Train resistance

When I run the train of the railroad, train resistance (れっしゃていこう) is resistance for the progress [^{source 1}]. The thing which falls down, and added up all the resistance by some factors including the resistance of air resistance and the wheel is train resistance.

Table of contents

Element of the train resistance

The train resistance is comprised of some elements. I show below an element.

• Starting resistance
• Run resistance
• Incline resistance
• Curve resistance
• Tunnel resistance

It is big and I am caused by necessary thing (starting resistance, run resistance), facilities physically to let a train accelerate and am classified in (incline resistance, curve resistance, tunnel resistance). In addition, you must turn the rotary parts of a wheel and the motor fast to accelerate, but this must let you accelerate rotary motion separately from acceleration of the going straight exercise as the whole train, and there is resistance in this. I may call this power acceleration resistance, acceleration resistance, an inertia coefficient.

The train resistance may measure power to act in a real vehicle by Newton unit, but expresses it in many cases in power (N/t) per train 1 ton in weight. I explain train resistance per this train 1 ton in weight in the following.

Starting resistance

By the resistance that acts when a train departs as for the starting resistance and begins to work, I am caused by the friction of an axle and the bearing. I may call it start resistance. Because the moment when it begins to work is the biggest and becomes small rapidly when speed rises, I usually bind a value at the age of 0km/h and a value at the age of 3km/h together by a straight line and express it and consider it to be run resistance after it. I express the starting resistance by power (unit N) per 1t in weight of the train.

The starting resistance is influenced by a kind and the stoppage time of the bearing. 30N/t is approximately 80-100N/t by vehicle of the plain bearing by vehicle of the roller bearing.

Run resistance

The run resistance is caused by the friction of air resistance and a wheel, the axle by resistance to occur on a train when a train runs. The run resistance divides it into vehicle resistance and air resistance more and thinks.

Vehicle resistance

Vehicle resistance is mechanical resistance by a vehicle running. When the vehicle resistance disintegrates more finely, there is the resistance of the slide part of turn resistance, others concerned with the motors such as frictional resistance, the motor of frictional resistance (by being able to rub a flange mainly), an axle and the bearing between a wheel and the rail. The resistance of an axle and the bearing decreases around the unit weight so that pressure to depend on a bearing becomes big. In addition, vehicle resistance increases because the viscosity of the lubricant is low so that temperature is high when generally it is winter.

Air resistance

As for the air resistance, a train top part pushes air aside by a train running and occurs by receiving resistance by the train side and friction of the air. I almost grow big in proportion to square of the speed. The size of the air resistance of the lead car consists of middle vehicles approximately approximately 10 times. In addition, because air becomes thin and pulls a vehicle on end side when a train moves even a vehicle of the end, resistance grows big in comparison with middle vehicle, and it is to approximately 2.5 times. Therefore, the air resistance per unit weight decreases so that a constitution dual number of the formation becomes long. In addition, I do not affect the air resistance even if a traveler and freight are put only on anything in in only the outside shape and materials of the vehicle influencing it. In other words, the weight does not influence air resistance.

In addition, air resistance in itself increases conspicuously in the tunnel, but this illustrates by a passage of the tunnel resistance.

Expression-style of the run resistance

Because it is a difficult value to analyze the run resistance theoretically, I make an expression to express this for the cause and use an actual value every form of the vehicle. The general formula,${\displaystyle r_{r}=g\times \left(a+bv+{\frac {cv^{2}}{W}}\right)}$である. Train mass (t), g are acceleration of gravity (m/s²) run speed (km/h), W run resistance (N/t), v r_r, and a, b, c are the fixed number.

a is the clause that is unrelated to the speed with a value depending on the friction of an axle and the bearing mainly. b is a value depending on the friction of a wheel and the rail mainly, and this part is a clause in proportion to speed. Because a tare does not influence c in a clause in proportion to square of the speed with a value depending on air resistance again, I break it at weight.

