The magic of 6 °

I once worked aboard a rusty tramp ship which steamed around the SouthPacific at a steady ten knots. For navigation equipment, we had littlemore than a sextant, chronometer and magnetic compass, but at ten knotsthere was plenty of time to find our position. At this speed, we had a verysimple and effective method of adjusting the course to counter the effectsof any tides and currents. It is easily adapted for use on slower sailingcraft, and may also be used to calculate the distance off various objects. Itis based on the figure of 6˚ and this is how it works.

Counteracting a current

At ten knots, if there is a cross-current of 1 knot, the course is adjusted by6˚ in the direction from which the current flows. If the cross-current is 2knots, the course is adjusted by 12˚ (2 x 6˚). If the cross-current is 3knots, the adjustment is 18˚ (3 x 6˚), and so on. Just how well thesefigures match up to the correct adjustments is shown in the table belowwhich assumes a boat speed of 10 knots.

Cross current Correction to 6˚ shortcut

rate (in knots) maintain course

1 5.7˚ 6˚2 11.5˚ 12˚3 17.5˚ 18˚4 23.6˚ 24˚5 30.0˚ 30˚6 36.9˚ 36˚

Though a small craft is unlikely to make ten knots, the basic principle isthe same. Calculate the current as a percentage of the boat’s speed and foreach 10% allow an adjustment of 6˚. For example, a 2 knots cross-currenton a craft making 5 knots equals 40% of the boat’s speed. The courseadjustment is 4 x 6˚ = 24˚ (Figure 1). The procedure works well up to across-current rate of 60%; thereafter, the system, and possibly the boat,are overwhelmed by the strength of the current.

But what if the current is on the bow or on the quarter? The influence isnot as strong as that of a cross-current and the correction is reduced to 4˚.So, for a 2 knots bow or quarter current on a craft making 5 knots, theadjustment is 4 x 4˚ = 16˚. Note that the adjustment is the same for bowor quarter current as the vector diagrams in Figure 1 show. The onlydifference is that the current speeds up the boat on the quarter and slowsit down on the bow.

Figure 1: courses to make good

Estimating current strength and direction is not an exact science so thesetwo figures of 6˚ and 4˚ should be sufficient for most situations. On asailing boat, a further adjustment for leeway may be necessary tomaintain the intended course. The next time you see a current problemsolved by vector solution in a magazine or textbook, try out thissimplified method and see how closely it matches the correct solution.

Estimating the distance off.

The 6˚ procedure with a multiplier of ten provides a handy way ofestimating your distance from an object with a known height. On a smallcraft, it is suitable for distances up to about 4 miles for beyond thatdistance the base of the object would be obscured by the horizon.

For example, when an object with a height above sea level of 100 metresis 6˚ above the horizon, it is approximately 1000 metres away (100metres x 10).

Working out the distance off for other angles is quite easy as long as youremember the indirect relationship between 6˚ and the multiplier of 10.For example, at 3˚ the multiplier of 10 is doubled to 20 so the distance offin the example is 2000 metres. At 12˚ the multiplier of 10 is halved to 5so the distance off is 500 metres.

This procedure for estimating the distance off from a vertical height mayalso be used horizontally when the width of an object, or the distancebetween two equidistant objects, is known or can be obtained from achart.

Some quick ways of estimating 6˚

The blink of an eye. Hold out a finger at arm’s length and line it up onan object with your right eye. Switch to your left eye and the finger willappear to have moved clockwise through a horizontal angle of 6˚. This isa typical figure but it is worth checking the angular shift of your winkwith the help of a sextant. This is also a useful trick for estimating leewayfrom your wake.

A finger sextant. Three fingers together at arm’s length will usuallycover an angle of about 6˚. Once again, check out your own angle with asextant.

Binoculars: Many binoculars have a field of vision in the region of 6˚.

A Kamal. The Kamal is one of the oldest angle measuring devices andwas used by Arab navigators to cross the Indian Ocean. It is very efficientat measuring small angles and consists of a small board with a knottedline passing through a hole drilled in the centre of the board. To make akamal for measuring 6˚, °drill a small hole in a piece of hardwood 6cm x

6cm. Take a length of line and tie an overhand knot at one end. Pull theother end of the line through the hole until the knot is hard against theboard. Tie another knot in the the line approximately 57 cms from the

board. When this knot is placed in or close to your mouth and the lineheld taut, the kamal will cover an angle of 6˚. A kamal may be adapted tomeasure other angles by extending the line, adding more knots or byaltering the dimensions of the board.

For more articles like this, see The Lo-Tech Navigator published bySeafarer (UK) and Sheridan House (USA)