Calculating the scale speed of OO gauge models

[Dungrange]

7 minutes ago, Nearholmer said:

Is it that our brains are capable of monitoring the near-imperceptible vertical, rather than horizontal, movements, and spotting that the rates of acceleration within them don't match gravity?

 

Probably.  I guess there is also the issue of things like air resistance.  In a vacuum, two items will fall at the same rate.  The problem is that we don't live in a vacuum, so although a hammer and a feather were observed to fall at the same rate on the moon, we don't see that in every day life on Earth.  You can therefore undertake a calculation as to how much you want to slow your film down by to correct for something like gravity, but any adjustment is never going to be wholly accurate for all properties.

 

@meil and I may disagree on the relevance of gravity to the calculation of a 'scale speed' for a model train on a horizontal track, but he is definitely correct when he says: 

 

On 20/04/2021 at 15:05, meil said:

the dynamics would be all to cock.

 

There are loads of things that don't scale correctly: inertia, momentum, drag, engineering tolerances, etc.  Therefore, I don't think it would ever be possible to film a model and not have something that makes it appear not quite like the prototype.

 

However, I don't think that changes the fact that you can calculate a scale speed in the horizontal plane along the line of our track and run our trains at that scale speed.

 

27 minutes ago, Nearholmer said:

I've been watching with fascination as the simple answer to a simple question has expanded into complex answers to complex questions - all very interesting.

 

That is the joys of RMWeb!!

 

 

[Dungrange]

4 minutes ago, Hroth said:

Its the snide "the calculation is a simple one" that amuses me.

 

I agree.  To be a simple calculation, surely there would need to be an integer number of telegraph poles in a mile: not 29.33 telegraph poles per mile. 

[Reorte]

25 minutes ago, Hroth said:

 

Its the snide "the calculation is a simple one" that amuses me.

 

Some aspects help - one yard a second is very close to 2 mph, so a telegraph pole every 2 seconds would be 60 mph. So it's then down to how good you are at doing a single division mentally - the sort of thing that might be simple for Holmes but isn't for the likes of me who's been using calculators and computers for those sorts of numbers for a long time!

Edited April 21, 2021 by Reorte

[Nearholmer]

The trad method was to count wheel-beats on jointed 60ft rail lengths over a minute. IIRC, 88 equates to 60mph, and I’ve certainly forgotten the rest, although 45mph (66bpm), 30mph (44bpm) etc are easy by proportion.

 

 

Edited April 21, 2021 by Nearholmer

[TheSignalEngineer]

1 hour ago, Reorte said:

Some aspects help - one yard a second is very close to 2 mph, so a telegraph pole every 2 seconds would be 60 mph. So it's then down to how good you are at doing a single division mentally - the sort of thing that might be simple for Holmes but isn't for the likes of me who's been using calculators and computers for those sorts of numbers for a long time!

And of course pole spacings weren't all the same. They could vary due to such factors as the weight of the route, positions of bridges, stations etc. Quarter mileposts are easy. 10 seconds = 90 mph.

14 minutes ago, Nearholmer said:

The trad method was to count wheel-beats on jointed 60ft rail lengths over a minute. IIRC, 88 equates to 60mph, and I’ve certainly forgotten the rest, although 45mph (66bpm), 30mph (44bpm) etc are easy by proportion.

 

 

Even easier, if you count the beats in 41 seconds that is the speed in mph on 60' jointed track to 99.78% accuracy.

[Nearholmer]

The obvious answer to the OP’s query then, is to saw all the track on his layout into scale 60ft lengths, buy a watch with a sweep hand, and count wheel beats.

 

Easy really.

[AndrueC]

2 hours ago, Reorte said:

Some aspects help - one yard a second is very close to 2 mph, so a telegraph pole every 2 seconds would be 60 mph. So it's then down to how good you are at doing a single division mentally - the sort of thing that might be simple for Holmes but isn't for the likes of me who's been using calculators and computers for those sorts of numbers for a long time!

Conversely 1 metre per second is 3,600 metres per hour or 3.6 kmh. The answer is in the question: 1 m/s = 3,600m/h = 3.6kmh. It's not even wrong to say that 1 metre per second is 3,600 metres per hour. It is. It's only convention that suggests replacing 'one thousand' with 'k' is better.

 

New York is approx 6,000km from London. It's also approx 6Mm from London. Or 6,000,000m from London. Whatever floats yer boat.

 

If we know that telegraph poles are 55 metres apart then:

 

55/2*3600 = 99kmh. Jobs a good 'un. Doesn't require much mathematical ability.

