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Natural hazard
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This article is about the natural hazards that might lead to disasters. For natural disasters, see natural disaster.
A natural hazard[1] is a natural phenomenon that might have a negative effect on humans or the environment. Natural hazard events can be classified into two broad categories[2]: geophysical and biological. Geophysical hazards[3][4] encompass geological and meteorological phenomena such as earthquakes, volcanic eruptions, wildfires, cyclonic storms, floods, droughts, and landslides. Biological hazards can refer to a diverse array of disease, infection, and infestation.
Many geophysical hazards are related;[5] for example, submarine earthquakes can cause tsunamis, and hurricanes can lead to coastal flooding and erosion. Floods and wildfires can result from a combination of geological, hydrological, and climatic factors. It is possible that some natural hazards are intertemporally correlated as well.[5][6] An example of the distinction between a natural hazard and a natural disaster is that the 1906 San Francisco earthquake was a disaster, whereas living on a fault line is a hazard. Some natural hazards can be provoked or affected by anthropogenic processes (e.g. land-use change, drainage and construction).[7]
Contents
[hide]
1 Geological hazards
1.1 Avalanche
1.2 Earthquake
1.3 Coastal erosion
1.4 Lahar
1.5 Landslide
1.6 Sinkholes
1.7 Volcanic eruption
2 Meteorological or climate hazards
2.1 Blizzard
2.2 Drought
2.3 Hailstorm
2.4 Heat wave
2.5 Cyclonic storm
2.6 Ice storm
2.7 Tornado
2.8 Climate change
2.9 Geomagnetic storm
3 Flood
4 Wildfire
5 Disease
6 Multi-hazard analysis
7 International campaigns
8 See also
9 References
10 External links
Geological hazards[edit]
Main article: Geohazard
Avalanche[edit]
An avalanche occurs when a large snow (or rock) mass slides down a mountainside.[8] An avalanche is an example of a gravity current consisting of granular material. In an avalanche, lots of material or mixtures of different types of material fall or slide rapidly under the force of gravity. Avalanches are often classified by the size or severity of consequences resulting from the event.[9]
Earthquake[edit]
See also: Lists of earthquakes and Soil liquefaction
San Francisco was devastated by an earthquake in 1906
An earthquake is the sudden release of energy stored as lithospheric stress that radiates seismic waves. At the Earth's surface, earthquakes may manifest with a shaking or displacement of the ground; when the earthquake occurs on the seafloor, the resulting displacement of water can sometimes result in a tsunami. Most of the world's earthquakes (90%, and 81% of the largest) take place in the 40,000-km-long, horseshoe-shaped zone called the circum-Pacific seismic belt, also known as the Pacific Ring of Fire, which for the most part bounds the Pacific Plate.[10] Many earthquakes happen each day, few of which are large enough to cause significant damage.
Coastal erosion[edit]
Coastal erosion is a physical process by which shorelines in coastal areas around the world shift and change, primarily in response to waves and currents that can be influenced by tides and storm surge.[11] Coastal erosion can result from long-term processes (see also beach evolution) as well as from episodic events such as tropical cyclones or other severe storm events.
Lahar[edit]
A lahar is a type of natural event closely related to a volcanic eruption, and involves a large amount of material originating from an eruption of a glaciated volcano, including mud from the melted ice, rock, and ash sliding down the side of the volcano at a rapid pace. These flows can destroy entire towns in seconds and kill thousands of people, and form flood basalt. This is based on natural events.
Landslide[edit]
A landslide is a mass displacement of sediment, usually down a slope.[12]
Sinkholes[edit]
A sinkhole is a localized depression in the surface topography, usually caused by the collapse of a subterranean structure such as a cave. Although rare, large sinkholes that develop suddenly in populated areas can lead to the collapse of buildings and other structures.
Volcanic eruption[edit]
Puʻu ʻŌʻō
A volcanic eruption is the point in which a volcano is active and releases its power, and the eruptions come in many forms. They range from daily small eruptions which occur in places like Kilauea in Hawaii, to megacolossal eruptions (where the volcano expels at least 1,000 cubic kilometers of material) from supervolcanoes like Lake Taupo (26,500 years ago) and Yellowstone Caldera. According to the Toba catastrophe theory, 70 to 75 thousand years ago, a supervolcanic event at Lake Toba reduced the human population to 10,000 or even 1,000 breeding pairs, creating a bottleneck in human evolution. Some eruptions form pyroclastic flows, which are high-temperature clouds of ash and steam that can travel down mountainsides at speed exceeding an airliner.
Meteorological or climate hazards[edit]
Young steer after a blizzard, March 1966
Blizzard[edit]
A blizzard is a severe winter storm with icy and windy conditions characterized by low temperature, strong wind and heavy snow.
