Tare mass of train is the mass of an empty train (without passengers).
The mass of passengers, baggage or goods conveyed by a train is called Pay or Net mass.
Total mass of train in tonne = Pay or Net mass of train in tonne + Tare mass of train in tonne
Generally, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. The difference between mass and weight is that mass is the measure of the amount of matter in an object, whereas weight refers to the force experienced by an object due to gravity.
WEIGHT = MASS * GRAVITY
Not to be confused with Ton / Tonne. In the United Kingdom, a long ton / gross ton (common name: ton) is defined as 1016.047 kilogram or 2240 pounds. In the United States and Canada, a short ton / net ton (common name: ton) is defined as 907.18 kg or 2000 lb. As per International System of Units, a metric tonne (common name: tonne) is defined as 1000 kg or 2204.623 lb.
Train resistance is the force resisting the motion of train on track. When the tractive force developed by train is greater than the train resistance, then the train will start to accelerate. Specific resistance is equivalent to the train resistance per tonne i.e. train resistance / mass of train. On straight & level track, train resistance consist of following resistances :
1. Friction Resistance
2. Rolling Resistance
3. Air Resistance
Starting resistance, appears at the time of starting, is to overcome the non-elastic effects of track & wheel surface, inertia and bearing friction. Starting Resistance depend upon the type of bearings, mass per axle & temperature of the bearing and drops rapidly as the train speed increases. Generally, Starting Resistance are taken as 4 and 6 kg/tonne.
Running resistance of a train can be calculated by using empirical expression TR= A+B*V+C*V2 Kg/tonne, where 'A', 'B' & 'C' are constants, V is speed in Kmph and TR is specific train resistance in Kg/tonne.
Constant 'A' mainly depend upon the mass of train and independent of speed. Constant 'B' mainly depend upon the sliding friction between the flange of the wheel & the inner face of the rail. Constant 'C' depend upon the cross-section area of train, space in-between coaches, equipment under the coaches, air resistance of the sides, draft and turbulence created by the train etc. Contribution of term "C*V2" is more visible with speed going more than 70 kmph
When the train travels upward, a component of its gravitational force works in a direction opposite to its motion and vice versa. Gradient Resistance is the force required to overcome train movement due to component of gravitational force acting on the train. If train is moving upward at a slope of θ, then the mass of the train (W in tonne) has two components; one perpendicular to the track (i.e. W*g*Cos θ) & the other along the track (i.e. W*g*Sin θ). The component along the track is known as gradient resistance.
Gradient Resistance = W*g*Sin θ Kilo Newton; For a up gradient of 1 in 'G', value of Sin θ is equal to 1/(1+G2)1/2. For higher value of 'G', value of Sin θ may be considered equal to 1/'G'. Hence, Gradient Resistance = W*g/G Kilo Newton
An upgrade produces a resistive force (+ve value) while a down grade produces an accelerating force (-ve value). Value of gradient resistance is independent of train speed.
When a train goes around a curve, a centrifugal force pushes the train outward which increases the sliding friction resistance between outer wheel flange & the inner face of the outer rail. In addition to this, the outer wheel rotates faster than the inner wheel causing transverse slip thus adding to sliding friction. To overcome curve resistance, outer rail is gradually lifted above the level of the inner rail and difference in height between the inner and outer rail on a curve is called superelevation or cant. The necessary cant in a curve depends on the expected speed of the trains and the radius. If a train goes around a curve at speed such that the component of centrifugal force in the lateral direction is equal to the component of gravitational force in the opposite direction there is very little curve resistance. This speed is called balancing speed of the curve. if train speed is either higher or lower from curve balancing speed, the curve resistance increases due to the unbalance in forces which tends to pull the vehicle sideways. Generally, curve resistance in Kg/tonne is given by :
Curve Resistance = 0.4 * Degree of curvature Kg/tonne;
Curve Resistance = (0.4 * Degree of curvature * g * mass of train in tonne)/1000 Kilo Newton;
Degree of curvature = 1750 / Radius of curvature in meters;
Total train resistance = Train resistance + Gradient resistance + Curve Resistance
Rotating mass of train is equivalent to the rotational Inertia of the train, transformed by gear ratio and wheel diameter respectively. The equivalent non-rotating mass of train may be defined as a function of its true static mass and its rotational inertia. It is based on the principle that the total energy stored in the object is a combination of its translational kinetic energy and its rotational kinetic energy and mentioned below:
Equivalent non-rotating mass of train = Static mass of train + Rotational inertia of train * (Gear ratio / wheel radius)2 ;
Note:
Rotational inertia of traction motor rotor will be transformed by gear ratio & wheel diameter, however rotational inertia of wheels will be transformed by wheel diameter only.
