On a compound the limb mainly changes how much force is needed, and changes the shape of the force-draw curve little

The summary today

The answer comes from models by a single author, calibrated on measured bows. The central work, from 2016, takes the limb of a commercial round-wheel compound and, in the calculation, changes its material, thickness, width and profile: what moves is mainly the height of the curve and the full draw, while the general shape stays much the same. Thickness weighs far more than width, because stiffness grows with its cube; the elastic modulus, estimated at about 34 gigapascals, scales the curve linearly; and the limb profile matters less than on a recurve, because on a compound the force always acts on the axle of the cam. There are exceptions: a curved limb gives a slightly gentler initial slope and more force at full draw, and thinning the limb at one point near the tip, so that it works almost like a hinge, shortens the full draw markedly. In 2017 another model, of the wheels, finds that the eccentric parameters are what weighs most on the curve. The picture fits the idea that the limb mainly supplies the force and the cams mainly the shape, but nobody has fitted different limbs to the same compound and measured the curve of each.

Also phrased as: "compound limbs and draw weight"; "do new limbs change the draw"; "limb thickness and draw weight"; "limbs and draw force curve"; "compound limb stiffness"

Evidence

• 2015
  Context Model Published later

  A 55-pound round-wheel compound has short, stiff limbs: 38.9 centimetres, a resting angle of 20.5 degrees, a spring constant of 1,032 newtons per radian, with 0.68 metres of travel to the bottom of the valley. The limb tip moves along an arc of a circle with a radius of 0.598 times the limb length, about 23 centimetres, against three quarters in the classical model. A description of the bow, with no different limbs compared.

  An advanced model of the round-wheel compound bow · M. Tiermas

• 2016
  For Model Published later

  Model of limb deformation calibrated on a commercial round-wheel compound, with the elastic modulus estimated at 33.75 gigapascals: in the calculation, changing the elastic modulus, thickness, width or profile of the limb mainly shifts the height of the force-draw curve and the full draw, while the general shape stays almost unchanged. The elastic modulus scales the curve linearly; thickness weighs more than width because stiffness grows with its cube. The only way found to shorten the full draw markedly is a limb with one very thin point near the tip, which works almost like a hinge.

  The limb deformation of the compound bow · M. Tiermas

• 2016
  Context Model Published later

  In the same work, three limb profiles (straight, curved, recurved) at equal stiffness and mounting: the recurved gives the highest peak and the curved the lowest, so much so that comparing the curves needs normalisation factors of 1.0, 1.611 and 0.654. Once normalised the curves differ little, apart from a gentler initial slope and a higher force at full draw for the curved limb. The author finds this surprising, since on a recurve the limb profile changes the curve a great deal, and explains it by the force on a compound always acting on the axle of the cam. In that compound 8.5 of the 38.9 centimetres of limb sit inside the riser pocket and do no work.

  The limb deformation of the compound bow · M. Tiermas

• 2016
  Context Model Published later

  On a commercial twin-cam compound measured in the laboratory, limbs of 39.2 centimetres with a spring constant of 1,135 newtons per radian and about a metre between the cam axles. The model built on it turns out to be particularly sensitive to the cam profile, and shows that the path of the limb tip is well described as that of a rigid rod with a single hinge even when the limbs are slightly recurved.

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

• 2017
  For Model Published later

  Extension of the round-wheel model, calculation only: of the twelve starting parameters, after preliminary runs those of the wheels (cable and string eccentrics) turn out to be the most influential on the curve, and the analysis concentrates on four of them; no values are given for the comparison with the other parameters. To obtain a more efficient curve without changing peak, draw length and let-off too much, the author modifies limbs and wheels together, with a calculated gain of 18.5 per cent in energy.

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

Status history

1. 2015 Not studied The first model of the round-wheel compound measures the limb of a 55-pound bow, 38.9 centimetres with a resting angle of 20.5 degrees and a spring constant of 1,032 newtons per radian, and finds that its tip moves along an arc of a circle whose centre lies closer to the tip than the classical model predicted. It describes the limb, but never changes it and never asks what happens to the curve if the limb is different: the question has not yet been put, hence not studied.
2. 2016 Transferred A model of limb deformation, calibrated on the measured curve of a compound, compares materials, thicknesses, widths and profiles in the calculation: what changes is mainly the height of the curve and the full draw, not its shape, and the case that changes the curve most is a limb thinned at one point near the tip, which works almost like a hinge and shortens the full draw markedly. Thickness matters far more than width, because stiffness grows with its cube; at equal stiffness recurved limbs give the highest peak force and curved limbs the lowest; and the profile weighs less than on a recurve, because on a compound the force always acts on the axle of the cam. In the same year a model of the twin-cam compound, with the same kind of short limbs, turns out to be particularly sensitive to the cam profile. All comparisons made in the calculation, on a single bow, with the elastic modulus obtained by fitting: transferred.
3. 2017 Transferred An extension of the round-wheel model starts from twelve parameters and, after preliminary runs, finds that those of the wheels, the cable and string eccentrics, are the ones that weigh most on the curve; to obtain a more efficient curve without moving the peak too much the author then has to modify wheels and limbs together, and the calculation gives 18.5 per cent more energy. It is another indirect confirmation, since it says where the shape lives rather than measuring the limb, and it is still a model by the same author: the status stays transferred.

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.

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

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• 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