In mathematics and physics, a brachistochrone curve, or curve of fastest descent, is the one lying on plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696; the brachistochrone curve is the same shape as the tautochrone curve. However, the portion of the cycloid used for each of the two varies. More the brachistochrone can use up to a complete rotation of the cycloid, but always starts at a cusp. In contrast, the tautochrone problem can only use up to the first half rotation, always ends at the horizontal; the problem can be solved using tools from the calculus of variations and optimal control. The curve is independent of the local strength of gravity. Only a parameter is chosen so that the curve fits the starting point A and the ending point B. If the body is given an initial velocity at A, or if friction is taken into account the curve that minimizes time will differ from the tautochrone curve.
Johann Bernoulli posed the problem of the brachistochrone to the readers of Acta Eruditorum in June, 1696. He said: I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, etc. I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise Bernoulli wrote the problem statement as: Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time. Johann and his brother Jakob Bernoulli derived the same solution, but Johann's derivation was incorrect, he tried to pass off Jakob's solution as his own.
Johann published the solution in the journal in May of the following year, noted that the solution is the same curve as Huygens's tautochrone curve. After deriving the differential equation for the curve by the method given below, he went on to show that it does yield a cycloid. However, his proof is marred by his use of a single constant instead of the three constants, vm, 2g and D, below. Bernoulli allowed six months for the solutions but none were received during this period. At the request of Leibniz, the time was publicly extended for a half. At 4 p.m. on 29 January 1697 when he arrived home from the Royal Mint, Isaac Newton found the challenge in a letter from Johann Bernoulli. Newton mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli recognized its author, exclaiming that he "recognizes a lion from his claw mark"; this story gives some idea of Newton's power. Newton wrote, "I do not love to be dunned and teased by foreigners about mathematical things...", Newton had solved Newton's minimal resistance problem, considered the first of the kind in calculus of variations.
In the end, five mathematicians responded with solutions: Newton, Jakob Bernoulli, Gottfried Leibniz, Ehrenfried Walther von Tschirnhaus and Guillaume de l'Hôpital. Four of the solutions were published in the same edition of the journal as Johann Bernoulli's. In his paper, Jakob Bernoulli gave a proof of the condition for least time similar to that below before showing that its solution is a cycloid. According to Newtonian scholar Tom Whiteside, in an attempt to outdo his brother, Jakob Bernoulli created a harder version of the brachistochrone problem. In solving it, he developed new methods that were refined by Leonhard Euler into what the latter called the calculus of variations. Joseph-Louis Lagrange did further work. Earlier, in 1638, Galileo had tried to solve a similar problem for the path of the fastest descent from a point to a wall in his Two New Sciences, he draws the conclusion that the arc of a circle is faster than any number of its chords, From the preceding it is possible to infer that the quickest path of all, from one point to another, is not the shortest path, namely, a straight line, but the arc of a circle....
The nearer the inscribed polygon approaches a circle the shorter is the time required for descent from A to C. What has been proven for the quadrant holds true for smaller arcs. Just after Theorem 6 of Two New Sciences, Galileo warns of possible fallacies and the need for a "higher science". In this dialogue Galileo reviews his own work; the actual solution to Galileo's problem is half a cycloid. Galileo studied the cycloid and gave it its name, but the connection between it and his problem had to wait for advances in mathematics. In a letter to Henri Basnage, held at the University of Basel Public Library, dated 30 March 1697, Johann Bernoulli stated that he had found 2 methods to show that the Brachistochrone was the "common cycloid" called the "roulette". Following advice from Leibniz, he only included the indirect method in the Acta Eruditorum Lipsidae of May 1697, he writes that this is because he believed it was suffi
Boardmasters Festival is an annual event held in Cornwall, United Kingdom held over four days in mid-August. The event is a combination of live music and surfing/skateboarding competitions in and around the town of Newquay; the festival has a heritage that goes back to 1981, although the music side of the festival has been running since 2005. It has a capacity of 53,000; the majority of the music performances take place to the north of Newquay near Watergate Bay. The Men's Pro 5 Star WQS surf competition takes place on Fistral Beach where a skate ramp is built for the BMX and Skateboard competitions. Other sporting events include The Women's Open, WSL Men's Longboard, WSL Women's Longboard, Boys/Girls Pro Junior and Under 12's; the event is managed by Vision Nine Group. The Watergate Bay site hosts all festival camping; the festival runs from Wednesday to Monday, with music performances running from Friday to Sunday across ten stages. Past years have seen acts performing such as Bastille, Chase & Status, Snoop Dogg, The Chemical Brothers, Stormzy, Ed Sheeran, Deadmau5, George Ezra, Cypress Hill, Calvin Harris, Fatboy Slim and Years and Craig David.