Drought[edit]
Scientists warn that global warming and climate change may result in more extensive droughts in coming years. These extensive droughts are likely to occur within the African continent due to its very low precipitation levels and high temperatures.
Hailstorm[edit]
A hailstorm is a natural hazard where a thunderstorm produces numerous hailstones which damage the location in which they fall. Hailstorms can be especially devastating to farm fields, ruining crops and damaging equipment.
Heat wave[edit]
A heat wave is a hazard characterized by heat which is considered extreme and unusual in the area in which it occurs. Heat waves are rare and require specific combinations of weather events to take place, and may include temperature inversions, katabatic winds, or other phenomena. There is potential for longer-term events causing global warming, including stadial events (the opposite to glacial "ice age" events), or through human-induced climatic warming.
Cyclonic storm[edit]
Hurricane Katrina
Hurricane, tropical cyclone, and typhoon are different names for the same phenomenon: a cyclonic storm system that forms over the oceans. It is caused by evaporated water that comes off of the ocean and becomes a storm. The Coriolis effect causes the storms to spin.74 mph (119 km/h). Hurricane is used for these phenomena in the Atlantic and eastern Pacific Oceans, tropical cyclone in the Indian, and typhoon in the western Pacific.
Ice storm[edit]
An ice storm is a particular weather event in which precipitation falls as ice, due to atmosphere conditions. It causes damage.
Tornado[edit]
A tornado is a natural disaster resulting from a thunderstorm. Tornadoes are violent, rotating columns of air which can blow at speeds between 50 mph (80 km/h) and 300 mph (480 km/h), and possibly higher. Tornadoes can occur one at a time, or can occur in large tornado outbreaks associated with supercells or in other large areas of thunderstorm development. Waterspouts are tornadoes occurring over tropical waters in light rain conditions.
Climate change[edit]
Climate change can increase or decrease weather hazards, and also directly endanger property due to sea level rise and biological organisms due to habitat destruction.
Geomagnetic storm[edit]
Geomagnetic storms can disrupt or damage technological infrastructure, and disorient species with magnetoception.
Flood[edit]
A flood results from an overflow of water beyond its normal confines of a body of water such as a lake, or the accumulation of water over land areas.[13]
Wildfire[edit]
Wildfire is a fire that burns in an uncontrolled and unplanned manner. Wildfires can result from natural occurrences such as lightning strikes or from human activity.[14]
Disease[edit]
Disease is a natural hazard that can be enhanced by human factors such as urbanization or poor sanitation. Disease affecting multiple people can be termed an outbreak or epidemic.
In some cases, a hazard exists in that a human-made defense against disease could fail, for example through antibiotic resistance.
Multi-hazard analysis[edit]
Each of the natural hazard types outlined above have very different characteristics, in terms of the spatial and temporal scales they influence, hazard frequency and return period, and measures of intensity and impact. These complexities result in "single-hazard" assessments being commonplace, where the hazard potential from one particular hazard type is constrained. In these examples, hazards are often treated as isolated or independent. An alternative is a "multi-hazard" approach which seeks to identify all possible natural hazards and their interactions or interrelationships.[15][5]
Many examples exist of one natural hazard triggering or increasing the probability of one or more other natural hazards. For example, an earthquake may trigger landslides, whereas a wildfire may increase the probability of landslides being generated in the future.[5] A detailed review of such interactions across 21 natural hazards identified 90 possible interactions, of varying likelihood and spatial importance.[5] There may also be interactions between these natural hazards and anthropic processes.[16] For example, groundwater abstraction may trigger groundwater-related subsidence.[17]
Effective hazard analysis in any given area (e.g., for the purposes of disaster risk reduction) should ideally include an examination of all relevant hazards and their interactions. To be of most use for risk reduction, hazard analysis should be extended to risk assessment wherein the vulnerability of the built environment to each of the hazards is taken into account. This step is well developed for seismic risk, where the possible effect of future earthquakes on structures and infrastructure is assessed, as well as for risk from extreme wind and to a lesser extent flood risk. For other types of natural hazard the calculation of risk is more challenging, principally because of the lack of functions linking the intensity of a hazard and the probability of different levels of damage (fragility curves).[18] ThinkHazard! is an online tool that provides an overview of the hazards from eight natural hazards (river floods, earthquakes, water scarcity, cyclones, coastal floods, tsunamis, volcanoes and landslides) developed by the Global Facility for Disaster Reduction and Recovery in partnership with other institutions.[19][20]
International campaigns[edit]
In 2000, the United Nations launched the International Early Warning Programme to address the underlying causes of vulnerability and to build disaster-resilient communities by promoting increased awareness of the importance of disaster risk reduction as an integral component of sustainable development, with the goal of reducing human, economic and environmental losses due to hazards of all kinds (UN/ISDR, 2000). The 2006-2007 United Nations International Disaster Reduction Day theme is “Disaster reduction education begins in school”. The Foundation of Public Safety Professionals has launched an international campaign giving everybody a chance to have their say, thought their international open essay or documentary competition “Disaster Risk Reduction Education Begins at School”.[citation needed]
See also[edit]
Act of God
Global catastrophic risk
List of environmental disasters
Ten Threats identified by the United Nations
Emergency management
Civil defense
Disaster relief
Disaster risk reduction
Standardized Natural Hazards Disclosure Statement
Social vulnerability
References[edit]
Jump up ^ Organization of American States, Department of Regional Development; Organization of American States, Natural Hazards Project; United States Agency for International Development, Office of Foreign Disaster Assistance (1990). Disaster, planning and development: managing natural hazards to reduce loss (PDF). Washington, D.C.: Organization of American States. Retrieved 21 July 2014.
