Curling Stone Research Articles

Development of a Curling Stone Delivery Robot with High Delivery Reproducibility

Curling is a two-player, zero-sum, finite, complete-information, uncertain game in which stones are delivered to a point approximately 37 m (120 ft). Despite its popularity, the dynamics of curling stones are unclear, and significant variations exist in the conditions of curling stones and curling sheets. It is essential to have a highly reproducible delivery apparatus that can perform tests in various environments to clarify stone dynamics and evaluate curling stones and sheets more accurately. In this study, we developed a delivery robot capable of delivering stones as quickly and accurately as, if not better than, a human using a large-diameter pneumatic cylinder. The delivery robot could deliver stones with high repeatability at 2.0 to 4.0 m/s by controlling the velocity of the pneumatic cylinder using multiple solenoid valves. In addition, we verified the accuracy of the robot’s velocity meter using motion capture to ensure that the throwing velocity measured by the delivery robot was sufficiently accurate. Finally, we conducted repeated delivery experiments using the delivery robot and demonstrated that the robot could deliver stones with high repeatability.

Gym machines for simulating training of technical movements in curling

Curling is a team sports game played on ice. The athletes slide stones one by one toward a marked target area. This is a sport in which the exactness of a throw is the base of technique and one of the main components of a successful play. In sport, technique means the way of making a physical action. Technical preparation is a process of education and improvement of movement skills, serving a mean of sports fighting. For making a throw of a curling stone an athlete has to push himself off a hack and slide in a deep lunge position holding a stone in his hand. In front of the hog line an athlete releases the stone. This paper describes the machines for training the technique of throwing a curling stone. Using empirical research methods we have created and used the machines which were used during the training process at the special preparation stage of the preparation period. A special training roller ground for throwing curling stones was developed. The useful model RU 192760 patent was published on September 30, 2019. The developed equipment allows to do imitative training of movements and technique of curling stones throwing. A training roller ground for a curling player’s boot was designed. The useful model RU 193702 patent was published on November 11, 2019. The conditions for simulating training of exactness of take-off force in curling were created

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

Why do curling stones curl? That is a question physicists are often asked, yet no answer has been established. Stones rotating clockwise curl right, contrary to our naive expectations. After a century of debate between contradicting hypotheses, this paper provides a possible answer based on experimental evidence. A digital image analysis technique was used to perform precision kinematic measurements of a curling stone’s motion to identify the curling mechanism. We observed a significant left–right asymmetric friction due to velocity dependence on the friction coefficient. Combined with the discrete point-like nature of the friction between ice and stone, swinging around slow-side friction points has been concluded as the dominant origin of the curling. Many new angular momentum transfer phenomena have been found, supporting this conclusion.

Taking Rocks for Granite: An Integrated Geological, Mineralogical, and Textural Study of Curling Stones Used in International Competition

ABSTRACTThe duopoly of curling stone sources suitable for international competition (Ailsa Craig, Firth of Clyde, Scotland and Trefor, Llŷn Peninsula, North Wales) has led to a long-held paradigm that the rocks from these localities are geologically unique. To evaluate this paradigm, we provide the first comprehensive, detailed analyses of the geological, mineralogical, and textural properties of curling stones, with a focus on three main areas: (1) the collective features of all curling stone lithologies, (2) the differences among the lithologies used for running bands versus striking bands, and (3) the presence of quartz, whose brittleness was previously considered to be undesirable in curling stones. The four curling stone varieties from the two localities (Ailsa Craig Blue Hone, Ailsa Craig Common Green, Blue Trefor, and Red Trefor) were analyzed using petrography, scanning electron microscopy, digital image analysis, powder X-ray diffraction, and normative mineralogy, with the following results: The curling stone varieties that are suitable for international competition can be broadly characterized as fine- to medium-grained, sparsely porphyritic to glomeroporphyritic, weakly to moderately altered, massive to weakly foliated, Phanerozoic granitoids (sensu lato). All four varieties are composed of feldspar (65–80 mod.%, with albite being the dominant component) and quartz (15–25 mod.%), along with mafic and accessory minerals (5–20 mod.%). The Ailsa Craig suite is classified as alkali feldspar quartz syenite, whereas the Trefor suite ranges from quartz monzogabbro (Blue Trefor) to granodiorite-granite (Red Trefor). None are strictly classified as granite.Predominantly equigranular textures are preferred for running bands (Ailsa Craig Blue Hone), whereas seriate to glomeroporphyritic textures are preferred for striking bands (Ailsa Craig Common Green, Blue Trefor, and Red Trefor). These are consistent with observations of used curling stones: pitting adversely affects larger grains in the running band, whereas a wider grain-size distribution correlates with fewer crescent-shaped fractures in the striking band.The appreciable abundance of unstrained, interstitial quartz (15–25 mod.%) in all curling stone samples challenges the longstanding belief of its absence and undesirability in curling stones. The degree of strain in quartz is likely to be a key criterion for selecting prospective curling stone materials.In conclusion, none of the examined characteristics of curling stones are unique in comparison to granitoids worldwide.

