Speed, time and distance

Know two, find the third

The last of the navigator’s four questions from Lesson 1 is when will I arrive? To answer it you need three things: how far you have to go, how fast you are going, and how long that will take. In Lesson 5 you met the units: distances at sea are measured in nautical miles (written M), and speed in knots (kn). One knot is a speed of one nautical mile per hour.

So a yacht making 5 knots covers 5 miles in one hour, 10 miles in two hours, and 2½ miles in half an hour. Distance, speed and time are tied together by a single relationship:

Know any two of distance, speed and time, and you can always work out the third.

The navigator’s form: 60D = ST

Most legs at sea take a number of minutes rather than a neat number of hours, and the clock is read in hours and minutes. So navigators measure time in minutes. There are 60 minutes in an hour, so time in hours is the minutes divided by 60. Put that into D = S × T, multiply both sides by 60, and you get the form every navigator knows by heart:

Rearranged, it answers all three questions:

If you like a picture, draw a triangle with 60D in the top and S and T side by side in the bottom. Cover the one you want and what is left is the sum: cover D and you see S × T (so D = ST ÷ 60); cover T and you see 60D over S; cover S and you see 60D over T.

T = 60 × D ÷ S
  = 60 × 7.5 ÷ 5
  = 450 ÷ 5
  = 90 min

The decimal-hours trap

Calculators work in tens; clocks work in sixties. If you work in hours with D = S × T, your calculator gives answers like 1.5 h or 2.3 h — and the part after the decimal point is a fraction of an hour, not a number of minutes.

This is the main reason navigators prefer 60D = ST: the time comes out in minutes, so there are no decimal hours to convert. To turn a long time in minutes into hours and minutes, take off whole sixties: 142 min = 120 + 22 = 2 h 22 min.

Clock times and ETAs

At sea, times are written on the 24-hour clock as four figures with no colon: 0930 is half past nine in the morning, 1415 is a quarter past two in the afternoon and 2340 is twenty to midnight. That is how they go into the logbook (Module 2) and how they appear in tide tables (Module 4).

Your estimated time of arrival (ETA) is your departure time plus the time the passage will take. Add hours to hours and minutes to minutes; if the minutes reach 60 or more, carry one hour. After 2359 the clock goes round to 0000 and you are into the next day.

The six-minute rule

Six minutes is one tenth of an hour. So in six minutes a boat covers one tenth of her speed in miles: just move the decimal point one place to the left. At 6 kn that is 0.6 M; at 7.5 kn, 0.75 M; at 12 kn, 1.2 M.

Build other times from it. Twelve minutes is two lots of six, so double it; eighteen minutes, treble it. Thirty minutes is five lots — half the speed. It works backwards too: at 5 kn you cover 0.5 M every six minutes, so each mile takes 12 minutes.

This is the navigator’s sanity check. If the calculator says 2 miles at 5 knots takes 2 hours, the six-minute rule tells you at once it should be about 24 minutes — so a button was pressed wrongly.

Measuring your speed

Turn the formula round and you can find your speed from the chart. Plot two positions, note the time at each, measure the distance between them with dividers, and use S = 60 × D ÷ T.

The longer the interval, the better the answer: a small error in plotting either position matters much less over three miles than over half a mile.

Dividers and 60D = ST also tell you when to expect the next mark. From the Kerran Approach buoy to Mew Rock beacon is 2.9 M; at 6 kn that takes 29 minutes, so leaving the buoy at 1000 you would expect to pass the beacon at 1029.

Log speed and GPS speed

A yacht has two ways of measuring speed, and they answer different questions.

In still water the two agree. When a tidal stream is running, the whole body of water moves over the seabed and carries the boat with it. Make 5 kn through the water with a 1.5 kn stream directly behind you and the GPS shows 6.5 kn; turn round into the same stream and it shows 3.5 kn. Either way, the log still reads 5 kn.

A speed worked out from two positions on the chart is also speed over the ground, like GPS. Tides are covered in Module 4 and allowing for them in Module 5; until then, the examples in this course assume no tidal stream, so log speed and speed over the ground are the same.

Rounding sensibly

• Distance to a tenth of a mile — 2.9 M, not 2.8947 M. That is about as well as dividers can measure.
• Time to the nearest whole minute.
• Speed to a tenth of a knot.
• Keep the full figures in the calculator and round only the final answer.