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| [[File:Braddley Wiggins, 2011 Critérium du Dauphiné, Stage 7.jpg|thumb|upright|right|Bradley Wiggins in the yellow [[Cycling jersey|jersey]], finishing the [[2011 Critérium du Dauphiné]].]]
| | Royal Votaw is my name but I by no means really liked that title. Interviewing is what she does but soon she'll be on her personal. My house is now in Kansas. Her friends say it's not good for her but what she loves doing is flower arranging and she is trying to make it a occupation.<br><br>My blog ... extended car warranty ([http://Lexhousing.com/ActivityFeed/MyProfile/tabid/56/userId/284/language/en-US/Default.aspx dig this]) |
| [[File:LongJohn08.jpg|right|thumb|Heavy duty [[freight bicycle]] made by SCO, Denmark. Can carry more than {{convert|100|kg}}.]]
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| A '''bicycle's performance''', in both biological and mechanical terms, is extraordinarily efficient. In terms of the amount of [[energy]] a person must expend to travel a given distance, investigators have calculated it to be the most efficient self-powered [[Mode of transport|means of transportation]].<ref>{{cite journal
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| | title = Bicycle Technology
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| | author = S.S. Wilson
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| | journal = Scientific American
| |
| |date=March 1973}}</ref> From a mechanical viewpoint, up to 99%
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| <ref name="whitt">{{cite book
| |
| | title = Bicycling Science
| |
| | edition = Third
| |
| | last = Wilson
| |
| | first = David Gordon
| |
| | coauthors = Jim Papadopoulos
| |
| | year = 2004
| |
| | publisher = Massachusetts Institute of Technology
| |
| | isbn = 0-262-23111-5
| |
| | pages = 343}}</ref>
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| of the energy delivered by the rider into the [[Bicycle pedal|pedals]] is transmitted to the [[Bicycle wheel|wheels]], although the use of [[Bicycle gearing|gearing mechanisms]] may reduce this by 10–15%.<ref>{{cite web
| |
| | title = Pedal Power Probe Shows Bicycles Waste Little Energy
| |
| | url = http://www.jhu.edu/~gazette/1999/aug3099/30pedal.html
| |
| | author = Phil Sneiderman Homewood
| |
| | publisher = Johns Hopkins Gazette
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| | date = August 30, 1999
| |
| | accessdate = 2010-02-21| archiveurl= http://web.archive.org/web/20100201184425/http://www.jhu.edu/~gazette/1999/aug3099/30pedal.html| archivedate= 1 February 2010 <!--DASHBot-->| deadurl= no}}</ref><ref name="Wilson1">{{cite book
| |
| | title = Bicycling Science
| |
| | edition = Third
| |
| | last = Wilson
| |
| | first = David Gordon
| |
| | coauthors = Jim Papadopoulos
| |
| | year = 2004
| |
| | publisher = The MIT Press
| |
| | isbn = 0-262-73154-1
| |
| | page = 318
| |
| | quote = When new, clean, and well-lubricated, and when sprockets with a minimum of 21 teeth are used, a chain transmission is highly efficient (at a level of maybe 98.5 percent or even higher).}}</ref> In terms of the ratio of [[cargo]] weight a bicycle can carry to total weight, it is also a most efficient means of cargo transportation.
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| | |
| ==Energy efficiency==
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| A human being traveling on a [[bicycle]] at 10–15 mph (16–24 km/h), using only the power required to walk, is the most energy-efficient means of transport generally available.{{citation needed|date=October 2011}} [[Air drag]], which increases with the square of speed,<ref name="Wilson2">{{cite book
| |
| | title = Bicycling Science
| |
| | edition = Third
| |
| | last = Wilson
| |
| | first = David Gordon
| |
| | coauthors = Jim Papadopoulos
| |
| | year = 2004
| |
| | publisher = The MIT Press
| |
| | isbn = 0-262-73154-1
| |
| | page = 126
| |
| | quote = aerodynamic drag force is proportional to the square of the velocity}}</ref> requires increasingly higher [[Power (physics)|power]] outputs relative to speed, power increasing with the cube of speed as power equals force times velocity. A bicycle in which the rider lies in a [[supine position]] is referred to as a [[recumbent bicycle]] or, if covered in an aerodynamic [[Bicycle fairing|fairing]] to achieve very low air drag, as a [[streamliner]].