 

But if you insist:

 

99/1.6 = 61.875 mph 

 

Familiarity counts for a lot but when you look at it from the perspective of global trade and mathematics metric seems to be the better answer. It would of course be better if we could all do arithmetic in our heads and were good at fractions but that's not how modern education leaves us. The metric system makes most things simpler and for sure having one globally agreed set of measurements has to be best.

 

It saves a tonne of bother and avoids a litre of tears

Edited April 21, 2021 by AndrueC

[Reorte]

1 hour ago, AndrueC said:

Familiarity counts for a lot but when you look at it from the perspective of global trade and mathematics metric seems to be the better answer. It would of course be better if we could all do arithmetic in our heads and were good at fractions but that's not how modern education leaves us. The metric system makes most things simpler and for sure having one globally agreed set of measurements has to be best.

 

It saves a tonne of bother and avoids a litre of tears

Oh gawd, not the metric debate again, which wasn't anything to do with the Sherlock Holmes example (yeah, it would if they were convenient fractions of a kilometer, but the same's true if they were convenient fractions of a mile, like the quarter mile posts are, no difference really).

 

As for "simpler", it would be if we all had the same everything and all individuality was destroyed, but once things do the job well enough I'm satisfied and generally find "improvement" just make the world a less interesting place for what are really generally quite trivial gains masquerading as "so much more convenient" (a phrase I've come to loathe).

Edited April 21, 2021 by Reorte

[Il Grifone]

20 hours ago, Nearholmer said:

The trad method was to count wheel-beats on jointed 60ft rail lengths over a minute. IIRC, 88 equates to 60mph, and I’ve certainly forgotten the rest, although 45mph (66bpm), 30mph (44bpm) etc are easy by proportion.

 

 

 

In the time of Sherlock Holmes rails were shorter than 60ft. Sixty yards in 4mm scale would be just under 2' 6". I suspect we place our telegraph poles at about a foot apart  (I do anyway - it looks about right to me, even if it isn't).

[JN]

On 21/04/2021 at 16:37, Hroth said:

 

Its the snide "the calculation is a simple one" that amuses me.

 

 

When poles are sixty feet/yards/chains/miles apart you can count the number passed in one minute aka 60 seconds.

 

The same ratio applies to any other number. For example, the number of forty-five foot rail joints in 45 seconds.

 

The .5 probably comes from averaging two or more measures or the average number from two or more minutes or possibly somehow knew that when one minute had passed Sherlock Holmes knew he was halfway between two telegraph poles.

[JN]

Tip(s) for anyone else calculating speed on an OO-gauge layout. For other gauges simply convert measurements to the appropriate scale.

 

o calculate distance, speed or time:

Distance = speed x time.

Speed = Distance/time.

Time = Distance/speed.

 

1 mile = 80 chains

1 chain = 22 yards

1 yard = 3 ft. Ad nauseam.

 

My Dad says 1 circuit of his symmetrical (no reverse curves etc) 6x4 layout is 5/8 of a mile, 50/80 chains, 1100/1760 yards. Which is also 1km.

12x8 = 10/8 of a mile (mile and 20 chains, a mile and a quarter).

18x12 = 15/8 of a mile or 1m and 70 chains. Ad nauseam.

 

Calculating speed on my dad’s layout:

(Time of circuit in seconds) x 8 = _ / 5 = _ mph

30 secs x 8 = 240/5 = 48mph or too fast for a vacuum fitted departmental train.

 

However, on a fiddle yard layout (or non symmetrical/with reverse curves etc). Scaling down:

23 pieces (and a bit more) of Peco flex track = 1 mile in OO gauge.

1 mile = 1760 yards (22y x 80ch) = 1760y. 1760 / 76.2 = 23y. One piece of Peco flex track = One yard.

To be exact: 1760/76.2 = 23.097112860892388.

 

60 mph = 1 mile in one minute

60 mph = 23.097112860892388 pieces of Peco flex track in one minute.

 

Scaling up;

One whole  Peco flex track = 1y (x76.2)  = 76.2y = 3.46ch (2dp) = 0.04325 mile (3.46ch/80).

 

60 mph = 1 mile in one minute. 60mph = 1 Peco flex track in 0.04325 seconds, two in 0.0865 seconds. Ad nauseam.

30 mph = 1 mile in two minutes, so double the seconds for the same length of track.

57 mph = (60 / 60) x 57. Ad nauseam.

 

To do this in metric is the same: 1000m / 76.2 = 13.12m (2dp). Best converting m(s) to km(s) rather than m(s) into mm(s). To convert km from miles:

(miles x 5) / 8.

Miles from km:

(km / 5) x 8.

