Calculating the scale speed of OO gauge models

[Pete the Elaner]

12 hours ago, melmerby said:

4.54 litres per gallon? Hardly moving the decimal point no easier than dividing by 2000 and knocking off 10% and yes I can do it mentally in probaly less than a minute.

Yes, that was the hardest bit. 4 x 4.5! The zeros came & went because I removed them for the calculation, added them back to get a figure in kilos then removed them again for a figure in tonnes.

You can do it in "probably less than a minute"? That would be about 59 seconds slower than me then!

 

I was brought up to work with both systems & Imperial is more awkward in 99% of situations.

[Colin_McLeod]

Just now, frobisher said:

 

Er nope. Time isn't the issue, gravity is...

 

The model is subject to full size gravity and full size time, because it is sitting on a baseboard which is sitting in a room in tbe full sized world.

 

If you make a pendulum 2 metres long and set it in motion in your living room you can observe the "tempo" of the oscillations.  Now make a 1:100 scale model of the pendulum, using the same materials and set it on your 1:100 scake model railway.  When you set that in motion you will observe a much faster "tempo".  This is because the real world gravity and the real world time, don't 'see' a 1:100 scale 2m pendulum; they "see' a 2cm pendulum and act on it accordingly.

[Reorte]

A lot of this is all very interesting but my idea of scale speed is - would a film of it look the same as a film of the real thing (realism of the modelling itself notwithstanding)?

 

The fact that to the laws of physics it's a small train rather than a scale model of a large one means things like moving water and smoke and loose coupled wagons don't behave in a scaled down way and it'll be hard (or impossible) to ever make them do so (you could probably power every individual wagon, individually computer-controlled but realistic scale smoke will need a holodeck), but when it comes to the train itself moving past the scenery does that matter?

[AndrueC]

Well that's what you get for poking the bear with a stick, lol. Hopefully I didn't offend anyone and it does us all good to get our hearts pumping with a lively but polite debate.

For my part I think driving and golf will remain imperial sadly. In theory changing golf sounds easy since there isn't much of a difference between a yard and a metre. Except that it's nearly 10% and that adds up fast enough that even with my amateur skills it will matter. There's a course near me that demonstrates that nicely. Rye Hill in Oxfordshire once hosted European Pro competitions so its distance markers are in metric (even though it's been a couple of decades since those heady days). I've known quite a few people come a cropper when assuming that 150 means yards.

What doesn't help is that several years ago they re-did the tee box information and used imperial values. So now you can tee off on 390yd hole, hit your ball 164 yards and find yourself alongside a 150 marker. That could lead to someone picking the wrong club and coming up 14 yards short of the green. I use a GPS so I avoid that problem at least.

Edited April 20, 2021 by AndrueC

[meil]

5 hours ago, Reorte said:

A lot of this is all very interesting but my idea of scale speed is - would a film of it look the same as a film of the real thing (realism of the modelling itself notwithstanding)?

 

No it wouldn't - the dynamics would be all to cock. That's why you need to run at about 8 times (1:76.2 scale) of what you think is scale speed and then show the film at 8 times less speed.

 

Think of the train falling from a bridge - do the sums and you will see the train hits the ground about 8 times faster than it should based on the naive definition of scale speed.

[meil]

7 hours ago, frobisher said:

 

Er nope. Time isn't the issue, gravity is...

And what is gravity? Length/time squared. So yes it is time that is the problem.

[Reorte]

10 minutes ago, meil said:

No it wouldn't - the dynamics would be all to cock. That's why you need to run at about 8 times (1:76.2 scale) of what you think is scale speed and then show the film at 8 times less speed.

 

Think of the train falling from a bridge - do the sums and you will see the train hits the ground about 8 times faster than it should based on the naive definition of scale speed.

But hopefully your trains aren't falling off bridges! Those dynamic effects aren't relevant in a model moving under control. It's true you'd have to do that if you were modelling something like hump shunting, but in most model railways the motion is fully under control, and it doesn't therefore matter than things like the momentum aren't in scale.