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| [[File:RacingBicycle-non.JPG|right|thumb|Racing bicycles are light in weight, allow for free motion of the legs, keep the rider in a comfortably aerodynamic position, and feature high gear ratios and low rolling resistance.]]
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| | |
| On firm, flat ground, a {{Convert|70|kg|lb|abbr=on}} person requires about 30 [[watt]]s to walk at {{Convert|5|km/h|mph|abbr=on}}{{Citation needed|date=August 2012}}. That same person on a bicycle, on the same ground, with the same power output, can average {{Convert|15|km/h|mph|abbr=on}}, so energy expenditure in terms of [[Calorie|kcal]]/(kg·km) is roughly one-third as much. Generally used figures are
| |
| * 1.62 [[Joule|kJ]]/(km∙kg) or 0.28 kcal/(mi∙lb) for cycling,
| |
| * 3.78 kJ/(km∙kg) or 0.653 kcal/(mi∙lb) for walking/running,
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| * 16.96 kJ/(km∙kg) or 2.93 kcal/(mi∙lb) for swimming.
| |
| | |
| Amateur bicycle racers can typically produce 3 [[watt]]s/kg for more than an hour (e.g., around 210 watts for a 70 kg rider), with top amateurs producing 5 W/kg and elite athletes achieving 6 W/kg for similar lengths of time{{Citation needed|date=August 2012}}. Elite track [[Sprint (cycling)|sprinters]] are able to attain an instantaneous maximum output of around 2,000 watts, or in excess of 25 W/kg{{Citation needed|date=August 2012}}; elite road cyclists may produce 1,600 to 1,700 watts as an instantaneous maximum in their burst to the finish line at the end of a five-hour long road race{{Citation needed|date=August 2012}}. Even at moderate speeds, most power is spent in overcoming the aerodynamic [[drag (physics)|drag]] force, which increases with the square of speed.<ref name="Wilson2"/> Thus, the power required to overcome drag increases with the cube of the speed.
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| | |
| ==Typical speeds==
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| In an urban environment, there are no typical speeds for a person riding a bicycle; an elderly person on a sit-up-and-beg style [[roadster (bicycle)|roadster]] might do less than {{convert|10|km/h|abbr=on}} while a fitter, younger person could easily do twice that on the same bicycle. For [[Cycling in Copenhagen|cyclists in Copenhagen]], the average cycling speed is {{convert|15.5|km/h|abbr=on}}.<ref>{{cite web|title=Bicycle statistics|url=http://subsite.kk.dk/sitecore/content/Subsites/CityOfCopenhagen/SubsiteFrontpage/LivingInCopenhagen/CityAndTraffic/CityOfCyclists/CycleStatistics.aspx|work=City of Copenhagen website|publisher=City of Copenhagen|accessdate=12 December 2013|date=13 June 2013}}</ref>
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| | |
| On a fast [[racing bicycle]], a reasonably fit rider can ride at {{convert|50|km/h|abbr=on}} on flat ground for short periods.{{citation needed|date=December 2013}}
| |
| | |
| ===Cycling speed records===
| |
| The highest speed officially recorded for any [[Human-powered vehicle#Related objects|human-powered vehicle]] (HPV) on level ground and with calm winds and without external aids (such as motor pacing and wind-blocks) is {{convert|133.78|km/h|abbr=on}} set in 2013 by [[Sebastiaan Bowier]] in the VeloX3, a streamlined recumbent bicycle.<ref>http://www.hptdelft.nl/en/index.php?option=com_content&view=article&id=508:hightech-recumbent-from-delft-breaks-world-record&catid=15:blog&Itemid=58</ref> In the 1989 [[Race Across America]], a group of HPVs crossed the United States in just 6 days.<ref name=wired>{{cite news
| |
| |title = World's Fastest Cyclist Hits 82.3 MPH
| |
| |last = Wired.com
| |
| |url=http://blog.wired.com/cars/2008/09/worlds-fastest.html