Above relationship is independent of the vehicle speed, so the consideration is valid at any velocity, and is independent of vehicle power. Generally, rotating mass of a metro train is considered 6 to 8 % of the tare mass of train.
Adhesion is caused by friction. Available adhesion between the driving wheels and the track depends on the weight per wheel, irregularities of contact surfaces, environmental conditions etc. and determine the force that can be applied before the wheels begin to slip or slide during traction or braking respectively. Adhesion value between rail wheel and track is observed between 35% to 50%, whilst under extreme conditions (i.e. slippery condition ) it can fall to as low as 5%. Generally, useable adhesion limit is kept below the maximum available adhesion limit and its general range is 12 to 22 % for metro trains. Hence, tractive effort per motor axle can be increased by increasing the motor torque but only upto a certain point, which design adhesion limit allows.
% Adhesion = Max. TE or BE of motor coach in tonne * 100 / Mass of motor coach in tonne ;
% Adhesion = Max. TE or BE per axle in tonne * 100 / Maximum axle load in tonne ;
Tractive effort of the train is equivalent to the force developed by the traction units at the wheel rims for moving the train. Tractive effort is generally higher than tractive force by the amount of rolling resistance present. Tractive effort develops necessary linear and angular acceleration to the train mass, overcome the gravity component of the train weight, overcome the wind, frictional and curve resistance of the train.
Tractive effort vs Speed graph may be classified as follow :
1. Constant Tractive Effort / Maximum Tractive Effort Zone
2. Quadrant portion of TE vs Speed graph; wherein, generally TE is inversely proportional of the speed
3. Quadrant portion of TE vs Speed graph; wherein, generally TE is Inverse Quadratic of the speed
Starting tractive effort is the tractive effort that can be generated at a standstill. It is important on railways because it determines the maximum train mass that a locomotive can set into motion. Tractive effort equivalent to constant power varies inversely with the speed. In this zone, relationship between power (P), velocity (v) and tractive effort (F) is described as below:
Power (kW) = Speed (m/s) * Tractive effort (kN) Similar to tractive effort graph, regenerative braking effort graph may be classified as follow :
1. Constant Regenerative Braking Effort Zone
2. Quadrant portion of Reg. BE vs Speed graph; wherein, generally Reg. BE is inversely proportional of the speed
3. Quadrant portion of Reg. BE vs Speed graph; wherein, generally Reg. BE is Inverse Quadratic of the speed
Regenerative braking effort is sub-set of total braking effort graph (Regenerative Braking Effort graph + Pneumatic Braking Effort graph)
Newton’s second law is applied to calculate the acceleration of the train.
Train acceleration at given speed = (Tractive effort of train - Train resistance) / Effective mass of train including rotating mass,
Starting resistance of the train should also be included in train resistance for calculation of starting acceleration of the train.
The residual acceleration of train is equivalent to the value of acceleration at maximum service speed. Trains which have low value of the residual acceleration cover longer distance to achieve the maximum service speed.
Balancing speed of train corresponds to the speed at which tractive effort of the train is equal to train resistance. At this speed, acceleration of train is supposed to zero. Balancing speed of metro train should be higher than its service speed / test speed. Higher value of the residual acceleration leads to higher value of the balancing speed as compared to maximum service speed of the train.
Service brake is used to apply and release of the brakes in a controlled way during normal operations of train. Generally, service brake deceleration of train is kept lower than the emergency brake deceleration of train.
Emergency brake is used for emergency stop of the train in the event of a brake pipe failure, control electronics failure or an emergency application by the train operator as a last resort. A completely separate mechanism from the service braking system is used to stop the train as quickly as possible. The emergency brake applies considerably more braking force than the full-service brake.
SEC of the train is the energy consumed (in KWh from the supply system) per tonne mass per km length of the run. SEC = (Energy consumed from the supply system during traction - Reg. energy fed to the supply system during braking) / (Mass of train * travelled distance), The specific energy consumption of a train is influenced by 1. Distance between stations 2. Gross mass of the train 3. No. of speed restrictions in sections 4. Acceleration & Deceleration 5. Maximum service speed 6. Auxiliary load of train 7. Shape of regenerated braking effort vs speed graph8. Efficiency of propulsion equipment Generally, percentage regeneration of a train for a given driving cycle is the ratio of regenerated electrical energy to consumed electrical energy measured at pantograph in presence of specified auxiliary load.
