| Types of tractive efforts | | | | cylinder dimensions and the time at which the steam |
| When a figure for tractive effort is quoted in | | | | inlet valves are open; if the steam inlet valves are |
| technical documentation it is either for the starting | | | | closed immediately after obtaining full cylinder |
| tractive effort (at a dead start with the wheels not | | | | pressure the piston force can be expected to have |
| turning) or as the continuous tractive effort which will | | | | dropped to less than half the initial force.[note 11] |
| be quoted at a particular speed. | | | | giving a low c value. If the cylinder valves are left |
| Maximum tractive effort | | | | open for longer the value of c will rise nearer to 1. |
| The maximum tractive effort is the maximum pulling | | | | For other numbers and combinations of cylinders, |
| force a vehicle or machine can exert under any | | | | including double and triple expansion engines the |
| (non-damaging) conditions. In general the maximum | | | | tractive effort can be estimated by adding the |
| tractive effort will be obtained at a standstill and/or | | | | tractive efforts due to the individual cylinders at their |
| low speeds. | | | | respective pressures and cylinder strokes.[note 12] |
| A variety of factors limit the maximum value: | | | | Values and comparisons for steam locomotives |
| The maximum tractive effort cannot exceed the | | | | Tractive effort is the figure most often quoted |
| 'Tractive mass (m)' x 'the coefficient of friction' () . If | | | | when comparing the power of different steam |
| a vehicle attempts to supply more force | | | | locomotives, but its use can be misleading, because |
| (Ftractive>m) this will cause Wheel spin[note 1]. | | | | tractive effort shows the ability to start a train, not |
| The gear ratios of drive components. | | | | the ability haul it. Possibly the highest figure for |
| The maximum power capable of being supplied to | | | | starting tractive effort ever recorded was for the |
| the drive systems. | | | | Virginian Railway's 2-8-8-8-4 Triplex locomotive, which |
| The safe working torques of the drive system | | | | in simple expansion mode had a starting T.E. of |
| components. | | | | 199,560 lbf (888 kN) but this did not translate into |
| Continuous tractive effort | | | | power, for the boiler was undersized and could not |
| The continuous tractive effort is the tractive effort | | | | produce enough steam to haul at speeds over |
| which is supplied at a given velocity. It may refer to | | | | 5 mph (8 km/h). |
| the tractive effort required to keep a vehicle rolling | | | | Of more successful large steam locomotives, those |
| without acceleration or the maximum force that can | | | | with the highest rated starting tractive effort were |
| be produced at given speed. | | | | the Virginian Railway AE-class 2-10-10-2s, at 176,000 |
| Because of the relationship between Power (P), | | | | lbf (783 kN) in simple-expansion mode. The Union |
| velocity (v) and force (F) of: | | | | Pacific's famous Big Boys had a starting T.E. of |
| P=vF or P/v=Fthe continuous tractive effort is | | | | 135,375 lbf (602 kN); the Norfolk & Western's |
| inversely proportional to the velocity for constant | | | | Y5, Y6, Y6a, and Y6b class 2-8-8-2s had a starting |
| power; the continuous tractive effort is therefore | | | | T.E. of 152,206 lbf (677 kN) in simple expansion mode |
| dependent on the power at rail[note 2] | | | | (later modified, resulting in a claimed T.E. of 170,000 |
| In vehicles which have a power source (diesel engine, | | | | lbf (756 kN)); and the Pennsylvania Railroad's freight |
| electrical supply etc) which is limited in terms of | | | | Duplex Q2 attained 114,860 lbf (511 kN) the highest |
| maximum total power (including steam engines[note | | | | for a rigid framed locomotive. Later two cylinder |
| 3]) the maximum continuous tractive effort at a | | | | passenger locomotives were generally 70,000 to |
| given speed is limited by the engine's power. | | | | 80,000 lbf (300 to 350 kN) of T.E. |
| Continuous tractive effort is quoted as a force at a | | | | Diesel and electric locomotives |
| given speed, and may be presented in graph form at | | | | For a diesel-electric locomotive or electric locomotive, |
| a range of speeds as part of a tractive effort curve | | | | starting tractive effort can be calculated from the |
| Maximum continuous tractive effort | | | | stall torque of the traction motors (the turning force |