| |
| |accessdate= 2008-09-26
| |
| |date=2008-09-25
| |
| | archiveurl= http://web.archive.org/web/20080926163047/http://blog.wired.com/cars/2008/09/worlds-fastest.html| archivedate= 26 September 2008 <!--DASHBot-->| deadurl= no}}</ref><ref>{{cite web
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| | url = http://www.ihpva.org/hpva/hpvarec3.html#nom01
| |
| | title = International Human Powered Vehicle Association Official Speed Records
| |
| | accessdate = 2008-03-04 | archiveurl= http://web.archive.org/web/20080412043822/http://www.ihpva.org/hpva/hpvarec3.html| archivedate= 12 April 2008 <!--DASHBot-->| deadurl= no}}</ref><ref>{{cite web
| |
| | url = http://www.wisil.recumbents.com/wisil/fastest_list.asp
| |
| | title = Fastest Human Powered Lists
| |
| | accessdate = 2008-03-04 | archiveurl= http://web.archive.org/web/20080308021037/http://www.wisil.recumbents.com/wisil/fastest_list.asp| archivedate= 8 March 2008 <!--DASHBot-->| deadurl= no}}</ref><ref>{{cite web
| |
| | url = http://www.legslarry.beerdrinkers.co.uk/tech/MLS.htm
| |
| | title = HPV And Bicycle Speed Records Men – Single Rider
| |
| | accessdate = 2008-03-04 | archiveurl= http://web.archive.org/web/20080412070636/http://www.legslarry.beerdrinkers.co.uk/tech/MLS.htm| archivedate= 12 April 2008 <!--DASHBot-->| deadurl= no}}</ref> The highest speed officially recorded for a bicycle ridden in a conventional upright position under fully faired conditions was {{convert|82.52|km/h|abbr=on}} over 200m.<ref>{{cite web
| |
| | url = http://www.moultonbicycles.co.uk/heritage.html#recordsracing
| |
| | title = Moulton Bicycle Company: Records and Racing
| |
| | accessdate = 2010-02-26| archiveurl= http://web.archive.org/web/20100412154319/http://www.moultonbicycles.co.uk/heritage.html| archivedate= 12 April 2010 <!--DASHBot-->| deadurl= no}}</ref><ref>{{cite web | url = http://pep.metapress.com/content/l323nr7267358864/ | title = Aerodynamic research using the Moulton small-wheeled bicycle |accessdate = 2010-02-26 }}</ref> That record was set in 1986 by Jim Glover on a [[Moulton Bicycle#Related objects|Moulton]] AM7 at the 3rd international HPV scientific symposium at Vancouver.
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| | |
| ==Weight vs power==
| |
| | |
| There has been major corporate competition to lower the weight of racing bikes. [[Bicycle wheel|Wheels]] are available with comparatively lower [[friction]] [[Bearing (mechanical)|bearings]] and other features to lower resistance, however in measured tests{{which|date=December 2012}} these components have almost no effect on cycling performance when riding on flat ground. The [[Union Cycliste Internationale|UCI]] sets a limit on the minimum weight of bicycles to be used in sanctioned races,<ref name=uci_rules>{{cite web
| |
| |title = UCI Rules
| |
| |last = uci.ch
| |
| |url=http://www.uci.ch/templates/UCI/UCI2/layout.asp?MenuId=MTkzNg
| |
| |accessdate= 2010-07-27
| |
| }}</ref> to discourage making structures so thin that they become unsafe. For these reasons recent designs have concentrated on lowering wind resistance by using aerodynamically shaped tubing, flat [[spoke]]s on the wheels, and [[Bicycle handlebar|handlebars]] that position the rider's torso and arms for minimal drag. These changes can impact performance dramatically{{quantify|date=December 2012}}, cutting minutes off a time trial.{{citation needed|date=December 2012}} Less weight results in larger time savings on uphill terrain.
| |
| | |
| ===Kinetic energy of a rotating wheel===
| |
| Consider the [[kinetic energy]] and "[[rotating]] mass" of a [[bicycle]] in order to examine the energy impacts of rotating versus non-rotating [[mass]].