Train operation modes may be classified as follow : 1. Full Traction mode : In this mode, master controller is kept in full traction position. 2. Driving in Allout mode : means full traction upto maximum service speed, operation at that speed followed by full service brake. 3. Cruising mode : In this mode, train is operated with constant speed and develop tractive effort equal to train resistance, hence value of acceleration is zero. 4. Coasting Mode : In this mode, no electric energy is supplied to traction motors and energy required to overcome train resistance is supplied from its kinetic energy, which result gradual reduction in train speed. 5. Full service brake : In this mode, master controller is kept in full service brake position.
Equinox:The equinox is the event when the Sun appears directly on the equator and the length of day and night are nearly equal all over the world i.e. 12 hours day and 12hours night. There are two equinoxes on the Earth every year i.e. Vernal equinox and Autumnal equinox. One equinox occurs around March 21 and another around September 22. The March equinox is the vernal equinox in the northern hemisphere, and the autumnal equinox in the southern hemisphere. The September equinox is the autumnal equinox in the northern hemisphere and the vernal in the southern hemisphere. At the time of equinoxes, solar declination is 0° and sun rays directly fall on the equator located at 0° latitude. Summer Solstice and Winter Solstice: A solstice is an event occurring when the Sun appears to reach its most northerly or southerly excursion relative to the equator. Two solstices occur annually, around June 21 and December 21 and can vary ± 1 day. The summer solstice has the longest daylight time and the winter solstice has the shortest daylight time. In the Northern Hemisphere, the summer solstice occurs on 21 June when the sun is directly over the Tropic of Cancer (which is located at 23.5° latitude North of the equator) and the winter solstice on 21 December. In the Southern Hemisphere, the summer solstice occurs on 21 Dec when the sun is directly over the Tropic of Capricorn (which is located at 23.5° south of the equator) and the winter solstice on 21 June. Alternative terms, with no ambiguity as to which hemisphere is the context, are "June solstice" and "December solstice", referring to the months in which they take place every year. Therefore, in the Northern Hemisphere, the June solstice is the summer solstice and December solstice is the winter solstice; whilst in the Southern Hemisphere, the June solstice is the winter solstice and December solstice is the summer solstice. On the solstice, the sun does not rise precisely in the east. Sun-Earth Distance: Earth's orbit around the Sun is an ellipse, therefore, distance between Earth and the Sun varies as Earth orbits the Sun, from a maximum distance (Aphelion) to a minimum distance (Perihelion) and back again once a year. For a planet, asteroid or comet orbiting the Sun, the point of least distance is the perihelion and the point of greatest distance is the aphelion. Astronomical unit (AU), a unit of length effectively equal to the average or mean distance between Earth and the Sun and it has been defined as 149,597,870 km or about 150 million kilometres (93 million miles). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. At perihelion, which occurred around 3 January, the Earth's is closest approach to the sun in its orbit, which is about 147,098,291 km (91,402,640 miles) from the Sun's center. At aphelion, which occurred around 4 July, the Earth's is farthest distance to the sun in its orbit, which is about 152,098,233 km (94,509,460 miles) from the Sun's center. The exact difference in the distance between Earth's closest and farthest points from the sun is 3,106,820 miles (5 million km), or 3.3 percent, which makes a difference in radiant heat received by the planet of nearly 7 percent, therefore, sunlight falling on the Earth in January is about 7% more intense than it is in July. But our warm weather doesn’t relate to our distance from the sun and it mainly depends on the tilt angle of Earth's revolution axis by 23.45 degrees. Solar Radiation: Solar radiation is radiant energy emitted by the sun in the space as electromagnetic wave. The spectrum of solar radiation is close to that of a black body with a temperature of about 5800 K. The complete solar radiation spectrum comprises the ultraviolet (UV), visible (Vis) and infrared (IR) wavelengths. Molecular Ozone in the upper layers of our atmosphere works as a filter for ultraviolet radiation and the effect increases with shorter wavelengths. Most of the emitted energy from Sun lies in the spectrum ranges from 2500 angstrom to 30000 angstrom (3 micrometer). About half of the radiation is in the visible short-wave part of the electromagnetic spectrum. The other half is mostly in the near-infrared part, with some in the ultraviolet part of the spectrum. The energy output of the Sun has its peak at a wavelength