Improved pivot–slide model of the motion of a curling rock

Abstract

The pivot–slide model (Shegelski and Lozowski) successfully predicts the slide and curl distances of a curling rock. However, in this model, there is no dependence of the curl distance on the initial velocity, because the ratio between the pivot to sliding times is constant. A refined model is presented, in which the ratio of the pivot to sliding times depends on the stone velocity via two parameters. Confidence limits for these parameters are deduced from experimental data, which show that the pivot–slide ratio depends on the stone velocity. However, precise values of these parameters could not be obtained with this study, as more precise experiment data are needed. The refined model allows one to qualitatively explain two characteristics of the stone trajectory observed in a curling game, namely the bigger final curl with lower initial velocity and the lower curl with the effect of sweeping the ice.

The Split Friction Model - Introducing Mixed Lubrication to Curling

“…[14] experimentally confirmed the importance of surface roughness supporting Scratch-Theory. Meanwhile, [16] published a paper that supported the Pivot-Slide model. Most recently, the original authors of the Pivot-Slide party published a comment [15] in which they pointed out mistakes in that supportive paper.…”

Study of curling mechanism by precision kinematic measurements of curling stone's motion

“…Therefore, possible hypotheses must include forwardbackward asymmetry [5][6][7][8] or left-right asymmetry [1,9] of the friction strength. In addition, surface roughness is often highlighted to be necessary, which may cause discrete frictioning such as pivoting due to pebble structures on ice [10][11][12][13][14] and dust and scratching on ice by the stone's rough bottom surface [15]. If we suppose the Coulomb friction law (the dynamic friction force must be opposite to the velocity direction), the left-right asymmetry of the continuum friction cannot transfer longitudinal to the transverse momentum [7].…”

The importance of the surface roughness and running band area on the bottom of a stone for the curling phenomenon

“…The curling phenomenon is primarily important in curling games because the amount of lateral displacement, called the curl distance, contributes to the strategy of games. Since the first scientific paper by Harrington 4 , several papers 5 – 27 have been published to propose a mechanism of the curling phenomenon. However, no established theory exists on the subject, because detailed measurements on a pebbled ice surface and a curling stone sliding on ice and detailed theoretical model calculations have yet to be available.…”

“…The curling behaviour of a stone sliding on ice has been explained by three models: a left-right asymmetry model (LR model, with different frictional forces on the left and right sides of a stone) 4-7 , a front-back asymmetry model (FB model, with different frictional forces on the front and back sides of a stone) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and a pivot-slide model (PS model, where brief pivots of a stone around a point between a stone and pebbles cause the curling behaviour) [25][26][27] .…”

“…The FB models are divided into six models, in which different mechanisms have been proposed for different front and back frictional forces: a pressure difference model (a larger pressure works on the front running band than on the back running band) [9][10][11] , a water layer model (a water layer is assumed to be produced by frictional heating, and the layer reduces the frictional forces at the front running band) [12][13][14] , a snowplow model (small ice debris are formed by a stone and accumulate at the front running band) 15 , an evaporation-abrasion model (with an asymmetrical effect on evaporation and abrasions on the tops of pebbles and the effects of ice debris) [16][17][18] , a scratch-guiding model (guiding of small scratches left on the tops of pebbles by a stone) [19][20][21][22] and an edge model (with different rake angles of a stone at the front and back of the stone) 23,24 . Recent papers discuss a possibility of the PS model [25][26][27] , which was originally suggested by Penner 8 . Scientific discussions between different modellers have been raised and published 28−35 .…”