[Tom D]

This is a website I found interesting regarding speed calculations, hope it is of interest;

 

https://www.elginmodelrailwayclub.co.uk/2010/articles/advice/model-railway-scale-speed-calculator.html#:~:text=The speed limit under the Light Railways Act was just 25mph.

 

I use the Accutrack II speedometer, which has been really helpful in regard to speed matching;

 

 

[frobisher]

35 minutes ago, meil said:

And what is gravity? Length/time squared. So yes it is time that is the problem.

 

No, that's an acceleration, and those scale just fine.  However for each acceleration there is an acting force (F=ma or F=mg in the gravitational sense), and for that due to gravity you have the following equation...

 

F = GmM/r^2

 

Where G is the universal gravitational constant, m the mass of the smaller body, M is the mass of the Earth in our instance, and r is radius of the Earth.

 

Dividing through by m to get the acceleration due to gravity g...

 

g = GM/r^2

 

meaning in scale units, we see a gravitational acceleration (in 00) 76.2 times what it should be to simulate our 1:1 world.  Time (as we use it) is really not the problem, but that our 1:76.2 models exist in our 1:1 world with its constraints.

Edited April 20, 2021 by frobisher

[frobisher]

7 hours ago, Colin_McLeod said:

When you set that in motion you will observe a much faster "tempo".  This is because the real world gravity and the real world time, don't 'see' a 1:100 scale 2m pendulum; they "see' a 2cm pendulum and act on it accordingly.

 

Precisely, certain real world methods of measuring time (the gravity based ones certainly) don't scale, time itself remains unconcerned being itself unscalable outwith relativistic effects.

[ejstubbs]

On 19/04/2021 at 17:34, Pete the Elaner said:

16 oz in 1lb, 14lb in 1 stone. 160 stones in a ton to make 2240lbs?

Base 14? 

I am sure units of 14 & 160 have their history but they are simply poor to use.

 

Should that not be 8 stones in a hundredweight (so 112lbs) and 20 hundredweight in a ton?  So the bases go 16, 14, 8, 20.

 

In the Good Ol' U.S. of A. it's different again of course.  They don't have stones (take that how you will) and a hundredweight is defined as 100lbs - but there are still 20 of them in a ton, so a ton (a.k.a. "short ton") is 2,000lbs.  It's almost as if they were fumbling towards the idea of using base 10 throughout but couldn't quite get themselves the whole way there...

Edited April 20, 2021 by ejstubbs

[meil]

6 hours ago, frobisher said:

 

No, that's an acceleration, and those scale just fine.  However for each acceleration there is an acting force (F=ma or F=mg in the gravitational sense), and for that due to gravity you have the following equation...

 

F = GmM/r^2

 

Where G is the universal gravitational constant, m the mass of the smaller body, M is the mass of the Earth in our instance, and r is radius of the Earth.

 

Dividing through by m to get the acceleration due to gravity g...

 

g = GM/r^2

 

meaning in scale units, we see a gravitational acceleration (in 00) 76.2 times what it should be to simulate our 1:1 world.  Time (as we use it) is really not the problem, but that our 1:76.2 models exist in our 1:1 world with its constraints.

But the units of G (the gravitational constant) is m^3.kg^-1.sec^-2. So time is there like it or not.

[Dungrange]

1 hour ago, meil said:

But the units of G (the gravitational constant) is m^3.kg^-1.sec^-2. So time is there like it or not.

 

Yes, but time is not the issue in that equation - it's mass that's the issue (ie the kg part).  That's the reason why you can't have things like 'scale momentum' or 'scale inertia' (albeit you can try to simulate these electronically).  Our models have a different mass from the prototype, but it isn't scaled down the same way as a linear distance because we use different materials and even if we did use the same materials, the atomic structure of these materials wouldn't scale down, so the density of the material doesn't scale.  Any issue of dynamics, which involves mass won't scale properly, which includes gravitational forces.  If we wanted to be able to scale gravitational forces, then we'd need to operate our scale models on a scaled down earth (which of course we can't do).

