With the same bow a heavier arrow receives more energy

The summary today

The measurements all point the same way: with the same bow the heavier arrow leaves more slowly but carries off more energy. The most controlled test mounts a laminated recurve on a mechanical shooting device and shoots it at 40, 45 and 50 lb with three arrows identical except for an internal weight, from 23 to 33 grams, 30 shots per combination: at every draw weight the heaviest is slower and carries more energy, 32.4 foot-pounds against 24.4 at 50 lb. A second experiment with the bow on a mechanical device finds the same on two 34 lb bows, with about 2 metres per second less and between 1 and 1.6 joules more for the heavy arrow, and earlier still the replicas of historical bows gave, with the Egyptian composite, about 46 joules for the 90 gram arrow against 34 for the 25 gram one. On a modern compound three arrows of different mass fit a model in which the bow behaves as if a mass of about five grams travelled with the arrow: with a 20.6 gram arrow 80 per cent of the available energy reaches the shaft. The models have given the reason since 1969: part of the energy is left moving the string and limbs, and that share falls the heavier the arrow. The limit is that nobody has measured the curve on an Olympic recurve with competition arrows, within the weight ranges used in competition, where a comparison between two shafts a quarter of a gram apart sees no difference; and the test with 30 shots per combination takes speed 20 metres from the bow, not at launch.

Also phrased as: "heavy arrow more kinetic energy"; "light or heavy arrow"; "arrow weight and bow efficiency"; "a heavy arrow is quieter"; "grains per pound"

Evidence

• 1933
  Context Model Published later

  An aerodynamic model of the arrow's flight: the curve of range against weight doubles back, so a heavier arrow carries further up to a point and then the advantage reverses. That arrow weight raises the bow's efficiency enters the calculation as a figure taken from earlier work, not as a result.

  The aerodynamics of an arrow · George Judson Higgins

• 1969
  For Model Published later

  A mathematical model of the modern recurve, integrated by computer: in the idealised case, with no friction and a string that does not stretch, all the stored energy goes to the arrow except the part needed to move the string, whose effect is the same as adding a third of the string's mass to the arrow; so the heavier the arrow, the larger the share it receives. With a 350 grain arrow the limbs take up part of the energy during the power stroke and give it back all at once, while with limbs ten times lighter the acceleration follows the draw curve. It is a calculation, with no measurements on equipment.

  Ballistics of the Modern-Working Recurve Bow and Arrow · Burton G. Schuster

• 1988
  For Equipment tests Published later

  Replicas of historical bows shot by a single expert archer, initial velocity measured with two optical screens at 3 and 6 metres, reporting the maximum of several shots: with the 28.8 kg Egyptian composite the 90 g arrow leaves at 32 m/s, the 50 g one at 40, 40 g at 47, 25 g at 52; with the 27.2 kg Tartar composite 50 g at 51 m/s, 30 g at 58, 25 g at 60. The authors do not give energies but they follow from the table: with the Egyptian bow about 46 joules for the 90 g arrow against 34 for the 25 g one, with the Tartar about 65 against 45. The light arrow is faster, the heavy one carries more energy.

  Experimental archery: projectile velocities and comparison of bow performances · C.A. Bergman, E. McEwen, R. Miller

• 1997
  For Model Published later

  A bow model validated on replicas: efficiency, that is the share of the stored energy passed to the arrow, depends on the ratio between the arrow's mass and the limbs', and a heavy arrow always gives high efficiency and a low initial velocity. No numerical values for a series of weights.

  An approach to the study of ancient archery using mathematical modelling · B. W. Kooi, C. A. Bergman

• 2007
  Context Model Published later

  A review chapter on the materials of the bow: the bow's virtual mass, which accounts for the energy left in limbs and string as the arrow leaves, is found by measuring speed as arrow mass changes and turns out constant for a given bow; on a Greenhorn recurve a 1992 laboratory test found it to be 4.6 grams per limb, 9.2 in all. With a constant virtual mass a heavier arrow takes a larger share of the energy. It takes up earlier measurements, with no new data.

  Design and materials in archery · B.W. Kooi

• 2009
  For Model Published later

  A dynamic model of a single-cam compound with arrows of different mass: the lighter arrow takes less energy from the bow and still undergoes a similar peak force, with a much less uniform acceleration. Below a mass of the order of 25 grams the final peak becomes sharp, and the author suggests staying towards the heavy end of the arrows in use, with a threshold he himself calls subjective. It is a calculation, with no measurements.

