# Find The Formula For Finding The Radius Of A Circle Impeller Logs and Compasses

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## Impeller Logs and Compasses

Sailing and navigation…Measuring Direction and Distance

For Measuring distance at sea, the old type of log that gave us the knot as unit of speed has long since given way to more sophisticated mechanical and electronic devices.

Walker logs

One of the oldest is the Walker log. This uses a torpedo-shaped spinner a few inches long towed behind the boat on a length of braided line. As it moves through the water, spiral fins on the torpedo make it spin, twisting the line. The on-board end of the line is hooked on to the back of the log instrument, where it turns a shaft connected to a reduction gear box. This in turn moves the hands on a series of dials, rather like those of an old fashioned gas meter, to give Direct reading of the distance the spinner has moved through the water.

Advantages of the Walker log are its rugged simplicity and the ease with which weed or debris can be cleared from the pinner. Its disadvantages are that its display has to be mounted right at the back of the boat; that the log line (usually 30 or 60 feet in length) has to be streamed before the log can be used, and recovered before entering harbour; it tends to under-read at very low speeds; and at speeds over about ten knots the spinner is inclined to jump out of the water and skitter along the surface. There are definite techniques for streaming and recovering a mechanical trailing log, intended to reduce the risk of the line tangling. To stream the log, first attach the on-board end to the hook on the back of the display unit. Then, keeping the spinner in hand, feed out all the line to form a long U-shaped loop astern before dropping the spinner overboard, well off to one side of the loop. Some owners like to hold on to the line just astern of the display unit for a few seconds, just to absorb the snatch as the load comes on to the line.

When recovering the log, speed is essential, especially if the boat is moving fast. Unclip the inboard end from the hook on the back of the display, and drop it overboard, allowing it to trail out astern while you pull in the log line. Then holding the spinner, gather in the line, coiling it as you go. Trailing the line astern like this allows any kinks to unravel.

Electrical trailing logs

The electrical trailing log is superficially similar to a Walker log, inasmuch as it uses a spinner towed astern of the boat on a long line. In this case, however, the spinner is in two parts, and the ‘log line’ is an electrical cable. The front part of the spinner is attached to the cable and only the rear part is free to rotate. As it does so, an electronic sensor in the front part makes and breaks an electrical circuit, so the on-board display unit receives a short pulse of electricity each time the spinner rotates. These pulses are counted electronically and are presented as a digital display of speed and distance run.

The advantages and disadvantages of this type of log are much the same as for the mechanical Walker log except that it is dependent on electrical power from internal dry batteries, which in return allows the display unit to be mounted almost anywhere on board, and that because the line itself is not twisting, it is rather easier to stream and recover.

Hull-mounted impeller logs

On cruising boats, hull-mounted logs are by far the most popular type, though in principle they are much the same as the electrical trailing log: a rotating impeller sends a stream of electrical impulses to a display unit mounted in the cockpit or near the chart table.

The impeller – which can be either a miniature version of the trailing log’s spinner, or a paddle wheel an inch or so in diameter – is mounted in a fitting called a transducer, which either protrudes through the bottom of the boat or hangs down below the transom.

The disadvantages of this system are that an impeller so close to the hull can be affected by the water flow around the hull itself, and that it is difficult and potentially dangerous to withdraw the transducer to clear weed or debris from it at sea. The reason in-hull logs are so popular is primarily the convenience of not having to stream and recover 30 feet or more of log line at the beginning and end of each passage.

Other logs

At the top of the scale of price and sophistication are several alternative methods of measuring speed through the water:

Electromagnetic logs are based on the same principle as generators and electric motors: that electricity is created if you move a magnetic field past an electrical conductor. In this case the conductor is sea water and the magnetic field is created by the transducer. As the transducer moves through the water a small electric current is set up, measured by sensors on the transducer.