| |
| | |
| The translational kinetic energy of an object in [[Motion (physics)|motion]] is:<ref>{{cite book
| |
| | title = Introduction to Statics and Dynamics
| |
| | last = Ruina
| |
| | first = Andy
| |
| | coauthors = [[Rudra Pratap]]
| |
| | year = 2002
| |
| | publisher = Oxford University Press
| |
| | url = http://ruina.tam.cornell.edu/Book/RuinaPratapNoProblems.pdf
| |
| | format = PDF
| |
| | accessdate = 2006-08-04
| |
| | page = 397
| |
| | archiveurl= http://web.archive.org/web/20060912103008/http://ruina.tam.cornell.edu/Book/RuinaPratapNoProblems.pdf| archivedate= 12 September 2006 <!--DASHBot-->| deadurl= no}}</ref>
| |
| | |
| :<math>E = \tfrac{1}{2}mv^2</math>,
| |
| | |
| Where <math>E</math> is energy in [[joule]]s, <math>m</math> is mass in kg, and <math>v</math> is [[velocity]] in meters per second. For a rotating mass (such as a wheel), the rotational kinetic energy is given by
| |
| | |
| :<math>E = \tfrac{1}{2}I \omega^2</math>,
| |
| | |
| where <math>I</math> is the [[moment of inertia]], <math>\omega</math> (pronunciation: omega) is the [[angular velocity]] in [[radians per second]]. For a wheel with all its mass at the outer edge (a fair approximation for a bicycle wheel), the moment of inertia is
| |
| | |
| :<math>I = m r^2</math>.
| |
| | |
| Where <math>r</math> is the radius in meters
| |
| | |
| The angular velocity is related to the translational velocity and the radius of the tire. As long as there is no slipping,
| |
| | |
| :<math>\omega = \frac{v}{r}</math>.
| |
| | |
| When a rotating mass is moving down the road, its total kinetic energy is the sum of its translational kinetic energy and its rotational kinetic energy:
| |
| | |
| :<math>E = \tfrac{1}{2}mv^2 + \tfrac{1}{2}I\omega^2</math>
| |
| | |
| Substituting for <math>I</math> and <math>\omega</math>, we get
| |
| :<math>E = \tfrac{1}{2}mv^2 + \tfrac{1}{2}mr^2 \cdot \frac{v^2}{r^2}</math>
| |
| | |
| The <math>r^2</math> terms cancel, and we finally get
| |
| :<math>E = \tfrac{1}{2}mv^2 + \tfrac{1}{2}mv^2 = mv^2</math>.
| |
| | |
| In other words, a mass on the tire has twice the kinetic energy of a
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| non-rotating mass on the bike.
| |
| This all depends, of course, on how well a thin hoop approximates the bicycle wheel. In reality, all the mass cannot be at the radius. For comparison, the opposite extreme might be a disk wheel where the mass is distributed evenly throughout the interior. In this case <math>I = \tfrac{1}{2}m r^2</math> and so the resulting total kinetic energy becomes <math>E = \tfrac{1}{2}mv^2 + \tfrac{1}{4}mv^2 = \tfrac{3}{4}mv^2</math>. A pound off the disk wheels = only 1.5 pounds off the frame. Most real bicycle wheels will be somewhere between these two extremes.
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| | |
| One other interesting point from this equation is that for a [[bicycle wheel]]
| |
| that is not slipping, the kinetic energy is independent of wheel radius. In
| |
| other words, the advantage of 650C or other smaller wheels is due to their
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| lower weight (less material in a smaller [[circumference]]) rather than their
| |
| smaller [[diameter]], as is often stated. The KE for other rotating masses on
| |
| the bike is tiny compared to that of the wheels. For example, pedals turn at
| |
| about <math>\tfrac{1}{5}</math> the speed of wheels, so their KE is about
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| <math>\tfrac{1}{25}</math> (per unit weight) that of a spinning wheel. As their center of mass turns on a smaller radius, this is further reduced.
