Gravity and air drag are enough to say where the arrow lands
5 studies
The summary today
Two equipment tests point the same way as the claim, but only one sets the calculation against the point of impact. Using a compound bow mounted on a shooting machine, a physicist found the sight setting that put the arrow in the centre at a range of distances and converted it into a launch angle: the points fall on the curve of a ballistic calculation that contains only gravity and air drag, with no need to add any lift. Four years earlier, three very different arrows timed with a chronograph out to 90 metres had slowed down just as the same kind of calculation predicts, though that checks speed rather than where the arrow lands. The calculation also shows how much small errors weigh: at seventy metres a one-metre mistake in distance moves the impact about seven centimetres up or down, and one metre per second more speed raises it by about thirteen. The limits are plain: no archer and no wind.
Also phrased as: "arrow trajectory"; "calculating sight marks"; "the arrow glides"; "lift from the vanes"; "arrow ballistics"; "arrow drop"
In practice
On the range the idea goes round that the vanes give the arrow a little lift that holds it up in flight, while sight-mark programs work only with speed, mass and drag.
Evidence
-
1933
For Model Published later
A purely theoretical model: drag is the friction of the air over the surface, proportional to the square of speed, and the arrow is assumed to stay aligned with its flight path. The approximate formulas follow the curves obtained graphically with a gap smaller than the difference in range, 26 feet, produced by 5 feet per second more or less at launch. For a 300-grain arrow launched at 180 feet per second the maximum range is 652 feet in 6.87 seconds, against the 1,007 it would reach without air. Agreement with measured shots is stated in one sentence, with a reference to a 1930 paper, and no values.
The aerodynamics of an arrow · George Judson Higgins
-
2008
Context Equipment tests Published later
A test with a launcher and Japanese bows of 13 and 15 kgf, target at 28 m: the arrow covers the distance in about half a second and drops meanwhile by roughly the archer's height, so the aim has to be set on the vertical through the target, marked in the test with a plumb line. It shows how much gravity weighs even at short range, but it does not test a calculation.
B4 Effect of Te-no-uchi in Japanese-style archery · Tetsuhiko Yamamoto, Hiroshi Kinjo, Motoki Tanaka
-
2011
For Equipment tests Published later
Three arrows very different in mass and diameter (Protour 470, LightSpeed 400 and Axis FMJ 400) shot from compound bows mounted on a shooting machine, with speed measured by a chronograph at distances of up to 90 m to an accuracy of about 0.3 m/s. The trajectory is calculated in steps of a thousandth of a second with gravity and air drag, recomputed at each step, and the calculated speed along the flight follows the measured one in a way the author judges satisfactory for all three arrows. It tests how much the arrow slows down, not where it lands.
The aerodynamic drag and axial rotation of an arrow · J L Park
-
2015
For Equipment tests Published later
A Hoyt compound on a shooting machine: at each distance the sight setting that puts the arrow in the centre, converted into a launch angle, falls on the curve of a Runge-Kutta ballistic calculation containing only gravity and air drag. Launch speed of the sample arrow 74.5 ± 0.2 m/s, the mean of ten readings two metres from the bow. For the author the agreement shows that no lift needs to be assumed.
Applications of Physics to Archery · H. O. Meyer
-
2015
Context Equipment tests Published later
From the same calculation, at 70 m with a launch angle of 0.068 radians: one metre more distance moves the impact about 7 cm vertically, one metre per second more launch speed raises it by about 13 cm, and a 20% change in the velocity decay rate or the drag coefficient shifts it by about 7 cm. The decay rate, measured with two microphones over 25 shots at seven distances between 27.4 and 82.3 m, is 0.00231 per metre, which corresponds to a drag coefficient of 1.94.
Applications of Physics to Archery · H. O. Meyer
-
2023
Context Model Published later
An analytical model with drag proportional to the square of the speed: it derives a closed formula for the elevation angle as a function of distance, launch speed and velocity decay, and with 74.5 m/s and 0.002 per metre states that the curve agrees with the numerical methods and measurements of the 2015 work. The agreement is described in words, without residuals, and the comparison data are those from 2015.
