Working with scales and numbers evolving from them can be confusing and a bother. In this article, I will eliminate some of the trouble by organizing pertinent information.
Knowing what the "Pictorial Ratio or Scale" is a good start. This will come to you via the industry in the form of a fraction or a ratio, such as 1/285 or 1:285, respectively. This is important information, as without it you would be unsure of what degree a life-sized representation has been reduced. You can find a "lost" pictorial ratio by using generic heights of a human being in millimeters. If you desire something more precise, however, I suggest you contact the manufacturer of the brand in question.
Some characteristics of scale differentiation that you should be directly aware:
- A. The higher the pictorial ratio/scale, the lower the brand
length, the higher the surface ratio.
B. The lower the pictorial ratio/scale, the higher the brand length, the lower the surface ratio.
As examples, 1/285 = 6mm with a surface ratio of 1 in. = 23.75 ft. and 1/108 = 16mm with a surface ratio of 1 in. = 9 ft.
OBTAINING SURFACE RATIOS
When converting lengths for distance relationships of sighting, weapons, and the such, and knowing both the "true" surface ratio and the "supplement" surface ratio, it's a good idea to know exactly how this is accomplished for better understanding. If I would like to check for these surface ratios, my math might look something like the following:
- 1:72 (1mm=72mm; 1mm=2.83 in.)
1mm(25.4mm) : 72mm(25.4mm)
1 in. = 1828.8mm/25.4mm
1 in. = 72 in./12
1 in. = 6 ft.
Therefore, the "true" surface ratio for the pictorial ratio/scale of 1:72 is for every inch of real measurement equals 6 feet of condension. You must, first , multiply both sides of the scale by 25.4mm, which is the number of millimeters in an inch. Since the inch is the standard measure in most rules in the U.S., converting to inches is a requirement. Then divide the new number of the right side by 25.4mm which gives you the number of inches. You will notice that the pictorial ratio's denomenator appears once again. This will give you a shortcut in your calculations. I'll discuss this later. Next, divide by 12 (number of inches to a foot) and your answer is 6 feet. For larger pictorial ratios/scales, this last figure could be numerous. Just, simply, divide by 3 (number of feet in a yard) to obtain the condensed number of yards.
When you become attuned and competent at these mathematical functions, you will deploy the shortcut method more often. This will look like something below:
- 1 in. = 72 in. / 12in/ft
1 in. = 6 feet
JUMPING SCALES
By exceeding or "jumping" your "true" surface ratio will create "supplement" surface ratio. Some rules use this method as a convenience to accomplish smaller table spaces, bigger games, and shorter ranges. To jump your "true" surface ratio of your chosen pictorial ratio/scale, you simply increase the condensed length of your "true" by whatever percentage. Say you what to increase your "true" by 300%. If your "true" surface ratio is 1 in. = 6 ft., an increase of 300% will produce a "supplement" surface ratio of 1 in. = 24 ft. which is equivalent to the pictorial ratio/scale of 1:288. You have to be careful as you increase your "true" as the new "supplement" surface ratio will become steadily distorted with the relationship of other components of the game and the rule sources.
To enable you to perform more efficiently with your calculations, I've put together a small table outlining some aspects of scale differentiation. Some examples will follow.
| Figure Size | Gauge Height (mm) | True Surf | Jump Ratio | Supp. Surf. | Notes |
|---|---|---|---|---|---|
| 6 | 285 | 23.75 | 100% | 47.5 | MicroArmor |
| 10 | 178 | 14.83 | 125% | 33.3 | - |
| 15 | 118 | 9.83 | 150% | 24.6 | Quality Castings |
| 16 | 108 | 9.00 | 175% | 24.75 | Quality Castings |
| 16 | 90 | 7.50 | 200% | 22.5 | - |
| 16 | HO 87 | 7.25 | 225% | 23.5 | - |
| 16 | HO 86 | 7.16 | 250% | 25.06 | - |
| 20 | OO 76 | 6.33 | 275% | 23.74 | Roskopf, Airfix |
| 72 | - | 6.00 | 300% | 24.00 | - |
| O | 48 | 4.00 | 325% | 17.00 | - |
| 35 | - | 2.91 | 350% | 13.09 | - |
| 54 | 32 | 2.66 | 375% | 12.63 | - |
| 2400 | - | 200 | 400% | 1000 | 66.66&333.33 yards |
| 3000 | - | 250 | 400% | 1250 | 83.33&416.66 yards |
Examples
An UK 25 pdr. artillery piece has a maximum range of 13,350 yards. To find the length in inches using 1/76 scaled miniatures, multiply 13350 by 3 which equals 40,050 in feet. The final math is: 40050/6.33 = 6327 inches, or 527.25 feet on the natural game surface.
To find the length of a Tiger I tank in 1:285 ratio, multiply its length in inches by the ratio's fraction. The final math looks like this: 272 inches (Tiger I's length) X .0035087 = .954 in. To find the length of a M4A3E8 Sherman tank in 1:108 pictorial ratio/scale, the final math is: 247 inches X .0092592 = 2.28 inches.
To find the range of a German AT gun, 50mm PAK 38, based on its "supplement" surface ratio, cross index the pictorial ratio/scale used with its "true" surface ratio and multiply by the appropriate percentage increase. The final math is: 14.83 (true) X 200% (jump) = 44.49 (supplement). 44.49 feet equals about 1:533 pictorial ratio/scale. The maximum range of a 50mm AT gun is 1090 yards or 3270 feet. 3270 / 44.49 =73 inches.
The following are additions to the previous text:
1. For OBTAINING SURFACE RATIOS: A "false" surface ratio is made by using random pictorial ratio/scales not otherwise standard manufacturer's classification or usage.
2. For JUMPING SCALES: Hyperbolic Coexistential Usage (HCU) may be an optional neologism identifying the usage of a "supplement" surface ratio that is informally related, or non-represented, in the context of rule source and game mechanical usage (e.g., a set of rules had been devised using a "supplement" surface ratio but did not formally announce this difference; a referee or moderator use a "supplement" surface ratio for a scenario and did not formally announce its difference or usage).
3. For TABLE I: 30mm 59 PR 4.9 ft. True Notes: Nuremberg sc.
4. For Ending: The "ronde bosse" was designed by Charles Stadden for a firm in 1953.
"Hyperpolemomorphics" (excessive + war (topic) + form) might be another neologism identifying the total range of historical warfare miniature renditions deployed by the Wargame Hobby market.
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