As well as music there is a variety of bars and fairground rides on the site, including a virtual reality hypercube. At Fistral Beach the surf, BMX and skate competitions take place along with more music during the evenings. A small mini-ramp is set up on the headland and the vert ramp is built in the beach car park. A purpose built beach bar hosts evening beach sessions. Full list of Boardmasters Festival line-ups 2019 Friday - Wu-Tang Clan, The Wombats, Razorlight, Mabel, DJ EZ, The Hunna, Ocean Wisdom, Sunset Sons, Bear's Den, SG Lewis, The Magic Gang, Bodega, Easy Life, Claude Vonstroke, Dennis Ferrer, Problem Central, Mason Maynard b2b Eli Brown, James Hype, Artful Dodger, The Menendez Brothers, Queen Zee, Ocean Alley, So Fresh So Clean Saturday - Florence + The Machine, Dizzee Rascal, Franz Ferdinand, Jax Jones & Martin Solveig, Sam Fender, Sleaford Mods, Ibibio Sound Machine, Lady Leshurr, Pete Murray, Self Esteem, Caravana Sun, Laurel, Sea Girls, My Nu Leng, Cakeboy, Barely Legal, Jaguar, Karen Harding, Mella Dee Sunday - Foals, Jorja Smith, Plan B, Michael Franti & Spearhead, Bugzy Malone, Wilkinson B2B Sub Focus, Dermot Kennedy, Lewis Capaldi, Gabrielle Aplin, House Gospel Choir, Grace Carter, Boy Azooga, Skeggs, The Dunwells, Mall Grab, Derrick Carter, Flava D, Ross From Friends, Dimension, Bradley Zero, Nathan Dawe, Echo Town, See Heart, DJ Proof2018 Friday Main Stage - Catfish and the Bottlemen, Miles Kane, Fun Lovin' Criminals, Has Baker, Samm Henshaw, Willie & The Bandits Unleashed - MK, Stefflon Don, DJ Zinc B2B MJ Cole, Fred V & Grafix, Audio Bullys, Will Clarke, Light Layers Land Of Saints - Everything Everything, The Amazons, Rae Morris, Kitty and Lewis, Phil Taggart, Hockey Dad The Point - Claptone, Idris Elba, Gene Farris B2B Doorly, OR:LA, Bronx Cheer, Ryan Platts Saturday Main Stage - The Chemical Brothers, Years & Years, Editors, MNEK, The Sherlocks, Isaac Gracie, Kele Okereke, Wildwood Kin, Newquay Male Voice Choir Unleashed - Annie Mac, Shy FX, Riton & Kah-Lo, Kelli-Leigh, Shapes, Cakeboy Land Of Saints - Lily Allen, Grandmaster Flash, Nadine Shah, Flyte, Balcony The Point - Skream, Denis Sultra, Steve Lawler, Krystel Klear, Two Tribes, Haai Sunday Main Stage - George Ezra, Rag N Bone Man, Fat Freddy's Drop, Declan Mckenna, Becky Hill, Tom Walker, King Tuff, Stereo Honey Unleashed - Craig David, Nadia Rose, Holy Goof, Bobii Lewis, DJ Proof, Danny Howard Land Of Saints - Friendly Fires, The Horrors, Songhoy Boys, Sam Fender, Confidence Man The Point - Bicep, Booka Shade, Dusky, Trance Wax, Shadow Child2017 Friday Main Stage - Two Door Cinema Club, The Flaming Lips, Frank Turner, Loyle Carner, Laura Mvula, Ten Tonnes, Ibibio Sound Machine Unleashed - Andy C, Giggs, TQD, High Contrast, Phil Taggart, Light Layers, Joe Fox Land Of Saints - DJ Shadow, Kurupt FM, Lower Than Alantis, Pulled Apart By Horses, Lucy Rose, Haunt The Woods The Point - Roger Sanchez, Patrick Topping, Purple Disco Machine, Carly Foxx, Luke Hassan Saturday Main Stage - Jamiroquai, The Vaccines, Lethal Bizzle, Tom Grennan, Newton Faulkner, Will Joseph Cook Unleashed - Gorgon City, Hannah Wants, Jax Jones, Conducta, Mad Villains, Dextric Land Of Saints - Jake Bugg, Kate Nash, Jagwar Ma, Wild Beasts, Daisy Clark, Palace The Point - Pete Tong, Idris Elba, Sonny Fodera, Boo Seeka Sunday Main Stage - Alt-J, Ziggy Marley, JP Cooper, Becky Hill, Kiko Bun, Sam Fender, Dutch Uncles Unleashed - Netsky, Armand Van Helden, Dub Pistols, Tonn Piper, Star One, Saint PHNX Land Of Saints - Wretch 32, Fickle Friends, The Amazons, A Blaze Of A Feather, Frances, Off Bloom The Point - Solardo, Hot Since 82, T.
