## Monday, August 6, 2012

### Scale Speed

When doing any scale modelling it is important to stick to the same scale throughout (as much as possible anyway) otherwise things start to look a bit odd. I'm currently modelling in OO gauge which means 4mm to the foot or a scale of 1:76 (although the track width is slightly wrong but that's a whole other kettle of fish). One thing that I never really considered before was scaling the speed of a locomotive correctly. Now I've always known that most of the engines run way too fast to be accurate, but I didn't really have any way of knowing just how inaccurate they were. My older locomotives tend to move at a more sedate pace than newer models. For example, the small 0-4-0ST that came with the starter set I bought goes off like the proverbial rocket.

So in an effort to try and model things accurately I set about working out how I could measure the scale speed of the various locomotives I own. Now this involves a bit of maths but it's nothing too complicated, honest!

Firstly I'm going to work in millimetres as I find both the maths easier and I have a nice accurate steel ruler that bizarrely doesn't show inches. This means that I'll end up calculating the speed in kilometres per hour (kph) although it's easy to convert kph to miles per hour (mph) for comparison with real steam engines:

mph = kph * 0.621371

Now firstly as were are going to calculate kilometres per hour we need to know what a kilometre of track at a specific scale would measure in millimetres.

scaleKilometer = 1000000/scale

We simply take a kilometres worth of millimeters and divide it by the scale (in the case of OO that would be 76 meaning I would need 13157.89mm of track to model a kilometre). Now that we know how many millimetres of track represent a kilometre we can work out what the distance between any two points on our layout represents

scaleDistance = distance/scaleKilometer

In my case I know that my two markers are 74 millimetres apart which means that they represent 0.005624 of a kilometre or more usefully 5.624 metres.

Now if I time the locomotive between the two markers I can finally calculate the speed by simply multiplying the distance the real locomotive would have travelled by the fraction of an hour that it took to cover the measured distance.

kph = scaleDistance*(3600000/time)

As an example, if it took 2 seconds to cover 74 millimetres that would be 2000 milliseconds which would be 1/1800 of an hour, which means that the real speed of the locomotive would be 10.1232 kilometres per hour or 6.29 miles per hour.

Now there are a number of websites that simplify the maths by providing you with a form where you simply fill in the distance, time and modelling scale and it gives you the speed, but manually measuring time with a stopwatch is never going to be particularly accurate, certainly not if you are trying to measure the speed of a fast moving locomotive.

The obvious solution (given my background) was to build a speed trap that could accurately measure the time taken for a locomotive to travel a set distance. I won't go into the technical details of how I built the speed trap here but if you want to build your own scale speed trap then I've posted full instructions over on one of my other blogs. All you really need to know is that I can set a speed limit and then a green light comes on if the locomotive is below that speed, otherwise a red light comes on. The actual speed is also fed back to the computer.

The photo to the left shows the current version installed on my layout. Now I know that it isn't pretty, but all the electronics apart from the two small sensors on the track could be hidden away off the layout so for a prototype of what I'll eventually include in my layout I'm happy with how it's turned out. In the photo you can also see one of my other locomotives which I haven't mentioned before. This is Mallard in BR green livery. Given Mallard's history she seemed the perfect locomotive with which to test a speed trap!

So how fast can the locomotives I own (or at least the ones I've blogged about so far) actually travel. I decided to measure the speed of each locomotive under two conditions: the locomotive on it's own and when pulling a train, which in this instance was made up of four LNER teak panelled coaches. In both cases I allowed each to run around the layout ten times and then took the highest recorded speeds which were...
Speed in mph
Engine OnlyA Train
CR 0-4-0ST163.38128.37
Mallard144.42118.68
Flying Scotsman110.3697.52
L&YR 0-4-0ST93.8856.96
Duchess of Abercorn84.4367.97

Now I think we can all agree that there is something seriously wrong with those numbers, i.e. running the locomotives at full speed means they are moving way two fast. Malard holds the world record for a steam locomotive at 126mph so nothing should be travelling faster than that, and certainly not a Caledonian Railways tank engine!

One thing to note from that table is that while it is sorted by decreasing speed of the loco only run, it's also ordered in the second column apart from the L&YR 0-4-0ST. The reason for this is that the engine is so small and light it doesn't have the weight to really pull the coaches, you could see the wheels slipping on the track. If I added some weight to the locomotive it could probably pull the coaches faster even though it would be heavier.

So now I know that I really don't want to run any of the locomotives anywhere near full power, unless I want to try and recreate Mallards record breaking run. Once I've decided exactly what my layout will include (rural or urban etc.) I can decide on a reasonable top speed and programme the speed trap accordingly so that I can keep an eye on the speeds and make the model as accurate as possible.