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dead reckoning

Abbreviated DR, it is the process of deducing a new position from a record of the course and distance sailed from a known position. If I am at buoy "Juliet" and sail due north for 3 miles and then turn and sail due west for 4 miles, then my "DR position" is then roughly northwest of "Juliet" and 5 miles from it.

Accurate DR is the key to successful navigation. It requires careful knowledge of your vessel and its performance, especially in varying conditions of current, leeway, and helming practices. It is also crucial to careful weather planning as we must always estimate by DR where we anticipate being at the time of the forecasted weather maps.

Accuracy evaluation and statistical errors in DR are covered in detail in the author's book on Emergency Navigation, because in an emergency without the aid of our accustomed instrumentation we are left with little but DR to go by.

As a practical guideline to the reliability of small craft ocean DR, it is safe to assume that with prudent log entries and calibrated instruments, your DR position will still grow uncertain by either some 7% of the distance run or by the drift of an error current equal to some 0.7 knots, whichever is larger.

If, for example, from a fixed position, you log 150 miles in 10 hours, you should consider that your DR position is uncertain by 11 miles (from 7% of log) since this is larger than the 7-mile uncertainty figured from a 0.7 knot error current acting for 10 hours. If the same 150-mile run took 30 hours, then the uncertainty estimate would be 21 miles based on the error current (0.7 knots x 30 hours), because this is now larger than the 11 miles figured as a percentage of logged miles.

These are only estimates of the errors that we propose you will find. Each navigator must do his own testing to see if 7% and 0.7 knots accounts for the DR-fix discrepancies they observe underway. The key point however is that there are two elements to consider, distance covered and time underway.

Some texts distinguish a final DR position obtained from log and compass only with an estimated position EP that they get by correcting this pure DR position for current, leeway or whatever else must be applied. We normally do not make this distinction in our teaching and generally consider a DR position as your best estimate of your position at the time, taking into account all you know about the navigation.

Our convention is in keeping with the golden age of sailing, where such a distinction was not made, and what we call here the DR is what was then called deduced position or "by account"... ie best estimate of where you are at the time, using all information at hand.

We might add that the often stated suggestion (including some of our own early writing!) that the "Dead" part of dead reckoning comes from the abbreviation "ded" (deduced) is not correct. The use of the term dead reckoning by English mariners predated the occasional appearance of the abbreviation ded. in 19th century logbooks by 200 years.

And we might add that our conclusions about typical DR error estimates (we first published in mid 80s') were based on our own experience at sea, but we have since ran across a historic comment on this topic by Lord Kelvin's "Lecture on Navigation" (Glasgow, Nov. 11, 1875):

"All things considered, a thoroughly skilled and careful navigator may reckon that, in the most favourable circumstances, he has a fair chance of being within five miles of his estimated place after a two hundred miles' run on dead reckoning; but with all his skill and with all his care, he may be twenty miles off it; and he will no more think of imperilling his ship and the lives committed to his charge on such an estimate, than a skilled rifleshot would think of staking a human life on his hitting a bull's-eye at five hundred yards."

Thus he claims 2.5% for most favorable conditions, but 10% as a real possibility and practical value. We agree with that, and stick with our summary above as a practical guideline. Note that we are proposing either/or on error current and log-compass errors, rather than summing these, which leads to our somewhat more conservative suggestion. Kelvin did not account for ocean current uncertainties in his estimates, but we know now these can be dominant factors.


Also this note on the two types of DR (ie compass and log alone, vs no distinction between DR and EP), we have this note from the Primer of Navigation by George Mixter in section 1201 of all editions.

"Many navigators correct the DR from time to time so it represents the navigator's best judgement of the ship's position, ie it is the estimated position. Under some circumstances this plan is best. In any case there is no rule that dictates either custom. The important point is to remember what the DR as you plot it represents."

See also Tricky Terms in Navigation.

Abbreviation:  DR

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