  A compound archery bow dynamic model, suggesting modifications to improve accuracy · J L Park

• 2013
  For Equipment tests Published later

  A laminated Browning Wasp recurve mounted on a mechanical shooting device with a mechanical release, shot at 40, 45 and 50 lb with three aluminium arrows identical except for an internal weight of 0, 5 and 10 grams, that is 23, 28 and 33 grams in all, 30 shots per combination and speed taken by chronograph 20 metres from the bow. At every draw weight the heavier arrow is slower, by about 3 metres per second between 23 and 33 grams at 50 lb, but carries more energy: 24.4, 30.0 and 32.4 foot-pounds at 50 lb, 17.2, 18.6 and 20.8 at 40. Speed is taken at 20 metres, not at launch, so it includes the loss over the first metres of flight.

  The Adoption of the Bow and Arrow: A Model Based on Experimental Performance Characteristics · Steve A. Tomka

• 2015
  For Equipment tests Published later

  A compound, three arrows of different mass shot from the same bow and measured with a chronograph: the velocities fit a model in which the bow has a virtual mass of about 5 grams, so efficiency is M/(M+m) and with the 20.6 gram arrow it is 0.80, that is 57.1 of the 71.0 joules available end up in the arrow. A heavier arrow therefore takes a larger share of the same energy. It is a preprint without peer review, on a single bow.

  Applications of Physics to Archery · H. O. Meyer

• 2015
  Context Equipment tests Published later

  The same compound returns 71.0 ± 0.5 of the 73.7 ± 0.5 joules put in during the draw: internal losses are 3-4 per cent, so the available energy is almost all of the draw's, and the difference between light and heavy arrows comes from how that energy is split between arrow and bow.

  Applications of Physics to Archery · H. O. Meyer

• 2016
  Context Equipment tests Published later

  A yew bow replica drawn at about 16 kg and a 9.7 g reed arrow, a single pair: from the measured force-draw curve it is estimated that only about a third of the bow's potential energy becomes the arrow's kinetic energy. It fits the low efficiency of very light arrows, but it does not compare different weights on the same bow.

  Archery by the Apaches – implications of using the bow and arrow in hunter-gatherer communities · Žiga Šmit

• 2020
  For Equipment tests Published later

  Two bows, one of wood and a Merlin reinforced with glass fibre, mounted on a mechanical device at a 23.5 inch draw and 34 lb, with two arrows of 25.66 and 30.35 grams and speed taken by chronograph one metre from the bow, 6 to 10 valid shots per arrow. With both bows the heavier arrow leaves about 2 metres per second more slowly but carries off more energy: with the Merlin 24.43 joules against 22.82, with the wooden bow 17.96 against 16.91. The authors put it down to the greater inertia of the heavier arrow, which takes the bow's energy better.

  The important role of bow choice and arrow fletching in projectile experimentation. A ballistic approach · Christian Lepers, Veerle Rots

• 2022
  Context Equipment tests Published later

  One archer, the same bow, two A/C/E arrows of almost equal weight, 18 shots each filmed at 3,000 frames per second: the 17.99 g one leaves at 59.21 m/s, the 17.73 g one at 59.67. The heavier one is slower, as expected, but the energy that follows is practically the same: with a quarter of a gram between them the expected gain is too small to see.

  Automatic image analysis of an archery arrow in free flight using high-speed video cameras · Riku Murakami, Hiroya Mamori, Takeshi Miyazaki, Naoya Takahashi