Williams, Patrick Nazemi, Digital Farm Animals2016 Friday Main Stage - Chase & Status and the Bottlemen, Lianne La Havis, Jack Savoretti, Nakho & Medicine For The People Unleashed - Wilkinson, Krept & Konan, Danny Howard, Playground Zero, Light Layers Land Of Saints - Wolf Alice, Maximo Park, Dinosaur Pile-Up, The Correspondents, Keir The Point - Eats Everything, Jonas Rathsman, Toucan, Carly Foxx, Danny Armstrong Saturday Main Stage - Deadmau5, Kaiser Chiefs, Protoje, Jamie Lawson, Michael Kiwanuka, Eliza & The Bear, The Steelers Unleashed - Cr
Nordic skiing encompasses the various types of skiing in which the toe of the ski boot is fixed to the binding in a manner that allows the heel to rise off the ski, unlike Alpine skiing, where the boot is attached to the ski from toe to heel. Recreational disciplines include Telemark skiing. Olympic events are cross-country skiing, ski jumping and nordic combined—competition in which athletes both cross-country ski and ski jump; the FIS Nordic World Ski Championships host these sports, plus Telemark skiing, at the championship level in the winter of every odd numbered year. Biathlon combines cross-country skiing and rifle shooting, but is not included as a Nordic discipline under FIS rules. Instead, it is under the jurisdiction of the International Biathlon Union; the biomechanics of competitive cross-country skiing and ski jumping have been the subject of serious study. Cross-country skiing requires strength and endurance and ski jumping requires aerodynamic efficiency, both of which requirements translate into specific skills to be optimized in training and competition
Skateboarding is an action sport which involves riding and performing tricks using a skateboard, as well as a recreational activity, an art form, an entertainment industry job, a method of transportation. Skateboarding has been influenced by many skateboarders throughout the years. A 2009 report found that the skateboarding market is worth an estimated $4.8 billion in annual revenue with 11.08 million active skateboarders in the world. In 2016, it was announced that skateboarding will be represented at the 2020 Summer Olympics in Tokyo. Since the 1970s, skateparks have been constructed for use by skateboarders, Freestyle BMXers, aggressive skaters, recently, scooters. However, skateboarding has become controversial in areas in which the activity, although illegal, has damaged curbs, steps, benches and parks; the first skateboards started with wooden boxes, or boards, with roller skate wheels attached to the bottom. Crate scooters preceded skateboards, having a wooden crate attached to the nose, which formed rudimentary handlebars.
The boxes turned into planks, similar to the skateboard decks of today. Skateboarding, as we know it, was born sometime in the late 1940s, or early 1950s, when surfers in California wanted something to do when the waves were flat; this was called "sidewalk surfing" – a new wave of surfing on the sidewalk as the sport of surfing became popular. No one knows; the first manufactured skateboards were ordered by a Los Angeles, California surf shop, meant to be used by surfers in their downtime. The shop owner, Bill Richard, made a deal with the Chicago Roller Skate Company to produce sets of skate wheels, which they attached to square wooden boards. Accordingly, skateboarding was denoted "sidewalk surfing" and early skaters emulated surfing style and maneuvers, performed barefoot. By the 1960s a small number of surfing manufacturers in Southern California such as Jack's, Kips', Bing's and Makaha started building skateboards that resembled small surfboards, assembled teams to promote their products.
