A competition bow passes about three quarters of the drawing work to the arrow

The summary today

The three-quarters figure starts out as a modelling parameter and only later finds a measurement. In 1990 the reference model for the competition recurve sets the efficiency at 0.75, meaning three quarters of the drawing work becomes kinetic energy of the arrow; the following year another model of the modern working recurve calculates it instead of setting it and finds 0.729, and in 1998 a more complete model takes up the same value, recalls that estimates fitted to filmed shots give 0.76 longitudinally and 0.71 transversely, and reports that on a modern bow the measured efficiency was a few points below the prediction. The first measurement on a bow shot by archers comes in 2001 and concerns kyudo: with ten archers and fifty shots per string, the Japanese bow passes between 67.7 and 69.4 per cent of its stored energy to the arrow. On a modern bow there is a single measurement, from 2015, in a preprint and on a compound the paper does not describe as a competition bow: the archer puts 73.7 joules into the draw, the bow gives back 71.0 and the 20.6 gram arrow receives 57.1, a little over three quarters of the drawing work and 0.80 of the energy returned. The order of magnitude holds, but the figure depends on how it is defined, against the drawing work or against the energy the bow gives back, and on the arrow, since the same bow is more efficient with a heavier arrow. For a competition bow, and for today's Olympic recurve in particular, there is no direct measurement.

Also phrased as: "bow efficiency"; "dynamic efficiency of the bow"; "how much energy reaches the arrow"; "stored energy and arrow energy"; "virtual mass of the bow"

Evidence

• 1937
  Context Model Published later

  The first study of bow dynamics in the bibliography: the calculations are made for a bow with 100 per cent efficiency, and the author adds that, taking the string into account, a purpose-built Osage bow reached 93 per cent, while most bows deliver much less. It gives no figure for a competition bow.

  The Dynamics of A Bow and Arrow · C. N. Hickman

• 1981
  Context Model Published later

  A model of the longbow from the 1937 calculations, with a 25-gram arrow, a 7-gram string and 93-gram limbs: with an elastic string only 78 per cent of the stored energy ends up in the arrow, against the 92 per cent predicted with an inextensible string. The author reports measurements between 70 and 85 per cent. It concerns a longbow, not a modern competition bow.

  Bow and arrow dynamics · W. C. Marlow

• 1990
  For Model Published later

  Mathematical model of the first phase of flight, checked against high-speed film of a leading Polish archer whose equipment is taken as the standard system: for the reference bow the efficiency, defined as the ratio between the arrow's kinetic energy at the start of flight and the work done in drawing, is 0.75, with a ratio of 1.3 between transverse and longitudinal elasticity. It is the value on which the nomogram for choosing shafts by draw weight and length is built.

  Experimental and theoretical research in archery · Roman Pekalski

• 1991
  For Model Published later

  A model of the modern working recurve in which efficiency is not set at the outset but comes out of the calculation: 0.729, with a static quality coefficient of 0.434, meaning a little under three quarters of the stored energy passes to the arrow, in line, according to the author, with values in the literature.

  On the mechanics of the modern working-recurve bow · B. W. Kooi

• 1998
  For Model Published later

  Model of the interaction between bow and arrow that treats the bow as a spring with its own efficiency: for the standard combination, a 66 inch Hoyt Pro Medallist T/D, it assumes 0.75 both longitudinally and transversely, and reports the estimates obtained by non-linear regression on the filmed arrow profiles, 0.76 and 0.71. It also reports that in experiments with a modern bow the measured efficiency was only a few percentage points below the model's prediction, without giving the figure.

  Bow-arrow interaction in archery · B. W. Kooi

• 2001
  Context Kyudo archers Published later

  Ten archers from a university kyudo club, fifty shots with each of four strings, with the same bow for all: the efficiency, calculated as the arrow's kinetic energy over the potential energy of the drawn bow, is 69.0 ± 3.3 per cent with a Kevlar string, 69.1 ± 3.5 with Technora, 69.4 ± 3.4 with Vectran and 67.7 ± 3.9 with hemp. It is the first measurement on a bow shot by archers, but on a long asymmetric Japanese bow rather than a Western competition bow, and the ratio is taken on the energy of the drawn bow rather than on the drawing work.

