1. How a speed generator turns wheel rotations into a speed reading
The rotation of train wheels and gears is turned into an electrical signal by a device called a speed generator. In 1964, Hitachi noted that the standard type for Japanese National Railways used a rotating magnet to produce an alternating voltage proportional to the rotation. For private railways, an inductor type counted the teeth of a gear using magnets and coils to create a voltage with a frequency proportional to the rotation speed [2].
Digital speedometers calculate the speed by multiplying the number of rotations counted in a set time by a factor based on the wheel diameter entered into the system [4]. A patent description gives an example where a rotation sensor sends out about 60 to 100 pulses per rotation. This is just one example, not a value for all vehicles [3]. Once the number of rotations is known, the rest is simple multiplication.
2. How far a train with 860 mm wheels travels in one rotation
A diagram in the 1964 Hitachi material shows an example with a wheel diameter of 860 mm. This is a condition for the diagram, not a standard for all trains. We use it here to practice the calculation [2].
The circumference of a circle is the diameter multiplied by 3.14. So, 0.86 m times 3.14 is about 2.7 m. If the wheel turns once per second, the speed is about 9.7 km/h. For a speed of 100 km/h (about 27.8 m per second), the wheel turns about 10 times per second. If the sensor sends 60 pulses per rotation, it counts about 600 pulses per second. One pulse represents about 4.5 cm of distance along the wheel’s edge. These calculations are examples for this article, not numbers taken directly from the source. But the method can be checked. If a new wheel displays the correct speed, what happens when the wheel gets thinner?
3. Why worn wheels shift the speed display and how registering the diameter fixes it
Train wheels wear down every time they run on the rails. Patent descriptions state that a weakness of counting rotations with a speed generator is that errors occur when the wheel diameter changes [5].
For example, if the diameter shrinks from 860 mm to 850 mm, a difference of 10 mm, the speedometer might show a speed about 1.2% higher if not adjusted. At 100 km/h, it would display about 101.2 km/h. This is a calculation example for this article.
Therefore, railway speedometers need a way to compensate for wheel diameter. The standard JIS E 4603 requires that the maximum compensation setting be no smaller than the new wheel diameter, and the minimum setting be no larger than the wheel diameter at its end of life. If the settings are switched, the interval between settings must be a maximum of 10 mm [6]. The 1964 Hitachi speedometer also used resistors with taps to compensate for changes in indication due to wheel wear [2]. The design is made to accept the range from new to worn wheels from the start.
4. How speed is measured when train wheels slip or slide
If the wheels spin without gripping the rail (slipping), the calculated speed based on rotation becomes higher than the actual speed. If the wheels slide while braking, the calculated speed becomes lower than the actual speed. Patent descriptions explain this mechanism [7].
One solution is to combine multiple values. A patent method uses the lower value during acceleration and the higher value during regenerative braking, averaging the speeds from multiple inverters to improve accuracy [7]. Another patent describes adding Doppler sensors (which do not touch the track) and acceleration sensors to the rotation sensor, switching calculations depending on the situation [3]. These are methods described in patents, not standards for all railways.
Doppler systems send radio waves or ultrasound and measure the difference in frequency of the reflected waves to find speed [1]. This measures speed relative to the ground, without relying on wheel rotation. In a test of a 24 GHz continuous wave radar, the error was within ±1 km/h for speeds under 100 km/h, and within ±1% for speeds over 100 km/h. This is the result of one radar test and does not apply to all radars [8].
There is also an unusual method. The Nagoya Railway M-type ATS places two ground devices on the track. It detects speed by measuring the time it takes for the train to pass between them. Because the devices are fixed, it can only measure one specific speed [9].
5. How the accuracy of a train speedometer is checked
The standard JIS E 4603 sets the overall accuracy of the speedometer at ±2.0% of the maximum scale value at a reference temperature of 20°C. For small instruments with a maximum indicated speed of 80 km/h or less, the tolerance is ±3.5% [6]. Note that this is ±2% of the maximum scale, not ±2% of the actual speed. If the maximum scale is 120 km/h, the allowed error is ±2.4 km/h. This is a calculation example for this article [6].
Inspection methods are also documented. A 2005 survey by the Ministry of Land, Infrastructure, Transport and Tourism found that management standards for operators were generally ±2 km/h or ±3 km/h, with some at ±1 km/h. Some small operators without measuring equipment, and the inspection of digital display units at JR West, checked speed by running a fixed distance and calculating speed from the time taken, then comparing it to the speedometer display [4]. This was the situation in 2005; current operations vary by operator.
On the electrical side, the idea of "fail-safe" was important. The speed generator for the Tokaido Shinkansen ATC system was designed to send a signal even when the train was stopped, allowing it to detect faults or broken wires while stationary, according to 1964 materials [2]. The design ensures that if something fails, it does not lean toward a dangerous state.
6. A bicycle activity to check wheel rotation and distance at home
Try this with an adult in a flat, safe place. Always perform this activity with a parent or guardian in a safe, flat area.
1. Measure the diameter of the bicycle wheel with a ruler or tape measure. Measure the outermost part of the tire.
2. Multiply the diameter by 3.14 to calculate the distance the wheel should travel in one rotation.
3. Push the bicycle and measure the distance traveled while the wheel turns 10 times.
Compare the distance from step 3 with 10 times the distance from step 2. If there is a difference, it might be due to the amount of air in the tire or how you pushed it. If the air pressure is low, the tire squashes, making the actual diameter smaller. Train wheels experience the same issue when they wear down. If you want to learn more, look for the speedometer standard (JIS E 4603) or the 1964 Hitachi Review article in the sources.