Jump up ^ Burton, I.; Kates, R.W.; White, G.F. (1993). The environment as hazard. Guilford Press. ISBN 9780898621594.
Jump up ^ Geography in the News - topical geography resources for teachers and students
Jump up ^ Kusky, Timothy M. (2003). Geological Hazards: A Sourcebook. Greenwood Press.
^ Jump up to: a b c d e Gill, Joel C.; Malamud, Bruce D. (December 2014). "Reviewing and visualizing the interactions of natural hazards". Reviews of Geophysics. 52 (4): 680–722. Bibcode:2014RvGeo..52..680G. doi:10.1002/2013RG000445.
Jump up ^ Graves, Philip E.; Bresnock, Anne E. (1 January 1985). "Are Natural Hazards Temporally Random?". Applied Geography. 5 (1): 5–12. doi:10.1016/0143-6228(85)90002-5. SSRN 1679224  .
Jump up ^ Gill, Joel C.; Malamud, Bruce D. (2017-03-01). "Anthropogenic processes, natural hazards, and interactions in a multi-hazard framework". Earth-Science Reviews. 166: 246–269. doi:10.1016/j.earscirev.2017.01.002.
Jump up ^ "Snow avalanches". All about snow. National Snow & Ice Data Center. Retrieved 22 July 2014.
Jump up ^ "North American Public Avalanche Danger Scale". Avalanche.org. American Avalanche Association. Retrieved 27 April 2015.
Jump up ^ Simkin, Tom; Tilling, Robert I.; Vogt, Peter R.; et al. (2006). This Dynamic Planet: World map of volcanoes, earthquakes, impact craters, and plate tectonics. U.S. Geological Survey Map I-2800. ISBN 1-411-30959-6. Archived from the original (map) on 7 Jan 2014. Retrieved 18 July 2014.
Jump up ^ Komar, Paul D. (1983). CRC handbook of coastal processes and erosion. CRC Press. ISBN 9780849302251.
Jump up ^ Koch, Nicholas K. (1995). Geohazards: natural and human. Prentice Hall. ISBN 9780023229923.
Jump up ^ "Flood". Meteorology glossary. American Meteorological Society. Retrieved 22 July 2014.
Jump up ^ "Wildfire". Cambridge dictionaries online. Cambridge University Press. Retrieved 22 July 2014.
Jump up ^ "Challenges of analyzing multi-hazard risk: a review". Natural Hazards. 64: 1925–1958. doi:10.1007/s11069-012-0294-2.
Jump up ^ http://meetingorganizer.copernicus.org/EGU2014/EGU2014-3049.pdf
Jump up ^ "Land Subsidence". USGS Water Science School. Retrieved 11 May 2017.
Jump up ^ Douglas, J. (2007-04-05). "Physical vulnerability modelling in natural hazard risk assessment". Nat. Hazards Earth Syst. Sci. 7 (2): 283–288. doi:10.5194/nhess-7-283-2007. ISSN 1684-9981.
Jump up ^ ThinkHazard!
Jump up ^ Global Facility for Disaster Reduction and Recovery
External links[edit]
Wikiquote has quotations related to: Natural hazard
Wikimedia Commons has media related to Natural hazard.
Natural hazard research from Bushfire and Natural Hazards CRC
Natural Hazards of the U.S. Geological Survey
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Rock Chalk, Jayhawk
From Wikipedia, the free encyclopedia
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"Rock Chalk, Jayhawk" (a.k.a. the "Rock Chalk" chant) is a chant used at University of Kansas Jayhawks sporting events. The chant is made up of the phrase "Rock chalk, Jayhawk, KU".