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| | |
| ===Convert to kilocalories===
| |
| Assuming that a rotating wheel can be treated as the mass of rim and [[tire]] and 2/3 of the mass of the spokes, all at the center of the rim/tire. For a 180 lb (82 kg) rider on an 18 lb (8 kg) bike (90 kg total) at 25 mph (40 km/h ; 11.2 m/s), the KE is 5625 [[joules]] for the bike/rider plus 94 joules for a rotating wheel (combined 1.5 kg of rims/tires/spokes). Converting joules to [[kilocalorie]]s (multiply by 0.0002389) gives 1.4 kilocalories ([[Food energy|nutritional calories]]).
| |
| | |
| Those 1.4 kilocalories are the energy necessary to [[accelerate]] from a standstill, or the heat to be [[dissipation|dissipated]] by the brakes to stop the bike. These are kilocalories, so 1.4 kilocalories will heat 1 kg of water 1.4 degrees Celsius. Since aluminum's [[heat capacity]] is 21% of water, this amount of energy would heat 800 g of alloy rims 8 °C (15 °F) in a rapid stop. Rims do not get very hot from stopping on flat ground. To get the rider's energy expenditure, consider the 24% efficiency factor to get 5.8 kilocalories—accelerating a bike/rider to <span style="white-space:nowrap">25 mph (40 km/h)</span> requires about 0.5% of the energy required to ride at <span style="white-space:nowrap">25 mph (40 km/h)</span> for an hour. This energy expenditure would take place in about 15 seconds, at a rate of roughly 0.4 kilocalories per second, while [[steady state]] riding at <span style="white-space:nowrap">25 mph (40 km/h)</span> requires 0.3 kilocalories per second.
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| | |
| ===Advantages of light wheels===
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| The advantage of light bikes, and particularly light wheels, from a KE standpoint is that KE only comes into play when speed changes, and there are certainly two cases where lighter wheels should have an advantage: [[Sprint (cycling)|sprints]], and corner jumps in a [[criterium]].<ref name="Zinn">{{cite web
| |
| | url = http://www.velonews.com/tech/report/articles/9662.0.html
| |
| | title = Technical Q&A with Lennard Zinn: The great rotating-weight debate
| |
| | accessdate = 2007-02-03 |archiveurl = http://web.archive.org/web/20061017095411/http://www.velonews.com/tech/report/articles/9662.0.html <!-- Bot retrieved archive --> |archivedate = 2006-10-17}}</ref>
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| | |
| In a 250 m sprint from 36 to 47 km/h to (22 to 29 mph), a 90 kg bike/rider with 1.75 kg of rims/tires/spokes increases KE by 6,360 [[joule]]s (6.4 kilocalories burned). Shaving 500 g from the rims/tires/spokes reduces this KE by 35 joules (1 kilocalorie = 1.163 [[watt-hour]]). The impact of this weight saving on speed or distance is rather difficult to calculate, and requires assumptions about rider power output and sprint distance. The [http://www.analyticcycling.com Analytic Cycling web site] allows this calculation, and gives a time/distance advantage of 0.16 s/188 cm for a sprinter who shaves 500 g off their wheels. If that weight went to make an aero wheel that was worth <span style="white-space:nowrap">0.03 mph (0.05 km/h)</span> at <span style="white-space:nowrap">25 mph (40 km/h)</span>, the weight savings would be canceled by the [[aerodynamic]] advantage. For reference, the best aero bicycle wheels are worth about <span style="white-space:nowrap">0.4 mph (0.6 km/h)</span> at 25, and so in this sprint would handily beat a set of wheels weighing 500 g less.
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| | |
| In a criterium race, a rider is often jumping out of every corner. If the rider has to brake entering each corner (no coasting to slow down), then the KE that is added in each jump is wasted as heat in braking. For a flat [[criterium|crit]] at 40 km/h, 1 km [[Race track|circuit]], 4 corners per lap, 10 km/h speed loss at each corner, one hour duration, 80 kg rider/6.5 kg bike/1.75 kg rims/tires/spokes, there would be 160 corner jumps. This effort adds 387 kilocalories to the 1100 kilocalories required for the same ride at steady speed. Removing 500 g from the wheels, reduces the total body energy requirement by 4.4 kilocalories. If the extra 500 g in the wheels had resulted in a 0.3% reduction in aerodynamic drag factor (worth a <span style="white-space:nowrap">0.02 mph (0.03 km/h)</span> speed increase at 25 mph), the caloric cost of the added weight effect would be canceled by the reduced [[Mechanical work|work]] to overcome the wind.
