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Arrow Flight Simulator

This page contains an arrow flight simulator, which can be used to plot ballistic trajectories of arrows fired with a handbow or crossbow. Several parameters can be varied. All values use the International System of Units, except the angle of fire, which is measured in degrees.

Air density	kg / m³	A good mean for dry air pressure at sea level is 1.225 kg/m³ at 15° Celcius. Several factors affect this mean: elevation, temperature and humidity. They all act together, but here are some rough guidelines for each indvidual factor: The air density decreases about 10% per 1000 m elevation above sea level. The air density increases/decreases about 0.023 kg/m³ per 5° temperatue decrease/increase. The air density increases/decreases about 0.0008 kg/m³ per 10% humidity decrease/increase.	Time	6.9	s
Launch height	m	A launch height of 1.6 m is average for a man of 1.8 m in length. Increase or decrease for different body lengths.	Distance	209.9	m
Launch angle	°	A launch angle of 2° is suitable for a shot a point blank range. Longer ranges require a greater angle. 5° is a reasonable estimate for effective range. The longest range can be achieved with a 45° angle.	Velocity	41.8	m / s
Launch speed	m / s	Launch velocity depends on how much energy is given to the arrow and its total weight. The energy is proportional to the draw length and the force required at that length. However note that on release, a large part of the energy is used in de-tensing the bow, rather than propelling the arrow. Most traditional bows reach a total energy transfer efficiency of only 28% - 31%, modern bows 33% - 34%.	Momentum	2.1	kg m / s
Arrow mass	kg	Arrow mass is the total mass of the arrow, including shaft, feathers and head. A light flight arrow weighs about 15 - 20 grams, but heavier war arrows can reach weights up to 100 grams. Heavier bows require heavier arrows to transfer energy with reasonable efficiency and to prevent the arrow from breaking under the strain.	Energy	43.6	J
Arrow diameter	m	Arrow diameter tends to vary little and usually is 0.008 - 0.013 m. Crossbow bolts are shorter and thicker, generally 0.008 - 0.018 m.
Arrow drag coefficient		The drag of the air on the arrow depends on its mass, its frontal area and also its profile, which is represented by the drag coefficient. The actual coefficient also depends on arrow rotation, twitching and other factors, but this is beyond the scope of the simulator. A value of 1.5 matches most arrows, but fast arrows can run into turbulence, yanking the coefficient up to 2.5 or more - at least for the first part of their flight. Crossbow bolts are generally shorter and thicker; for these a value of 1.2 seems right.