Heeling Error

92. Ship's head N.E. × E. and heeling 10° to port; the heeling error observed was 5° 30' east.

Required the probable heeling error, ship's head S.S.E., and heeling 8° to starboard.

Formula

Heeling error =

Log. heeling error =

observed error X cos. new course x new heel

cos. old course x old heel

Log. observed error + log. cos. new course + log. new heel + log. sec. old course + arith.-co. log. old heel tens

The circle represents the compass, N C S the compass needle, ≤ N CB first compass course, SC H second compass course, C A heeling error for 1° of heel at NE x E, CB heeling error for 1° of heel at N or S, C J the heeling error for 1° of heel at S.S.E. It is obvious that the heeling error varies as the cosine of the compass course, as shown in the formula.

Ship's head N.E. × E. and heeling 10° to starboard, the heeling erior observed was 6° west.

Required the probable heeling error, ship's head north and heeling 10° to

port.

Fig. 6. Let C A heeling error at N.E. x E., then CB will be the heeling error for ship's head north, equal to CN, both being radii of the same circle.

Then in the right angled plane triangle, C A B, Fig. 6, given ▲ C and side CA: to find side C B.

Let us suppose that the ship, in the last example, had been heeling, say, 13° on north; you would have to multiply the error just found by 13° and divide the product by 10°, thus—

10°.8
13°

324 108

The heeling error for 13° of port heel head North 14°E.
The error would be the same at South but would be West.
At East or West there should be no heeling error.

=

10°)140'4

14°0 E.

Examples for Practice

1. Ship's head S.E. and heeling 6° to starboard, the heeling error observed was 8° East.

Required the probable heeling error, ship's head N.N.E. and heeling 10° to port.

Ans. Heeling error 17° 42 East.

2. Ship's head N.N.E. and heeling 10° to port, the heeling error observed was 17° 42 East.

Required the probable heeling error, ship's head S.E. and heeling 6° to

port.

Ans. Heeling error 8° West.

3. Ship's head S.E. and heeling 6° to starboard, the heeling error observed was 8° East.

Required the probable heeling error, ship's head N.N.E. and heeling 10° to starboard.

Ans. Heeling error 17°42 West.

4. Ship's head north heeling 7° to port, the heeling error observed was 11° West.

Required the probable heeling error, ship's head south and heeling 10° to port.

Ans. Heeling error 15°7 East.

The heeling error changes its name if on both tacks her head is either northerly or southerly; it retains the same name if on one tack her head is southerly and on the other tack northerly. A ship with a heavy list to port or starboard would change the name of the heeling error on changing from a northerly to a southerly course, or from a southerly to a northerly

course.

568

Table I. inserted by kind permission of J. D. Potter, 145, Minories, E.