A compound bow stores between 70 and 100 joules and sheds about two thirds of the force at full draw

The summary today

There are three measurements, each on a single bow, and only one of them gives the let-off. In 2015 a physicist measured the force-draw curve of a production compound, a Hoyt Contender, in the laboratory: the force rises to about 200 newtons, stays almost constant over much of the draw and then drops sharply, with a let-off of about 65 per cent at full draw; integrating the curve, the bow stores 73.7 joules, returns 71 at the release and 57 end up in the arrow. In 2016 another study measured the curve of a production twin-cam compound and, with a model that reproduces it well, derived 96.5 joules up to full draw. In 2020 a third compound, a target model of 53.5 pounds and measured as a starting input in a study on wind, stores 92.8 joules, about twice the recurve tested alongside, but the paper does not report the let-off. A 2017 model adds that the two figures are design choices rather than constants: in compounds with eccentric wheels the holding force is usually about a third of the peak, but changing the eccentrics moves the let-off from under 50 to about 80 per cent, and at the same peak and draw, with different eccentrics and limbs, one virtual bow stores 18.5 per cent more energy with a let-off of about 61 per cent instead of 67, while another gains 6 per cent with almost the same let-off. The energy also depends on draw weight and draw length, which differ across the four works. Nobody has measured more than one specimen, so the figures describe single bows, not the compound in general.

Also phrased as: "compound let-off"; "energy stored by a compound"; "compound valley"; "holding weight"; "compound force-draw curve"

Evidence

• 2015
  For Equipment tests Published later

  A production compound (Hoyt Contender) measured in the laboratory, with a brace height of 0.185 m and an actual draw length of 0.665 m: the force at the string rises to about 200 N and the let-off at full draw is about 65 per cent. Integrating the force-draw curve, the energy put into the bow is 73.7 ± 0.5 J, the energy returned at the release 71.0 ± 0.5 J, and the 20.6 g arrow receives 57.1 J.

  Applications of Physics to Archery · H. O. Meyer

• 2015
  Context Equipment tests Published later

  In the same bow string tension goes the opposite way to the draw force: it is highest with the bow at rest, 307 ± 5 N, and falls to about 50 N at full draw.

  Applications of Physics to Archery · H. O. Meyer

• 2016
  For Model Published later

  Force-draw curve measured on a commercial twin-cam compound and reproduced by a mathematical model of the cams: the energy stored up to a draw of 0.764 m is 96.5 J, with a cross-check against a second formula within 0.1 per cent. With cams redesigned on the computer, at the same peak and draw, the model reaches 106.5 J, 10 per cent more.

  A model of the twin-cam compound bow with cam design options · M. Tiermas

• 2017
  Context Model Published later

  Static model of an eccentric-wheel compound: the holding force is usually about a third of the peak, but changing the eccentrics moves the let-off from under 50 to about 80 per cent. Three virtual bows with the same 223.9 N peak and the same draw store 61.7, 65.5 and 73.1 J and hold 73.1, 70.6 and 88.3 N at full draw, that is a let-off of about 67, 68 and 61 per cent: the most energetic, +18.5 per cent, has the lowest let-off, but the second also stores more energy than the first with almost the same let-off.

  The round-wheel compound bow model revisited: a new extension · Marko Tiermas

• 2020
  For Equipment tests Published later

  A Hoyt Pro Comp Elite compound with Spiral cams, measured as a starting input for a study on wind: peak draw force 237.9 N (53.5 pounds), a draw length of 700 mm, and an X10 Protour arrow of 24.86 g leaving at 78.9 m/s. The stored energy calculated by the author is 92.8 J, about twice the 45.1 J of the recurve tested alongside. Let-off is not reported.

  The dynamic behaviour of an arrow in wind · James L Park

Status history

1. 2015 Reported The first direct measurement on a production compound arrives: the force at the string rises to about 200 newtons and falls by about 65 per cent at full draw, while string tension goes the opposite way, 307 newtons with the bow at rest and about fifty at full draw. Integrating the curve, the bow stores 73.7 joules and returns 71. A let-off of about two thirds is measured, and the energy falls within the claim's range, but it is a laboratory test on a single bow: reported.
2. 2016 Reported A second group measures the force-draw curve of a production twin-cam compound, reproduces it with a model of the cams and derives 96.5 joules stored up to full draw, with a cross-check within 0.1 per cent. Between them the two bows give 73.7 and 96.5 joules: figures consistent with the claim, but from two different specimens, each measured only once, so the status holds.
3. 2017 Reported A model of an eccentric-wheel compound shows that energy and let-off are not constants of the bow but design choices: the holding force is usually about a third of the peak, but changing the eccentrics moves the let-off from under 50 to about 80 per cent, and at the same 223.9 newton peak and the same draw, with different eccentrics and limbs, the stored energy goes from 61.7 to 65.5 joules with almost the same let-off, and to 73.1 joules, 18.5 per cent more, with let-off falling from about 67 to 61 per cent. The model brings no new measurements: the status stays reported, with the two figures to be read as typical rather than as a rule.
4. 2020 Reported A third measurement arrives, taken as a starting input in a study on wind: a target compound with a peak of 53.5 pounds and a 700 millimetre draw stores 92.8 joules, about twice the 45.1 of the recurve measured alongside. With three bows, at 73.7, 92.8 and 96.5 joules, the energy falls entirely within the claim's range; let-off, though, is still measured on a single bow, the 2015 one, and each specimen was tested once. The status does not change: reported.

Related

Related articles

• The compound on the draw: what the cams, the limbs and the nocking point doCompound cams, limbs and nocking point: what shapes the force-draw curve, the let-off and the path of the nock, according to what studies have measured.
• Bow tuning in archery: how to tune your bow, backed by scienceBow tuning and the research: spine, centre shot, button, nocking point, brace height and tiller. What models and machine tests show, and how precise you need to be.
• 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

• 12 studiesCompound mechanics: cams, limbs and symmetry
• 22 studiesHow much energy passes from bow to arrow: models and measurements since 1937

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 damper tuned to the tremor frequency reduces the bow's vibration while aiming1 studyStatus since 2017

See all claims on equipment and tuning