 

The other issue is of course that our models interact with other real world things that aren't scaled, such as the atmosphere.  So therefore things like drag won't scale.

 

There is then the fact that engineering tolerances aren't scaled down either, albeit those modelling in P4 try to work to tolerances that are closer to a scaled down version of the prototype tolerances.  Things like the wear that occurs in bearings wont scale down either.  That therefore means that a model train will never truly operate like a scaled down version of the prototype that it represents.  

 

8 hours ago, meil said:

 That's why you need to run at about 8 times (1:76.2 scale) of what you think is scale speed and then show the film at 8 times less speed.

 

I don't understand your logic here.  If you drive a train eight times faster than 'scale speed' and film it, then show that film at one eighth of the speed it was recorded at, you'll see the model travel at 'scale speed', but all you've actually achieved is a higher frame rate for your film.  So for example, if you were filming with a frame rate of 24 frames per second, by running your train eight times too fast and then playing the film eight times slower, you'll increase your frame rate to 192 frames per second.  That will make the playback smoother, but it doesn't really change the observed speed and it's not really any use to those who just want to watch their models travel at a scale speed.

 

Perhaps we should actually be talking about scale velocity, since that's a vector quantity with both magnitude and direction and confirm that the scale velocity that we are trying to calculate is along the line of the track, which means that things like gravity or speed of falling to the floor when the train runs off the end of the layout become irrelevant. 

[Michael Hodgson]

Should you scale sound?  OO Locos chuffing away at 1:76 the wavelength .. or the freqency?  Is either in the audible range?

Or should a little plastic station announcer make his announcements as a high-pitched squeak, perhaps at 76 times times full size speed?  

The diddy-de-doing of coaches over rail joints - which should of course be correctly spaced.

And the volume should be in scale decibels - and how do you apply scale to a logarithmic measurement?

[Colin_McLeod]

8 hours ago, Dungrange said:

So for example, if you were filming with a frame rate of 24 frames per second, by running your train eight times too fast and then playing the film eight times slower, you'll increase your frame rate to 192 frames per second.

 

I think you may have that tbe wrong way round.  If I film something at 24 frames per second and play it back eight times slower, then I would be playing it back at three frames per second.

 

Though I agree with you that I can't understand the logic.  Why eight times? Why not ten times? Why do it at all?

 

If I film a model train (with perfect modelling including scenery etc) travelling at 30 scale miles per hour, then when I play it back it should look like a real train travelling at 30 mph.

[Reorte]

10 hours ago, Dungrange said:

I don't understand your logic here.  If you drive a train eight times faster than 'scale speed' and film it, then show that film at one eighth of the speed it was recorded at, you'll see the model travel at 'scale speed', but all you've actually achieved is a higher frame rate for your film.  So for example, if you were filming with a frame rate of 24 frames per second, by running your train eight times too fast and then playing the film eight times slower, you'll increase your frame rate to 192 frames per second.  That will make the playback smoother, but it doesn't really change the observed speed and it's not really any use to those who just want to watch their models travel at a scale speed.

 

If you slow a film down (by whatever the numbers work out to be) then, say, a wagon rolling down a gradient will appear to be accelerating at a more convincing speed (and the pendulum would swing slower, closer to how it would appear at full size). But to have your powered trains in the same scene appear to be going at the right speed in that film they'd need to be run faster.

[Il Grifone]

The observer in this case is in the real world, so the time involved is also real and not speeded up in any way.

Discussions of mass, weight, etc. would have to be recalculated for an Earth scaled down in size, with subatomic particles* also scaled down. I have no intention of going into the results of that!

 

I'll settle for a simple linear scaling of speed. The result looks right to me.

 

(The factory test for Hornby Dublo locomotives involved a maximum scale speed of about 100mph for the Express types. They look like they are going very fast at that speed, as one would expect. Tri-ang locomotives are under geared** and capable of about a scale 150mph which looks far too fast, again as one would expect.)

