(08-04-2019, 01:12 PM)gnemeth1980 Wrote: Hi All,

I have a question regarding section G.7 (effects of gradient on braking) and I haven't found any response on the forum. For me it is not really clear when is it required to calculate average gradient using the given formula.

I understand how it can influence the braking rate and the stopping distance, but can somebody explain to me, in which case and how to apply the averaging formula in terms of the distance (variable D in the formula)? is it the length of the train or the calculated braking distance or anything else.

Also, is the referred formula coming from a particular standard applied in the UK?

Thanks

Gabor

I can't remember the last time that the exam actually required candidates to take the gradient into account; you are normally told that it is level n one year there was an underpass that the gradient down and up averaged to level.

However it could just come up in the mod 2 exam and is certainly worth understanding anyway.

You need to average the gradient over the entire length the train is traversing whilst it is undertaking its braking. One of the practical problems is if the gradient is quite variable; without knowing the gradient you can't work out the braking distance and unless you know the distance that the braking will take you can't work out the correct average gradient. Welcome to the job of calculating where to put a warning board for a Temporary Speed Restriction. In the 1980s this was done with the aid of a simple pocket calculator, but otherwise manually. So it was a matter of making an approximate assumption, work on that basis and see what the result was and then tweak appropriately. In other words, an iterative approach- trial and error.

It actually didn't often make a huge difference, but if there was quite a steep rising gradient to a summit and then an equally steep fall the other side then it could actually be very significant where the warning board had to be placed.

I remember the arguments whether to calculate just from the front of the train or from half way along its length; in most cases it made pretty little difference. If the route was particularly undulating I think we calculated for the front and also for the back of the longest expected train and then compared the results and went with the worst.

The way it was (and as far as I know still is but I haven't done the task for decades) was to use the empirical tables / graphs, rather than the Newton's Laws of motion formulae, since modelling as constant brake rate is far too crude an assumption. Make pessimistic assumption re gradient (most steeply downhill / least steeply uphill) and determine an approximate braking distance. Then use that braking distance to calculate a better approximation to the average gradient; look up the braking distance at that gradient. So yes the method did involve working out the total height gain or loss over the full length by summing all the amounts at each of the separate gradients within that distance; then divide that total height by the total length travelled. At the sort of gradients that railways typically traverse, there is very little difference between the horizontal distance and the hypostomes of the triangle