Status history

1. 1933 Not studied An aerodynamic model of the arrow's flight builds into the calculation that arrow weight changes the bow's efficiency, but it takes this from earlier work rather than deriving it; its result concerns range, which grows with heavier arrows up to a point and then doubles back. On the energy the arrow receives from the bow there is still no evidence.
2. 1969 Transferred The first mathematical model of the modern recurve supplies the reason: in the idealised case all the stored energy goes to the arrow except the part needed to move the string, which counts as a third of the string's mass added to the arrow, so the heavier the arrow the larger the share it receives. It is a calculation, with no measurement on equipment, and the claim rests on the model: transferred.
3. 1988 Reported Ballistic tests on replicas of historical bows, with the same shooter: with the Egyptian composite the 90 gram arrow leaves at 32 metres per second and the 25 gram one at 52, so the light one is much faster, but kinetic energy goes the other way, about 46 joules against 34 (the energies follow from the table, the authors do not give them). With the Tartar composite the same: 50 grams at 51 metres per second against 25 grams at 60. It is a direct test on equipment, but from a single study, with maximum velocities and no statistics: reported.
4. 1997 Reported A bow model supplies the reason and the same direction: efficiency depends on the ratio between the arrow's mass and the limbs', so a heavy arrow absorbs a larger share of the bow's energy and leaves more slowly. A model does not raise the status, and a carefully measured series of weights on the same bow is still missing: reported.
5. 2009 Reported Two calculation papers explain the mechanism from two sides. A 2007 chapter notes that the bow's virtual mass, which accounts for the energy left in limbs and string, is constant for a given bow, 9.2 grams on a recurve tested in the laboratory in 1992, and with a constant mass the arrow's share grows with its weight; in 2009 a compound model shows that the lighter arrow takes less energy from the bow, with a less uniform acceleration. No new measurement on equipment: reported.
6. 2013 Reported The first well-controlled test arrives: a laminated recurve mounted on a mechanical shooting device, three arrows identical except for the added weight, from 23 to 33 grams, three draw weights and 30 shots per combination. At every draw weight the heavier arrow is slower but carries more energy, 32.4 foot-pounds against 24.4 at 50 lb. With the 1988 replicas there are now two direct tests in agreement, but the 1988 ones give the maximum velocities of a single shooter with no statistics, and this one takes speed 20 metres from the bow rather than at launch: reported for now.
7. 2015 Reported Measurements on a compound put a figure on the share: three arrows of different mass, shot from the same bow, fit a model in which the bow has a virtual mass of about five grams, so with a 20.6 gram arrow 80 per cent of the available energy ends up in the arrow. The same work shows the bow returning 71 of the 73.7 joules put in during the draw. There are now three direct tests and they agree, but this one is a preprint on one bow and three arrows: the status stays reported.
8. 2016 Reported With a 9.7 gram reed arrow a wooden bow transfers only about a third of the stored energy, estimated from the force-draw curve measured on the replica. It fits the low efficiency of very light arrows, but it is an indirect estimate on a single bow-arrow pair, with no different weights on the same bow: reported.
9. 2020 Reported A second experiment with the bow mounted on a mechanical device, in a peer-reviewed journal, repeats the comparison on two 34 lb bows: with both, the 30.35 gram arrow leaves about 2 metres per second more slowly than the 25.66 gram one but carries off more energy, 24.43 joules against 22.82 with the glass-fibre bow and 17.96 against 16.91 with the wooden one. There are now two independent, well-controlled tests alongside the two weaker ones, and none points against; but none was done on an Olympic recurve with competition arrows, one takes speed 20 metres from the bow and this one counts 6 to 10 shots per arrow: the status stays reported.
10. 2022 Reported A comparison within the same archer and the same bow, 18 shots per arrow filmed at high speed: the 17.99 gram shaft leaves at 59.21 metres per second against 59.67 for the 17.73 gram one. The heavier one is slower, as expected, but with a quarter of a gram between them the energy that follows is practically the same: the result adds nothing and takes nothing away, and the status stays reported.

Related

Related articles

• How fast an arrow flies: the metres per second, what decides them and how much they matter on the targetHow many metres a second recurve and compound arrows fly, what decides launch speed, and how much speed matters on the target and for the score.
• How much energy actually reaches the arrow, and where the rest goesHow much of the drawing work reaches the arrow: models say about three quarters, while the few measurements show where the rest goes and what the arrow changes.

Research lines

• 22 studiesHow much energy passes from bow to arrow: models and measurements since 1937
• 32 studiesArrow aerodynamics: drag, boundary layer, vanes

Other claims in this domain

• CorroboratedAlong its flight the arrow loses an appreciable part of its launch speed12 studiesStatus since 2011
• CorroboratedAs it leaves the bow, the arrow flexes and snakes around the riser instead of leaving straight19 studies · 47 archers measuredStatus since 2012
• ReportedA camera-based scoring system misreads some arrows: the ones barely sticking out and the ones that shift the target face7 studies · 2 archers measuredStatus since 2017
• ReportedA chest band with fibre optic sensors measures breathing and mean heart rate with small errors, and an archer can wear it while shooting2 studiesStatus since 2019
• ReportedA compound bow stores between 70 and 100 joules and sheds about two thirds of the force at full draw4 studiesStatus since 2015

See all claims on equipment and tuning