Trace operator - Revision history

67.241.66.231 at 03:05, 27 February 2014

2014-02-27T03:05:45Z

← Older revision		Revision as of 05:05, 27 February 2014
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	~~{{Unreferenced\|date=May 2008}}~~		Alyson Meagher is the title her parents gave her but she doesn't like when people use her full name. Office supervising is where her primary income comes from but she's currently utilized for another 1. To play lacross is one of the issues she enjoys most. Her family members life in Ohio but her husband desires them to transfer.<br><br>Review my blog post - psychics online ([http://help.ksu.edu.sa/node/65129 help.ksu.edu.sa])

	~~The term '''"cant deficiency"'''~~ is ~~defined in~~ the ~~context of travel of a [[rail transport\|rail vehicle]] at constant speed on a constant radius curve~~. ~~[[Cant (road/rail)\|Cant]] itself~~ is ~~a British synonym for the superelevation of the curve, that is, the elevation of the outside rail minus the elevation of the inside rail. Cant deficiency is present when a vehicle~~'s ~~speed on a curve is greater than the speed at which the components of wheel to rail [[force]] normal to the plane of the track would be the same in aggregate~~ for ~~the outside rails as for the inside rails.~~

	~~The forces that bear on the vehicle in this context are illustrated in the following figure.~~

	~~[[File:Ltk balance diagram w alpha.jpg\|thumb\|centre\|300px]]~~

	~~A vehicle's motion at speed ''v'' along a circular path embodies [[centripetal]] acceleration of magnitude ''v''<sup>2</sup>/''R'' toward the center of the circle, the curvature of that path being~~ 1~~/''R'' where ''R'' is the radius of the circle~~. ~~This centripetal acceleration~~ is ~~produced by horizontal forces applied by the rails to the wheels~~ of the ~~vehicle, directed toward the center, and having sum equal to ''Mv''<sup>2</sup>/''R'' where ''M'' is the mass of the vehicle~~.

	~~The net horizontal force producing the centripetal acceleration is generally separated into components that are respectively~~ in ~~the plane of the superelevated (i.e., banked) track and normal thereto.~~

	The component normal to the track acts together with the much larger component of [[gravitational]] force normal to the track and is generally neglected. It can slightly increase the vertical load seen by the vehicle suspension but ~~it does not create lateral acceleration as perceived by passengers or and does not cause lateral deflection of the vehicle suspension.~~

	~~The track is superelevated so that the component of the [[acceleration]] of gravity in the plane of the track will provide some fraction of the horizontal acceleration in the plane of the track due~~ to ~~the circular motion~~. Referring to the figure above, it can be seen that the components of gravitational and centripetal acceleration in the plane of the track will be equal when the following balance equation is satisfied, where α is the bank angle.

	~~:<math>{v^2\over R} \cos \alpha = g \sin \alpha</math>~~

	~~For a given curve radius and bank angle (i.e., superelevation) the speed V that satisfies the balance equation is called the balancing speed and is given by~~

	:<~~math~~>~~V_{bal} = \left ( {R g \tan \alpha} \right ) ^ \tfrac{1}{2}~~<~~/math~~>

	For reasons that will be mentioned below, passenger vehicles usually traverse a curve at a speed higher than the balance speed. The amount by which the actual speed exceeds the balance speed is conveniently expressed via the so-called cant deficiency, i.e., by the amount by which the superelevation would need to be increased to raise the balance speed to the speed at which the vehicles actually travel. Letting ''gauge<sub>se</sub>'' denote the rail gauge from low rail gauge side corner to high rail field side corner, letting ''super_el'' denote the actual superelevation, and letting ''V<sub>act</sub>'' denote the actual speed, it follows from the definition that the cant deficiency, ''CD'', is given by the formula

	~~:<math>CD = { gauge_{se}~~
	~~\over { \left~~ (~~1 + {R^2 g^2~~
	~~\over {V_{act}^4} } \right ) ^ \tfrac{1}{2} } } - super\_el</math>~~

	Taking an example, a curve with curvature 1.0 degree per 100 ft chord (radius 1,746.40 m = 5,729.65 ft), gauge_se = 1511.3 mm (59.5 inches), and super_el = 152.4 mm (6.0 inches) will have
	~~:<math> V_{bal} = \sqrt{1746.4 \cdot 9.80665 \cdot \tan( \arcsin( 152.4 / 1511.3 ) )}</math>:~~
	:~~<math> = 41.6638\,\mathrm{m~~/~~s} = 149.99\,\mathrm{km~~/~~h} = 93.20\,\mathrm{miles/h}</math>~~

	~~If a vehicle traverses that curve at a speed of 55.880 m/s (= 201.17 km/h = 125 mph), then the cant deficiency will be~~

	~~:<math> CD = \frac{1511~~.~~3}{\sqrt{1 + (1746~~.~~4^2 \cdot 9~~.~~8066^2~~ / ~~55.8^4)}}- 152.4 <~~/~~math>~~
	~~:<math> = 118.7\,\mathrm{mm} (= 4.67\,\mathrm{inches})</math>~~

	On routes that carry freight traffic in cars with the maximum allowed axle loads it will be desirable to set superelevations so that the balancing speed of each curve is close to the speed at which most such traffic runs. This is to lessen the tendency of heavy wheel loads to crush the head of either rail.