| For vehicles propelled by electric motors the | | | | it can produce while at a dead stop), the gearing, and |
| maximum continuous tractive effort can be less than | | | | the wheel diameter. For a diesel-hydraulic locomotive |
| the short term maximum tractive effort[note 4] at a | | | | the starting tractive effort depends on the stall |
| given speed. The maximum continuous tractive effort | | | | torque of the torque converter. |
| is defined as: | | | | In general, it is more common for heavy freight trains |
| "the tractive force delivered at full throttle notch | | | | (such as Class 59, Class 60 and Class 66 locomotives) |
| (power) after the traction system has heated to | | | | to have a high maximum tractive effort due to the |
| maximum operating temperature" | | | | mass which they haul. Passenger trains (such as Class |
| Similar considerations also apply to hydrodynamic | | | | 43 / Intercity High Speed Train locomotives) usually |
| transmissions such as fluid couplings and torque | | | | have much lower maximum tractive efforts due to |
| converters which create more heat at stall than | | | | the higher gear ratio required for a higher top speed. |
| when free running. (see also Stall torque). | | | | See alsofactor of adhesion, which is simply the |
| Tractive effort curves | | | | weight on the locomotive's driving wheels divided by |
| Technical specifications of locomotives often include | | | | the starting tractive effort |
| tractive effort curves, which show the relationship | | | | Tractor pulling,Bollard pull - articles relating to tractive |
| between tractive effort and velocity. | | | | effort for other forms of vehicle |
| Schematic diagram of tractive effort vs. speed for a | | | | Rail adhesionpower classification - British Railways and |
| hypothetical locomotive with power at rail of | | | | London, Midland and Scottish railway classification |
| ~7000kW | | | | scheme |
| The basic shape of the graph is shown schematically | | | | References and notes |
| (diagram right). The line AB shows the operation at | | | | Notes |
| the maximum tractive effort, the line BC shows the | | | | ^ Wheel spin can damage the wheel and rail. Low |
| relationship of continuous tractive effort being | | | | frictional coefficients can be a problem for rail vehicles |
| inversely proportional to speed. | | | | - eg see Slippery rail; Most locomotives carry a |
| Tractive effort curves will often have graphs of | | | | sandbox for use when the wheels are likely to slip |
| rolling resistance superimposed on them - the | | | | ^ quoted figures will usually refer to the maximum |
| intersection of the rolling resistance graph[note 5] and | | | | continuous tractive effort - IE when the engine or |
| tractive effort graph gives the maximum velocity (ie | | | | other power source is operating at its maximum. ie at |
| when the net tractive effort is zero). | | | | the maximum available power at rail. |
| Rail vehicles | | | | ^ Although it may seem that the maximum power |
| For a long, heavy train to accelerate from a | | | | of a conventional steam engine is limited at the rate |
| stationary position at a satisfactory rate of | | | | at which the fireman can shovel coal into the steam |
| acceleration, the locomotive must apply a large force. | | | | engine, in fact the power will be limited by a variety |
| In general the resistive forces increase with velocity, | | | | of other factors, including - the rate of combustion |
| so at a some given rate of movement the tractive | | | | of the fuel, the rate at which heat can be |
| effort will equal the resistive forces and the train will | | | | transferred across the heat exchanging mechanism |
| not be able to accelerate further - this gives rise to a | | | | from fire to water boiler etc |
| limit in any train's top speed. | | | | ^ For electric motors higher torques require higher |
| For a train running at a desired velocity, the | | | | currents, which also produce greater resistive heating, |
| locomotive needs only to provide enough forward | | | | the term maximum continuous current is a related |
| force to counteract the counteracting forces of | | | | figure for traction motors. In the short term currents |
| friction (wheels on rails, axles in bearings) and wind | | | | higher than the maximum continuous current may not |
| resistance (a small force compared to the other | | | | cause damage by overheating. |
| forces at work) on level track, plus the | | | | ^ The graphs will typically show rolling resistance for |
| parallel-to-track vector component of gravity's | | | | standard train lengths or weights, both on the level |