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

Curling is a sport in which players deliver a cylindrical granite stone on an ice sheet in a curling hall toward a circular target located 28.35 m away. The stone gradually moves laterally, or curls, as it slides on ice. Although several papers have been published to propose a mechanism of the curling phenomenon for the last 100 years, 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. Here we show using our precise experimental data that the curl distance is primarily determined by the surface roughness and the surface area of the running band on the bottom of a stone and that the ice surface condition has smaller effects on the curl distance. We also propose a possible mechanism affecting the curling phenomena of a curing stone based on our results. We expect that our findings will form the basis of future curling theories and model calculations regarding the curling phenomenon of curling stones. Using the relation between the curl distance and the surface roughness of the running band in this study, the curl distance of a stone sliding on ice in every curling hall can be adjusted to an appropriate value by changing the surface roughness of the running band on the bottom of a stone.

Path Planning of a Sweeping Robot Based on Path Estimation of a Curling Stone Using Sensor Fusion

In this paper, we proposed an enhanced path planning strategy for sweeper robots, which were created for the curling Olympic games. The main task for the multi-robot system is to clean the ice surface making a smooth path for a curling stone. The sweeping robots should have a motion planning on how to follow the curling stone slide and to prevent any collisions. In order to find the next position of the sweeping robot, it needs to establish the current position and to compute the next position of the curling stone. The initial and goal points of the sweeping robots are found and set up based on the simulation results from the main server. While the curling stone moves, the sweeping robots measure its position and adjust their motions according to the stone position trajectory. If the distance between the current and the next positions of a curling stone exceeds the threshold value, the sweeping robots should activate the sweeping mechanism preventing collisions with the stone. Since the estimation of the sweeping robot motion solely depends on the stone’s trajectory, the accumulation of errors is undesirable. Thus, the stone trajectory should be recalculated in a certain time step using the trend-adjusted exponential smoothing method. Then, the formation of the sweeping robot system can be calibrated according to the stone path computation. The obtained experimental results proved the efficiency of the proposed path planning method.

氷の切削メカニズムとカーリング・ストーン運動のエッジ・モデル（2）

氷の切削メカニズムとカーリング・ストーン運動のエッジ・モデル（2）

氷上を進むストーンの曲がり幅に対する ストーンのランニングバンドの表面粗さ, 氷面, 角速度の影響

氷上を進むストーンの曲がり幅に対する ストーンのランニングバンドの表面粗さ, 氷面, 角速度の影響

Edge Model of the Motion of a Curling Stone (2)

This paper presents further development of the new edge model of a curling stone introduced in our previous paper. Precise measurements of edge angles of curling stones showed that the edge angles of each running band are about 10 degrees and the inner edge angles are larger than the outer edge angles. The cutting force by edges was formulated as a function of inner and outer edge angles, band width, translational and angular velocities based on various experimental results of ice, metal, plastic and other materials. The force increases with the edge angles and decreases with the increasing translational and angular velocities.

A surface topography analysis of the curling stone curl mechanism

The curling motion of the curling stone on ice is well-known: if a small clockwise rotational velocity is imposed to the stone when it is released, in addition to the linear propagation velocity, the stone will curl to the right. A similar curl to the left is obtained by counter-clockwise rotation. This effect is widely used in the game to reach spots behind the already thrown stones, and the rotation also causes the stone to propagate in a more predictable fashion. Here, we report on novel experimental results which support one of the proposed theories to account for the curling motion of the stone, known as the “scratch-guiding theory”. By directly scanning the ice surface with a white light interferometer before and after each slide, we observed cross-scratches caused by the leading and trailing parts of the circular contact band of the linearly moving and rotating stone. By analyzing these scratches and a typical curling stone trajectory, we show that during most of the slide, the transverse force responsible for the sideways displacement of the stone is linearly proportional to the angle between these cross-scratches.