	~~{{Unreferenced section\|date=June 2011}}~~
	For passenger traffic superelevations and authorized speeds can be set so that trains run with as much cant deficiency as is allowed, based on safety, on relevant regulations and on passenger comfort. As of 2007 the US [[Federal Railroad Administration]] regulations limit CD to 7.0 inches for tilting passenger vehicles, 3.0 inches for conventional vehicles. {{Citation needed\|date=June 2011}} This FRA regulation is based on AAR standards based on a single study in the 1950s on a rail line in Connecticut. {{Citation needed\|date=June 2011}} In Germany, where axle loads are typically lower than those in the USA, [[tilting train]]s are allowed to operate with 12.0 inches CD in some cases{{Citation needed\|date=June 2011}}.

	Allowed CD is set below the value that would be allowed based on safety in order to reduce wheel and rail wear and to reduce the rate of degradation of geometry of ballasted track. Choice of design CD will be less constrained by passenger comfort in the case of vehicles that have tilting capability. One historical approach to determining safe cant deficiency was the requirement that the projection to the plane of the track of the resultant of the centrifugal and gravitational forces acting on a vehicle fall within the middle third of the track gauge. Contemporary engineering studies would likely use vehicle motion simulation including cross wind conditions to determine margins relative to derailment and rollover.

	~~If the superelevation determined for a dedicated passenger route curve on regulatory and safety bases is below 6.0 inches (152~~.4 mm) it may be desirable to increase the superelevation and reduced the cant deficiency. However, if on such a curve some trains regularly travel at low speeds, then raising the superelevation may be inadvisable for passenger comfort reasons.

	On a mixed traffic route owned by a freight rail company, freight considerations are likely to prevail. On a mixed traffic route owned by a passenger rail company some kind of compromise may be needed.

	~~Cant deficiency is generally looked at with respect to ideal [[track geometry]]~~. ~~As geometry of real track is never perfect it may be desirable to supplement the static considerations laid out above with simulations of vehicle motion over measured geometries of actual tracks~~. ~~Simulations are also desirable for understanding vehicle behaviour traversing [[track transition curve\|spiral]~~]s, turnouts, and other track segments where curvature changes with distance by design. Where simulations or measurements show non-ideal behaviour traversing traditional linear spirals, results can be improved by using advanced spirals. Good track geometry including advanced spirals is likely to foster passenger acceptance of higher CD values.

	~~==See also==~~
	*[[Cant (road/rail)]]

	~~{{Railway track layouts}}~~

	~~[[Category:Track geometry]]~~

223.67.153.23: /* Informal discussion */

2013-02-23T10:32:03Z

Informal discussion

← Older revision		Revision as of 12:32, 23 February 2013
Line 1:		Line 1:
	The ~~name~~ of the ~~writer~~ is ~~Jayson~~. ~~Distributing manufacturing has been his occupation~~ for ~~some time~~. ~~Doing ballet~~ is ~~something she would~~ by ~~no means give up~~. ~~Some time ago she chose~~ to ~~live~~ in ~~Alaska~~ and ~~her mothers~~ and ~~fathers live close~~ by.<br><br>~~Here~~ is ~~my website~~ ... ~~best psychics~~ (~~[http~~://~~netwk~~.~~hannam~~.ac.kr/xe/~~data_2~~/~~85669 click~~ the ~~up coming website page~~])		{{Unreferenced\|date=May 2008}}

			The term '''"cant deficiency"''' is defined in the context of travel of a [[rail transport\|rail vehicle]] at constant speed on a constant radius curve. [[Cant (road/rail)\|Cant]] itself is a British synonym for the superelevation of the curve, that is, the elevation of the outside rail minus the elevation of the inside rail. Cant deficiency is present when a vehicle's speed on a curve is greater than the speed at which the components of wheel to rail [[force]] normal to the plane of the track would be the same in aggregate for the outside rails as for the inside rails.

			The forces that bear on the vehicle in this context are illustrated in the following figure.

			[[File:Ltk balance diagram w alpha.jpg\|thumb\|centre\|300px]]

			A vehicle's motion at speed ''v'' along a circular path embodies [[centripetal]] acceleration of magnitude ''v''<sup>2</sup>/''R'' toward the center of the circle, the curvature of that path being 1/''R'' where ''R'' is the radius of the circle. This centripetal acceleration is produced by horizontal forces applied by the rails to the wheels of the vehicle, directed toward the center, and having sum equal to ''Mv''<sup>2</sup>/''R'' where ''M'' is the mass of the vehicle.

			The net horizontal force producing the centripetal acceleration is generally separated into components that are respectively in the plane of the superelevated (i.e., banked) track and normal thereto.

			The component normal to the track acts together with the much larger component of [[gravitational]] force normal to the track and is generally neglected. It can slightly increase the vertical load seen by the vehicle suspension but it does not create lateral acceleration as perceived by passengers or and does not cause lateral deflection of the vehicle suspension.