One of the earliest Skateboard exhibitions was sponsored by Makaha's founder, Larry Stevenson, in 1963 and held at the Pier Avenue Junior High School in Hermosa Beach, California. Some of these same teams of skateboarders were featured on a television show called "Surf's Up" in 1964, hosted by Stan Richards, that helped promote skateboarding as something new and fun to do; as the popularity of skateboarding began expanding, the first skateboarding magazine, The Quarterly Skateboarder was published in 1964. John Severson, who published the magazine, wrote in his first editorial: Today's skateboarders are founders in this sport—they're pioneers—they are the first. There is no history in Skateboarding—its being made now—by you; the sport is being molded and we believe that doing the right thing now will lead to a bright future for the sport. There are storm clouds on the horizon with opponents of the sport talking about ban and restriction; the magazine only lasted four issues, but resumed publication as Skateboarder in 1975.
The first broadcast of an actual skateboarding competition was the 1965 National Skateboarding Championships, which were held in Anaheim and aired on ABC's Wide World of Sports. Because skateboarding was a new sport during this time, there were only two original disciplines during competitions: flatland freestyle and slalom downhill racing. One of the earliest sponsored skateboarders, Patti McGee, was paid by Hobie and Vita Pak to travel around the country to do skateboarding exhibitions and to demonstrate skateboarding safety tips. McGee made the cover of Life magazine in 1965 and was featured on several popular television programs—The Mike Douglas Show, What's My Line? and The Tonight Show Starring Johnny Carson—which helped make skateboarding more popular at the time. Some other well known surfer-style skateboarders of the time were Danny Bearer, Torger Johnson, Bruce Logan and Mark Richards, Woody Woodward, & Jim Fitzpatrick; the growth of the sport during this period can be seen in sales figures for Makaha, which quoted $10 million worth of board sales between 1963 and 1965.
By 1966 a variety of sources began to claim that skateboarding was dangerous, resulting in shops being reluctant to sell them, parents being reluctant to buy them. In 1966 sales had dropped and Skateboarder Magazine had stopped publication; the popularity of skateboarding remained low until the early 1970s. In the early 1970s, Frank Nasworthy started to develop a skateboard wheel made of polyurethane, calling his company Cadillac Wheels. Prior to this new material, skateboards wheels were "clay" wheels; the improvement in traction and performance was so immense that from the wheel's release in 1972 the popularity of skateboarding started to rise again, causing companies to invest more in product development. Nasworthy commissioned artist Jim Evans to do a series of paintings promoting Cadillac Wheels, they were featured as ads and posters in the resurrected Skateboarder magazine, proved immensely popular in promoting the new style of skateboarding. In the early 1970s skateparks hadn't been invented yet, so skateboarders would flock and skateboard in such urban places as The Escondido reservoir in San Diego, California.
Skateboarding magazine would publish the location and Skateboarders made up nicknames for each location such as the Tea Bowl, the Fruit Bowl, the Rabbit Hole, Bird Bath, the Egg Bowl, Upland Pool and the Sewer Slide. Some of the development concepts in the terrain of skateparks were taken from the Escondido re
Freestyle BMX is bicycle motocross stunt riding on BMX bikes. It is an extreme sport descended from BMX racing that consists of five disciplines: street, vert and flatland. In June 2017, the International Olympic Committee announced that it was to be added as an Olympic event to the 2020 Summer Olympics; the earliest photographic documentation of BMX freestyle shows Devin and Todd Bank in 1974 riding BMX bikes on an eight foot tall skateboard ramp they built at their childhood home in West Los Angeles, California. This was the birth of BMX ramp riding. Devin Bank was documented doing 360 degree freestyle spinning tricks on the street and in the air by jumping off curbs. Skateboarder Magazine published photos of kids on bikes riding in empty household swimming pools in 1975.. In 1975 kids started riding bikes in concrete reservoir channels in California. In 1976 Devin and Todd Bank began riding BMX bikes inside the Runway Skatepark in Carson California. And, bike riders were seen in 1976 riding at Carlsbad Skatepark in Carlsbad, California..
