4.8 Dead Reckoning: Speed-Time-Distance

Dead Reckoning Defined

Dead reckoning (DR) is the process of determining position by advancing from a known position using course, speed, and time—without yet applying current. The name’s history is debated; the skill is not. For a Master of vessels under 100 GRT on near-coastal routes, DR is how you stay oriented between fixes, brief the next turn point, and compute whether you will make the inlet before the tide turns.

On Q162 you will see formula and concept items. On Q163 Chart Plot you will draw the DR track as the backbone of every problem set.

The Master Formula: D = S × T

With consistent units:

Distance = Speed × Time

• Speed in knots (nautical miles per hour)
• Time in hours
• Distance in nautical miles (NM)

Unit conversions for time

Example 1. Speed 8 kn, distance 24 NM → time = D/S = 24/8 = 3 hours.
Example 2. Speed 12 kn, time 40 minutes (40/60 = 2/3 h) → distance = 12 × 2/3 = 8 NM.
Example 3. Distance 15 NM, time 1.5 h → speed = 15/1.5 = 10 kn.

These three rearrangements—D = S×T, S = D/T, T = D/S—are the entire arithmetic core. The exam dresses them in word problems about legs, ETAs, and fuel planning.

The 60-D-ST Triangle

Navigators often remember the relationship with the 60-D-ST (or D-ST) triangle used with a nautical slide-rule style layout or mental proportion:

• Place 60 as the time base for “minutes vs hours” thinking: in 60 minutes, distance run equals speed in knots.
• Distance relates to Speed and Time so that any one unknown is found from the other two.

Practical minute form many mariners use:

Distance (NM) = Speed (kn) × Time (min) / 60

Example 4. 9 kn for 20 min → D = 9 × 20 / 60 = 3.0 NM.
Example 5. How long to cover 6 NM at 8 kn? T_min = D × 60 / S = 6 × 60 / 8 = 45 minutes.

On the TI-30XIIS (REC-approved calculator family), keep parentheses clean: (6*60)/8 not fragmented steps that drop a zero.

ETA — Estimated Time of Arrival

ETA is clock time of arrival based on remaining distance and planned speed (and later, current).

Example 6. At 1300 you have 18 NM to the sea buoy. Speed 9 kn. Time needed = 18/9 = 2.0 h → ETA 1500 (if no current and track is straight).

Example 7. Same 18 NM but you slow to 6 kn for fog. Time = 18/6 = 3 h → ETA 1600. Update the log and any passenger schedule promises—Master responsibility includes not advertising impossible arrivals.

When the route has multiple legs, compute time per leg and sum. Do not average speeds carelessly across unequal distances.

DR Track vs Estimated Position (EP)

Plotting convention (standard teaching):

• DR labeled with time, often a semicircle or labeled point on the course line.
• EP labeled distinctly when current is applied.
• Fix labeled with full time and often a circle or standard fix symbol.

Never call a pure DR a “fix.” Exam writers punish that vocabulary swap.

When to Plot DR

Professional practice—and exam expectation—is to update DR at least:

1. Every course change
2. Every speed change
3. Every fix (restart DR from the fix)
4. At regular intervals on a long steady leg (e.g., each hour) so the plot does not go stale

Example 8 — multi-leg DR.

• 1000 fix at Point A. Steer 090°T at 10 kn for 1 hour → 1100 DR is 10 NM east of A.
• At 1100 alter to 180°T at 10 kn. At 1130, DR is 5 NM south of the 1100 DR.
  Always measure from the last DR or fix, not from a mental average.

Leeway

Leeway is the sideways drift of the vessel through the water caused primarily by wind acting on hull and superstructure (and for sail, by sail force). The vessel’s path through the water is downwind of the heading by the leeway angle.

• Leeway ≠ current set. Current is water motion over ground; leeway is vessel motion relative to the water due to wind.
• Small passenger vessels with high cabins can take noticeable leeway in a beam wind.
• On exams, if leeway is given (e.g., “3° leeway”), apply it to heading to get course through the water before building the DR track.

Example 9. Heading 000°T, wind from port causing 5° leeway (path pushed to starboard) → course through water approximately 005°T (direction of leeway depends on wind side—read the problem carefully).

Near-Coastal Master 100 Context

Your typical operating picture:

• Short coastal legs between inlets, islands, and sea buoys
• Frequent course changes near ATON and traffic
• Need for ETA discipline for passengers, connecting tours, and daylight/tide windows
• GPS available but DR retained as integrity check and exam skill

If GPS fails in rain squalls, the DR you have been maintaining from the last visual fix is your bridge back to the next buoy. If you never plotted DR, you are guessing.

Formula practice block (exam reps)

Set and drift teaser (full treatment in Chart Plot / currents)

DR ignores current. Set is the direction toward which the current flows; drift is current speed in knots. Applying set/drift to DR yields course and speed over ground and an EP. Do not mix “steer 090°” with “made good 100°” without a current triangle—that skill is expanded in the chart-plotting chapter, but the vocabulary starts here: DR first, current second, fix whenever possible.

Common exam traps

• Using statute miles or mph when the problem is in nautical units
• Forgetting to convert minutes to hours (using 30 min as 30 h is rare; using 30 min as 0.3 h instead of 0.5 is common)
• Calling a DR position a fix
• Failing to restart DR after a plotted fix
• Ignoring a stated speed change mid-leg

Bridge resource habit

On a two-person watch, one officer plots DR while the other handles traffic and ATON. On a single-handed small passenger vessel, you still need a mental DR refreshed at every turn: “Last fix abeam the outer marker at 1400, 8 kn, heading 350—should be 4 miles out at 1430.” That sentence is dead reckoning. Master it on paper so it is trustworthy under stress.

Dead reckoning will not replace a good fix, but without DR you cannot even know when your fix is late or your ETA is fiction.