On a compound the two limbs do not bend by the same amount at full draw

The summary today

Both studies that have measured it find that the two limbs of a compound do not bend identically, and the cause is the same: the nocking point sits above the centre of the string, so the string reaches the two limbs at different angles and loads them differently. The 2010 work explains it in those terms; in the 2012 one the difference between the two branches of the string is the only thing that sets top apart from bottom in the model. Where they part company is the size. In 2010, on several compounds with different cam configurations, the deflections of the two limbs matched to within half a degree over the whole draw, and in the worst case, a short axle-to-axle bow, the calculated difference was 0.22 degrees, small enough to shift the path of the nocking point by half a millimetre. In 2012 a model that does not impose symmetry, checked against a photograph of a compound at full draw, finds limb angles of 0.124 and 0.110 radians, measured at 0.125 and 0.106: a difference of 12 per cent of the mean angle, roughly one degree, which the author judges many times larger than the measurement errors. The same work shows, though, that treating the bow as symmetrical changes only the angles and the transverse quantities, while the forces on string and cables stay the same to within two parts in a thousand. The difference is there in both studies, measured on few bows; how much it matters for tuning or on the target nobody has measured.

Also phrased as: "compound limb asymmetry"; "upper and lower limb bend"; "uneven limb deflection"; "limb flex at full draw"; "compound tiller"; "compound limb symmetry"; "limbs working as a pair"

Evidence

• 2010
  For Equipment tests Published later

  On several compounds with different cam configurations the deflections of the upper and lower limbs matched to within half a degree over the whole draw. The author points out that they are not identical: with the nocking point above the centre of the string, the string meets the two limbs at different angles and applies different moments. In the worst case, a short axle-to-axle bow at full draw, the string-limb angles were 44 and 46 degrees, the calculated difference in deflection 0.22 degrees and the largest error in the nocking-point path 0.5 millimetres; the stiffness at the nocking point was above 8,400 newtons per metre.

  Compound-archery-bow nocking-point locus in the vertical plane · J L Park

• 2012
  For Equipment tests Published later

  Model of the compound with no symmetry constraint, checked against a photograph of the same bow loaded at the nock to 0.738 metres: limb angles of 0.124 and 0.110 radians in the model and 0.125 and 0.106 in the measurement, a difference of 0.014 radians, 12 per cent of the mean angle. The error of the photographic measurement is put at about 1 per cent, and the author judges the difference many times larger than the measurement errors.

  Compound archery bow asymmetry in the vertical plane · Ihor Zanevskyy

• 2012
  Context Equipment tests Published later

  On the same bow at full draw, the two branches of the string between cam and nocking point measure 0.631 and 0.699 metres: with the nocking point above the centre, the two branches already differ in the design of the bow, by 0.080 metres at brace.

  Compound archery bow asymmetry in the vertical plane · Ihor Zanevskyy

• 2012
  Context Equipment tests Published later

  Against the photographic measurement the model with no symmetry constraint is closer: for the angle of the upper limb the gap is -0.001 radians against -0.008 for the symmetric model, for the lower limb 0.004 against 0.011. The overall difference between model and measurement reaches 7 per cent.

  Compound archery bow asymmetry in the vertical plane · Ihor Zanevskyy

• 2012
  Context Equipment tests Published later

  One consequence of the asymmetry: at full draw the bow force has a component along the arrow of 104.5 newtons and a transverse one of 9.4, about 9 per cent, and the line between grip and nock is inclined with a tangent of 0.088 measured and 0.090 calculated.

  Compound archery bow asymmetry in the vertical plane · Ihor Zanevskyy

• 2012
  Context Equipment tests Published later

  Comparing the asymmetric model with one that imposes symmetry, the forces on string and cables change by 0.1 to 0.2 per cent and the other longitudinal quantities by about 0.05, the size of the measurement errors; what does change is the limb angles, by more than 5 per cent, the transverse component of the force, by 2.1, and the transverse displacement of the nock, by 1.5.

  Compound archery bow asymmetry in the vertical plane · Ihor Zanevskyy

Status history

1. 2010 Reported The first measurement comes inside a study of the nocking-point path. To build the model the author assumes the two limbs bend in the same way, then points out that they do not: with the nocking point above the centre of the string, the string meets the limbs at different angles and applies different moments. Measuring several compounds with different cam configurations, the two deflections matched to within half a degree over the whole draw; in the worst case, a short axle-to-axle bow, the string-limb angles at full draw were 44 and 46 degrees and the calculated difference in deflection 0.22 degrees. A difference exists but it is small, and it is reported by a single work that uses it to justify an approximation: reported.
2. 2012 Reported A second author builds a model of the compound without the symmetry constraint and checks it by photographing a bow loaded at full draw: the model predicts limb angles of 0.124 and 0.110 radians, a difference of 12 per cent of the mean angle, and the photograph measures 0.125 and 0.106; the author judges the difference many times larger than the measurement errors. The direction is the same as in 2010, the size is not: there it stayed under half a degree, here it reaches roughly one degree. The same work finds that the asymmetry affects the angles and the transverse quantities, not the forces on string and cables. Two studies that agree the difference exists but not on its size, each on few bows and with different methods, are not enough to move up: it stays 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.

Research lines

• 12 studiesCompound mechanics: cams, limbs and symmetry

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