Bob Haro and John Swanguen rode BMX bikes at Skateboard Heaven, a concrete skatepark in San Diego, late 1976. They transformed freestyle beyond skateparks by creating new bike tricks on flat streets. In the fall of 1977 Bob Haro was hired as a staff artist at BMX Action Magazine where he be friended R. L. Osborn, son of the magazine publisher Bob Osborn. Haro and R. L. practiced freestyle moves in their free time. In the summer of 1978, Paramount and other Southern California skateparks began reserving sessions or whole days for BMX bikes. BMX racer Tinker Juarez was innovating freestyle moves in vert bowls at Lakewood Ca Park, while William "Crazy Lacy" Furmage was innovating freestyle at the Paramount Ca Skatepark. BMX Action Magazine published the first freestyle how to article in their January/February 1979 issue which showed Bob Haro doing a "rock walk." BMX bike riders performed a demonstration freestyle show in 1979 during a skate competition at Rocky Mountain Surf Skatepark in Salt Lake City, Utah.
Towards the end of 1979, William "Crazy Lacy" Furmage and Tony Ray Davis formed the Super Style II BMX Trick Team and began performing freestyle shows at BMX races and other events. After the Super Style II BMX Trick Team became known, other organized trick teams were founded and gained prominence; the freestyle movement at this point was all underground. Although several BMX manufacture-sponsored freestyle teams were touring the US, they were promoting the sport of BMX in general, not freestyle; the American Freestyle Association was the first governing body for BMX freestyle, founded by Bob Morales in 1982. Bob Osborn founded a slick quarterly magazine devoted to freestyle BMX. In the summer of 1984, Freestylin' Magazine made its debut; the BMX world noticed the sport's massive potential. Manufacturers hurried to the drawing boards to develop new freestyle bikes and accessories, began searching for talented riders to sponsor. Bike shops began stocking freestyle products; the AFA began to put on organized quarter-pipe competitions.
From 1980 until 1987, freestyle BMX increased in popularity to a peak in 1987. During this period, the sport progressed with the release of new bike models and accessories designed for freestyle. For example, Haro released the Haro FST, Master each year, with blazing graphical colors, new look, new frame designs. In the early 1990s, BMX freestyle suffered a decline in its commercial popularity. In this economic climate, communities of new rider-owned companies and initiatives began to re-define the sport according to their own needs and interests, paving the way for what is now a new lead in the industry with clothing companies and material companies; this decline and subsequent new phase of the sport's development into an independently driven industry was notably referenced in the introduction to the BMX video Ride On. Freestyle BMX riders participate in several well-established disciplines; as in the other forms of freestyle riding, there are no specific rules. Street riders make use of public spaces to perform tricks.
These tricks can be performed on curbs, stairs, ledges and other obstacles. Styles among street riders vary, as riders depend upon their own urban surroundings. BMX street rose to prominence as an defined discipline in the late 1980s. In modern BMX, the progression of more technical tricks on street obstacles has led to this discipline becoming more divided from other freestyle disciplines. BMX bikes aimed at street riding have steeper angles and shorter wheelbases, making them easier to maneuver, but less stable at the higher speeds associated with ramp and dirt riding. Within street BMX there are a handful of competitions, however the majority of professional street riders tend to focus on making videos for DVDs and YouTube videos on behalf of their sponsors. Only a handful of riders tend to focus on both, with competition courses and corporate sponsorships not considered'core' street riding by many riders. One rider that has succeeded in both competitions and video projects is Garret Reynolds.
Garret has won 13 X Games medals, as well as Ride BMX Nora Cup Awards for Video Part of The Year and Street Rider of the Year, is considered one of the best BMX Street riders ever. Park denotes the BMX discipline of riding skateparks with an emphasis on riding bowl transitions or ramp jumps. Skateparks are us
Encinitas is a beach city in the North County area of San Diego County, California. Located within Southern California, it is 25 miles north of San Diego and about 95 miles south of Los Angeles; as of the 2010 census, the city had a population of 59,518, up from 58,014 at the 2000 census. Encinitas is a Spanish name meaning "little oaks"; the city was incorporated by 69.3% of the voters in 1986 from the communities of historic Encinitas, new Encinitas, Cardiff-by-the-Sea, Olivenhain. The communities retain distinctive flavors. Encinitas can be divided into five areas: Old Encinitas: a small beachside area featuring a mix of businesses and housing styles. Sitting along Coast Highway 101, the Encinitas welcome arch, the famous surf break Swamis, the early 20th century La Paloma Theater are located here. Old Encinitas is divided from New Encinitas by a low coastal ridge. New Encinitas: a newer region which features a golf course, many shopping centers, is composed of larger tract homes. Olivenhain: a semi-rural region in eastern Encinitas, composed of single family homes, an active 4-H Club, several private equestrian facilities.
