Calculate arrow flex amplitude and spine rating based on draw weight and shaft stiffness.
The archer's paradox is the snake-like flex an arrow undergoes as it leaves the bow: the shaft bends around the riser at release and keeps oscillating in flight. Enter your peak draw weight in pounds, arrow length in inches, and the shaft's static spine deflection in inches (a 500-spine shaft deflects 0.500 inches under the standard test load).
The flex amplitude estimate in millimeters equals draw weight × length² × deflection ÷ 5000. Amplitude rises linearly with draw weight and deflection but with the square of arrow length — going from a 28-inch to a 30-inch shaft adds roughly 15% more flex with everything else unchanged. As a worked example, 50 lb of draw weight on a 29-inch shaft with 0.300-inch deflection yields about 2.5 mm of flex.
The spine verdict uses a window that scales with draw weight: deflections between 0.3 × (draw weight ÷ 100) and 0.6 × (draw weight ÷ 100) inches rate as ideal. For a 50 lb bow that window is 0.150–0.300 inches; a stiffer shaft below it is flagged too stiff, a softer one above it too weak.
At release the string pushes the arrow before it can clear the riser, so the shaft bends around the bow and keeps oscillating in flight — yet still arrives where it was aimed. This calculator estimates the amplitude of that flex in millimeters from your draw weight, arrow length, and spine deflection.
More than any other input: flex amplitude grows with the square of length in this model. Moving from a 28-inch to a 30-inch shaft adds roughly 15% more flex even though the length itself only increased by about 7%.
The window scales with draw weight: from 0.3 to 0.6 times (draw weight ÷ 100) inches of deflection. For a 40 lb bow that means 0.120–0.240 inches; stiffer shafts below the window are flagged 'too stiff' and softer shafts above it 'too weak'.