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Distance run, corrected for log error

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Log error: the corrected distance on a mile scale, an under-reading log corrected upwardThe log showed 268 nm for the day and under-reads by 3.5 %. The correction is 268 × 3.5 ÷ 100 = 9.38 nm, a share of the distance the log shows. An under-reading log is corrected upward: 268 + 9.38 = 277.4 nm. Subtracting instead gives 258.6 nm, the same distance the wrong way.ONE DAY'S RUN, TO SCALElog shows 268 nmcorrection = 3.5 % of the log's 268 nm = 9.38 nmmagnified below+ 9.38 nm3.5 % of 268− 9.38 nmwrong way255260265270275280285log 268277.4 nmdistance runnot 258.6Under-reading log: she ran further than it shows, so add.

The rule

  • Turn the percentage into miles: correction = log distance × error ÷ 100.
  • Say what the log did: it under-reads, so she went further than it says, and the correction is added. An over-reading log is the other way.
  • The correction is a percentage of the whole distance the log shows, so it grows with the day and is applied once to all of it.

Formula

  • Correction = log distance × error % ÷ 100
  • Corrected distance = log distance + correction (log under-reading)

Worked example

Distance shown by the log over the day268 nm
Log error from the last speed trial, under-reading3.5 %
The percentage the error is expressed against100 %
  1. Correction = 268 × 3.5 ÷ 100 = 9.38 nm
  2. The log under-reads: she went further than it shows, so add
  3. Corrected distance = 268 + 9.38 = 277.4 nm

Answer277.4 nm

Common mistake

Taking the correction off an under-reading log.

The log already showed too little; subtracting makes it worse, not better: 258.6 nm is twice the error away from the 277.4 nm she really ran.