Calculate how your arrow slows down over distance and how it affects KE and momentum.
Enter your chronographed launch speed in feet per second, the total finished-arrow weight in grains, and the shaft's outside diameter in millimeters. The calculator builds a table showing retained velocity, kinetic energy, and momentum at 10-yard intervals out to 60 yards.
Behind the table sits an exponential air-drag model: velocity at distance d equals the launch speed multiplied by e^(−kd). The decay constant k combines a drag coefficient of 1.5 — typical for a fletched carbon arrow with a field point, where measured values fall in the 1.3–1.7 range — sea-level air density of 1.225 kg/m³, the shaft's frontal area, and the arrow's mass. Because frontal area grows with the square of diameter while mass sits in the denominator, a heavier arrow on a skinnier shaft holds its speed noticeably better.
Watch how the three columns diverge: kinetic energy depends on velocity squared, so in percentage terms it bleeds off at twice the exponential rate of momentum, which is linear in velocity. That is why hunters who care about downrange energy floors check the 40–60 yard rows rather than the chronograph reading at the riser.
It depends on mass and shaft diameter. With this calculator's default-style setup — a 420-grain arrow on a 5.6 mm shaft launched at 290 fps — the exponential drag model predicts roughly 277 fps at 60 yards, about a 4.5% loss. A lighter or fatter arrow loses a larger fraction.
Kinetic energy depends on velocity squared while momentum is linear in velocity, so under exponential speed decay KE falls at twice the rate. In the 420-grain example above, the arrow keeps about 95.5% of its speed and momentum at 60 yards but only about 91% of its kinetic energy.
Yes — drag is proportional to frontal area, which grows with the square of diameter. A 4 mm micro-diameter shaft presents only about 38% of the frontal area of a 6.5 mm shaft, so at equal weight its drag constant, and therefore its speed loss, is correspondingly smaller.