Jump to content
 

Calculating the scale speed of OO gauge models


Recommended Posts

Good morning.

 

An internet search produces many confusing offerings so I thought I'd ask the knowlagebile folk here.

 

I want to calculate the speed of my OO gauge trains over say 24 inches of track.

I get that speed= Speed = distance divided by time.

 

So if my train takes 10 seconds to travel 24 inches that would be 24/10 = 2.4  Which I think is real world speed? Lost after this.

 

Many thanks

Link to post
Share on other sites

  • RMweb Gold

If I convert to mm, lets say it travelled 600mm. At 4mm to a ft in 10 seconds it travelled 150 ft (600mm/4mm) which in turn is 0.03 of a mile as 1 mile contains 5280 ft, so that's a pretty slow speed that in turn converts to around 10 mile per hour. (0.03 * 6 to get distance travelled in a minute and then * that by 60 to get mile per hour)

 

I think my logic is correct as it seems to align to the calculator in Knapper blog.

  • Like 1
  • Thanks 1
Link to post
Share on other sites

  • RMweb Premium

Think on the basis of 36" of track (1 yard) represents 76 yds of track in real life.

 

A mile a minute (60mph) is 1760 yds per minute in real life.

Therefore a model should travel 1760/76 yds in 1 minute = 23 yds/min (roughley 70 feet)

Taking your 24" , then 60mph should take 1/35 of a minute, just under 2 seconds.

 

But should you take time into account with scale as well?:o

Edited by melmerby
  • Agree 1
  • Thanks 1
Link to post
Share on other sites

29 minutes ago, mikesndbs said:

So if my train takes 10 seconds to travel 24 inches that would be 24/10 = 2.4  Which I think is real world speed? Lost after this.

 

The speed you measured is 2.4 inches per second.  Multiply by 3600 to get inches per hour, divide by 36 (inches per yard), divide again by 1760 (yards per mile) to get miles per hour.  The answer is 0.136mph - which is a real world speed, as you say.

 

I had it drummed in to me as a kid that "there is no such thing as scale speed" as time does not scale.  But distance does, so you can get an equivalent speed for a life-sized train by multiplying the miles by 76 (00 being a linear scale of 1/76) which gives you 10.36 "scale" miles per hour.  (The actual business of extrapolating measurements obtained from scale models up to life size - for example in fluid dynamics e.g. airframe models in wind tunnels - can be a lot more complicated than just multiplying by the linear scale factor.)

 

So, the actual train on your layout is still only travelling at a 0.136mph.  It might help to think of how that would translate to life size by thinking in terms of the size of the object concerned.  Let's say that, for example, your model train was itself 24" long.  By your measurement it travelled its own length in 10 seconds, which is an actual (real world) speed of 0.136mph.  If a 1:1 scale i.e. life-sized train made up the same vehicles (which would be around 152ft long) travelled its own length in 10 seconds then it would be travelling at a real world speed of 10.36mph.

 

(For the avoidance of doubt: I know that the precisions to which I've quoted the results of the calculations above are waaaay optimistic, but it's easier to work with a few otherwise unjustifiable decimals rather than start faffing around quoting error ranges or the like.)

  • Friendly/supportive 1
Link to post
Share on other sites

As we model stations with platforms shorter than they should be and distances between stations much closer than scale, the speed is somewhat meaningless.  These foreshortened distances are one of the reasons that layouts working to a model timetable also scale time - by using speeded up clocks.  I think it's fair to say we usually scale the acceleration and braking rates too.  The other reason for doing this is that a lot of the time there's nowt happening on a real railway and that isn't very interesting at a show, whether you're a visitor or the operator. 

Link to post
Share on other sites

  • RMweb Gold

Hello Mike

 

Another way to approach the subject is to fix your eye on a fixed point on the layout - a signal post for example - then run the train past.

 

Ask yourself, does that passing speed 'look right' for the type of train? 

 

Yet another way is to listen to the how fast the vehicle axles cross any track gaps and compare that to real railway sounds.

 

In my experience, modellers run trains far faster than 'real' ones.

 

If you play such as a Peter Handford recording while observing as above, you will soon 'get the feel' for what is right for your trains.

 

Brian

  • Like 2
Link to post
Share on other sites

7 hours ago, melmerby said:

But should you take time into account with scale as well?:o

 

Not unless you are trying to accurately scale mass and physical effects (unless you can somehow modify local gravitational interaction).