Contents
[hide]
1 History
2 Usage
3 References
4 External links
History[edit]
The chant was first adopted by the university's science club in 1886. Chemistry professor E.H.S. Bailey and his colleagues were returning by train to Lawrence after a conference. During their travel, they discussed a need of a rousing yell. They came up with "Rah, Rah, Jayhawk, Go KU",[1] repeated three times, which later became "Rock Chalk Jayhawk, KU".
By 1889, "Rock Chalk"—a transposition of chalk rock, a type of limestone, that exists in the Cretaceous-age bedrocks of central and western parts of the state as well as on Mount Oread, where the University is located, which is similar to the coccolith-bearing chalk of the white cliffs of Dover—later replaced the two "rahs." Those responsible for the change are unknown, with Bailey himself crediting the geology department,[2] and others an English professor.[3]
Kansas troops have used it in the Philippine-American War in 1899, the Boxer Rebellion, and World War II.[4] In the 1911 Border War football game, over 1,000 fans gathered in downtown Lawrence to listen to a "broadcast" of the game by telegraph and participated in cheers including the Rock Chalk.[5]
In the 1920 Summer Olympics, Albert I of Belgium asked for a typical American college yell, and gathered athletes replied with the chant.[4]
Former United States President Theodore Roosevelt called the Rock Chalk chant the greatest college chant he ever heard.[6]
Usage[edit]
Fans have used the phrase "Rock Chalk" in creative ways, such as Rock "Chocolate" Jayhawk ice cream.
It is best known as being loudly chanted at basketball games at Allen Fieldhouse and football games at University of Kansas Memorial Stadium. During pregame, the refrain of "Rock chalk... Jay-Hawk... KU," is repeated twice slowly, and then three times quickly. It is usually preceded by the Kansas alma mater "Crimson and the Blue,” and followed by the fight song, "I'm a Jayhawk.” Since the early 1990's, Kansas fans have been known to do the slow repetition of "Rock chalk... Jay-Hawk... KU" when the Jayhawks are believed to be safely ahead, and victory is guaranteed.
"Rock chalk" is also often used on campus as a way to say goodbye, with the reply being "Jayhawk.”
References[edit]
Jump up ^ "Rock Chalk K-State? Kind of, a century ago". The Topeka Capital-Journal. 2007.
Jump up ^ KUhistory.com - A Swell Yell
Jump up ^ "The Rock Chalk Chant". RockChalk.com. Archived from the original on September 8, 2012. Retrieved April 5, 2008.
^ Jump up to: a b DeReus, Bailey and Betsy McLeod (May 20, 2005). "The Land of the Jayhawks". The University Daily Kansan. Archived from the original on March 19, 2006. Retrieved April 5, 2008.
Jump up ^ "100 years ago: Football fans enjoy mechanized reproduction of KU-MU game". Lawrence Journal-World. November 27, 2011. Retrieved December 27, 2011.
Jump up ^ "The Chant". KU.edu.
External links[edit]
MP3 of the chant
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Gear train
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train.
A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage.
Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next.[1]
The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio.
Features of gears and gear trains include:
The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set.
A planetary gear train provides high gear reduction in a compact package.
It is possible to design gear teeth for gears that are non-circular, yet still transmit torque smoothly.
The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing.
An Agricola illustration from 1580 showing a toothed wheel that engages a slotted cylinder to form a gear train that transmits power from a human-powered treadmill to mining pump.
Contents
[hide]
1 Mechanical advantage
2 Analysis using virtual work
3 Gear trains with two gears
3.1 Formula
4 Double reduction gear
5 Speed ratio
6 Torque ratio
7 Idler gears
7.1 Formula
7.2 Example
8 Belt drives
9 Automotive applications
9.1 Example
9.2 Wide-ratio vs. close-ratio transmission
10 See also
11 References
12 External links
Mechanical advantage[edit]
Gear teeth are designed so the number of teeth on a gear is proportional to the radius of its pitch circle, and so the pitch circles of meshing gears roll on each other without slipping. The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and the ratio of the number of teeth on each gear.
Two meshing gears transmit rotational motion.
The velocity v of the point of contact on the pitch circles is the same on both gears, and is given by
v = r A ω A = r B ω B , {\displaystyle v=r_{A}\omega _{A}=r_{B}\omega _{B},\!}
where input gear A with radius rA and angular velocity ωA meshes with output gear B with radius rB and angular velocity ωB. Therefore,
ω A ω B = r B r A = N B N A . {\displaystyle {\frac {\omega _{A}}{\omega _{B}}}={\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
where NA is the number of teeth on the input gear and NB is the number of teeth on the output gear.
