Simplified representation of rigging efficiency in brake force calculation

A method is presented for predicting brake shoe force of a rail vehicle as a linear function of effective brake cylinder pressure. Historically, the braking force has been calculated as the product of cylinder pressure, cylinder area, rigging leverage ratio, and an overall system efficiency factor. The efficiency factor, which takes into account frictional forces and other losses, is a non-linear function of brake cylinder pressure. The method presented here uses a modified formulation for braking force that does not require a non-linear representation of efficiency. Instead, the braking force is represented as a linear function of effective (or net) cylinder pressure. Effective cylinder pressure is the actual cylinder pressure reduced by the initial cylinder pressure required to set the brake shoes against the wheels with no net force transmitted to the wheels. This method of determining the braking force allows a clearer understanding of the role of rigging efficiency, breaking it into fixed losses (such as return spring force) and purely frictional losses that are directly proportional to load (such as pin friction). This approach for calculating brake shoe force as a function of effective cylinder pressure has several advantages over the conventional method (as described above) using nonlinear rigging efficiency: the mathematical formulation is a more appropriate representation of the pertinent physical aspects of the brake cylinder and rigging; complex curve-fit representations of efficiency for different rigging types are avoided; shoe force as a function of cylinder pressure is characterized (for a given vehicle) by just two parameters, each of which has a clear physical meaning and may be readily determined for any particular car using common brake system measurement techniques. Published discussions of efficiency and its approximation to measured data for various types of car rigging are compared with predictions from the subject method and show close correlation.