Curling

Nevertheless, today a rock which deviates from a straight line is said to curl. Note that this power spectral density corresponds to a delta function for the covariance function of w(t). One possible derivation is that it came from the old verb "curr" which describes a low rumble, a sound that is strongly associated with the game (curling is often called the roaring game). so that w(t) is a white noise random process with zero mean and constant, unit power spectral density. It was first used in print in 1630 in Perth, Scotland. The final form of the whitening procedure is as follows:. The origins of the word "curling" are not known. Additionally, we must be sure that H(ω) is strictly positive for all so that H_inv(ω) does not have any singularities.

In the early history of curling, the rocks were simply flat-bottomed river stones which were sometimes notched or shaped; the thrower had little control over the rock, and relied more on luck than skill to win. We choose the minimum phase filter so that the resulting inverse filter is stable. Curling probably does not take its name from the motion of the stones. Choosing the minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then whiten x(t) with the following inverse filter. Curling is the provincial sport of Saskatchewan, home of one of the most famous curlers, the late Sandra Schmirler, who led her team to what was believed, until 2006, to be the first ever gold medal in the 1998 Winter Olympics. We factor the power spectral density S_x(ω) as described above. However there are many young teams who turn heads, and junior curling is quite popular, with national finals being televised nationwide in Canada. We can whiten this signal using frequency domain techniques.

Because accuracy, strategy, skill, and experience are more valuable in curling than traditional sports virtues of speed, stamina, and strength, most competitive curlers are older than their counterparts in other sports. Suppose we have a wide-sense stationary, continuous-time random process defined with the same mean μ, covariance function K_x(τ), and power spectral density S_x(ω) as above. Curling survives as a people's sport, making its Winter Olympic Games debut in 1998 with men's and women's tournaments (some sources also include the competition held in 1924 as an official Olympic tournament). Thus, the resultant signal has the same 2nd moment properties as the desired signal x(t). While Canadian bonspiels (tournaments) offer cash prizes, there are no full-time professional curlers. where w(t) is a continuous-time, white-noise signal with the following 1st and 2nd moment properties:. The first ever world title was won by the Canadian team from Regina, Saskatchewan skipped by Ernie Richardson. We can simulate x(t) by constructing the following linear, time-invariant filter.

The first world curling championship in the sport was limited to men and was known as the "Scotch Cup" held in Falkirk and Edinburgh, Scotland, 1959. Choosing a minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then simulate x(t) with H(ω) as the transfer function of the filter. The Tournament of Hearts and the Brier are contested by provincial and territorial champions, and the world championships by national champions. If S_x(ω) is a rational function, we can then factor it into pole-zero form as. Despite its small population, the Brier has been won by the province of Manitoba more times than any other province. if and only if S_x(ω) satisfies the Paley-Wiener criterion. Improvements in ice making and changes in the rules to increase scoring and promote complex strategy have increased the already high popularity of the sport in Canada, and large television audiences watch frequent curling telecasts, especially the Tournament of Hearts (the national championship for women), the Brier (the national championship for men), and the women's and men's world championships. Because K_x(τ) is Hermitian symmetric and positive semi-definite, it follows that S_x(ω) is real and can be factored as.

Curling is most popular in Canada, but is played in other countries including the United States, Scotland, Norway, Sweden, Switzerland, Denmark and even Japan, all of which, with other countries, compete in the world championships. We can simulate this signal using frequency domain techniques. If no independent officials are available, the thirds measure the distances. and power spectral density. An independent official then measures the distances using a specially designed device that pivots at the center of the button. We can simulate any wide-sense stationary, continuous-time random process with constant mean μ and covariance function. In tournament play the most frequent circumstance in which a decision has to be made by someone other than the third is the failure of the thirds to agree on which rock is closest to the button. For whitening, we feed any arbitrary random signal into a specially chosen filter so that the output of the filter is a white noise signal.

No players other than the third from each team should be in the house while score is being debated. We choose the filter so that the output signal simulates the 1st and 2nd moments of any arbitrary random process. However, all scoring disputes are handled by the third, or vice-skip. For simulating, we create a filter into which we feed a white noise signal. Most decisions about rules are left to the skips. We can extend the same two concepts of simulating and whitening to the case of continuous time random signals or processes. Scoring without the hammer is commonly referred to as stealing, or a steal, and is much more difficult. Thus, with the above transformation, we can whiten the random vector to have zero mean and the identity covariance matrix.

This is called a blank end. By diagonalizing K_xx, we get the following:. If only one point is possible, the skip will often try to avoid scoring at all in order to retain the hammer until the next end, when two or more points may be possible. and covariance matrix. Naturally, it is easier to score points with the hammer than without; in tournament play, the team with the hammer generally tries to score two or more points. Thus, the output of this transformation has expectation. In the event that neither team scores, the hammer remains with the same team. The method for whitening a vector with mean and covariance matrix K_xx is to perform the following calculation:.