Olivenhain connects to Rancho Santa Fe via Encinitas Boulevard. Leucadia: a coastal community of the city. Leucadia features tree-lined boulevards; the community features art galleries, unusual stores, restaurants, along with single family homes. This contains beaches such as Beacons and Grandview. Cardiff-by-the-Sea: Encinitas' southernmost oceanfront community, which features streets named after British cities and classical composers, the Lux Art Institute, the San Elijo Campus of Mira Costa College. Encinitas is located at 33°2′40″N 117°16′18″W. According to the United States Census Bureau, the city has a total area of 20.0 square miles. 18.8 square miles of it is land and 1.2 square miles of it is water. The city's elevation ranges between 180 feet above sea level. Encinitas lies on rugged coastal terrain; the city is bisected by a low-lying coastal ridge that separates Old Encinitas. In the north of the city, the coast rises in elevation and the land is raised up in the form of many coastal bluffs.
The city is surrounded by Batiquitos Lagoon and San Elijo Lagoon to the north and south, respectively. Encinitas has a mild, Mediterranean climate. Average daily high temperature is 72 °F. Temperatures below 40 °F and above 85 °F are rare. Average rainfall is about 10 inches per year; the wet season lasts during the winter and spring, when temperatures are cool. Average daytime temperatures hit 65F in spring, when rain and marine layer are common. Nighttime lows range from 45-55F; the dry season lasts from summer through fall, with average daytime temperatures ranging from 75-85F, nighttime lows being from the upper 50s–60sF. Ocean water temperatures average 60F in winter, 64F in spring, 70F in summer, 66F in fall. In winter, strong Pacific storms can bring heavy rain. During the winter of 2015-2016, the area saw rounds of severe thunderstorms. Tornados touched down nearby; the 2010 United States Census reported that Encinitas had a population of 59,518. The population density was 2,977.5 people per square mile.
The racial makeup of Encinitas was 51,067 White, 361 African American, 301 Native American, 2,323 Asian, 91 Pacific Islander, 3,339 from other races, 2,036 from two or more races. Hispanic or Latino of any race were 8,138 persons; the Census reported that 58,990 people lived in households, 123 lived in non-institutionalized group quarters, 405 were institutionalized. There were 24,082 households, out of which 6,997 had children under the age of 18 living in them, 12,113 were opposite-sex married couples living together, 1,950 had a female householder with no husband present, 981 had a male householder with no wife present. There were 1,359 unmarried opposite-sex partnerships, 169 same-sex married couples or partnerships. 6,303 households were made up of individuals and 2,118 had someone living alone, 65 years of age or older. The average household size was 2.45. There were 15,044 families; the population was spread out with 12,285 people under the age of 18, 3,767 people aged 18 to 24, 16,584 people aged 25 to 44, 19,239 people aged 45 to 64, 7,643 people who were 65 years of age or older.
