I wanted to leave a reply in the comments to the guide "Structured Approach To Braking Distances" but my comment was too so I decided to make it into a guide.

First I'd like to give credit to nerazzurri2014 for taking the time to make the guide. It is a subject that comes up intermittently on this and other forums but there are few guides to find.

The reason for why I decided to write this guide is that I think the problem that was brought up in the initial guide can be attacked from a different angle with, in my opinion, better results.

• These tables are for UK trains so they do not hold for other trains like German or NA trains (maybe you mentioned this and I missed it).
  
• The tables are taken as minimum stopping distances and don't say very much about the real stopping distance of a UK train other than it should (if modelled correctly) stop within these distances using full service application.
  
• If stopping for a platform or a signal, it is not advised to use full service in normal situations because it will have an adverse affect on passenger comfort and could lead to flat spots on the wheels. Also if brake force happens to be lower than expected you have no "fall back".
  
• This approach to finding the braking distance is more empirical and does not rely on the trains behaving exactly as their real world counterparts.

What I would recommend instead is to find a deceleration rate that is comfortable for the passengers and test what brake pipe pressure (or step) is closest to this value, and then calculate the stopping distance using this deceleration.

A common deceleration rate that upholds passenger comfort is between 0.5 m/s^2 and 0.8m/s^2.

Some high school physics gives the stopping distance from this formula:

d = v^2/2a

where v is the speed and a is the deceleration. To get a distance that is in units of meters you need to divide km/h by 3.6 or multiply mph by 0.447.

Because trains don't instantly apply the brakes but rather it takes time for the pressure drop to propagate through the train, an added delay T can be implemented to calculate the stopping distance as:

d = vT + v^2/2a

Let's take an example. You've decided on braking with a comfortable 0.6m/s^2, the brakes take 5 seconds to apply and your speed is 100 km/h. Divide 100 km/h by 3.6 to get the speed in meters per second and plug in the values in the formula:

d = 28m/s * 5s + (28m/s)^2 / (2*0.6m/s^2) ~ 800m. This is the distance before the stopping point you need to apply the brakes.

If you want to decelerate but not stop this formula will be appropriate:

d = v_0T + (v_0^2 - v_1^2)/2a,

where v_0 is the initial speed and v_1 the final.

Let's say we want brake the train from 100 km/h to 50 km/h. We calculate the braking distance by converting the speeds and putting them into the above formula like this:

d = 28m/s * 5s + ((28m/s)^2 - (14m/s)^2)/(2*0.6m/s^2) = 630m. You'd need to start braking at least 630 meters before the speed restriction.

[h4] Measuring Deceleration [/h4]
When first taking control of a train you might not know what brake pressure or setting to use to achieve the desired deceleration. An easy way to find out how much brake force to use is to measure the deceleration the following way.

Take the train you want to drive and get it up to a relatively high speed on a flat bit of track (check the grade in the F3 or F4 HUD). Now apply step 2 on a UK style 3-stepped EMU/DMU or decrease the brake pipe pressure by 1 bar (around 15 psi) on other kinds of trains.

When the brakes have taken hold simply use a stop watch or the ingame clock to record the time it takes to decelerate between two speeds (I'll call the initial speed v_0 and the final speed v_1). Then use the following formula to calculate the deceleration:

a = (v_0 - v_1)/t

This value will be in either mph/s or kmh/s so if you want to get the value in m/s^2 convert by:

(m/s^2) = mph / s * 0.447 = km/h / s / 3.6

Then you can retest with a lower or higher brake pressure depending on what value you got.

Final points: This value you got will be for flat grade, if braking in a descending grade you will need to apply more brake or brake earlier and vice versa for an ascending grade.

Hope that was of some help. Please feel free to give criticism or point out any errors I've made.