Link to post
Share on other sites

  • RMweb Gold

I am fairly cogniscent of the sound of wheels over joints and the noise made by steam locomotives, so I can assess the scale speed of my 4mm trains fairly accurately by listening to the wheel beat and making mental chuff chuff noises (you'll get funny looks if you actually make the noises) at the rate of 4 chuffs per each revolution of the driving wheels, or a  chuff per quarter revolution with the crank turning through 90 degrees.  This works for 2 or 4 cylinder locos, and all of mine are 2 cylinder beasts. you need 6 chuffs per revolution for 3 cylinder locos (Gresleys, Jubilees, Bullied pacifics, Patriots), and 8 for the Southern Railway Lord Nelson class.  You can get the idea from visiting a heritage railway and listening to the locos accelerating out of stations or doing running around movements at about 15mph, and trying to match the exhuast chuffs, which will be slower the  larger the driving wheel diameter, to the wheel beats on the rail joints.

 

For non-steam locos, things are a bit more involved as you only have the wheel beats to indicate speed.  This approach relies on experience, and listening closely to real trains, videos of them, or webcams footage, in situations where you know or have a fair idea of the speeds. 

 

The other way to do it is to time your train over a known distance.  Let us say your train takes 20 seconds to travel 10 feet on your layout (time it from the moment one point, the obvious one being the leading buffer beam of the loco, passes the start mark to the moment that same point passes the finish mark).  Now, my maths are pretty hopeless, but I make this 6 inches per second,  6 inches in 4mm represents 76 (4mm to the foot is 1 76th scale) x 6 = 456 inches in real life.  38 feet travelled in real life per second.  There are 3,660 seconds in an hour, so the distance that would have been travelled by your 4mm train had it been a full size real train at that speed would be 139,080 feet, the calculator on my phone says.  If you divide that by the number of feet in a mile, 5,280, you get 26.3409091, let's say 26 mph near enough for jazz. 

 

Things are much easier in metric of course, but the principle is the same.  I'll continue with my chuff chuffs, adequate for assessing speeds on a smallish BLT where nothing is ever going to be doing much over about scale 40mph tops.

 

My view is that most modellers drive their trains far too fast, and acellerate or decellerate far too rapidly as well.  Jerky starts and brick wall stops destroy the illusion of reality, as real trains are heavy and have considerable inertia when they are stopped which translates into considerable momentum when they are moving.  This sort of dampens and smooths out any changes in speed, so good  model driving technique is to be as gentle as possible on the control knob, and slow down in good time for stopping; the added attraction of this is that it's what real drivers do.  I have seen many otherwise excellent exhibition layouts ruined by people driving trains as if they were cars.

 

I've also seen the opposite, every move carried out at a crawl, so that shunting a goods yard takes forever.  There are some movements on real railways that have to be carried out very slowly and with extreme caution, such as propelling wagons in to a goods shed; the driver cannot see what is happening inside the shed and there may be men unloading or loading vehicles, so any contact must be made gently.  Similarly, a loco backing on to a train with passengers boarding will do so with a degree of circumspection.  But everybody wants to finish job and go home, within the limits of safety, so most shunting takes place at about 15mph, as does most movement in loco shed yards.  Good drivers (and they are not all as good as they think they are) will take trouble to stop trains as smoothly as possible, and keep couplings on loose coupled freight trains taut while running, an very skilled job indeed to do properly.  We should emulate such practice as far as possible. 

 

We are aided by current RTR models that are built to very high standards and are capable, if carefully run in and their wheels and pickups are kept clean and in good order and the track is laid smoothly between adjoining pieces and as level as possible, of giving very good slow running and smooth stop/starts.

  • Like 2
Link to post
Share on other sites

  • RMweb Gold
11 hours ago, mikesndbs said:

Good morning.

 

An internet search produces many confusing offerings so I thought I'd ask the knowlagebile folk here.

 

I want to calculate the speed of my OO gauge trains over say 24 inches of track.

I get that speed= Speed = distance divided by time.

 

So if my train takes 10 seconds to travel 24 inches that would be 24/10 = 2.4  Which I think is real world speed? Lost after this.

 

Many thanks

 

Just use one of the online calculators, such as this one

 

https://www.modelbuildings.org/scale-speed-calculator/

 

Ans = 10.39 mph

 

I also have a .exe file that does the same things but I can't remember where I got it from.

Link to post
Share on other sites

Speed = distance / time

It is more accurate to measure the speed over the longest distance possible.

It is easiest to measure the speed in  the speed in mm/s & most of us will understand it in mph, so we need to do some conversions.

 

There are 1609000 mm in a mile (close enough). This needs to be a denominator.

There are 3600 seconds in a hour. This needs to be a numerator.

