On the Reverse Engineering of Big Old Machines

Estimating Your Uncertainty

( An ad hoc Scale )

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In methods guided by (Popperian) science, we never know absolute truth. In the analog world of old machinery, we never know anything with either complete precision or complete accuracy. These are actually all (three) complex concepts with many intellectual dimensions. But to be practical, I need a simple scale for estimating the uncertainty of my measurements - something I can jot down on my notes to keep me honest.

I'll use a scale from 1 to 10, 1 being least certain and 10 being most certain (but not absolutely certain). I'll cite this in my notes as "UL1" to "UL10" (for Uncertainty Level). This scale is nonlinear.

This scale applies to machines generally on the scale of common machine tools (and, for me, typecasting machines) from benchtop sizes up to about 10,000 pounds / 4500 kilograms. It is not intended for very small machines (e.g., watch movements) or larger engineering projects such as dams (though it might work for things up to the size of 18th century stationary steam engine installations).

1. Hypothetical. Reconstructed in the absence of existing objects (example: reconstructing the machines of Hero of Alexandria).

2. From visual observation without measurements, from woodcuts or engravings, or from engineering drawings before about 1880.

3. From photographs. This may or may not include photogrammetric techniques to extract more or less precise measurements.

4. From physical machines which cannot be disassembled, using semiprecision measuring tools (steel rules, spring calipers, tape measures, etc.) Errors up to 1/8" or 3 mm to be expected (if greater, estimate them and record this).

5. From physical machines which can be partially disassembled, but which must generally be measured in place, using semiprecision measuring tools as in Level 4. Errors over 1/16" or 2 mm to be expected.

6. From physical machines which can be partially disassembled, but which must generally be measured in place, using common precision measuring tools (micrometers, vernier/digital calipers, fixed gauges, etc.) Generally errors less than 1/16" or 2 mm.

7. From physical machines which can be disassembled, measuring individual parts on the bench using common precision measuring tools as on Level 5 plus machines such as optical comparators as appropriate. Error levels approaching 0.001" or 0.01 mm.

8. Very good precision, very good accuracy measurements of physical machines. Near 0.001" or 0.01 mm error. Done with good quality measuring tools in favorable conditions (like Level 7, but you trust your work more).

9. High-precision, high-accuracy measurements of physical machines. >= 0.001" or 0.01 mm error. Done in controlled conditions, using high-end tools such as Coordinate Measuring Machines or (good) 3-D scanners

10. Surviving original engineering drawings from about the 1880s on, regardless of the survival of physical machines.

Note that there are inconsistencies within this scale. For example, originial engineering drawings for Uncertainty Level 10 need to be interpreted according to reconstructions of the manufacturing practices of their time, while high-precision, high-accuracy measurements of Level 9 may well come closer to existing objects. You could use Level 9 measurements to build a working replacement part - put it in the machine and go - but a part made to Level 10 specifications, from the original engineering drawings, might well require hand fitting.

At the higher levels of this scale (lower degrees of uncertainty) it is also a good idea numerically to estimate errors in your measurements and record them. This is especially important in UL6 through UL8, which use common precision measuring tools. Sometimes you're certain of the results of a vernier or digital caliper measurement to within 0.001", but sometimes you're so contorted trying to get the measurement inside the machine that you know it only to 0.1". Sometimes you're measuring a casting rib (say) which varies by more than 1/16 inch in thickness - maybe this matters and you should record it, maybe it doesn't and you can just supply one estimate of error. If you know the patternmaker must have made an error, do you correct it? This linear UL scale is intended to be a useful shorthand - easy to record - but it conceals the subtleties of real machines and their making.