Fascinating post, Jeff. I especially like your th...

2008-10-22T06:57:00.000-07:00

Fascinating post, Jeff. I especially like your thoughts about how we are happy with scaled lengths but not scaled durations.

I guess it makes sense from an evolutionary perspective. We're used to scaled lengths just because we often see the same thing from different distances. But we didn't evolve in an environment where traveling at relativistic speeds was routine, so we're not used to seeing the same events take different subjective durations.

I can't comment on your post, only because I was l...

2008-10-17T03:42:00.000-07:00

I can't comment on your post, only because I was lost after the second sentence! I wanted to thank you for the comment on my blog and for the suggestion to add the link to the white pigment.

Jeff,

We're not trying to be physicists (or...

2008-07-16T17:57:00.000-07:00

Jeff,

We're not trying to be physicists (or spellers), just model railroaders. We are simple minded enough to go with RATE x TIME = DISTANCE all over 87.1.

Thanks for chuckle, Steve (wesolint)

Ross: That's a wonderfully written assessment that...

2008-07-16T10:27:00.000-07:00

Ross: That's a wonderfully written assessment that comes to (mostly) the exact same conclusions I did, except written in a more intuitive,and less mathematical way. (Something tells me I should re-write my blog article to follow some of your lead!) :)

Indeed, this morning I was thinking about the conclusion that should really be drawn from all this, now that I've had time to see other people's thoughts on the matter, and I think I came to two things:

1. Modelers should understand that there is not one way to scale speed and/or time, but instead many different ways to do it based on the requirements at hand.

2. A modeler should understand why they use the model that they do, and what the problems are.

I plan on supplementing and/or re-writing my blog entry to reflect these conclusions.

It also dawned on me why, exactly, the standard transformation is used. I had the right idea before with it "feeling" right, but I think I understand more scientifically now.

It is rooted in an interesting asymmetry in the way our brain works. We are able to perceive symbols. For example, a map. It is a symbolic miniature representation of a real place. Our brain has no problem with that. But with time, we are not. Conceiving time running at a different rate is something that our brain is not wired to do.

So when we are in our basements with our model trains, we have no trouble perceiving that the distance is, in an abstract sense, a symbolic representation of the real, bigger space. However our perception of time (and hence speed) is not so flexible, and results in us needing to not scale time in any way in order to make things feel correct to your brain.

There are a ton of things that don't work in any s...

2008-07-16T03:04:00.000-07:00

There are a ton of things that don't work in any scaled model. The only things we can truly count on is the scale size and nothing more at least not on this world (I will go on into details later). I have been asked many times why real trains derail when going to fast around a corner of 4-8 degrees curve in the real world when in models they can sail around a 20 - 40 degree or more curve traveling at 5 times the speed. The answer you'll find in all the problems in the scaled world is our planets gravity (g). For everything to work like it should you would have to have a scaled world to build it on. Also if someone could also figure out how to manipulate gravity in an efficient way that could help too. We can't use scaled time because we live on a planet that has too much mass. If you scale built a HO planet you would find it would rotate the same scaled distance in our time factor to equal the scaled (g) of our own planet. I believe time would be the same on both if everything was truly scaled down. The only time you would want to scale time is if gravity in our world were to take over, like when falling off the table. But still time shouldn't be messed with and at this point the only logical thing to do is scale (g). Astronauts do this all the time when doing their physicals before entering space. They do this by fling in a jet in a negative g maneuver. Following are some examples of problems and facts in an HO world.

About Weight and Length

If you have a SD40-2 @ 68 ft 10 in (21.0 m) over the coupler pulling faces when you scale it by a factor of 1/87th you will get a scaled size of 68 ft 10 in (21.0 m) over the coupler pulling faces. We also know that a mile is 5280ft, in the real world we can fit 76.7 SD40-2's all coupled up in both the HO and the real worlds mile. Now that we know these things match our real world 1:1 measurements we can move on and (g)& (t) never said a word of influence. When dealing with scaled speeds (g) is not a factor since we're just looking at how many feet we have traveled in the given time frame. We scaled the model down but we still live in the same big world, so time is a constant for us and the model due to our world's (g).

With (g) this measurement is constant in our scale 1:1 and the model scale being 1/87 with g = 9.8 m/s^2 you will find there is a weight problem. The problem here is if we measure this engine in scale weight on our planets (g) it would crush the rail it would sit on due to the fact it would now weigh not 368,000 lb (167,000 kg) but 3,201,600 lb (1,452,900 kg) scaled weight on our planet. With a scaled 110 lb or 130 lb rail it would crush it like it was a pop can. Now take that same engine and scale the planet it sits on to the same scaled (g), you would find the weight would be the same.