 

* There's a theory that there is only one electron (and presumably one each of the other particles?) that moves forward and back in time so that it appears as all the observed electrons. This would explain why all electrons have identical mass and charge. The maths is beyond me, so I'll leave it to those would understand these things. (I was lost around partial differential equations....)

 

** Off load specification for an X.04 motor is around 20,000 r.p.m and a ratio of only 20:1 gives the scalded cat syndrome!

 

I don't follow the reasoning for scaling factors having units. Metre/metre is meaningless as the terms cancel out.

 

 

Edited April 21, 2021 by Il Grifone

[meil]

3 hours ago, Colin_McLeod said:

 

I think you may have that tbe wrong way round.  If I film something at 24 frames per second and play it back eight times slower, then I would be playing it back at three frames per second.

 

Though I agree with you that I can't understand the logic.  Why eight times? Why not ten times? Why do it at all?

 

If I film a model train (with perfect modelling including scenery etc) travelling at 30 scale miles per hour, then when I play it back it should look like a real train travelling at 30 mph.

8 times? Because it is the square root of the scale. So for S scale (1:64) it is 8 and for 76.2 it is 8.7.

 

If you drop a ball from a cliff 98.1m high it will take 4.5sec to reach the ground. If you drop a ball from your S scale cliff (ie 1.55m high) it will take .55sec. 4.5/.55 ~8. So if you want to see your “scale” ball fall from your scale cliff in 4.5 sec then you shoot your film at 8 times the play back speed ie for 25 FPS play back you shoot at 200fps.

Edited April 21, 2021 by meil

[Dungrange]

2 hours ago, meil said:

If you drop a ball from a cliff 98.1m high it will take 4.5sec to reach the ground. If you drop a ball from your S scale cliff (ie 1.55m high) it will take .55sec. 4.5/.55 ~8. So if you want to see your “scale” ball fall from your scale cliff in 4.5 sec then you shoot your film at 8 times the play back speed ie for 25 FPS play back you shoot at 200fps.

 

Okay, I now understand what you are saying, but I try very hard not to drive my trains off a scale 80m cliff (ie the baseboard edge) and if I inadvertently did drive a locomotive off the end of the baseboard, I certainly don't want to film the 0.5 seconds that it takes to hit the ground (just so that I can slow the film down and watch it take eight times as long to hit the floor).

 

I still don't agree that you can't scale velocity and acceleration in a direction that is parallel with the rails.  The reason that you are changing the rate of the passage of time in the above calculation is not because of time itself, but because you haven't scaled the mass of the earth, which is what determines the gravitational constant - it's the same in the model and in real life.

 

However, if you were to build your scale model railway layout on the Moon, where the gravitational constant is less because the Moon is like a scaled down Earth, then when you drove your model locomotive off the end of your baseboard, it would hit the ground in a more similar time to what the prototype would on Earth.  However, I don't think the gravitational effects are relevant to the concept of 'scale speed' in the horizontal direction on a model railway, with the exception of the example below.

 

4 hours ago, Reorte said:

If you slow a film down (by whatever the numbers work out to be) then, say, a wagon rolling down a gradient will appear to be accelerating at a more convincing speed.

 

But to have your powered trains in the same scene appear to be going at the right speed in that film they'd need to be run faster.

 

The point here is how many of us undertake gravity shunting?  I'd see a model wagon rolling down a gradient as incompetent baseboard construction - it's not something that I'd be trying to model.  I want to uncouple a wagon and it shouldn't move - just like on the real 21st Century railway.  I therefore have no need to run powered trains faster to account for gravitational effects that I've tried to eliminate.

 

In a vertical sense, you are correct, simply because we have no control over the rate at which an object moves towards the centre of the Earth (because we can't scale the mass of the Earth).  However, in the horizontal direction (ie parallel to the rails), the rate at which a model accelerates is within our control: it's determined by how fast we turn the controller knob.  However, even that is a slightly different discussion to 'scale speed', as when talking about 'scale speed' we're usually referring to a constant speed, where the rate of acceleration is zero.