The mechanical advantage of a pair of meshing gears for which the input gear has NA teeth and the output gear has NB teeth is given by
M A = N B N A . {\displaystyle \mathrm {MA} ={\frac {N_{B}}{N_{A}}}.}
This shows that if the output gear GB has more teeth than the input gear GA, then the gear train amplifies the input torque. And, if the output gear has fewer teeth than the input gear, then the gear train reduces the input torque.
If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a speed reducer. In this case, because the output gear must have more teeth than the input gear, the speed reducer amplifies the input torque.
Analysis using virtual work[edit]
For this analysis, we consider a gear train that has one degree-of-freedom, which means the angular rotation of all the gears in the gear train are defined by the angle of the input gear.
The size of the gears and the sequence in which they engage define the ratio of the angular velocity ωA of the input gear to the angular velocity ωB of the output gear, known as the speed ratio, or gear ratio, of the gear train. Let R be the speed ratio, then
ω A ω B = R . {\displaystyle {\frac {\omega _{A}}{\omega _{B}}}=R.}
The input torque TA acting on the input gear GA is transformed by the gear train into the output torque TB exerted by the output gear GB. If we assume the gears are rigid and there are no losses in the engagement of the gear teeth, then the principle of virtual work can be used to analyze the static equilibrium of the gear train.
Let the angle θ of the input gear be the generalized coordinate of the gear train, then the speed ratio R of the gear train defines the angular velocity of the output gear in terms of the input gear:
ω A = ω , ω B = ω / R . {\displaystyle \omega _{A}=\omega ,\quad \omega _{B}=\omega /R.\!}
The formula for the generalized force obtained from the principle of virtual work with applied torques yields:[2]
F θ = T A ∂ ω A ∂ ω − T B ∂ ω B ∂ ω = T A − T B / R = 0. {\displaystyle F_{\theta }=T_{A}{\frac {\partial \omega _{A}}{\partial \omega }}-T_{B}{\frac {\partial \omega _{B}}{\partial \omega }}=T_{A}-T_{B}/R=0.}
The mechanical advantage of the gear train is the ratio of the output torque TB to the input torque TA, and the above equation yields:
M A = T B T A = R . {\displaystyle \mathrm {MA} ={\frac {T_{B}}{T_{A}}}=R.}
The speed ratio of a gear train also defines its mechanical advantage. This shows that if the input gear rotates faster than the output gear, then the gear train amplifies the input torque. And if the input gear rotates slower than the output gear, the gear train reduces the input torque.
Gear trains with two gears[edit]
The simplest example of a gear train has two gears. The "input gear" (also known as drive gear) transmits power to the "output gear" (also known as driven gear). The input gear will typically be connected to a power source, such as a motor or engine. In such an example, the output of torque and rotational speed from the output (driven) gear depend on the ratio of the dimensions of the two gears.
Formula[edit]
The teeth on gears are designed so the gears can roll on each other smoothly (without slipping or jamming). In order for two gears to roll on each other smoothly, they must be designed so the velocity at the point of contact of the two pitch circles (represented by v) is the same for each gear.
Mathematically, if the input gear GA has the radius rA and angular velocity ω A {\displaystyle \omega _{A}\!} , and meshes with output gear GB of radius rB and angular velocity ω B {\displaystyle \omega _{B}\!} , then:
v = r A ω A = r B ω B , {\displaystyle v=r_{A}\omega _{A}=r_{B}\omega _{B},\!}
The number of teeth on a gear is proportional to the radius of its pitch circle, which means the ratios of the gears' angular velocities, radii, and number of teeth are equal. Where NA is the number of teeth on the input gear and NB is the number of teeth on the output gear, the following equation is formed:
ω A ω B = r B r A = N B N A . {\displaystyle {\frac {\omega _{A}}{\omega _{B}}}={\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
This shows that a simple gear train with two gears has the gear ratio R given by:
R = ω A ω B = N B N A . {\displaystyle R={\frac {\omega _{A}}{\omega _{B}}}={\frac {N_{B}}{N_{A}}}.}
This equation shows that if the number of teeth on the output gear GB is larger than the number of teeth on the input gear GA, then the input gear GA must rotate faster than the output gear GB.
Double reduction gear[edit]
Double reduction gears
A double reduction gear comprises two pairs of gears, as single reductions, in series.[3] In the diagram, the red and blue gears give the first stage of reduction and the orange and green gears give the second stage of reduction. The total reduction is the product of the first stage of reduction and the second stage of reduction.
It is essential to have two coupled gears, of different sizes, on the intermediate layshaft. If three gears were used, the overall ratio would be simply that between the first and final gears, the intermediate gear would only act as an idler gear: it would reverse the direction of rotation, but not change the ratio.