Physics Application in Traditional Archery: Sight-lines Method for Aiming Using a Traditional Bow · Ibnu Jihad
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2023
Context Model Published later
Sensitivity analysis of the same model, at 70 m with 60 m/s and a decay of 0.002 per metre: estimating the decay at 0.001 sends the arrow 35 cm below the centre, estimating it at 0.003 sends it 38 cm above; misjudging the speed by 3 m/s moves the impact by 69-80 cm.
Physics Application in Traditional Archery: Sight-lines Method for Aiming Using a Traditional Bow · Ibnu Jihad
Status history
- 1933 Transferred The question starts life as a calculation. An aeronautical engineer writes the equations of the arrow's flight with only two forces, gravity and the friction of the air over its surface, and finds approximate formulas that follow the exact curves with a gap smaller than the one a slightly slower shot would produce. He says the results agree with experimental tests, but he says it in one sentence and without numbers, and no measurement on equipment has yet put the calculation to the test: the claim rests on a model.
- 2008 Transferred A study of the Japanese bow uses the trajectory without testing it: at twenty-eight metres the arrow flies for about half a second and drops meanwhile by roughly the archer's height, so the aim has to be set on the vertical line through the target. It shows how much gravity weighs even at short range, but nobody has yet compared a calculation with measured shots, and the claim still leans on the 1933 model.
- 2011 Reported The first measurement on equipment arrives. Three very different arrows, shot from compound bows mounted on a shooting machine, pass over a chronograph at distances of up to 90 metres, and the measured speed follows that of a calculation containing gravity and air drag, recomputed every thousandth of a second. It is a direct test, but of only part of the claim: it checks how much the arrow slows down, not where it lands.
- 2015 Reported The first test arrives that sets the calculation against the point of impact. With a compound on a shooting machine, the sight marks found at a range of distances and converted into launch angles match a ballistic calculation containing only gravity and drag: no lift is needed to explain them. The same calculation says that at seventy metres a one-metre error in distance moves the impact by about seven centimetres, and one metre per second more speed raises it by about thirteen. There are now two equipment tests in favour, but the 2011 one measured speed and this is the only one on the point of impact, with one bow, one arrow and no wind: the evidence is still limited.
- 2023 Reported An analytical model built on the same two forces derives a closed formula for the launch angle and states that its curve agrees with the 2015 measurements, without publishing the residuals. It adds a measure of how much drag matters: at seventy metres, with an arrow at sixty metres per second, estimating drag at half its correct value sends the arrow 35 centimetres below the centre. It is a calculation that reuses the 2015 data, not a new test, and the status does not move.
Related
Related articles
- Why do your groups open up with distance?Double the distance and the group doubles, or a little more: what geometry and competition scores say, and how to use two distances to find what opens your group.
- Wind and weather conditions in archery: how to read and manage themHow far the wind moves an arrow and why, how many points it costs, how to read and correct for it, and what the data say about rain, cold and heat.
- How much the air slows an arrow down, and what really changes the dragHow much speed an arrow loses in flight, how much the shaft, vanes and point add to air drag, and how much of it actually reaches the target.
Research lines
Cite
Campagna, M. (2026). Gravity and air drag are enough to say where the arrow lands (Version 2). In Evidence Registry. Retrieved 16 October 2026, from https://matteocampagna.com/en/registry/equipment/arrow-trajectory-gravity-drag
@misc{campagna2026_traiettoriagravitaresistenza,
author = {Campagna, Matteo},
title = {Gravity and air drag are enough to say where the arrow lands},
year = {2026},
howpublished = {Evidence Registry, matteocampagna.com},
url = {https://matteocampagna.com/en/registry/equipment/arrow-trajectory-gravity-drag},
note = {Version 2; accessed 2026-10-16}
}
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