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Steady bearing: what the range will be at the next plot

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Relative plot on a steady bearing: the previous, present and next plots on one line towards own shipOwn ship is fixed. The target was at 21.48 nm on the previous plot and 18.96 nm on the present one, on a steady bearing: 2.52 nm in 0.3 h is 8.4 kn, the relative speed, so the two plots agree. Run the present range on at the relative speed for 0.4 h: 8.4 × 0.4 = 3.36 nm, so the range at the next plot is 18.96 − 3.36 = 15.6 nm. Own ship's speed, 12.6 kn, is not the closing rate.RELATIVE PLOT · OWN SHIP FIXEDprevious 21.48 nmpresent 18.96 nmnext plot 15.6 nm2.52 nm in 0.3 h= 8.4 kn: check8.4 × 0.4 = 3.36 nmrelative speed × intervalbearing steadyOwn shipown speed 12.6 kn:not the closing rate

The rule

  • A steady compass bearing with a closing range means risk of collision exists (Rule 7(d)(i)): the relative track runs at you, so the CPA is about zero; the range figure tells you how long you have to act.
  • Check the plots first: (previous range − present range) ÷ time between plots must equal the relative speed. If not, she has altered or an echo was misread.
  • Run the present range on, never an older one: the latest plot is where she is now.
  • Closing distance = relative speed × interval to the next plot; take it off the present range. Own ship's speed is not the closing rate unless the other ship is stopped.
  • This holds only while the bearing is steady; a drawing bearing closes more slowly and has to be plotted.

Formula

  • Next range = present range − relative speed × interval to the next plot
  • Check: (previous range − present range) ÷ time between plots = relative speed

Worked example

Range of the target on the present plot18.96 nm
Range of the target on the previous plot21.48 nm
Relative speed from the plot8.4 kn
Own ship's speed12.6 kn
Time between the two plots0.3 h
Interval to the next plot0.4 h
  1. Check: 21.48 − 18.96 = 2.52 nm in 0.3 h = 8.4 kn, the plot's relative speed
  2. Closing distance = relative speed 8.4 × 0.4 = 3.36 nm
  3. Next range = present range 18.96 − 3.36 = 15.6 nm

Answer15.6 nm

Common mistake

Closing the range at own ship's 12.6 kn instead of the relative speed.

Two moving ships close at the rate the gap between them shrinks, which is what the plot measured: with 12.6 kn the next range comes out 13.9 nm, a target you would expect much closer than she will be.