| acceleration of the train's mass on grades (which is | | | | or on an uphill gradient |
| fighting against the locomotive on uphill grades, and | | | | ^ It can be shown as a first approximation that half |
| pushing it forward on downhill grades). | | | | the stroke distance is approximately the same as the |
| As well as been calculated theoretically from the | | | | radial distance from the coupling of the driving rod to |
| characteristics of the engine, transmission system | | | | the centre of the driven wheel |
| and the wheel diameter and mass of a locomotive, | | | | ^ The relationship is simply Torque = Forcepiston x R |
| the tractive effort can also be obtained | | | | (the radial distance to the point of connection of the |
| experimentally through combinations of drawbar | | | | driving rod) x cos(A) where A is the angle the driving |
| strain sensors and a dynamometer car. | | | | rod makes with the tangent to the radius from |
| Power at rail is a railway term for the available power | | | | wheel centre to driving rod attachment |
| for traction. | | | | ^ As with any physical formula, consistent units of |
| Steam locomotives | | | | measurement are required: pressure in psi and lengths |
| An approximate theoretical value for the tractive | | | | in inches give tractive effort in lbf, while pressure in |
| effort of a single cylinder steam locomotive can be | | | | Pa and lengths in metres give tractive effort in N. |
| obtained by considering the cylinder pressure, cylinder | | | | ^ For a 'perfect' locomotive with cylinder piston |
| area, and stroke of the piston[note 6] and the | | | | pressure equal to boiler pressure (independent of |
| diameter of the wheel. The torque developed by the | | | | stroke) and with no frictional losses the constant c |
| action of the linear motion of the piston depends on | | | | can be taken as 1 |
| the angle that the driving rod makes with the | | | | ^ note that the boiler pressure may be greater than |
| tangent of the radius on the driving wheel.[note 7] | | | | the cylinder pressure |
| For a more useful value an average value over the | | | | ^ See Gas laws for an explanation. |
| rotation of the wheel is used. The driving force is | | | | ^ The value of the constant c for a low-pressure |
| simply the torque divided by the wheel radius. | | | | cylinder is taken to be 0.80 (when the value for a |
| For a two cylinder locomotive the average force is | | | | high pressure cylinder is taken to be 0.85 |
| twice that of a single cylinder locomotive. | | | | References |
| Thus as an approximation the following equation can | | | | ^ Article : "So just what do terms used to describe |
| be obtained (for a 2 cylinder locomotive)[note | | | | the performance of locomotives and multiple units like |
| 8]:wheret is tractive effortc is a constant | | | | Maximum Tractive Effort, Power At Rail, and |
| representing losses in pressure and friction; normally | | | | Continuous Power mean?" Tony Woof B.Eng C.Eng |
| 0.85 is used[note 9] | | | | MIEE |
| P is the boiler pressure[note 10]d is the piston | | | | ^ Handbook of Railway Vehicle Dynamics , Simon |
| diameter (bore)s is the piston stroke | | | | Iwnicki , page 256 , Google books ^ a b Handbook |
| D is the driving wheel diameter | | | | of Railway Vehicle Dynamics, Simon Iwnicki, |
| The constant 0.85 was the Association of American | | | | Illustrated, CRC Press, 2006, ISBN 0849333210, |
| Railroads (AAR) standard for such calculations, and | | | | 9780849333217. Google books link: |
| certainly over-estimated the efficiency of some | | | | ^ XPT: Delivery, test runs and demonstration runs |
| locomotives and underestimated that of others. | | | | railpage.au.org see graph |
| Modern locomotives were equipped with roller | | | | ^ The Gravita Locomotive Family voithturbo.de (page |
| bearings were probably underestimated. | | | | 2) |
| European designers used a constant of 0.6 instead of | | | | ^ EURO 4000 Freight Diesel-Electric Locomotives |
| 0.85, so the two cannot be directly compared | | | | (page 2) |
| without a conversion factor. In Britain, the main-line | | | | ^ Eurorunner ER20 BF and ER20 BU, Diesel electric |
| railways generally used a constant of 0.85 but builders | | | | platform locomotives for Europe siemens.dk (page 3) |
| of industrial locomotives often used a lower figure, | | | | ^ Marks' Standard Handbook for Mechanical Engineers |
| typically 0.75. | | | | By Eugene A. |
| The value of the constant c also depends on the | | | | |