|Work in progress on recent Bring-and-Buy acquisitions. I've made|
the Spanish into a single composite, probably anachronistic
20-figure unit. The stove-pipe officer I have added is Minifigs;
the rest might be Hinchliffe, but I don't actually know.
Let me tell you about Kleiber's Law. It comes from the field of biology, and the observations made in the 1930s by one Max Kleiber. It states that the metabolism rate of most animals is proportional to the fourth root of the cube of their mass. Symbolically:
...where R is the animal's metabolic rate, and M is its mass. Now the thing about M3/4 is that the ratio M/M3/4 is the same as M3/4/√M.
Now, how does this relate to war games and rule set design? You will recall from way back (link) that I discussed the relationship between ground and time scale, that the latter was (i.e. should approximate) the square root of the former.
Ground scale = G = 1:3600
Time scale = T = √G = 1:60.
Then I found that the movement rates according to ground scale alone and according to time alone just would not work. Intuitively I came up with the notion that movement rates 'm' ought to be such that
G/m = m/T;
and, therefore, as it has transpired:
m = G3/4 = 1:√216,000~ 1:465.
|British Fusiliers. who might yet be elevated to Guards status.|
This is an 18-figure unit; further off you see a 16-figure unit that
includes10 'genuine' guards figures. Minifigs.
Quite how 'mass' and 'metabolic rate' fits with ground and time scales is a bit obscure - I have my doubts about it myself. But it does go towards scaling. It works.
Here is a 'thought experiment' I carried out whilst pondering this back in July. Imagine a small insect a half-millimeter in length (1:3600 my height in fact). You watch for one minute it walking across a flat surface. It would certainly travel farther than 1.2 inches (Sorry about mixing measuring scales, here, but I'm going for measures easiest to imagine. Can you imagine 2/100ths of an inch?). Will the little wight travel as far as as 6 ft though? I don't think so.
|Too lazy to strip the original paint job, I'm planning to keep|
as much of the original, but add the white belts,straps, wings and
flounders etc. The quick white dry brush identifies highlights
as a visual aid to me in touching up these guys.
Here was my problem. In an hour, a human being might walk, pretty briskly, 4 miles - 72 inches (6ft) at the 1:3600 scale. That is the length of my war games table. As my moves represent 1 hour, that's the length of the table in just one move. 'We can't be having with that,' quoth Granny Weatherwax.
Of course, the time scale I'm using is that 1 minute represents 1 hour. But in one minute, at 4mph, one will travel maybe 120 yards, which at my chosen ground scale is 1.2". Hardly what you'd call 'stepping out', eh? The answer had to lie somewhere in between. It was sheer intuition and no more that led me to the movement value m that satisfied the condition 3600/m = m/60, or, more specifically in inches:
72/m = m/1.2.
|They sure look rough, don't they? I admit this is a very |
experimental technique, but I'm hoping the final product
will pass muster.
The last equation gave us the ballpark figure for a standard move (numbers in inches):
72/m = m/1.2
72x1.2 = m^2
m = √86.4,
m ~ 9.3
|Russian howitzer and crew. I'm not sure how 'Russian' the|
piece is, but as the two guns that came with it were
definitely French, this is how they will go. Minifigs.
Of course, 9.3, approximate anyway, isn't a particularly tractable number to work with, but it is in the right ballpark. So, as a 'first pass' I rounded it to 10 inches. Now, some quick research indicated that a standard 'quick march' would take a foot soldier 100 yards (120x30-inch paces), which approximates to an 8-inch (7.75") move under my proposed scaling scheme. 'Double time' takes a soldier about 180 yards (180x36" paces). This would be as near to 14 inches as makes no never mind.
|French 8pr cannon and crew.|
At this point I am inclined to bring this 14-inch 'double time' down to a 12-inch (30mm) maximum, for march column along a road. Cross country, let us reduce it to 10-inch (25cm - our 'standard), to take into account the casual irregularities of the ground. Our 'column of manoeuvre', 'assault column', column of companies', or however it is to be styled, has an 8-inch move; line (single rank) is down to 6-inch. Back in July I formulated my movement rules as follow:
"Just to make things simple, and as 6km an hour is a pretty fast rate of travel, I'm inclined therefore to round things down, thus:
Infantry in march column: 25cm (10 inch) + 5cm (2 inch) on a roadway. The assumption here is that nearing the battlefield, the troops are probably moving 'at the double'. All other movement is geared around this benchmark.
Infantry in skirmish order: 25cm (10 inch) (I have some doubts about this provision)
Infantry in battlefield (or assault) column: 20cm (8 inch).
Infantry in line: 15cm (6 inch).
Infantry in square: 5cm (2 inch).
Light Cavalry in march column: 50cm (20 inch) + 10cm (4 inch) on a roadway.
Light Cavalry in battlefield column: 40cm (16 inch).
Light Cavalry in line: 30cm (12 inch)
Heavy Cavalry (includes 'heavy' Dragoons) in March Column: 40cm (16 inch)
Heavy Cavalry in battlefield column: 35cm (14 inch)"
Horse Artillery (3-4pr, 'light' 6pr) limbered: 35cm (14 inch)
Horse Artillery manhandled: 10cm (4 inch)
Foot Artillery ('heavy' 6pr, 8-9 pr, 5.5"-7" howitzers) limbered: 30cm (12 inch)
Foot Artillery manhandled: 5cm (2 inch)
Heavy Foot Artillery (12pr; 8" howitzer): 25cm (10 inch).
Heavy Foot Artillery may not be manhandled except to change front.
At the scale we are looking at, this might well be too much detail. In that case, the default rules for all artillery will be those for the 'Foot Artillery'.
Foot Routing: 30cm (12 inch) These guys aren't hanging around!
Light Horse Routing: 60cm (24 inch)
Heavy Horse Routing: 50cm (20 inch)
Heavy cavalry in line: 30cm (12 inch)