Measure the distance between the 2 places you are start & stopping your watch. If you always use the same points, then this can be a constant for your layout.

Measure the time it takes your train to pass between these 2 points.

We don't have this in scale, so we need to scale the speed up by 76 for OO. This needs to be a numerator.

 

(Distance * 3600 * scale) / (time * 1609000).

 

I wrote a short program in Python so I can run this on one of my Raspberry PIs, but that was as much of an exercise in programming than anything else. You could easily use Excel to do the calculations for you.

 

 

  • Like 1
Link to post
Share on other sites

Sorry, I could have gone further, you mentioned 24", which is 609.6mm

 

speed = (Distance * 3600 * scale) / (time * 1609000).

 

speed = (609.6 * 3600 * 76) / (time * 1609000)

 

speed =  (166786560 /1609000) / time

speed = 103.658 / time

 

24" is not very far though. If you can, use a bigger distance if possible. My measured distance is my scenic section, 6'5". If I start & stop my watch to an accuracy of 0.1s, then I can measure speeds to the nearest 2-3mph.

 

 

 

 

 

Link to post
Share on other sites

On my previous layout, I timed all my loco's over a scale 1/10th mile, which just happened to be from a barrow crossing to the end of a viaduct. Maximum speed was set, using DCC, according to the type of loco. Passenger loco's to between 50-60mph, mixed traffic at 40-50 and freight as low as 20.

Link to post
Share on other sites

One mile is 5280 ft.

 

We model at 4mm/1ft.

 

5280 time 4 gives you a scale mile in mm. (1 mph)

 

Divide that number by 60 will give you the distance per minute for 1mph in mm

 

Divide that number by 60 again will give you the distance per mm second for mph in mm.

 

Once you know what 1mph is in mm per second, just times that by what speed you want to get the distance per second, then time them over that distance.

 

1mph works out at 5.86mm per second.

Link to post
Share on other sites

There seems to be as many ways of doing this as members in the forum!

 

There must be a set formula taking the knowns of scale 1/76th distance and time in seconds.

 

LOL I am more confused than when I started. Easily done I guess

Link to post
Share on other sites

  • RMweb Gold

Distance/time = speed. That's it ;)

 

However...

 

As you'll be measuring in seconds you need to add a conversion to get hours:

 

Distance/time*3600 = speed per hour.

 

Since we are modelling at scale we probably want to adjust the distance accordingly. So it becomes:

 

scale factor * distance / time*3600.

 

For most of you that's 76*distance. For me as diminutive cousin it's 148*distance.

 

However for those people still using the imperial system (shakes head sadly) you then have the confusion of converting between multiple units (that whole inches/feet/yards/miles nonsense). In metric there is no need to do that. Metric only has one unit for length (as it has only one unit for everything) so all you have to do is choose an appropriate prefix. For trains speeds are generally described in 'thousands of metres per hour' or 'kmh'.

 

If you want that in mph the approximate conversion is to divide by 1.6 since there are approximately 1,600 metres in a mile.

Edited by AndrueC
Link to post
Share on other sites

Right, drawing on everything else I have worked out the following:

 

So, for 121.92cm (or 4 feet)  divide 207.2727 by time in seconds = MPH scaled. Phew! got there

 

(based upon

 

scale 0.013157894736842 1/76th as decimal.


30480cm (1000 feet)
(1000 real feet = 401.0526315789 cm scaled)

30480 X 0.013157894736842 = 401.0526315789 cm

401.0526315789 cm is scale 1000 feet or 30480cm)

Edited by mikesndbs
Link to post
Share on other sites

  • RMweb Premium
26 minutes ago, AndrueC said:

Distance/time = speed. That's it ;)

 

 

However for those people still using the imperial system (shakes head sadly) you then have the confusion of converting

As i said in my first post. But it does need scaling.

 

As to converting from metric to imperial. Why use metric in the first place?

Pirouet's convoluted post shows why that is not a good idea.

00 is for British models. British models run on track measured in inches, speed is in mph.

Stick to imperial

 

BTW I use metric for everything else and have done for decades.

Link to post
Share on other sites

  • RMweb Premium
5 minutes ago, mikesndbs said:

Right, drawing on everything else I have worked out the following:

 

So, for 121.92cm (or 4 feet)  divide 207.2727 by time in seconds = MPH scaled. Phew! got there

 

(based upon

 

scale 0.013157894736842 1/76th as decimal.


30480cm (1000 feet)
(1000 real feet = 401.0526315789 cm scaled)

30480 X 0.013157894736842 = 401.0526315789 cm

401.0526315789 cm is scale 1000 feet or 30480cm)

No No No.