High-precision measurement of friction coefficient of a curling stone by motion analysis

High-precision measurement of friction coefficient of a curling stone by motion analysis

Motion analysis of a curling stone by image analysis

Motion analysis of a curling stone by image analysis

Comparison of IMU Measurements of Curling Stone Dynamics with a Numerical Model

Despite almost a century of research, the question of what causes a curling stone to curl (move perpendicular to its initial direction of motion) has no complete answer. Many hypotheses have been formulated, but none has been able to account quantitatively for the full magnitude of the observed curl. The objective of this research was to equip a curling stone with an inertial measurement unit (IMU) and measure its motion, in order to verify a previously published, numerical model of curling stone dynamics. Low cost, small size, accuracy, ease of programming and operation, wireless data communication, and a data-sampling rate near 1kHz, were selection criteria and constraints for the instrument package. We used the MicroStrain 3DM-GX4-25 system. This is a MEMS-based IMU with a tri-axial gyroscope and a tri-axial linear accelerometer. It was mounted and interfaced with a Bluetooth transmitter, on a curling stone handle. The data were streamed to a host laptop and displayed graphically in real time. Post-processing of the data included filtering and time-integration in order to obtain linear and angular velocities, and displacements. We have compared our experimental results with trajectory data calculated using a previously published numerical model, based on a thermodynamic approach to ice friction. While the observed longitudinal and angular motions are captured reasonably well by the model (errors of about 5% or less), no curl is predicted by the model.

スウィーピングのカーリング・ストーン運動に対する影響

スウィーピングのカーリング・ストーン運動に対する影響

D-9 ディジタル画像解析によるカーリング・ストーンの摩擦係数の精密計測(カーリング)

D-9 ディジタル画像解析によるカーリング・ストーンの摩擦係数の精密計測(カーリング)

D-7 カーリング・ストーン動力学の新実験(カーリング)

Recent high-precision measurements of curling stone dynamics have revealed several funcamental behaviors of a curling stone on an ice sheet. The main results obtained so far are briefly reviewed and some novel experiments are suggested to obtain deeper insight into the curling stone dynamics.

Erratum to: Dynamics and curl ratio of a curling stone

Erratum to: Dynamics and curl ratio of a curling stone

Dynamics and curl ratio of a curling stone

An attempt to develop a dynamic model for the motion of a curling stone is reported. Characteristic forms of the ice surface covered with many small pebbles and the narrow annular running band at the bottom of a stone lead to the increase in the force exerting on ice, resulting in the reduction of friction coefficient of ice and the production of ice fragments to increase the effective friction coefficient at the rear running band. In this paper, a numerical model is presented to compute the dynamic motion of a curling stone on the base of the evaporation–abrasion mechanism. The friction magnification factor, A, was introduced to evaluate the asymmetry that the friction coefficient of the rear running band is larger by a factor of A than that of the front. Numerical computations showed that curl distances and trajectories experienced in usual curling games were reproduced by magnitudes 5 ≤ A ≤ 20. Another physical quantity, curl ratio, C, was introduced to describe quantitatively the amount of curl of a stone moving with definite translational and angular velocities. C specifies the direction to which a stone moves at any instant. It increases with decreasing translational velocity and increasing angular velocity. In other words, a stone curls more at smaller speeds and higher turns.

Calculated Trajectories of Curling Stones Sliding Under Asymmetrical Friction: Validation of Published Models

In the sport of curling, stones are slid across an ice sheet, aimed towards a target area. A sliding stone does not move in a straight line, but follows a curled trajectory, deviating in a direction determined by its rotation. As yet, no satisfactory explanation for this motion has been presented, although many attempts have been made. In many of them, the curling motion has been attributed to an asymmetrical distribution of the friction force acting on the sliding stone, typically such that the friction on the rear of the stone (as seen in the direction of motion) is higher than that on the front. In this paper, the motion of a rotating curling stone sliding over ice is calculated, for different assumed distributions of the coefficient of friction in the contact between stone and ice, using a numerical method. It is shown that no redistribution of the friction, no matter how extreme, can explain the observed motion of a real curling stone.

The asymmetrical friction mechanism that puts the curl in the curling stone

Curling is an Olympic winter sport in which two teams slide stones across a sheet of ice towards a target area, some 28m away from the release line. The sport has its name from the fact that the trajectory of a rotating stone becomes slightly curled, a fact used to reach open spots or take out opponent stones behind hindering “guarding” stones, etc. By slowly turning the stone clockwise when it is released, it will curl to the right, and vice versa. The resulting sideward deviation is typically slightly more than a metre. This intriguing tribological phenomenon has so far lacked a satisfactory explanation, although many attempts have been presented. In many of them, the curling motion has been attributed to an asymmetrical distribution of the friction force acting on the sliding stone, such that the friction on the rear of the stone (as seen in the direction of motion) is higher than that on the front. In a recent paper, we could show that no such redistribution of the friction, no matter how extreme, can explain the magnitude of the observed motion of a real curling stone. The present work presents an alternative asymmetrical mechanism that actually is strong enough to account for the observed motion. Further, in contrast to previous models, it satisfies other observed phenomena, including the independence of rotational speed of the stone and the strong dependence of the roughness of the stone. The model is backed up by experimental evidence and is based on the specific tribological conditions presented by the contact between a scratched curling stone and a pebbled ice sheet.