  BOWSTRING EVALUATION BASED ON Kansei ENGINEERING TECHNOLOGY · Satoshi Hosoya, Takashi Kawamura, Yosuke Horiba

• 2007
  For Model Published later

  A review chapter by the author of the 1991 paper, applying the model to a 68-inch, 30 lb Greenhorn Comet recurve with an 18.3-gram Easton arrow: 32.9 joules available, predicted efficiency 72.9 per cent, speed 51.39 metres per second. Efficiency and static coefficient match those of 1991, so it is the same calculation applied to a real bow, not a measurement.

  Design and materials in archery · B.W. Kooi

• 2015
  Context Equipment tests Published later

  A compound bow, a Hoyt Contender, measured in the laboratory and in the field: the draw curve gives 73.7 ± 0.5 joules of work, the return curve 71.0 ± 0.5 (between 3 and 4 per cent is lost to internal friction) and the 20.62 gram arrow leaves with 57.1 ± 0.8 joules. Against the drawing work this is a little over three quarters; the author defines efficiency against the energy returned and obtains 0.80. The difference corresponds to a virtual bow mass of about 5 grams, half of it in the string, the serving, the D-loop and the peep, and the formula says the same bow is more efficient with a heavier arrow. A single bow, which the paper does not describe as a competition bow, in a preprint: for a claim about competition bows it stays as context.

  Applications of Physics to Archery · H. O. Meyer

Status history

1. 1937 Not studied The first study of bow dynamics works with an efficiency of 100 per cent and warns that this is not realistic: taking the string into account, a purpose-built Osage bow reached 93 per cent, and most bows deliver much less. Efficiency enters the discussion, but there is still no figure for a competition bow.
2. 1981 Not studied A model of the longbow adds an elastic string and efficiency falls to 78 per cent, against 92 predicted with a rigid string; the author reports measurements between 70 and 85 per cent. The three-quarters order of magnitude appears, but on a longbow and in a calculation, and nobody has yet studied a competition bow.
3. 1990 Transferred The first figure for a competition bow is a model parameter: for the reference competition recurve the efficiency is 0.75, meaning three quarters of the work done in drawing ends up as kinetic energy of the arrow. The model is checked against film of a leading archer, but the value is set to build the calculation, not measured on the bow: with models alone the status is transferred.
4. 1991 Transferred A model of the modern working recurve calculates efficiency instead of setting it: 0.729, a little under the three quarters assumed the year before. The figure now comes from two different models, but they remain calculations with no measurement on the bow, so the status is still transferred.
5. 1998 Transferred A more complete model assumes the same 0.75, reports the estimates fitted to filmed shots, 0.76 longitudinally and 0.71 transversely, and states that on a modern bow the measured efficiency was a few points below the prediction. The value holds, but the measurement cited comes without figures and the rest is calculation: transferred.
6. 2001 Transferred The first measurement on a bow shot by archers arrives, but it is a kyudo bow: ten archers, fifty shots per string, and the Japanese bow passes between 67.7 and 69.4 per cent of the drawn bow's energy to the arrow. The figure is close to three quarters without being it, and above all it concerns a long asymmetric bow very different from a competition bow: it confirms the order of magnitude without testing the claim, so the status stays transferred.
7. 2007 Transferred The same model as in 1991, applied to a 30 lb recurve with an 18.3-gram arrow, predicts an efficiency of 72.9 per cent. It is the same calculation on a real bow, not a measurement: the only measurement with figures on a bow actually shot is still the kyudo one, and the status stays transferred.
8. 2015 Transferred The first measurement on a modern bow comes from a compound: 73.7 joules of drawing work, 71.0 returned by the bow, 57.1 to the 20.6 gram arrow, a little over three quarters of the work and 0.80 of the energy returned. The same work shows that efficiency rises with arrow mass, so the figure is not a constant of the bow. It is a single bow, though, a compound the paper does not describe as a competition bow, in a preprint: it confirms the order of magnitude without measuring it on a competition bow, and the status stays transferred.

Related

Related articles

• 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
• 29 studiesThe archer's paradox in research: from 1987 to today

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