Stick to imperial

Link to post
Share on other sites

Ok, how about this for imperial.

 

5280 ft (1 mile) times 12 (reduced to inches)

 

Divide by 76.2

 

Then divide by 60

 

Then divide by 60

 

That would give you inches per second for 1mph

 

Roughly 1mph is one quarter of a inch per second.

Edited by cheesysmith
Stupid tablet spell checker
  • Like 1
  • Informative/Useful 1
Link to post
Share on other sites

  • RMweb Premium
1 minute ago, mikesndbs said:

 

lol you can, just convert back so 121.92 cm = 4 feet

?

That's not sticking to imperial.

"00" track is made in inch lengths e.g. 36" or Yard lengths.

 

The fact that the scale is a hybrid 4mm/ft is irrelevant, just use a factor of 76 and do it all in yards or feet

e.g. 60mph is a mile a minute 1760yards in 60 seconds or 88ft per second. work from there.

  • Agree 1
Link to post
Share on other sites

The time compression is an interesting feature. My unfinished layout is meant to represent an imaginary Birmingham Terminus to Wolverhampton to an imaginary Telford Terminus, a distance of say 50 km. This is represented by 21M of track. Allow for scale and this 21M becomes 1.6 km, so the real world distance is still 31x the modelled distance. So if a real world express in 1960 completed the journey with the intermediate stop in an hour, my model train would have to do it in 60/31.25 minutes, or 1 minute 54 seconds. Non stop at constant speed that is 10.94 metres per minute. The time to pass a 91.25cm piece of flexi would be 2.6 seconds.

 

This data is appropriate to my layout and its correspondence to the real world. At its most basic level the time compression of 1 min 54s per hour applies to my scale distances only, and massive corrections would be needed to allow for typical start/stop and acceleration/deceleration phases. For a layout with no such distance references there is no way to calculate these values, although many exhibition layouts are carefully scaled and would be able to do so.

 

A further feature of my layout is that it contains a continuous loop so I can pass trains through Wolverhampton any number of times on their way to their destinations, should I wish to do so. This is either an imaginary rescaling of the inter terminus distance or extending the journey to a time comparable to the real world. While for an observer in the intermediate station, they would have to be subjected to a Groundhog Day process so that they observed the train pass only once.

 

In the very distant future I may be able to use this analysis to specify the correct loco speeds – I am hoping to run at least partly in automatic mode.

Link to post
Share on other sites

44 minutes ago, RobinofLoxley said:

The time compression is an interesting feature.

 

That is the reason why some people operate fast clocks.  Time cannot be scaled: one second in our model is the same as one second in the prototype.  It doesn't scale the way linear dimensions do.  When people start talking about 'scale time', it's usually obvious that they don't know what they are talking about.  If using a fast clock, the speed of the clock has nothing to do with the scale of the model.

 

To calculate the scale speed, do as others have said: speed = distance / time, adjusted for the fact that linear distance is scaled at 1:76.2 or whatever, and the measured distances and times are often not in the desired units and need to be converted (millimetres, inches or feet to kilometres or miles and seconds to hours).  The calculation of scale speed is obviously more accurate if measured over a longer distance.

 

However, as you've pointed out, the running length of your layout has been compressed, which in your case is by a factor of 31.  That therefore means that once you've got your trains running at a 'scale speed', you'd need to speed up time by a factor of 31, so that your train has a correct departure and arrival time.  Of course the problem with speeding up time in proportion to linear compression in the model (as opposed to the nonsense of 'scale time') is that our models are not compressed uniformly.  We tend to model the more interesting / important parts like the station platforms much closer to scale than the open countryside between stations. 

 

Therefore, as a train is pulling out of your near to scale length platform, the speed at which a fast clock should run should be only slightly faster than reality, but the model clock should then get faster and faster as the compression in your model becomes more obvious and would then have to start slowing down again as your train approaches it's destination because of less linear compression at the destination station. 

 

If you only had one train running on the layout, and could determine where your model was closest to scale and where it was most compressed, you could, in theory, devise a formula to determine how fast the model clock should be running at any point in time, but as soon as you progress to a layout with multiple trains, that becomes impossible, because the clock should be running 40 times faster than reality for your Birmingham to Telford express when it's in open countryside, but should be running just 50% faster than reality for the shunter that's marshalling stock in the nearer to scale station.  That's why I prefer operating trains to a schedule, rather than operating to a timetable.

Edited by Dungrange
  • Like 2
Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...