Scale Speed Calculator
Scale speed on both conventions — divide by the scale, or by its square root — and why no running speed fixes a model clock.
The railroad figure is the one to set a throttle by. The film figure is the one to match a falling, swinging or splashing model against. Neither is a correction of the other — they answer different questions and the tool declines to pick. Nothing is uploaded.
Two defensible scale speeds, and they disagree badly
Divide by the scale and the model covers a scale mile in the time the real thing takes to cover a mile — the railroad convention. Divide by the square root of the scale and the model's dynamics match instead, because gravity was not scaled down with it. At 60 mph in HO those are 0.69 mph and 6.43 mph.
| Scale | Railroad | On the track | Film | Apart by |
|---|---|---|---|---|
| G (1:22.5) | 2.67 mph | 46.9 in/s | 12.65 mph | 4.74× |
| O (1:48) | 1.25 mph | 22.0 in/s | 8.66 mph | 6.93× |
| S (1:64) | 0.94 mph | 16.5 in/s | 7.50 mph | 8.00× |
| HO (1:87) | 0.69 mph | 12.1 in/s | 6.43 mph | 9.33× |
| TT (1:120) | 0.50 mph | 8.8 in/s | 5.48 mph | 10.95× |
| N (1:160) | 0.38 mph | 6.6 in/s | 4.74 mph | 12.65× |
| Z (1:220) | 0.27 mph | 4.8 in/s | 4.05 mph | 14.83× |
The gap is exactly the square root of the scale, so it is worst in the smallest scales — 14.8× in Z. There is no scale small enough for the choice not to matter: even in garden scale the two answers are 4.7× apart. S is the one worth memorising, because 1:64 has a whole number for a root and the two figures sit exactly 8× apart.
And no running speed fixes the clock
Gravity is the same on the layout as it is outside, so anything the model drops, swings or spills happens 9.3 times too fast in HO. That is a property of the model's size, not of how fast it is driven — which is why it cannot be tuned out with a throttle, and why miniature effects are filmed with the camera instead.
| Scale | Clock runs | A 2-second fall takes | Film at |
|---|---|---|---|
| G (1:22.5) | 4.74× fast | 0.42 s | 114 fps |
| O (1:48) | 6.93× fast | 0.29 s | 166 fps |
| S (1:64) | 8.00× fast | 0.25 s | 192 fps |
| HO (1:87) | 9.33× fast | 0.21 s | 224 fps |
| TT (1:120) | 10.95× fast | 0.18 s | 263 fps |
| N (1:160) | 12.65× fast | 0.16 s | 304 fps |
| Z (1:220) | 14.83× fast | 0.13 s | 356 fps |
Shoot at that frame rate, play back at 24, and model time stretches by the same root that compressed it. The figures assume 24 fps playback and treat the motion as governed by gravity alone — which is fair for a fall or a swing, and not for anything where air resistance, surface tension or a motor is doing the work. Water in particular does not scale at all.
How to use
- Enter the prototype speed in miles per hour.
- Enter the scale as the number after the colon.
- Read both conventions and the gap between them.
- Add a run of track for the crossing time.
Frequently asked questions
What is scale speed?
The prototype speed divided by the scale. At 1:87, sixty miles an hour is 0.69 miles an hour — slower than a walk, and yet about twelve inches of track every second, which is why it does not look slow.
Why is there a second answer?
Because gravity was not scaled down with the model. Matching the DYNAMICS rather than the distance means dividing by the square root of the scale instead, which at 1:87 gives 6.43 mph. Both answers are right about different things.
Which one should I use?
The railroad figure to set a throttle by, because it makes the model cover a scale mile in the time the real thing takes to cover a mile. The film figure to match a falling, swinging or rocking model against. The tool declines to pick for you.
How far apart are they?
Exactly the square root of the scale, so the gap grows as the scale shrinks: 9.3 times in HO, 12.6 in N, 14.8 in Z. Even in garden scale they are 4.7 times apart, so there is no scale where the choice does not matter.
Why does a model look wrong at the right speed?
Because its clock runs fast. Anything gravity governs happens about 9.3 times too quickly in HO — a two-second fall takes a fifth of a second. That is a property of the model size, not of how fast it is driven.
Can I fix that with the throttle?
No. The compression depends only on the scale, so it is identical at any running speed. Miniature effects fix it with the camera instead: shoot at the square root of the scale times the playback rate, which is 224 frames a second for HO at 24.
Does this work for water and smoke?
Not really. Froude scaling assumes gravity is doing the work, which is fair for a fall or a swing. Water has surface tension that does not scale, smoke has viscosity that does not scale, and both look like exactly what they are.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.