · ½ m v²

Arrow energy32.6 JCh 6 · why ranges have rules

Flight time1.23 sCh 2 · distance ÷ speed

Drop if shot level7.37 mCh 2 · ½ g t²

Launch angle needed6.1°Ch 2 · ½ asin(g d ÷ v²)

Bar = arrow speed on a 0–80 m/s scale. Try a heavier arrow, then a longer distance. Only ever shoot at a supervised range (Ch 6).

CH 1

How a bow stores energy

A bow is a spring you load with your back muscles.

Drawing the string does work: force × distance. If the force rose evenly from zero to the draw weight F over the power stroke s (from brace height to full draw), the stored energy would be E ≈ ½ F s. Real bows store somewhat more because of their force–draw curve. Not all of it reaches the arrow: some stays in the limbs and string as vibration and sound.

Worked example · 28-inch draw, 8.75-inch brace height, 75% of stored energy to the arrow (illustrative)

Draw weight	Arrow	Stored energy	Arrow energy	Arrow speed
30 lb (133 N)	20 g	≈ 32.6 J	≈ 24.5 J	≈ 49.5 m/s
40 lb (178 N)	20 g	≈ 43.5 J	≈ 32.6 J	≈ 57.1 m/s
40 lb (178 N)	25 g	≈ 43.5 J	≈ 32.6 J	≈ 51.1 m/s
50 lb (222 N)	20 g	≈ 54.4 J	≈ 40.8 J	≈ 63.9 m/s

40 lb × 4.448 = 177.9 N; power stroke (28 − 8.75) × 0.0254 = 0.489 m; ½ × 177.9 × 0.489 ≈ 43.5 J; × 0.75 ≈ 32.6 J; v = √(2 × 32.6 ÷ 0.020) ≈ 57.1 m/s.

✋

Feel the numberHolding 40 lb at full draw is like holding an 18 kg bag on three fingers, steady enough to aim at a 12 cm circle 70 m away.

A longer draw (30 in) on the same 40 lb bow: what stored energy?

Power stroke (30 − 8.75) × 0.0254 ≈ 0.54 m; ½ × 177.9 × 0.54 ≈ 48 J.

↑ Back to the challenge

CH 2

Arrow flight & gravity

From the moment it leaves the string, the arrow is falling.

Ignoring drag, an arrow flies at constant horizontal speed and falls under gravity: flight time t = d ÷ v and drop ½ g t² below the line it was launched along. To land on target you launch slightly upward, at θ = ½ asin(g d ÷ v²).

Worked example · 20 g arrow at 57.1 m/s, no drag (from our Arrow Lab)

Distance	Flight time	Drop if shot level	Launch angle
18 m	≈ 0.32 s	≈ 0.49 m	≈ 1.6°
30 m	≈ 0.53 s	≈ 1.35 m	≈ 2.6°
50 m	≈ 0.88 s	≈ 3.76 m	≈ 4.3°
70 m	≈ 1.23 s	≈ 7.37 m	≈ 6.1°
90 m	≈ 1.58 s	≈ 12.2 m	≈ 7.9°

70 m: t = 70 ÷ 57.1 ≈ 1.23 s; ½ × 9.81 × 1.23² ≈ 7.4 m. World Archery's standard distances are 70 m for recurve and 50 m for compound, with competition distances of up to 90 m.

Why the sight moves

Drop grows with t², so it more than doubles from 30 m to 50 m. Archers set the sight lower for longer distances, which raises the bow arm and the launch angle. Drag slows the arrow along the way, adding a little more drop than this model shows.

What launch angle would 57.1 m/s need at 30 m?

½ asin(9.81 × 30 ÷ 57.1²) ≈ 2.6°.

↑ Back to the challenge

CH 3

Spine, the archer's paradox & fletching

The arrow bends around the bow and still flies straight. That's no accident.

On release, the string drives the back of the arrow forward while the front sits beside the riser. The shaft bends and oscillates as it clears the bow: the archer's paradox. An arrow with the right stiffness (spine) for the bow's draw weight recovers and flies true; too stiff or too weak and it leaves at an angle.

Fletching keeps the point forward

Vanes or feathers at the back move the centre of drag behind the centre of mass. If the arrow turns sideways, the extra drag on the tail swings it back in line, like a weathervane. Slightly angled vanes also spin the arrow, averaging out small flaws.

Worked example · the same energy, different arrows (40 lb, 28 in)

Arrow mass	Speed	Momentum	Drop if shot level at 70 m
20 g	≈ 57.1 m/s	≈ 1.14 kg·m/s	≈ 7.4 m
25 g	≈ 51.1 m/s	≈ 1.28 kg·m/s	≈ 9.2 m

Same 32.6 J: the heavier arrow is slower but carries more momentum (m × v), which helps it hold its line in wind. 25 g: t = 70 ÷ 51.1 ≈ 1.37 s; drop ≈ 9.2 m.

