Error in a taped distance measured in n tape lengths, against a single EDM shot
The same 648 ft line measured two ways. Series propagation over seven tape settings against one EDM observation with a constant-plus-ppm specification, and what the comparison says about when taping is still adequate.
Recall· about 16 minutes by hand· 4 steps
Given
A line measures 648.55 ft horizontally.
Method A - taping. The line is taped with a 100 ft steel tape in six full tape lengths plus a partial length of 48.55 ft, so seven independent settings of the tape are made. Systematic effects (tape standardisation, temperature, tension, sag) have already been corrected. The residual random error of each setting - marking, plumbing and reading - is ±0.008 ft.
Method B - EDM. One observation with an instrument specified at ±(0.010 ft + 2 ppm), the constant and proportional parts to be combined in quadrature as the manufacturer intends.
The two methods are to be compared as they stand, one pass each.
Required
The standard error of the taped distance.
The standard error of the EDM observation.
The relative precision each method delivers, and how many tape settings the taped method could tolerate before it falls behind.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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