Speed ratio[edit]
Gear teeth are distributed along the circumference of the pitch circle so the thickness t of each tooth and the space between neighboring teeth are the same. The pitch p of the gear, which is the distance between equivalent points on neighboring teeth along the pitch circle, is equal to twice the thickness of a tooth,
p = 2 t . {\displaystyle p=2t.\!}
The pitch of a gear GA can be computed from the number of teeth NA and the radius rA of its pitch circle
p = 2 π r A N A . {\displaystyle p={\frac {2\pi r_{A}}{N_{A}}}.}
In order to mesh smoothly two gears GA and GB must have the same sized teeth and therefore they must have the same pitch p, which means
p = 2 π r A N A = 2 π r B N B . {\displaystyle p={\frac {2\pi r_{A}}{N_{A}}}={\frac {2\pi r_{B}}{N_{B}}}.}
This equation shows that the ratio of the circumference, the diameters and the radii of two meshing gears is equal to the ratio of their number of teeth,
r B r A = N B N A . {\displaystyle {\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
The speed ratio of two gears rolling without slipping on their pitch circles is given by,
R = ω A ω B = r B r A , {\displaystyle R={\frac {\omega _{A}}{\omega _{B}}}={\frac {r_{B}}{r_{A}}},}
therefore
R = ω A ω B = N B N A . {\displaystyle R={\frac {\omega _{A}}{\omega _{B}}}={\frac {N_{B}}{N_{A}}}.}
In other words, the gear ratio, or speed ratio, is inversely proportional to the radius of the pitch circle and the number of teeth of the input gear.
Torque ratio[edit]
A gear train can be analyzed using the principle of virtual work to show that its torque ratio, which is the ratio of its output torque to its input torque, is equal to the gear ratio, or speed ratio, of the gear train.
This means the input torque ΤA applied to the input gear GA and the output torque ΤB on the output gear GB are related by the ratio
R = T B T A , {\displaystyle R={\frac {T_{B}}{T_{A}}},}
where R is the gear ratio of the gear train.
The torque ratio of a gear train is also known as its mechanical advantage
M A = T B T A . {\displaystyle {\mathit {MA}}={\frac {T_{B}}{T_{A}}}.}
Idler gears[edit]
In a sequence of gears chained together, the ratio depends only on the number of teeth on the first and last gear. The intermediate gears, regardless of their size, do not alter the overall gear ratio of the chain. However, the addition of each intermediate gear reverses the direction of rotation of the final gear.
An intermediate gear which does not drive a shaft to perform any work is called an idler gear. Sometimes, a single idler gear is used to reverse the direction, in which case it may be referred to as a reverse idler. For instance, the typical automobile manual transmission engages reverse gear by means of inserting a reverse idler between two gears.
Idler gears can also transmit rotation among distant shafts in situations where it would be impractical to simply make the distant gears larger to bring them together. Not only do larger gears occupy more space, the mass and rotational inertia (moment of inertia) of a gear is proportional to the square of its radius. Instead of idler gears, a toothed belt or chain can be used to transmit torque over distance.
Formula[edit]
If a simple gear train has three gears, such that the input gear GA meshes with an intermediate gear GI which in turn meshes with the output gear GB, then the pitch circle of the intermediate gear rolls without slipping on both the pitch circles of the input and output gears. This yields the two relations
ω A ω I = N I N A , ω I ω B = N B N I . {\displaystyle {\frac {\omega _{A}}{\omega _{I}}}={\frac {N_{I}}{N_{A}}},\quad {\frac {\omega _{I}}{\omega _{B}}}={\frac {N_{B}}{N_{I}}}.}
The speed ratio of this gear train is obtained by multiplying these two equations to obtain
R = ω A ω B = N B N A . {\displaystyle R={\frac {\omega _{A}}{\omega _{B}}}={\frac {N_{B}}{N_{A}}}.}
Notice that this gear ratio is exactly the same as for the case when the gears GA and GB engage directly. The intermediate gear provides spacing but does not affect the gear ratio. For this reason it is called an idler gear. The same gear ratio is obtained for a sequence of idler gears and hence an idler gear is used to provide the same direction to rotate the driver and driven gear. If the driver gear moves in the clockwise direction, then the driven gear also moves in the clockwise direction with the help of the idler gear.
Example[edit]
2 gears and an idler gear on a piece of farm equipment, with a ratio of 42/13 = 3.23:1
In the photo, assuming the smallest gear is connected to the motor, it is called the drive gear or input gear. The somewhat larger gear in the middle is called an idler gear. It is not connected directly to either the motor or the output shaft and only transmits power between the input and output gears. There is a third gear in the upper-right corner of the photo. Assuming that gear is connected to the machine's output shaft, it is the output or driven gear.