A 30 g arrow from the same bow (32.6 J): what speed?

v = √(2 × 32.6 ÷ 0.030) ≈ 46.6 m/s.

↑ Back to the challenge

CH 4

Aiming, angles & scoring

At 70 m, the 10-ring is a tenth of a degree wide.

World Archery's recurve face at 70 m is 122 cm across with a 12.2 cm 10-ring; the compound face at 50 m is 80 cm with an 8 cm 10-ring. The angle a ring covers is angle ≈ size ÷ distance (in radians).

Worked example · how small the 10 really is

Division	Distance	10-ring	Angle covered
Recurve	70 m	12.2 cm	≈ 1.74 mrad ≈ 0.10°
Compound	50 m	8 cm	≈ 1.60 mrad ≈ 0.09°

0.122 ÷ 70 ≈ 0.00174 rad. A sight pin 0.8 m from your eye that drifts 1 mm moves the impact about 1 × 70 ÷ 0.8 ≈ 88 mm at 70 m.

The five-colour target

Ten scoring zones: yellow 10 and 9, red 8 and 7, blue 6 and 5, black 4 and 3, white 2 and 1; a miss scores 0. On the compound face the outer four rings are usually removed, leaving yellow, red and blue.

What angle does the compound 10-ring cover, in degrees?

0.08 ÷ 50 = 0.0016 rad × 57.3 ≈ 0.09°.

↑ Back to the challenge

CH 5

Holding, breathing & let-off

The steadiest bow is held by bones and back, not by arm muscles alone.

A recurve archer holds the full draw weight while aiming. A compound bow's cams give let-off: the holding weight at full draw is only a fraction of the peak. Either way, small movements at the bow become big misses at the target (Ch 4), so archers build a repeatable posture: bow arm extended, drawing with the back, a consistent anchor point and a settled breath.

Worked example · what you hold at full draw

Bow	Peak draw weight	Let-off	Holding force
Recurve	40 lb	none	≈ 178 N
Compound	60 lb	80%	≈ 53 N

20% of 60 lb = 12 lb × 4.448 ≈ 53 N. Let-off values vary by bow; 80% is illustrative.

Breathing and the shot sequence

Settle the breath before the final aim: chest movement shifts the bow arm.
Hold only as long as it's steady. If you start to shake, let down safely and start again.
Clean release: relax the string fingers so the string leaves smoothly, and keep the bow arm still through the follow-through.

A 50 lb compound with 75% let-off: what's the holding weight?

25% of 50 lb = 12.5 lb (about 56 N).

↑ Back to the challenge

CH 6

Wind, drag & range safety

An arrow is a projectile with real energy. Ranges are designed around that.

A crosswind pushes the arrow sideways for its whole flight. Light arrows are pushed around more by the same force, and slow arrows are exposed for longer, so both drift further. Drag also slows every arrow, so the drop at long range is a little more than the no-drag model.

Worked example · energy an arrow carries

Bow	Arrow	Speed	Energy
30 lb	20 g	≈ 49.5 m/s	≈ 24.5 J
40 lb	20 g	≈ 57.1 m/s	≈ 32.6 J

½ × 0.020 × 57.1² ≈ 32.6 J. Launched at 45°, a no-drag arrow from this bow could fly about v² ÷ g ≈ 330 m: one reason ranges need clear zones well behind the targets.

Range rules

Shoot only at a supervised range. Nock and draw only on the shooting line and only towards the targets. Nobody goes forward of the line until every archer has stopped and the signal is given. Never "dry-fire" a bow (release without an arrow): the energy goes into the limbs and can break them.

Doubling arrow speed multiplies its energy by how much?

E ∝ v², so by 4.

↑ Back to the challenge

Store the energy. Release it clean. Let gravity do its part.

How well do you know the physics of archery?

Six chapters. Every number worked out.

Set the bow, the draw and the arrow, then pick a distance and see how far the arrow falls

How a bow stores energy

Arrow flight & gravity

Why the sight moves

Spine, the archer's paradox & fletching

Fletching keeps the point forward

Aiming, angles & scoring

The five-colour target

Holding, breathing & let-off

Breathing and the shot sequence

Wind, drag & range safety

Range rules

First arrows → club & registration → state & national events → academy → India selection → coach or judge

Who sets the rules

Global

World Archery

World Archery coaching & judging

India

Archery Association of India (AAI)

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