MY SIMULATOR

Archery Bow Physics
Limb Energy & Arrow Flight

Find your aim. Follow the flight.

INTERACTIVE 3D

Launch 0 m/s

Stored energy 0 J

Last shot –

Move DRAW / ANGLE / WIND / DISTANCE, then press Start practising (Space). Drag to orbit, wheel to zoom.

Draw

85%

Angle

12°

Wind

3 m/s

Distance

30 m

Bow & arrow

Bow draw weight35 lbf

Arrow mass26 g

Arrow spine (static deflection)0.500 in

Wind directioncrosswind →

Aim off (windage)0.0°

Fletching Place

Camera & quality

Readouts

Force – draw curve (energy = area)

Flight path (side view)

■ with drag & wind ■ vacuum parabola ■ target

Arrow flex during the power stroke

Score (end of 6 arrows)

Experiment: what angle for 30 m?

Press Auto-aim: it solves the full drag model for the elevation that centres the arrow at the target and compares it with the textbook no-drag formula. Air drag always asks for a slightly higher angle. Switch Place to Moon (no air): the two answers coincide.

The science

What you see. A practice bow in a stand pitched by the ANGLE control. The string is drawn by the DRAW fraction and loosed at a round straw target. Everything is virtual and for physics learning only; the target is an inanimate disc.

F(x) = F_full [ (1−s) u + s u³ ],  u = x / X      force–draw (s = 0.25 limb stiffening)
U(x) = F_full X [ (1−s) u²/2 + s u⁴/4 ]     stored limb energy
η U = ½ (m_a + m_v) v²                    launch speed (η = 0.80, m_v = 30 g virtual mass)
dv/dt = g − k |v−w| (v−w),  k = ρ C_d A / 2m_a   flight with drag and wind
no drag: R = v² sin 2θ / g
f₁ = (βL)² / (2πL²) √(EI/μ),  βL = 4.730   first flex mode of the shaft
EI = F L³ / (48 δ)    from the static spine test (1.94 lbf, 26 in span)
t_power ≈ 2 s_p / v         power-stroke time (uniform acceleration)

Assumptions. Draw force curve and efficiency are typical model values, not a measured bow; limbs are an energy store plus a 30 g virtual mass; arrow is a point mass with quadratic drag (C_d for the fletching styles is illustrative); wind is uniform; the flex amplitude (4 mm start), damping (3 %) and the small yaw coupling (0.05) are illustrative constants and the flex shown on screen is exaggerated 12×. Historic details of old bows are not modelled.

Checks. running…

Virtual sport-archery model for education. Not instructions for real equipment; real archery needs qualified supervision and a safe range.

Archery Bow PhysicsLimb Energy & Arrow Flight

Archery Bow Physics
Limb Energy & Arrow Flight