of 4700 angstrom. Solar constant is the amount of solar radiation received outside the earth’s atmosphere on a unit area perpendicular to the sun’s rays, at the mean distance of the Earth from the Sun. The radiation from the Sun travels in the space as electromagnetic wave. Above the earth’s atmosphere, sunlight carries 1367 watts of power per square meter. It is most accurately measured from satellites where atmospheric effects are absent. Due to atmospheric effects, the peak solar radiation received on a terrestrial surface oriented normal to the Sun at noon is in the order of 1000 watts per square metre on a clear day. Geographic North-South Pole of Earth: The geographic north and south poles are determined by the points where the earth's rotation axis intercepts earth's surface. Magnetic north and south poles are determined by the direction a compass points. The Magnetic Pole is a point in Northern Canada where the northern lines of attraction enter the Earth. Magnetic variance, or declination, is the difference between geographic north and magnetic north. This is a difference of about 500 kilometres between the Geographic North and Magnetic North poles. As an approximation, the earth magnetic dipole tilts about eleven degrees with respect to Earth's rotational axis, and sits in the Arctic Ocean north of Alaska. But the Magnetic North Pole is actually moving kilometres every year. The angle made by geographic north and magnetic north pole on the observer location depends on the longitude and latitude value of the observer location. Magnetic declination angle is smaller at the equator and greater at higher latitudes. As a result, at locations close to the poles, compass readings are not very valuable unless one knows the exact declination. The declination is positive when the magnetic north is east of true north.
Latitude and Longitude: The latitude and the longitude angles are used to define the any location on the surface of the earth. Latitude is a measurement of location north or south of the Equator. The latitude of a location on the Earth is the angle between the line joining that location to the center of the earth and the equatorial plane. The north of the equator is positive and the south of the equator is negative and it varies between -90º ≤ Ø ≤ 90º. Longitude is a similar measurement east or west of the Greenwich meridian. Longitude ranges from 0° to 180° East and 0° to 180° West. The zero point of longitude is defined as a point in Greenwich, England called the Prime Meridian. Declination AngleDeclination angle (δ) is the angle between the equator plane and Sun lights (orbital plane). It is positive at north & negative at south and varies between +23.45º to -23.45º. Declination angle is at its highest point on 21st June (+23.45º) in summer while it is at its lowest point (-23.45º) on 22nd December in winter. Sun lights fall on the equator with steep angle twice a year. This condition is called as equinox. Vernal equinox is on 20th March and autumnal equinox is on 23rd September. Daytime and night time durations are equal on equinox dates (12hrs day and 12hrs night at all places of the world) and the respective declination angle is zero on equinox dates. The Sun declination angle has the range of – 23.5° to + 23.5° during its yearly cycle. Hour Angle: Hour Angle (ω) is the angle between the longitude of sun lights and the longitude of the location. The angle before noon and after noon are taken as -ve and +ve respectively. This angle is zero at solar noon and the hour angle increases by 15 degrees every hour. The hour angle is defined as the difference between noon and the desired time of the day. Zenith Angle: Zenith angle (θz) is the angle between the line to the sun and the vertical axis. Zenith angle is 90º during sunrise and sunset whereas it is 0º at noon. Solar Elevation Angle: Solar elevation angle (α) is the angle between the line to the sun and the horizontal plane. This angle is the complement of the zenith angle. Two angles are complementary when they add up to 90 degrees (A Right Angle). Solar Azimuth Angle: Solar azimuth angle (γ) is the angle on a horizontal plane between the due-south direction line and the horizontal projection of the Sun's rays. The angle is referenced to due south in the northern hemisphere and to due north in the southern hemisphere. This angle is assumed to be -ve from south to east and to be +ve from south to west and varies between -180º and 180º. Values to the east of the north–south meridian are negative and westward is designated as positive. Incidence Angle: For a particular surface orientation, the sun's incidence angle (θ) is the angle between the radiation falling on the surface directly and the normal of that surface. For a horizontal surface, the incidence angle is equal to the zenith angle. Tilt Angle: Tilt angle (β) is the angle between the panels and the horizontal plane. This angle is south oriented in the northern hemisphere and north oriented in the southern hemisphere.