(In tournaments, this is typically assigned, giving every team the hammer first in half of their games.) In all subsequent ends, the hammer belongs to the team that did not score in the preceding end. and covariance matrix. Before the game, teams typically decide who gets the hammer in the first end by coin toss or similar method. Thus, the output of this transformation has expectation. The last rock in an end is called the hammer. where. This is often accompanied with saying "Good game!" Hands are also shaken before the game and is accompanied by saying "Good curling!" to the opposing team. We can simulate the 1st and 2nd moment properties of this random vector with mean and covariance matrix K_xx via the following transformation of a white vector :.

When a game is ended by normal means, both teams will shake hands as well. where E is the orthogonal matrix of eigenvectors and Λ is the diagonal matrix of eigenvalues. This may occur at any point during the game, but usually happens near the end. Since this matrix is Hermitian symmetric and positive semidefinite, by the spectral theorem from linear algebra, we can diagonalize or factor the matrix in the following way. When a team feels it is impossible or near impossible to win a game, they will shake hands with the opposing team to indicate surrender. Suppose that a random vector has covariance matrix K_xx. This is called a blank end and the end number usually goes in the furthest column on the right in the row of the team who has the hammer (last rock advantage). These concepts are also used in data compression.

However, some confusion can exist if no team gets points in an end. These two ideas are crucial in applications such as channel estimation and channel equalization in communications and audio. This scoreboard works because only one team can get points in an end. To whiten an arbitrary random vector, we transform it by a different carefully chosen matrix so that the output random vector is a white random vector. If they score two more in the second end, then a two will be placed beside the five in the red row indicating that the red team has five points in total (3+2). We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. If the red team scores 3 points in the first end (called a three-ender), then a one (indicating the first end) is placed beside the number three in the red row. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix.

The numbers placed are indicative of the end. Two theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. It is set up in the same way, except the numbered row indicated points not ends, and it can be found between the rows for the team. Since this power spectral density is the same at all frequencies, we call it white as an analogy to the frequency spectrum of white light. The other form of scoreboard is the one used in most curling clubs (see photo). since the Fourier transform of the delta function is equal to 1. The number of points each team gets in an end is marked this way. The above autocorrelation function implies the following power spectral density.

Below this are two rows — one for each team. I.e., it is a zero mean process for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function. On this scoreboard the ends are marked by columns 1 through 10 (or 11 for the possibility of an extra end to break ties) plus an additional column for the total. A continuous time random process w(t) where is a white noise process if and only if its mean function and autocorrelation function satisfy the following:. One is the baseball type scoreboard, which is usually used for televised games. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation. There are two different types of scoreboards used for curling. I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix.

The score is usually marked on a scoreboard of some sort. A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:. Since the bottom of the rock is rounded, a rock just barely in the house will not have any actual contact with the ring, which will pass under the rounded edge of the stone, but it still counts.) The winner is the team with the highest score after an even number of ends — usually in high-level curling this is ten; however, at club play it is usually eight, or less. White noise machines are sold as privacy enhancers and sleep aids. (A rock is considered in the house if any portion of its edge is over any portion of the 12-foot ring. White noise can be used to disorient individuals prior to interrogation and may be used as part of sensory deprivation techniques. Rocks that are not in the house (further from the center than the outer edge of the 12-foot ring) do not score even if no opponent's rock is closer. White noise is used as the basis of some random number generators.

After both teams have delivered eight rocks each, the team with the rock closest to the button is awarded one point for each of its own rocks that is closer than the opponent's closest rock. He or she can then adjust the overall EQ to ensure a balanced mix. While a sound strategy, this made for an unexciting game. To set up the EQ for a concert or other performance in a venue, a short burst of pink noise is sent through the PA system and monitored from various points in the venue so that the engineer can tell if the acoustics of the building naturally boost or cut any frequencies. The team with the hammer could peel rock after rock, which would blank the end, keeping the last rock advantage for another end. It is also used to generate impulse responses. This rule, a relatively recent addition to curling, was added in response to a strategy of "peeling" opponents' guard stones (knocking them out of play at an angle that caused the shooter's stone to also roll out of play, leaving no stones on the ice) that skilled teams leading a game would employ to prevent their opponents from "stealing" an end (scoring without having the last rock, or hammer) by placing guard stones and later trying to draw around them and using them for protection. It is used extensively in audio synthesis, typically to recreate percussive instruments such as cymbals which have high noise content in their frequency domain.