The input gear in this gear train has 13 teeth and the idler gear has 21 teeth. Considering only these gears, the gear ratio between the idler and the input gear can be calculated as if the idler gear was the output gear. Therefore, the gear ratio is driven/drive = 21/13 ≈1.62 or 1.62:1.
At this ratio, it means the drive gear must make 1.62 revolutions to turn the driven gear once. It also means that for every one revolution of the driver, the driven gear has made 1/1.62, or 0.62, revolutions. Essentially, the larger gear turns slower.
The third gear in the picture has 42 teeth. The gear ratio between the idler and third gear is thus 42/21, or 2:1, and hence the final gear ratio is 1.62x2≈3.23. For every 3.23 revolutions of the smallest gear, the largest gear turns one revolution, or for every one revolution of the smallest gear, the largest gear turns 0.31 (1/3.23) revolution, a total reduction of about 1:3.23 (Gear Reduction Ratio (GRR) = 1/Gear Ratio (GR)).
Since the idler gear contacts directly both the smaller and the larger gear, it can be removed from the calculation, also giving a ratio of 42/13≈3.23. The idler gear serves to make both the drive gear and the driven gear rotate in the same direction, but confers no mechanical advantage.
Belt drives[edit]
Belts can have teeth in them also and be coupled to gear-like pulleys. Special gears called sprockets can be coupled together with chains, as on bicycles and some motorcycles. Again, exact accounting of teeth and revolutions can be applied with these machines.
Valve timing gears on a Ford Taunus V4 engine — the small gear is on the crankshaft, the larger gear is on the camshaft. The crankshaft gear has 34 teeth, the camshaft gear has 68 teeth and runs at half the crankshaft RPM.
(The small gear in the lower left is on the balance shaft.)
For example, a belt with teeth, called the timing belt, is used in some internal combustion engines to synchronize the movement of the camshaft with that of the crankshaft, so that the valves open and close at the top of each cylinder at exactly the right time relative to the movement of each piston. A chain, called a timing chain, is used on some automobiles for this purpose, while in others, the camshaft and crankshaft are coupled directly together through meshed gears. Regardless of which form of drive is employed, the crankshaft-to-camshaft gear ratio is always 2:1 on four-stroke engines, which means that for every two revolutions of the crankshaft the camshaft will rotate once.
Automotive applications[edit]
Illustration of gears of an automotive transmission
Automobile drivetrains generally have two or more major areas where gearing is used. Gearing is employed in the transmission, which contains a number of different sets of gears that can be changed to allow a wide range of vehicle speeds, and also in the differential, which contains the final drive to provide further speed reduction at the wheels. In addition, the differential contains further gearing that splits torque equally between the two wheels while permitting them to have different speeds when travelling in a curved path. The transmission and final drive might be separate and connected by a driveshaft, or they might be combined into one unit called a transaxle. The gear ratios in transmission and final drive are important because different gear ratios will change the characteristics of a vehicle's performance.
Example[edit]
A 2004 Chevrolet Corvette C5 Z06 with a six-speed manual transmission has the following gear ratios in the transmission:
Gear
Ratio
1st gear 2.97:1
2nd gear 2.07:1
3rd gear 1.43:1
4th gear 1.00:1
5th gear 0.84:1
6th gear 0.56:1
reverse −3.38:1
In 1st gear, the engine makes 2.97 revolutions for every revolution of the transmission’s output. In 4th gear, the gear ratio of 1:1 means that the engine and the transmission's output rotate at the same speed. 5th and 6th gears are known as overdrive gears, in which the output of the transmission is revolving faster than the engine's output.
The Corvette above has an axle ratio of 3.42:1, meaning that for every 3.42 revolutions of the transmission’s output, the wheels make one revolution. The differential ratio multiplies with the transmission ratio, so in 1st gear, the engine makes 10.16 revolutions for every revolution of the wheels.
The car’s tires can almost be thought of as a third type of gearing. This car is equipped with 295/35-18 tires, which have a circumference of 82.1 inches. This means that for every complete revolution of the wheel, the car travels 82.1 inches (209 cm). If the Corvette had larger tires, it would travel farther with each revolution of the wheel, which would be like a higher gear. If the car had smaller tires, it would be like a lower gear.
With the gear ratios of the transmission and differential and the size of the tires, it becomes possible to calculate the speed of the car for a particular gear at a particular engine RPM.
