The Split Friction Model - Introducing Mixed Lubrication to Curling

Abstract

In general, the curling stone is subject to mixed lubrication, resulting in the characteristic Stribeck -curve. As velocity increases, the friction force falls quadratically just to rise linearly yet almost flat after the minimum. In the case of a rotating curling stone this results in a torque. Due to isotropy , the lateral force arises as a delta of asymmetric friction forces opposite to the centripetal forces. \par This in turn allows a split friction model that splits up the quadratic curve into two rather constant values for the friction force on the advancing and the retreating side below a critical velocity difference of these sides: the flee force on the advancing side must not exceed the normal force of the retreating side. Only then a curl can happen. This explains why a stone curls towards the end of the throw. \par Following basic static considerations, the stone may theoretically rest on up to three points during a throw. Each single static case is investigated. These results are discussed with additional heuristic calculations that involve Scratch-Theory. Lastly, the influence of gyroscopic precession yields a graph that reflects established experimental observations: A desired flat curve within deviations ranging from 0.80 to 1.02 meter for up to 20 rotations just to rise linearly up to 2 meters for 80 rotations.

An examination of studies related to the sport of curling: a scoping review

“…The five in Maeno's ( 92 ) review are the “Pressure Difference Model”, the “Water Layer Model”, the “Snowplow Model”, the “Evaporation Abrasion Model”, and the “Scratch Guide Model”. In order of novelty, the two newly proposed models are the “Pivot-Slide Model” (Shegelski, & Lozowski ( 79 ) and the “Split Friction Model with mixed lubrication” by Ziegler ( 87 ).…”

“…To date, no unanimous theory exists to explain the lateral displacement of the curling stone ( 72 , 75 ). Various physical models present conflicting proposals including: (1) the “front-back” and “right-left asymmetrical models” ( 2 , 74 , 75 , 81 , 97 , 98 ); (2) the “evaporation-abrasion model” ( 86 , 92 , 96 ); (3) the “snowplow model” ( 81 , 92 ); (4) the “pressure difference model” ( 92 ); (5) the “scratch-guide model” ( 73 , 75 , 89 , 90 ); (6) the “pivot-slide model” ( 79 , 85 , 88 ); (7) the “split friction model” ( 87 ); and (8) the “water layer model” ( 76 – 78 , 91 – 93 ). There is also a large variation in the different mathematical equations used in analysis across studies, as currently no numerical model of curling stone dynamics can satisfactorily predict all observed stone translations ( 80 ).…”

“…There is also a large variation in the different mathematical equations used in analysis across studies, as currently no numerical model of curling stone dynamics can satisfactorily predict all observed stone translations ( 80 ). Further controversy remains on the influence of the stone running band ( 72 ), speed of rotation ( 76 , 87 ), and pebbled ice surface on the lateral displacement. Many studies have considered this domain of the sport, but few have observed the mechanisms experimentally or been able to provide concrete data.…”

“…Several studies introduced the "pivot-slide model" which describes lateral displacement as a sequence of pivots about individual ice pebbles followed by slides (79,85,88). Finally, two studies evaluated "split friction/granular models", describing factors of mixed lubrication (76,87). Numerical models used to describe and validate the above theories were considered across studies (91,92).…”

The Split Friction Model - The Isotropic Origin of the Lateral Force in Curling

“…A preprint version of this original manuscript [18] then first presented a quantified combination of asymmetry mechanisms as a solution to the curling problem. The mechanisms arranged were split friction which by itself was also presented first and an adaption of Scratch Theory that closely followed Nyberg et al [2].…”