Supplementary information Calculations




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Supplementary information

Calculations. The centripetal acceleration required when running at a speed V around a bend of radius r combines with gravity g (9.81 m s-2) to provide an acceleration requirement, or 'effective gravity', a:



During the straight, the centripetal acceleration term V2/r is zero (r is infinite). While the exact form of the ground reaction force profile cannot be calculated from these kinematic data, the assumption that each limb experiences an approximately half-sine profile, and conservation of momentum, allows an estimation for the peak reaction forceS1 Fmax for running and gallopingS2. Expressed as a proportion of body mass m, this results in

Fmax/m = ppa/4b 

for quadrupeds running at a duty factor (proportion of stride the foot is on the ground) . The term p in this expression represents a proportion, used to distinguish the impulse distribution between forelegs and hind (taken to be 0.6:0.4 from a study on trottingS3). No account is made for left/right differences, or deviations from the sine force profile assumption; however, such inaccuracies have little bearing on the conclusions.

S1. Alexander, R. McN., Maloiy, G. M. O., Hunter, B., Jayes, A. S. & Nturibi, J. Mechanical stresses during fast locomotion of buffalo (Syncerus caffer) and elephant (Loxodonta africana). J. Zool. Lond. 189, 135-144 (1979).

S2. Witte, T. H., Knill, K. & Wilson, A. M. Determination of peak vertical ground reaction force from duty factor in the horse (Equus caballus). J. Exp. Biol. 207, 3639-3648 (2004).

S3. Lee, D. V., Bertram, J. E. A. & Todhunter, R. J. Acceleration and balance in trotting dogs. J. Exp. Biol. 202, 3565-3573 (1999).



Filming details

Foot contact timings were measured from high-speed video (250 frames per second, Troubleshooter HR (Fastec Imaging, San Diego, CA)) for 17 Greyhounds at the end of the first straight and at the apex of a bend of radius 22.37m with minimal banking. A further 23 Greyhounds were subsequently recorded at the start of the second straight, directly after the first bend. Mean speeds for 6.84 to 8.00m intervals (from the time taken for Greyhounds to move past posts and appropriate geometry to account for the slightly wider path of the dog) were measured for the Greyhounds at these positions. The second population of measurements, for the start of the second straight, confirmed that those for the end of the first straight were not unduly influenced by the slight acceleration observed at this position. Sarah Williams helped with filming.


SI Table Foot timings (Mean +/- 1SE, periods in ms) for Greyhounds at the end of the first straight and then at the apex of the bend. Values for the start of the 2nd straight come from similar ability dogs in separate trials.




1st straight

Bend

2nd straight




Stance period

Swing period

Stance period

Swing period

Stance period

Swing period

N


17 (paired)

23

Speed (m/s)

16.33+/-0.31

17.57+/-0.185

15.19+/-0.08

Fore non-lead

40.2+/-0.7

243.5+/-4.2

42.4+/-1.2

236.9+/-3.0

44.5+/-1.0

247.8+/-2.8

Fore lead

44.5+/-0.5

239.3+/-4.4

42.4+/-1.6

236.9+/-4.0

48.1+/-0.5

244.3+/-2.9

Hind non-lead

48.9+/-1.1

234.8+/-4.7

59.1+/-1.7

220.2+/-3.5

50.8+/-0.8

241.6+/-2.8

Hind lead

45.6+/-0.9

238.1+/-4.9

45.9+/-1.4

233.4+/-3.2

48.9+/-0.6

243.5+/-2.9


Walthamstow Greyhound Stadium kindly provided access during trials, and Simon Townsend and Jonathan Bamford contributed to greyhound observations.


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