We have taken a model and built it on our planets mass and not on the scaled planets mass. Therefore to make this work we would have to scale (g) down to the scale we are modeling. Good luck with that one!

About pendulum clocks and time (The Tompion clocks at Greenwich)

Richard Towneley and with the help from John Flamsteed's, the pendulum clock was only to prove to their own satisfaction that the Earth rotated at a constant speed. They didn't create it for the time piece we use it for today. To scale a pendulum clock and make it work correctly to the specs of Towneley. It would only work if the (g) in the HO model world was 1/87th of our own planet's (g).

If you were to put that same clock 1:1 on a different planet you would get a very different time due to gravity and mass and the rotation of that planet telling us (g) drives this clock. You could however calibrate the clock by converting its pendulum length and mass to match that of the new planets (g) so it would track time the same as it did on earth. Scaling the pendulum clock here on earth on a layout doesn't work as the earth is way to big for it to function the same way, in fact it will run faster by a factor of 8.7 times or maybe more. You would have to put that clock on a planet that was 1/87th scaled in everyway to make it work and at that point time would equal our time.

So really (g) could be described as the motor for the clock. We made the object it is designed to propel a big and heavy one so that the motor runs it at the speed we need it to. We didn't change the power of the motor to make it work, we changed what it is driving. Now when we scaled the clock down but forgot to scale the motor that powers it down you will find this will makes the clock run way too fast. To scale one thing down you must do it for all the components. We don't leave the 3200HP prime mover EMD 16-645-E3 motor in the scaled model train, doing so would cause us some big problems.

Falling off the tracks and why (g) is so important

Take a jet, put it in a negative 8.7 of gravity spin on it. The model now would fall off the table at the same rate scaled speed feet per second as the prototype would if it were to fall off a cliff. You also would find it derails a lot easier like the prototype when going around a curve.

When the train is on the track it is as close to 1/87th (scale) as we can get it here on earth. No one can afford to build a layout in a manipulated-gravity room to make it truly correct.

In the real world when it leaves the track and it falls off the table you then transfer that 1/87th scale model while on the rails to our world and at a rate of g = 9.8 m/s^2 = 32.2 ft/s^2. This is not of the scaled (g) for the model, its our worlds (g) and speed. If someone had the time they could do the math and figure what (g) would be in a 1/87th scaled world. I'm going to guess it would be in the neighborhood of g = 1.25 m/s^2 but remember this is a guess and not fact.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the objects surface. With 9.8 m/s (32.2ft/s or 22 mph) for each second of its descent we cannot use this equation for our 1/87th world cause (g) is not scaled down.

If you decrease (g) to the scale you will find that all the math will then work out. With the correct scaled down (g) model trains derail just like the real ones do when they're going too fast around a curve. They fall at the same scaled speed even in our time. And last they weight the same without crushing the rail at where they sit. By converting gravity you will find it fixes every problem in a scaled world. With the scaling of (t) time you can compensate (g) and the rate of the train falling like in Back to the Future III. It will even prove that the time speed increase of the same will cause the train to derail going around a 4-8 degree curve if speeding. It does not and will not make a change in the weight of the locomotive and with that your pendulum clock is still running to fast. (t) doesn't solve the problem but (g) does.

They slowed the film back down to our time because it didn't look realistic and if I remember correctly they filmed the layout section on a angle so the train wouldn't travel a ridicules distance once it fell off the end of the tracks. By doing this the added (g) due to the fact they added (t). Once it was slowed down it looked great. Just like a bullet you have speed over time equals fall rate or Spd/t = fr. When your object is moving faster it tends to fly a bit longer making its falling out of the sky rate too slow for the distants it just traveled. This proves once again we see gravity took place and if they had filmed it in a jet with the right -g they wouldn't have had to speed up the train to make it look right.

I so need to get to bed, great topic though!

Comments on blog.PaplooTheLearned.net: Essay: Scale Railroading (Part 2: Time)

Fascinating post, Jeff. I especially like your th...

I can't comment on your post, only because I was l...

Jeff,We're not trying to be physicists (or...

Ross: That's a wonderfully written assessment that...

There are a ton of things that don't work in any s...

Jeff,

We're not trying to be physicists (or...