Martin Wynne wrote:How are you calculating the sideways force on the flange?

I promised earlier to dig out some sums, so here we go.

Imagine a typical prototype 3' wheel (weight 500kg, say) striking an 'immovable object' like a check or a wing knuckle at a sedate 15mph. If the the impact takes place over a duration of say 0.25s, the impact force is 26.8kN. That impact force will be transmitted laterally, because that is the shape of the interaction between the rear of the flange and the railhead, and the transmitted lateral will accelerate the wheelset toward the running rail, where the push will be resisted only when the wheeltread root collides, in a sort of dynamic glancing blow, with the running rail shoulder. For the sake of argument, let's take the common tangent of the flange root and rail shoulder at approximately 45 degrees (see diagram above), so the resulting force components will be 50% lateral and 50% vertical. Very simplistically, one can say the impact force will therefore result in a resultant vertical force on that wheel of 13.4kN, which will be transmitted to the body via the wheel spring. The ratio of that force to the weight the wheel is supporting, say one quarter of a 10t wagon, is a significant 54%.

For a model wheel (say 3g, which is too generous) of a 40g wagon at an equivalent scale speed (0.09m/s) but over the same impact duration, the resultant vertical impact force is 0.001N. The ratio of the vertical force to the weight being supported then becomes an insignificant 1%.

I accept the above impact analysis is crude, but it is the comparison of the prototype 50-plus% and model 1% ratios that is illuminating.

Guy Rixon wrote:So the fact that we tend to run our models faster than the prototype round sharp curves is raising L/V, maybe by factors of two or three. This may account for some flange-climbing derailments in models.

I don't think so.

Let's compare the same 10t prototype wagon travelling at 15mph around a 90m radius curve. The centripetal force is approximately 5kN. If this is apportioned equally between the front and the rear wheelsets of the wagon, a reasonable assumption I hope, each wheelset would be undergoing approximately 2.5kN sidethrust, which is approximately 10% of the 25kN vertical force on each wheel. In other words, for that speed and that flange angle (70 degrees is a reasonable value to take for our prototype and model profile), it is comfortably below the Nadal

*L*/

*V* limit, even in high friction situations. For an equivalent 40g model wagon traversing a 1.2m radius curve, the ratio of lateral to vertical force is, again, an insignificant 1%. (Even if the model speed is increased to 60smph, the model lateral to vertical force ratio becomes a very low 4%.)

In both the impact force analysis and via a Nadal analysis, the sums indicate our models should therefore be far more stable than the prototype. (For the model case, however, coupling forces will easily counter the opposing, but small, centripetals, and are likely to dominate the flange sidethrust situation.)

I'm still scratching my head a bit. Something doesn't add up.