This rule is known as the four-rock rule or the free-zone rule; some people and leagues play with a three-guard rule, where the rule is in place until three rocks are played. White noise has also been used in electronic music, where it is used either directly or as an input for a filter to create other types of noise signal. If they are removed, they are replaced and the opponent's rock is removed from play. urban traffic noise). Until four rocks have been played, guard rocks left in the area between the hog and tee lines, excluding the house — known as the free guard zone — may not be removed by an opponent's stone. White noise is used by some sirens for emergency vehicles, due to its ability to cut through background noise (e.g. A player in the house, either the skip (captain) or vice-skip (also known as the third), will often coach the sweepers as to when they should sweep. Here in order to submerge distracting, undesirable noises (for example conversations, etc.,) in interior spaces, a constant low level of noise is generated and provided as a background sound.

On each shot, two players are equipped with brushes or brooms with which they can vigorously sweep the ice in front of the rock so as to alter its trajectory or increase the distance of travel. One use for white noise is in the field of architectural acoustics. When throwing the rock, it must be released before the near hogline is reached (players usually slide while releasing their shots) and must cross the far hogline; otherwise it is removed from play. There are also other "colors" of noise, the most commonly used being pink and brown. In each end each player on each team throws two rocks in turn, the players on each side alternating shots. White noise is the generalized mean-square derivative of the Wiener process or Brownian motion. A competitive game usually consists of ten ends, while recreational games are more commonly only eight or even six ends. Gaussian white noise has the useful statistical property that its values are independent (see Statistical independence).

Curling is played between two teams of four curlers. These models are used so frequently that the term additive white Gaussian noise has a standard abbreviation: AWGN. Brooms are also used by some curlers as a balancing aide during delivery of the stone. Gaussian white noise is a good approximation of many real-world situations and generates mathematically tractable models. Today, brushes have replaced traditional corn brooms at every level of curling, but are universally referred to as brooms. Thus, the two words "Gaussian" and "white" are often both specified in mathematical models of systems. Brushes were used primarily by elderly curlers as a substitute for corn brooms. However, neither property implies the other.

In earlier days, brooms were made of corn strands and were similar to household brooms. It is often incorrectly assumed that Gaussian noise (see normal distribution) is necessarily white noise. The skip will also hold the broom at the opposite end of the rink from the delivering player to show the deliverer where to aim the rock. Noise having a continuous distribution, such as a normal distribution, can of course be white. The broom can also be used to clean debris off the ice, and is also used by the skip to show where she or he wants the rock to go. For example, a binary signal which can only take on the values 1 or 0 will be white if the sequence of zeros and ones is statistically uncorrelated. Agressive sweeping in front of the rock momentarily melts the pebble, which lessens the deceleration of the rock, and also straightens the trajectory of the rock. Any distribution of values is possible (although it must have zero DC component).

The curling broom is used by the sweepers to sweep the ice surface in front of the rock. Being uncorrelated in time does not however restrict the values a signal can take. Another piece of equipment is the curling broom. The image to the right displays a finite length, discrete time realization of a white noise process generated from a computer. This piece of equipment is needed when a player is sweeping, and needs traction with both feet. the distribution of a signal across all angles in the night sky). This is also usually made of rubber. The signal is then "white" in the spatial frequency domain (this is equally true for signals in the angular frequency domain, e.g.

An additional piece of footwear is the gripper, which can slide on and off the shoe with the slippery surface. The term white noise is also commonly applied to a noise signal in the spatial domain which has zero autocorrelation with itself over the relevant space dimensions. The other foot has a thin layer of rubber, to maximize traction on the ice. . Left-handed curlers have this special shoe on their right foot, while right-handed curlers have it on their left foot. In practice, a signal can be "white" with a flat spectrum over a defined frequency band. This enables curlers to slide out of the hack when delivering a rock. By having power at all frequencies, the total power of such a signal is infinite.

Inexpensive sliders can be purchased that can be attached to any shoes by means of an elastic band. An infinite-bandwidth white noise signal is purely a theoretical construct. The sole of one shoe has a thin strip of Teflon or another type of smooth surface, called a slider. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. When curling, players need to wear special shoes. White noise (Sample (help·info)) is a random signal (or process) with a flat power spectral density. The two remaining players follow the rock and assist in guiding its trajectory by sweeping the ice before the rock, usually under direction from the skip and their own instincts for the weight of the rock, as well as stopwatch split timing.

Thus, each time a rock is thrown, there is one player throwing the rock, and another player at the far end. While the first three players throw their rocks, the skip remains at the far end of the ice to guide the players; while the skip is throwing, the vice takes this role. The lead for each team throws first, followed by the second, third (vice skip or vice or mate), and the skip who is the team captain; this order is not mandatory, and some prominent teams (for example, Randy Ferbey's) reverse the order in which the skip and third throw. The team members are named according to the order in which they throw in each end.

Curling is a team game, played between two teams of four curlers each. Because of the particular rarity of Ailsite, costs for curling stones can reach as much as $500 (CAD). Most curling stones are made from this granite. The Scots in particular believe that the best quality curling stones are made from a specific type of granite called "Ailsite", found on the Ailsa Craig, an island off the Ayrshire coast.