 

From a WTT I have noticed trains seem to be scheduled to run about 0.75 of maximum permissible line or train speed (whichever is the lower). A train timetabled to run at 7.5mph could run quicker (or slower), so long as the driver followed the usual or periodic regulations.

 

As ever, model railways are more art than science unless you have the space for a scaled down prototype copy.

 

To add a bit of realism into your pool of locos, perhaps use the best performer for each class to measure and use that standard (using a piece of acetate or paper to overlay on your non-dcc controller) for the rest of the class. Not all locos ran the same and each manufacturer may gear the model differently. Art rather than science. DCC users can just programme in a speed through a programme which seems more of chore than having fun with the imagination. My Dad also draws back on the regulator I mean analogue controller when simulating going up a gradient.

 

The person who suggested elephants and dairy milk bars is correct: distance/speed/time is more about ratios and tolerances of compromise between model and railway.

 

For people wanting the clickety-clack from 60ft rail, one 60ft rail piece is 240mm or 24cm.

 

Imperial or metric? I prefer cubits. However, I think of distance in terms of time. How far away is London? Two, two and half or seven hours (depending on the mode of transport) and/or cost rather than London is x miles/kms etc.

[The Johnster]

I use (for steam engines, I only have steam engines, and all are GW or BR two-cylinder types, DC controlled) the 4 chuffs per revolution of the driving wheel rule, and make suitable chuffing noises (The Squeeze is fully conversant with my mental condition) or vacuum pump noises.  If these sound close enough to my memory of steam in service and preserved examples, then I reckon I'm somewhere in the region of ball-park accurate, whilst simultaneously accepting that 'somewhere in the region of ball-park' is exactly the description of inaccurate...  It helps that the overwhelming majority of my locos have the GW's standard 4'7" driving wheels, with only the large prairies and BR 3MT breaking the mould. 

 

Of course, my industrials have smaller driving wheels, but industrials generally chuffed a bit more quickly than big railway engines at the same speed, so that's ok.  I note that some layout operators at shows seem to run steam locos quite slowly, and I suspect that this is because they are of generations that only have experience of them on heritage lines where 25mph is the order of the day.  In daily service, steam could be pretty quick; a 56xx, for example, leaving Cardiff General with 5 Collett coaches heading for Queen Street would be up to the 35mph allowed over the bridge at the eastern end of the station well before the last coach had cleared the platform, well up to the standard of modern traction and a bit smarter than the 116s that dominated this route for nearly 40 years.  This is borne out by the section timings, largely unaltered since steam days.  The large prairies, with 5'8" driving wheels, were not exactly tardy either!

[DCB]

Almost all the speed measuring charts are for passengers riding on trains. so they time over a known distance while moving with the train.

I did a train speed chart some years ago.  It relies on timing a known length of train past a fixed point, which is dead easy if standing at the lineside.  Generally you can guestimate train length , so  I worked it out in units of 75 and 64ft coaches and short 9ft wheelbase Mineral wagons and 10ft wheelbase merchandise wagons   It works for any scale, 303mm/ft to half Z 

Like timing music start with zero as the front of the first vehicle passes your timing point and then one as the first passes,two etc
You can "scale" time by running slower with diesels and electrics without side rods,  but revolutions per minute of side rods are a fixed ratio. 

A speeded up clock can work for models as many prototypes had very sparse services. but it mainly serves to compress the time when nothing happens.  The bigger problem is when  trying to timetable trains when 12 actual feet equals 30 miles.    I wonder if a variable speed clock would be useful.  or do able, I have quite a large stock of dead clocks so I might have a play.  One which can be stopped and started, can be whizzed on an hour or two and maybe run at real time, or 2X or 3X maybe.

 

Edited May 24 by DCB

[Chimer]

Did anybody ever just answer the OP's question?  If D = distance travelled (in inches) and T = time taken (in seconds) then

 

S (speed in mph) = (D/63360)*(3600/T).

 

This is true for model railways (in any scale), real railways, motor cars, you, me and Usain Bolt!  Speed, like time, does not scale.

Edited May 26 by Chimer
Ooops!

[Dungrange]

28 minutes ago, Chimer said:

Speed, like time, does not scale.

 

I agree that time doesn't scale, but since speed = distance / time and we scale distance, speed does scale when talking about model railways.

[Chimer]

22 minutes ago, Dungrange said:

 

I agree that time doesn't scale, but since speed = distance / time and we scale distance, speed does scale when talking about model railways.

 

Yes, you're right of course - I realised I was talking twaddle but you beat me to the correction!  So multiply the actual speed (S above) by the scaling factor (76 for 00) for scale speed.

Edited May 26 by Chimer