For example, it is possible to determine the distance the car will travel for one revolution of the engine by dividing the circumference of the tire by the combined gear ratio of the transmission and differential.
d = c t g r t × g r d {\displaystyle d={\frac {c_{t}}{gr_{t}\times gr_{d}}}}
It is also possible to determine a car's speed from the engine speed by multiplying the circumference of the tire by the engine speed and dividing by the combined gear ratio.
v c = c t × v e g r t × g r d {\displaystyle v_{c}={\frac {c_{t}\times v_{e}}{gr_{t}\times gr_{d}}}}
Gear
Distance per engine revolution
Speed per 1000 RPM
1st gear 8.1 in (210 mm) 7.7 mph (12.4 km/h)
2nd gear 11.6 in (290 mm) 11.0 mph (17.7 km/h)
3rd gear 16.8 in (430 mm) 15.9 mph (25.6 km/h)
4th gear 24.0 in (610 mm) 22.7 mph (36.5 km/h)
5th gear 28.6 in (730 mm) 27.1 mph (43.6 km/h)
6th gear 42.9 in (1,090 mm) 40.6 mph (65.3 km/h)
Wide-ratio vs. close-ratio transmission[edit]
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Main article: Close-ratio transmission
A close-ratio transmission is a transmission in which there is a relatively little difference between the gear ratios of the gears. For example, a transmission with an engine shaft to drive shaft ratio of 4:1 in first gear and 2:1 in second gear would be considered wide-ratio when compared to another transmission with a ratio of 4:1 in first and 3:1 in second. This is because the close-ratio transmission has less of a progression between gears. For the wide-ratio transmission, the first gear ratio is 4:1 or 4, and in second gear it is 2:1 or 2, so the progression is equal to 4/2 = 2 (or 200%). For the close-ratio transmission, first gear has a 4:1 ratio or 4, and second gear has a ratio of 3:1 or 3, so the progression between gears is 4/3, or 133%. Since 133% is less than 200%, the transmission with the smaller progression between gears is considered close-ratio. However, the difference between a close-ratio and wide-ratio transmission is subjective and relative.[4]
Close-ratio transmissions are generally offered in sports cars, sport bikes, and especially in race vehicles, where the engine is tuned for maximum power in a narrow range of operating speeds, and the driver or rider can be expected to shift often to keep the engine in its power band.
Factory 4-speed or 5-speed transmission ratios generally have a greater difference between gear ratios and tend to be effective for ordinary driving and moderate performance use. Wider gaps between ratios allow a higher 1st gear ratio for better manners in traffic, but cause engine speed to decrease more when shifting. Narrowing the gaps will increase acceleration at speed, and potentially improve top speed under certain conditions, but acceleration from a stopped position and operation in daily driving will suffer.
Range is the torque multiplication difference between 1st and 4th gears; wider-ratio gear-sets have more, typically between 2.8 and 3.2. This is the single most important determinant of low-speed acceleration from stopped.
Progression is the reduction or decay in the percentage drop in engine speed in the next gear, for example after shifting from 1st to 2nd gear. Most transmissions have some degree of progression in that the RPM drop on the 1-2 shift is larger than the RPM drop on the 2-3 shift, which is in turn larger than the RPM drop on the 3-4 shift. The progression may not be linear (continuously reduced) or done in proportionate stages for various reasons, including a special need for a gear to reach a specific speed or RPM for passing, racing and so on, or simply economic necessity that the parts were available.
Range and progression are not mutually exclusive, but each limits the number of options for the other. A wide range, which gives a strong torque multiplication in 1st gear for excellent manners in low-speed traffic, especially with a smaller motor, heavy vehicle, or numerically low axle ratio such as 2.50, means the progression percentages must be high. The amount of engine speed, and therefore power, lost on each up-shift is greater than would be the case in a transmission with less range, but less power in 1st gear. A numerically low 1st gear, such as 2:1, reduces available torque in 1st gear, but allows more choices of progression.
There is no optimal choice of transmission gear ratios or a final drive ratio for best performance at all speeds, as gear ratios are compromises, and not necessarily better than the original ratios for certain purposes.
See also[edit]
Machine (mechanical)
Mechanism (engineering)
Powertrain
Wheel train (horology)
Outline of machines
Epicyclic gearing - related to turboprop reduction gear boxes
Continuously variable transmission (CVT)
Virtual work
References[edit]
Jump up ^ Uicker, J. J.; G. R. Pennock; J. E. Shigley (2003). Theory of Machines and Mechanisms. New York: Oxford University Press.
Jump up ^ Paul, B. (1979). Kinematics and Dynamics of Planar Machinery. Prentice Hall.
Jump up ^ https://www.quora.com/What-is-double-reduction-gearing
Jump up ^ Cangialosi, Paul (2001). "TechZone Article: Wide and Close Gear Ratios". 5speeds.com. Medatronics. Retrieved 28 October 2012.
External links[edit]
Gear ratio at How Stuff Works
Online Motorcycle gear train calculator with Help pages
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