Assessment of Broken Rail Protection in Audio Frequency Track Circuits

In addition to the vital function of train detection, a track circuit is also expected to provide an indication of a broken rail within its boundaries. Ability to detect a broken rail in a double rail track circuit is a result of the failsafe design principle, which interrupts the flow of track signal current and drops the track relay in the presence of any credible component failure. The overall result of such an event is identical to that of track occupancy, which causes the associated signals to be set to the most restrictive aspect. In the case of electrified territory, the ability to detect a broken rail may be compromised by the presence of crossbonds between parallel tracks. These additional connections, which are intended to minimize potential differences in the negative return system, also provide a sneak path for track signal current to flow from transmit to receive ends of the track circuit under broken rail conditions. In most cases involving 2 parallel tracks, application of a simple rule of thumb (described in this paper) regarding crossbond spacing and track circuit length is sufficient to ensure broken rail protection. In situations which are marginal, or where complex track work is involved, a more detailed analysis is necessary. Evaluation of the broken rail protection in such cases requires that the sneak path impedance be calculated and compared to the normal track circuit impedance. A formal method for this impedance calculation, based upon the classical circuit analysis techniques, is presented. To completely characterize the behavior of the track circuit under broken rail conditions, the operational characteristics of the track circuit must also be considered. In this paper a digital jointless AF track circuit, operating in the 9.5–20.7 kHz range, is used as a basis for this discussion. The operational characteristics of the S-bond, O-bond, as well as the role of overdrive are considered in the context of broken rail (BR) protection. The mathematical methods described for the simplified examples in this paper can readily be expanded to include any number of parallel tracks.

SENARIET, A Water Hammer Software for Analyzing Hydraulic Transients in Complex Circuits

Water hammer transients are a danger for piping integrity and represent an important safety issue. In the design of pipeline systems it is necessary to take into account the magnitudes of pressure waves associated with water hammer phenomena and, therefore, it is important that these water hammer effects are calculated with the appropriate accuracy. SENARIET is a programme to study fluid transients in pipeline systems to obtain pressure and velocity distributions along a circuit. When a transient process occurs in periods of the same order of the pressure waves’ travelling time along a circuit (the order of the circuit length divided by the effective propagation speed), the compressibility effects in liquids have to be considered. Taking this effect into account, the appropriate equations of continuity and momentum are solved by the method of characteristics, to obtain pressure and velocity along pipes as a function of time. The programme considers different devices that usually take part in complex circuits, such as pumps, motorized valves, check valves, elbows, change of sections, bifurcations, vacuum valves, damping devices, reservoirs, etc. The simulated results have been compared to theoretical and experimental ones to validate and evaluate the precision of the software. The results help to perform efficient and accurate predictions in order to define the pipelines.

Some remarks on a paper by Vizing on critical graphs

In papers (7, 8), Vizing studied graphs which are critical with respect to edge colourings. In particular, he obtained bounds on the number of edges and on the circuit length of such graphs in terms of its maximum valency. The object of this paper is to improve these bounds by obtaining others which also take into account the order of the graph.