Lights at the base of the handle indicate whether contact was sustained past the line or not. The handle is coated in metallic paint; the circuitry detects the relative charge of the thrower's hand contact to determine if they are still in contact, and a linear field is established at the hog line to indicate its location to the internal sensor. A special handle has recently been developed for high-level tournament play, which integrates electronics to ensure a rock is released before it crosses the hog line. According to the Canadian Curling Association Rules of Curling, "The use of a curling aid commonly referred to as a 'delivery stick' which enables the player to deliver a stone without placing a hand on the handle is considered acceptable.".

This allows the game to be played by handicapped players, as well as those unable to crouch comfortably. Such a stick is designed to attach to the handle so that it can be released without requiring the player to place a hand on the handle in a crouched position. Although the rock is designed to be delivered by players grasping the handle as they slide down the ice, a special "delivery stick" may be used by players incapable of delivering the rock in this fashion. Ice on which the rocks curl well is said to be swingy.

The degree of curl depends on several factors, including the preparation of the ice and the flattening of common paths to the house during the game. On properly prepared ice the rock's path will bend (curl) in the direction the front edge of the rock is turning, especially toward the end of its trip. This small running surface allows the pebble applied to the ice to have an effect on the action of the rock. A special feature of the rock is that its bottom is not flat, but concave and the actual running surface of the rock is only ¼ to ½ inch (6 to 12 mm) wide on the rim of the concave bottom.

If the handle is rotated away from the body, the shot is said to be an in-turn, and if rotated across the body, it is an out-turn. The curling stone or rock used in the game weighs a maximum of 44 lb (19.96 kg) and is fitted with a handle on top allowing it to be rotated as it is released.
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A single moveable hack may also be used. On indoor rinks there are usually two fixed hacks, rubber-lined holes, one each side of the centre line with the inside edge no more than three inches (7.6 cm) from the center line and the front edge on the hack line. The hack is a device used to provide traction to the curler making a shot; the curler places the foot he or she will push off with in the hack. Twelve feet behind the junction of the centre and tee lines, the centre line is crossed at right angles by the hack line.

more than 12 feet from the centre) is not in the house and therefore does not score. The inner rings are merely a visual aid for judging which stone is closer to the centre; they do not affect scoring; however, a stone that is not at least touching the outside of the 12-foot ring (i.e. They are usually distinguished by colour. The rings that surround the button are defined by their diameter as the four-foot, eight-foot, and twelve-foot rings.

Two other lines, the hoglines, are drawn parallel to each backboard and 37 feet (11.3 m) from it. The two lines are the centre line, which is drawn lengthwise down the centre of the sheet, and the tee line, drawn 16 feet (4.9 m) from the backboard and parallel to it. The centre of the house, marked by the junction of two lines which divide the house into quarters, is known as the pin, tee, or spit. On the rink, a 12 foot (3.7 m) wide set of concentric rings, called the house, is painted near each end of the rink.

The curling action of rocks/stones changes during a game as the pebble evens out from wear. As the bottom catches on the pebble, it turns to the inside or outside, causing the stone's path to 'curl'. The pebble creates friction with the bottom of the stone. A key part of the preparation is the spraying of fine water droplets on the ice to create what is called pebble.

The curling arena is a sheet of ice 146 feet (45.5 m) long by 14 feet 2 inches (4.32 m) wide, and is carefully prepared to be absolutely level and to allow the "rocks" or "stones", as the polished granite is called, to glide with as little friction as possible. . Curling was on that occasion played outdoors. Previous opinion had been that all sports then had been demonstration events.

In February 2006 the IOC included the winning curling teams in the 1924 Winter Olympic Games, originally called Semaine des Sports d'Hiver ("International Winter Sports Week"), as medal winners in an official Olympic tournament. Curling has been an official sport in the Winter Olympics since the 1998 Winter Olympic Games. Today, curling is played all over Europe and has spread to Japan, Australia, New Zealand, and even China and Korea. The first curling club in the United States began in 1832, and the game was introduced to Switzerland and Sweden before the end of the nineteenth century.

The Royal Montreal Curling Club, the first sporting club of any kind in North America, was established in 1807. The game is currently most firmly established, however, in Canada. Whatever the truth of the matter, outdoor curling was very popular in Scotland between the 16th and the 19th centuries when the climate was cold enough to ensure good ice conditions every winter, and as a result the international governing body for curling, the World Curling Federation, is based in Perth, Scotland. The game is generally believed to have been invented in 16th century Scotland, although two paintings by Pieter Brueghel the Elder depict Dutch peasants curling.

Curling is a precision sport similar to bowls or bocce, but played on ice with polished heavy stones rather than plastic balls.