 

If you want to consider scale rates of acceleration and deceleration, I think most of us probably increase and decrease the speed of our trains too quickly, because we're not constrained by the dynamics of the prototype.  Our 2 Kg train just doesn't have the same momentum as the 500 tonne prototype we are trying to represent.

[Dungrange]

6 hours ago, Colin_McLeod said:

I think you may have that the wrong way round.  If I film something at 24 frames per second and play it back eight times slower, then I would be playing it back at three frames per second.

 

Though I agree with you that I can't understand the logic.  Why eight times? Why not ten times? Why do it at all?

 

Yes, you are correct, I have got that the wrong way around - you'd need to film at 192 frames per second to get a more watchable 24 frames per second when slowed down by a factor of eight.

 

As to the logic, I get it now, but don't think it's relevant.  We have no control over the rate at which an object accelerates towards Earth (model and prototype would fall at the same rate (ie not scaled)), but we have complete control over how our models accelerate along the line of the track (because it's based on how we turn the knob on the controller).  Since I only drive my trains on a horizontal baseboard and try not to drop them on the floor, I don't think the fact that you'd have to film the fall to the floor and slow it down to make it appear like a more realistic accident is particularly relevant.

[Nearholmer]

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.

 

Now, can I throw a subjective spanner in the works?

 

My observation is that if I run a model train at unrealistically high speed*, then use the "slo-mo" function on my phone camera to film it, thereby slowing down its apparent speed to something realistic, rather than looking realistic, it looks as if the whole scene is taking place inside a tank of very viscous, transparent fluid ........ any fool can spot that what they are looking at is slo-mo. The same seems true of many old films, where it is quite obvious from the motion when a slowed-down film of a model is being used.

 

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?

 

*Hard to do otherwise with most vintage clockwork trains.

[Dungrange]

15 hours ago, Michael Hodgson said:

Should you scale sound?  OO Locos chuffing away at 1:76 the wavelength .. or the freqency?  Is either in the audible range?

Or should a little plastic station announcer make his announcements as a high-pitched squeak, perhaps at 76 times times full size speed?  

The diddy-de-doing of coaches over rail joints - which should of course be correctly spaced.

And the volume should be in scale decibels - and how do you apply scale to a logarithmic measurement?

 

I guess the answer depends on who is listening.  Since I am a full scale person, then I'd say sound shouldn't be scaled.  However, if I was to have an unfortunate accident with a shrink ray and dropped onto a model railway, then the sound would have to be scaled if it were to sound authentic to my 1:76.2 scale ear.  Thankfully, I don't posses the technology to shrink myself to any model railway scale.

[Hroth]

Or, space your telegraph poles at a scale 60 yards.

 

Holmes and Watson are on a train going to Exeter. Holmes has been reading all the papers have to say about the disappearance of the horse, Silver Blaze. Apparently satisfied, he thrusts the papers under the seat and comments to Watson:

 

“We are going well,” said he, looking out of the window, and glancing at his watch. “Our rate at present is fifty-three and a half miles an hour.”

“I have not observed the quarter-mile posts,” said I.

“Nor have I. But the telegraph posts upon this line are sixty yards apart, and the calculation is a simple one.

from "Silver Blaze"

 

So there!

 

[Reorte]

16 minutes ago, Hroth said:

Or, space your telegraph poles at a scale 60 yards.

 

Holmes and Watson are on a train going to Exeter. Holmes has been reading all the papers have to say about the disappearance of the horse, Silver Blaze. Apparently satisfied, he thrusts the papers under the seat and comments to Watson:

 

“We are going well,” said he, looking out of the window, and glancing at his watch. “Our rate at present is fifty-three and a half miles an hour.”

“I have not observed the quarter-mile posts,” said I.

“Nor have I. But the telegraph posts upon this line are sixty yards apart, and the calculation is a simple one.

from "Silver Blaze"

 

So there!

 

Hmm, try that to keep the kids quiet? Should take them a nice long time to find a telegraph post on the modern railway

[Hroth]

1 minute ago, Reorte said:

Hmm, try that to keep the kids quiet? Should take them a nice long time to find a telegraph post on the modern railway

 

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