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| | |
| Another place where light wheels are claimed to have great advantage is in climbing. Though one may hear expressions such as "these wheels were worth 1–2 mph", etc. The formula for [[Power (physics)|power]] suggests that 1 lb saved is worth <span style="white-space:nowrap">0.06 mph (0.1 km/h)</span> on a 7% [[Grade (slope)|grade]], and even a 4 lb saving is worth only <span style="white-space:nowrap">0.25 mph (0.4 km/h)</span> for a light rider. So, where is the big savings in wheel weight reduction coming from? One argument is that there is no such improvement; that it is "[[placebo effect]]". But it has been proposed that the speed variation with each [[Bicycle pedal|pedal]] stroke when riding up a hill explains such an advantage. However the energy of speed variation is conserved; during the power phase of pedaling the bike speeds up slightly, which stores KE, and in the "dead spot" at the top of the pedal stroke the bike slows down, which recovers that KE. Thus increased rotating mass may slightly reduce speed variations, but it does not add energy requirement beyond that of the same non-rotating mass.
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| Lighter bikes are easier to get up hills, but the cost of "rotating mass" is only an issue during a rapid acceleration, and it is small even then.
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| | |
| ==Aerodynamics vs power==
| |
| | |
| Heated debates over the relative importance of weight savings and aerodynamics are a fixture in [[cycling]]. This is an attempt to at least get the equation-based parts of the debate clarified. There will always be those who argue that "experience trumps mathematics" on this issue, so this will attempt to highlight those areas where experience might disagree with the math. From this, perhaps further discussion can focus on the topics of dispute rather than questioning known physics. To be as clear as possible, this will cover 1) the power requirements for moving a bike/rider, 2) the energy cost of acceleration, and then 3) why experience and the math might disagree.
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| | |
| ===Power required===
| |
| | |
| There is a well-known equation that gives the [[Power (physics)|power]] required to push a bike and rider through the air and to overcome the friction of the drive train:
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| | |
| :<math>P = g m V_g (K_1+s) + K_2 V_a^2 V_g</math>,
| |
| | |
| where <math>P</math> is in [[watt]]s, <math>g</math> is [[Earth's gravity]], <math>V_g</math> is ground speed (m/s), <math>m</math> is bike/rider mass in kg, <math>s</math> is the [[Grade (slope)|grade]] (m/m), and <math>V_a</math> is the rider's speed through the air (m/s). <math>K_1</math> is a lumped constant for all [[friction]]al losses (tires, bearings, chain), and is generally reported with a value of 0.0053. <math>K_2</math> is a lumped constant for aerodynamic drag and is generally reported with a value of 0.185 kg/m.<ref>Corresponding to a surface area of 0.4m^2 with a drag coefficient of 0.7: [[Drag (physics)#Power]]</ref> If there is no wind, <math>V_g=V_a</math> and the result simplifies to:
| |
| | |
| :<math>P = g m V_g (K_1+s) + K_2 V_g^3</math>,
| |
| | |
| which is proportional to the ground speed cubed in its leading term.
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| | |
| Note that the power required to overcome friction and gravity is proportional only to rider weight and ground speed. The aerodynamic drag is roughly proportional to the square of the relative velocity of the air and the bike. Being that the total power requirement to propel the bike forward is a sum of these two variables multiplied by speed, the degree of proportionality between power requirement and speed varies according to their relative magnitude, in an interval between the linear and cube: at higher speeds (riding fast on a flat road) power required will be close to being a cube function of speed, at lower speeds (climbing a steep hill) it will be close to being a linear function of speed.
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| The human body runs at about 24% efficiency for a relatively fit athlete, so for every kilojoule delivered to the pedals the body consumes 1 kcal (4.2 kJ) of food energy.{{Citation needed|date=May 2011}}
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| | |
| Obviously, both of the lumped constants in this equation depend on many variables, including drive train efficiency, the rider's position and drag area, aerodynamic equipment, tire pressure, and [[Pavement (material)|road surface]]. Also, recognize that air speed is not constant in speed or direction or easily measured. It is certainly reasonable that the aerodynamic lumped constant would be different in cross winds or tail winds than in direct head winds, as the profile the bike/rider presents to the wind is different in each situation. Also, [[wind speed]] as seen by the bike/rider is not uniform except in zero wind conditions. [[Weather forecasting|Weather report]] wind speed is measured at some distance above the ground in free air with no obstructing trees or buildings nearby. Yet, by definition, the wind speed is always zero right at the road surface. Assuming a single wind velocity and a single lumped drag constant are just two of the simplifying assumptions of this equation. [[Computational fluid dynamics|Computational fluid dynamicists]] have looked at this bicycle modeling problem and found it hard to model well. In layman's terms, this means that much more sophisticated models can be developed, but they will still have simplifying assumptions.