The median age was 41.5 years. For every 100 females, there were 97.9 males. For every 100 females age 18 and over, there were 95.3 males. Females comprise the majority of Encinitas' population at 50.5% as of April 2010. There were 25,740 housing units at an average density of 1,287.7 per square mile, of which 15,187 were owner-occupied, 8,895 were occupied by renters. The homeowner vacancy rate was 1.0%. 39,101 people lived in owner-occupied housing units and 19,889 people lived in rental housing units. As of the census of 2000, there were 58,014 people, 22,830 households, 14,291 families residing in the city; the population density was 3,035.6 inhabitants per square mile. There were 23,843 housing units at an average density of 1,247.6 per square mile. The racial makeup of the city was 86.60% White, 0.59% Black or African American, 0.46% Native American, 3.10% Asian, 0.12% Pacific Islander, 6.28% from other races, 2.85% from two or more races. 14
A grain elevator is an agrarian facility complex designed to stockpile or store grain. In grain trade, the term grain elevator describes a tower containing a bucket elevator or a pneumatic conveyor, which scoops up grain from a lower level and deposits it in a silo or other storage facility. In most cases, the term grain elevator describes the entire elevator complex, including receiving and testing offices and storage facilities, it may mean organizations that operate or control several individual elevators, in different locations. In Australia the term grain elevator describes only the lifting mechanism. Before the advent of the grain elevator, grain was handled in bags rather than in bulk. Dart's Elevator was a major innovation, it was invented by Joseph Dart, a merchant, Robert Dunbar, an engineer, in 1842 and 1843, in Buffalo, New York. Using the steam-powered flour mills of Oliver Evans as their model, they invented the marine leg, which scooped loose grain out of the hulls of ships and elevated it to the top of a marine tower.
Early grain elevators and bins were built of framed or cribbed wood, were prone to fire. Grain-elevator bins and silos are now made of steel or reinforced concrete. Bucket elevators are used to lift grain to a distributor or consignor, from which it falls through spouts and/or conveyors and into one or more bins, silos, or tanks in a facility; when desired, silos and tanks are emptied by gravity flow, sweep augers, conveyors. As grain is emptied from bins and silos it is conveyed and weighted into trucks, railroad cars, or barges, shipped to grain wholesalers, and/or local end-users, such as flour mills and ethanol and alcohol distilleries. In Australian English, the term "grain elevator" is reserved for elevator towers, while a receival and storage building or complex is distinguished by the formal term receival point or as a "wheat bin" or "silo". Large-scale grain receival and logistics operations are known in Australia as bulk handling. In Canada, the term "grain elevator" is used to refer to a place where farmers sell grain into the global grain distribution system, and/or a place where the grain is moved into rail cars or ocean-going ships for transport.
There are several types of grain elevators under Canadian law, defined in the Canadian Grain Act, Section 2. Primary elevators receive grain directly from producers for forwarding, or both. Process elevators store grain for direct manufacture or processing into other products. Terminal elevators receive grain on or after official inspection and weighing and clean and treat grain before moving it forward. Transfer elevators transfer grain, inspected and weighed at another elevator. In the Eastern Division, transfer elevators receive and store eastern or foreign grain, it was both necessity and the prospect of making a lot of money that gave birth to the steam-powered grain elevator in Buffalo, New York, in 1843. Due to the completion of the Erie Canal in 1825, Buffalo enjoyed a unique position in American geography, it stood at the intersection of two great all-water routes: one extending from New York Harbor, up the Hudson River, to Albany and, beyond it, the Port of Buffalo. All through the 1830s, Buffalo benefited tremendously from its position.
In particular, it was the recipient of most of the increasing quantities of grain, being grown on farms in Ohio and Indiana, shipped on Lake Erie for transshipment to the Erie Canal. If Buffalo hadn't been there, or when things got backed up there, that grain would have been loaded onto boats at Cincinnati and shipped down the Mississippi River to New Orleans. By 1842, it was clear, they still relied upon techniques, in use since the European Middle Ages: work teams of stevedores would use block and tackles and their own backs to unload or load each and every sack of grain, stored or was to be stored in the boat's hull. It would take several days, sometimes a week, to service a single grain-laden boat. Grain shipments were going down the Mississippi River, not over the Great Lakes/Erie Canal system. A merchant named Joseph Dart, Jr. is credited as being the one who adapted Oliver Evans' grain elevator for use in a commercial framework, but the actual design and construction of the world's first steam-powered "grain storage and transfer warehouse" was executed by an engineer named Robert Dunbar.
Thanks to the historic Dart's Elevator, which worked seven times faster than its non-mechanized predecessors, Buffalo was able to keep pace with—and thus further stimulate—the rapid growth of American agricultural production in the 1840s and 1850s, but after the Civil War, with the coming of the railroads. It wasn't by accident that the world's second and third grain elevators were built in Toledo and Brooklyn, New York, in 1847. Fledgling American cities, they were connected through an emerging international grain trade of unprecedented proportions. Grain shipments from farms in Ohio were loaded onto ships by elevators at Toledo.