On a compound bow the shape of the force-draw curve is governed by the cam profile

The summary today

Everything known comes from three mathematical models by the same author, calibrated on real bows but never tested by actually changing the cams. The first, in 2015, rebuilds the measured curve of a 55-pound round-wheel compound from the geometry of wheels, limbs and cables alone, with a small gap near full draw. The second, in 2016, on a commercial twin-cam compound, finds the calculation particularly sensitive to the cam profile, and redesigning the cams for the same peak force and draw length would raise the stored energy from 96.5 to 106.5 joules, about 10 per cent more, gained almost entirely by steepening the first part of the curve. The third, in 2017, goes back to round wheels and confirms that the geometry of the eccentrics moves the peak, changes its shape and sets the let-off: with the cable eccentric offset by 16.7 millimetres the let-off reaches about 80 per cent, but the curve becomes less full. Over the same period a model of the limb finds that material and thickness mostly change the height of the curve, not its shape. The direction is consistent, but these are calculations: nobody has fitted different cams to the same bow and measured what happens, and the energy gains are simulation figures, not measurements.

Also phrased as: "soft cams versus aggressive cams"; "cam profile and draw force curve"; "compound let-off and cams"; "how cams change the draw"; "aggressive cams are faster"

Evidence

• 2015
  For Model Published later

  Static model of a 55-pound round-wheel compound built on the geometry of wheels, limbs and cables: it follows the force-draw curve measured on the same bow well, with a slight gap near full draw (0.68 metres) put down to string and cable stretch, which the model leaves out. The wheel geometry is enough to reproduce the curve; different wheels are not compared.

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

• 2016
  For Model Published later

  Static model of a commercial twin-cam compound, with the cams described by splines taken from photographs: the model turns out to be particularly sensitive to the cam profile. For the same peak force and draw length the most energetic possible curve is a rectangle, and redesigning the cams by trial and error raises the energy up to 0.764 metres of draw from 96.5 to 106.5 joules (+10 per cent), mainly because the first part climbs more steeply; the starting draw gets shorter. Calculation only: the modified cams were never built.

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

• 2016
  Context Model Published later

  The same work sets a design constraint: for string and cable to stay seated without jumping, the profile of both cams has to be convex everywhere. A single radius value out of line makes the contact point jump and the calculation fail, so much so that the profiles measured from the photographs had to be smoothed.

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

• 2016
  Context Model Published later

  Model of limb deformation calibrated on a round-wheel compound: changing the elastic modulus, thickness, width or profile of the limb mainly shifts the height of the curve and the full draw, while the general shape stays much the same. It is the complementary half of the question: if the limb does not draw the shape, that leaves the system of cams and wheels.

  The limb deformation of the compound bow · M. Tiermas

• 2017
  For Model Published later

  Extension of the round-wheel model, with no new measurements: after preliminary runs on twelve parameters, those of the eccentrics turn out to be the most influential on the curve. With the cable eccentric offset by 16.7 millimetres the let-off reaches about 80 per cent and the quality coefficient falls to 0.589 against 0.619 for the reference bow; with a starting angle of 100 degrees on the cable eccentric the let-off is about 50 per cent and the coefficient rises to 0.685, and with the string eccentric at 0 degrees it reaches 0.737 with a let-off under 50 per cent. Modifying the eccentrics and limbs of an example bow gives +18.5 per cent energy and +18.8 per cent quality coefficient.

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

Status history

1. 2015 Transferred The first static model of the round-wheel compound derives the force-draw curve from the geometry of wheels, limbs and cables alone, and on a 55-pound bow it follows the measured curve well, with a small gap near full draw, at 0.68 metres, which the author puts down to the stretch of string and cables, left out of the calculation. It shows that the geometry is enough to explain the curve, not how much each part weighs in, and it does not compare different wheels: it is a model, hence transferred.
2. 2016 Transferred A model of the twin-cam compound, calibrated on a commercial bow, turns out to be particularly sensitive to the cam profile: when redesigning them a single stray point is enough to break the calculation, and both cams have to be convex everywhere for string and cable to stay seated. Redesigning the cams for the same peak force and draw length, the energy up to 0.764 metres of draw would go from 96.5 to 106.5 joules, 10 per cent more, gained mainly by steepening the first part; under the same constraints the theoretical limit would be a rectangular curve. In the same year a model of the limb finds that material, thickness and width mostly shift the height of the curve, not its shape. The modified cams exist only in the calculation: transferred.
3. 2017 Transferred An extension of the round-wheel model varies the eccentric parameters one at a time and finds that they weigh most on the curve, moving its peak and changing its shape. Offsetting the cable eccentric by 16.7 millimetres takes the let-off to about 80 per cent but hollows out the curve, with the quality coefficient falling from 0.619 to 0.589; changing the starting angles of the eccentrics, the fullest curves have a let-off of around 50 per cent or less. Modifying eccentrics and limbs together on an example bow, the calculation gives 18.5 per cent more energy for the same peak and draw length. It is the third confirmation, again by calculation and again 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.

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

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