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| | |
| Given this simplified equation, however, one can calculate some values of interest. For example, assuming no wind, one gets the following results for kilocalories required and power delivered to the pedals (watts):
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| | |
| * 175 W for a 90 kg bike + rider to go 9 m/s (20 mph or 32 km/h) on the flat (76% of effort to overcome aerodynamic drag), or 2.6 m/s (5.8 mph or 9.4 km/h) on a 7% grade (2.1% of effort to overcome aerodynamic drag).
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| | |
| * 300 W for a 90 kg bike + rider at 11 m/s (25 mph or 40 km/h) on the flat (83% of effort to overcome aerodynamic drag) or 4.3 m/s (9.5 mph or 15 km/h) on a 7% grade (4.2% of effort to overcome aerodynamic drag).
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| | |
| * 165 W for a 65 kg bike + rider to go 9 m/s (20 mph or 32 km/h) on the flat (82% of effort to overcome aerodynamic drag), or 3.3 m/s (7.4 mph or 12 km/h) on a 7% grade (3.7% of effort to overcome aerodynamic drag).
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| | |
| * 285 W for a 65 kg bike + rider at 11 m/s (25 mph or 40 km/h) on the flat (87% of effort to overcome aerodynamic drag) or 5.3 m/s (12 mph or 19 km/h) on a 7% grade (6.1% of effort to overcome aerodynamic drag).
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| Shaving 1 kg off the weight of the bike/rider would increase speed by 0.01 m/s at 9 m/s on the flat (5 seconds in a <span style="white-space:nowrap">20 mph (32 km/h)</span>, <span style="white-space:nowrap">25-mile (40 km)</span> TT). Losing 1 kg on a 7% grade would be worth 0.04 m/s (90 kg bike + rider) to 0.07 m/s (65 kg bike + rider). If one climbed for 1 hour, saving 1 lb would gain between 225 and <span style="white-space:nowrap">350 feet (107 m)</span> – less effect for the heavier bike + rider combination (e.g., <span style="white-space:nowrap">0.04 mph (0.06 km/h)</span> * 1 h * <span style="white-space:nowrap">5,280 ft (1,609 m)</span>/mi = 225 ft). For reference, the big climbs in the [[Tour de France]] have the following average grades:
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| * [[Col du Tourmalet|Tourmalet]] = 7%
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| * [[Col du Galibier|Galibier]] = 7.5%
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| * [[Alpe D'Huez]] = 8.6%<ref>{{cite journal
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| |url = http://www.velonews.com/article/80615
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| |title = Sastre wins the 2008 L'Alpe d'Huez stage
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| |date = July 23, 2008
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| |accessdate = 2009-01-14
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| |page = Velo News| archiveurl= http://web.archive.org/web/20090219103919/http://www.velonews.com/article/80615| archivedate= 19 February 2009 <!--DASHBot-->| deadurl= no}}</ref>
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| * [[Mont Ventoux]] = 7.1%.
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| The equation can be separated into ''level ground power''
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| :<math>P_{level} = g m V_g K_1 + K_2 V_a^2 V_g </math>,
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| and [[Potential energy#Calculation of gravitational potential energy|vertical climbing power]] given by
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| :<math>P_{climbing} = mg(h/t) \approx gm (V_g s)</math>.
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| ===Energy cost of acceleration===
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| :<math>P_{accelerating} = m*a*V </math>
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| ==See also==
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| *[[Bicycle]]
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| *[[Bicycle and motorcycle dynamics]]
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| *[[Cycling power meter]]
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| *[[Cyclocomputer]]
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| * [[List of cycling topics]]
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| ==References==
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| {{Reflist|2}}
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| * [http://wiki.vanguardsw.com/bin/browse.dsb?det/Engineering/Mechanical/Bike%20Race%20Simulation Physics-bases simulation of bicycle race performance]
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| {{DEFAULTSORT:Bicycle Performance}}
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| [[Category:Cycling]]
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