			The track is superelevated so that the component of the [[acceleration]] of gravity in the plane of the track will provide some fraction of the horizontal acceleration in the plane of the track due to the circular motion. Referring to the figure above, it can be seen that the components of gravitational and centripetal acceleration in the plane of the track will be equal when the following balance equation is satisfied, where α is the bank angle.

			:<math>{v^2\over R} \cos \alpha = g \sin \alpha</math>

			For a given curve radius and bank angle (i.e., superelevation) the speed V that satisfies the balance equation is called the balancing speed and is given by

			:<math>V_{bal} = \left ( {R g \tan \alpha} \right ) ^ \tfrac{1}{2}</math>

			For reasons that will be mentioned below, passenger vehicles usually traverse a curve at a speed higher than the balance speed. The amount by which the actual speed exceeds the balance speed is conveniently expressed via the so-called cant deficiency, i.e., by the amount by which the superelevation would need to be increased to raise the balance speed to the speed at which the vehicles actually travel. Letting ''gauge<sub>se</sub>'' denote the rail gauge from low rail gauge side corner to high rail field side corner, letting ''super_el'' denote the actual superelevation, and letting ''V<sub>act</sub>'' denote the actual speed, it follows from the definition that the cant deficiency, ''CD'', is given by the formula

			:<math>CD = { gauge_{se}
			\over { \left (1 + {R^2 g^2
			\over {V_{act}^4} } \right ) ^ \tfrac{1}{2} } } - super\_el</math>

			Taking an example, a curve with curvature 1.0 degree per 100 ft chord (radius 1,746.40 m = 5,729.65 ft), gauge_se = 1511.3 mm (59.5 inches), and super_el = 152.4 mm (6.0 inches) will have
			:<math> V_{bal} = \sqrt{1746.4 \cdot 9.80665 \cdot \tan( \arcsin( 152.4 / 1511.3 ) )}</math>:
			:<math> = 41.6638\,\mathrm{m/s} = 149.99\,\mathrm{km/h} = 93.20\,\mathrm{miles/h}</math>

			If a vehicle traverses that curve at a speed of 55.880 m/s (= 201.17 km/h = 125 mph), then the cant deficiency will be

			:<math> CD = \frac{1511.3}{\sqrt{1 + (1746.4^2 \cdot 9.8066^2 / 55.8^4)}}- 152.4 </math>
			:<math> = 118.7\,\mathrm{mm} (= 4.67\,\mathrm{inches})</math>

			On routes that carry freight traffic in cars with the maximum allowed axle loads it will be desirable to set superelevations so that the balancing speed of each curve is close to the speed at which most such traffic runs. This is to lessen the tendency of heavy wheel loads to crush the head of either rail.

			{{Unreferenced section\|date=June 2011}}
			For passenger traffic superelevations and authorized speeds can be set so that trains run with as much cant deficiency as is allowed, based on safety, on relevant regulations and on passenger comfort. As of 2007 the US [[Federal Railroad Administration]] regulations limit CD to 7.0 inches for tilting passenger vehicles, 3.0 inches for conventional vehicles. {{Citation needed\|date=June 2011}} This FRA regulation is based on AAR standards based on a single study in the 1950s on a rail line in Connecticut. {{Citation needed\|date=June 2011}} In Germany, where axle loads are typically lower than those in the USA, [[tilting train]]s are allowed to operate with 12.0 inches CD in some cases{{Citation needed\|date=June 2011}}.

			Allowed CD is set below the value that would be allowed based on safety in order to reduce wheel and rail wear and to reduce the rate of degradation of geometry of ballasted track. Choice of design CD will be less constrained by passenger comfort in the case of vehicles that have tilting capability. One historical approach to determining safe cant deficiency was the requirement that the projection to the plane of the track of the resultant of the centrifugal and gravitational forces acting on a vehicle fall within the middle third of the track gauge. Contemporary engineering studies would likely use vehicle motion simulation including cross wind conditions to determine margins relative to derailment and rollover.

			If the superelevation determined for a dedicated passenger route curve on regulatory and safety bases is below 6.0 inches (152.4 mm) it may be desirable to increase the superelevation and reduced the cant deficiency. However, if on such a curve some trains regularly travel at low speeds, then raising the superelevation may be inadvisable for passenger comfort reasons.

			On a mixed traffic route owned by a freight rail company, freight considerations are likely to prevail. On a mixed traffic route owned by a passenger rail company some kind of compromise may be needed.

			Cant deficiency is generally looked at with respect to ideal [[track geometry]]. As geometry of real track is never perfect it may be desirable to supplement the static considerations laid out above with simulations of vehicle motion over measured geometries of actual tracks. Simulations are also desirable for understanding vehicle behaviour traversing [[track transition curve\|spiral]]s, turnouts, and other track segments where curvature changes with distance by design. Where simulations or measurements show non-ideal behaviour traversing traditional linear spirals, results can be improved by using advanced spirals. Good track geometry including advanced spirals is likely to foster passenger acceptance of higher CD values.

			==See also==
			*[[Cant (road/rail)]]

			{{Railway track layouts}}

			[[Category:Track geometry]]

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