The concrete run resistance calculating formula is given, for example, by a Shinkansen 100 system train with rr = g (1.273 + 0.001v + 0.0001381v²).

Incline resistance

When a train approaches the ascent, I work in the direction that the ingredient of the incline parallelism direction of the gravity stops in spite of the progress of the train by the degree of leaning of the point. This power is called incline resistance. This power can express W (t), acceleration of gravity at train weight with Wg sinθ when I assume the angle of the g (m/s²) incline θ. Using being sinθ ≒ tanθ, the incline resistance at the incline of the h par mil is expressed in Wgh by permillage (gone thick-haired codium) that is used generally to express the degree of the incline in a railroad as far as θ is small enough when I rearrange it. Incline resistance of 245 (N/t) will act at 98 (N/t), 25 soft-headed mil inclines at 10 soft-headed mil inclines. This works in the direction letting a train slow down in the ascent, but works in the direction letting, on the contrary, you accelerate a train in the downslope.

Curve resistance

When a train runs a curve, a flange touches it, and a wheel is slippery with an outside rail to absorb that the length of the rail of the outside and the inside is different. From this, when I run a tangent, I compare it, and train resistance increases. This power is called curve resistance. Is affected by various elements, but to the public${\displaystyle r_{c}=g\times {\dfrac {1000\mu (G+L)}{2R}}}$I am given in an expression of の Morrison. In r_c, in curve resistance (N/t), G, in (m), L between the gauge, as for wheelbase (m), μ of the cart, coefficient of friction, R of a wheel and the rail are curve radius (m) here.

The expression that substituted a general value by Japanese JR old line, and took the result of the examination into consideration, and simplified this,${\displaystyle r_{c}={\dfrac {K}{C}}\times g}$となる. K uses 800 by the JR old line with the fixed number. C is a curve radius of the point. Therefore, it becomes around 19.6N/t with 9.8N/t, the curve of 400m with the curve of a radius of 800m.

Tunnel resistance

When I run the tunnel, when I run the tunnel outside (I call it a light section), I compare it, and air resistance of the run resistance is enhanced by influence of the wind pressure. I call this increase tunnel resistance. I am influenced by values such as a shape, the speed of a cross section and the vehicle of the tunnel.

In the Shinkansen, I am 270km/h in resistance increase of around 30-50N/t when I break into the tunnel of the double track section when I run. This is degree same as an ascent of the 3-5 soft-headed mil degree. On the other hand, when an old line train breaks into the tunnel of the single line section by a 160km/h run, there is resistance increase of around 80-120N/t, and this is equivalent to the ascent of the 8-12 soft-headed mil degree.

In a real calculation, I often set expression itself of the run resistance particularly for tunnel sections. The run resistance calculating formula in the tunnel of the Shinkansen 100 system train is given with rr = g (1.273 + 0.001v + 0.0002569v²).

Use of the train resistance

The value of the train resistance makes the general formula that expressed it based on an actual value well, and what I demand by the expression is common. This ceremony is used for the making of the driving curve. The driving force (tension) of the train at a certain point in time is decided by the performance of the train and the driving of the driver. The acceleration of the train is provided by dividing the value that deducted train resistance from this driving force by the mass of the train. The driving curve adds the driving method of the driver at the point in time while calculating train resistance to change by a curve or the incline of the route at any time and is provided by calculating the speed at each point of the train. I calculate the standard driving time that is the standard time required between the station for the cause in this.

References

• "Electric railroad handbook" electric railroad handbook editing Committee, CORONA PUBLISHING CO.,LTD., 2007. ISBN 978-4-339-00787-9。 pp.391 -393
• Run resistance investigation subcommittee "run resistance Japan Society of Mechanical Engineers Vol.67 No. 543 (April, 1964) pp.620 -630 of the railroad carriage of the railroad carriage"

Source

1. ^ JIS E 4,001:1,999 13019

Allied item

• Adhesion-type railroad

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