Being British, we didn't question the BS 276 specification, asssuming that the basic shape of wheel flange was sort of universal. I have since endeavoured to ascertain how the standard was arrived at, without any conclusion. Note the BS 276 profile is in fact different from the AAR diagram, showing that there are in fact differences between continents.
There are many factors which influence the performance of wheelsets other than the depth of flange. The wheel profile works as follows: the treads of wheels are coned at 1 in 20 and the rails are inclined inwards at the same angle. When the wheelset rolls along a straight track the coning attempts to centre the wheelset between the running rails and clear of them. In practice, the wheelset veers to one side until the flange root radius of one wheel makes contact with the running rail shoulder radius (In this position the distance between the edge of the running rail and the back of the flange gives the Effective Flange dimension, any further movement in the same directrion will cause the tread to lift from the rail head). As the wheel does continue to climb up the shoulder radius the wheelset motion reverses and starts to travel in the opposite direction where the same effect takes place, resulting in a sinusoidal motion of the wheelset along the track.
Note too the rail shoulder radius and the flange root radius are important in that the point of contact gives a tangent angle which affects wheel performance; a shallow tangent angle allows the wheel to more readily rise up, a steeper tangent angle will do the opposite, giving rise to a more abrupt change of direction and shock of motion. The rail shoulder radius must never be greater than the flange root radius. On the other hand in modelling terms the rail should never have a sharp corner between its edge and the head, which itself should be radiused as is the prototype.
Still with a prototype wheelset, in normal straight line motion the only contact of flanges with rails is at the root radii. Wheel bounce occurs at rail joints and crossings and in these cases the part of the flange adjacent to the root radius ensures the wheel is guided back to its rightful place.
The only time that the rest of the flange makes contact with the rail is on curved track. Here the design of the flange is most important. See Figure 2 which illustrates the section of BS 276 / P87 flange taken at the point of rail contact and compare this with the profile in Figure 1. When this flange moves to angle with the rail there is contact between the two, gradually moving down to the tip. If the flange profile were more square, as in for example the BRMSB design, the rail/flange would make initial contact near the root and lose contact until almost the tip. This indicates that it is not so much the depth of the flange that is important but the design or shape.
With Protofour, we adopted the BS 276 profile without question at the time, though looking back now we made the right choice. It is interesting to note that the shape and dimensions of the flange front face (the rail side) of the BS276 and AAR are identical and that other designs are similar.