Sonic logs use accurate measurements of the speed of sound between two transducers mounted one ahead of the other. Each transducer emits a continuous stream of clicks, inaudible to the human ear, while listening for clicks transmitted from the other. When the boat is moving, the movement of the water past the hull slows down the clicks travelling forward whilst speeding up those travelling aft. The instrument accurately measures the time taken for each click to make the trip, compares them, converts the results into a display of speed through the water, and from this calculates the distance run.

Another type of sonic log uses sophisticated echo sounder technology to measure the rate at which plankton and debris are moving past its transducer.

The big advantages of all three types are that they are much less susceptible to fouling than ordinary in-hull logs and that they can go on working at very high speeds or in rough sea conditions, when turbulence or air bubbles make impeller logs unreliable.

Calibrating logs

No log can be relied upon to be 100 per cent accurate. This is particularly true of hull mounted logs because – quite apart from any inherent inaccuracies in the instrument itself – the gradual build-up of fouling as the season progresses means that the boat is dragging an ever-thickening layer of water along with it, so the water flow past the impeller will be slower than the boat speed through the water. Conversely, around some parts of the hull, such as alongside a sailing boat’s keel or near the propellers of a motor boat, the water flow may actually be accelerated, making the log over-read.

Errors can always be allowed for if you know about them, and most electronic logs have a calibration facility that allows them to be adjusted to take account of these variations. Finding, and if necessary, correcting, log error is known as calibration. In principle it involves measuring the time taken to cover a known distance, using this to calculate true speed, and comparing this with the speed indicated by the log. Any accurately-known distance can be used, though the best are undoubtedly the measured distances’ set up specially for the purpose. They consist of two (or sometimes three) pairs of transit posts, marking the start and finish of a precisely-measured distance, and shown on the appropriate chart. The course to steer to cover the Measured distance is also shown.

Settle the boat on course and at a steady speed before crossing the first transit line; note the time at which you cross the start ine and hold that course and speed without making any allowance for wind or tide until you cross the finish line, and note the time taken. Note the actual log reading at intervals of, say, 15 seconds so that you can work out the average log speed for the whole run.

As perfectly still water is rare, it is important to repeat the process in the opposite direction. Having found the speed over the ground in both directions, the speed through the water can be calculated by taking the average, by adding the two speeds together and dividing by two.

A more accurate result can be obtained by making four or six runs, but this can be a very

time-consuming process, especially as log errors are not necessarily the same at all speeds, so the calibration runs need to be carried out at a range of different speeds, and repeated as a double check after the log has been adjusted.

A common mistake is to work out the average time taken and divide the distance by this. The result invariably understates the boat’s speed, because it must have been travelling in the ‘slow’ direction longer than in the ‘fast’ direction.

Some large scale charts (harbour plans) have a clearly marked scale of distance – rather like the one you might find on a road atlas – usually printed somewhere near the bottom edge. But this is not always the case, and on the smaller scale charts used for coastal and offshore navigation it would be impractical to provide such a scale because the scale of the chart varies slightly from top to bottom. One sea mile, however, is by definition one minute of latitude, so the latitude scales on each side of the chart constitute a scale of distance.

The slight difference between a sea mile and an international nautical mile is so small that for normal navigation it can be ignored: what is important, on small scale charts, is the distortion caused by the Mercator projection, which means that distance has to be measured at the latitude at which it is to be used. The longitude scale on the top and bottom edges of the chart is useless as a scale of distance.

It is relatively rare to find ourselves faced with the job of measuring distance in an exactly north-south line, so we need some means of transferring the distance between any two points on the chart to the latitude scale. Dividers are the tool for the job. For classroom navigation the kind of dividers used in technical drawing are perfectly adequate, and their sharp needle points give a reassuring sense of precision, but for practical navigation, traditional bow dividers have the big advantage that they can be opened and closed with one hand, by squeezing the bow to open them, and squeezing the legs to close them.

Sometimes it is necessary to draw arcs of measured radius on the chart, for which it is useful to have a drawing compass. Again, the type intended for technical drawing can be used so long as it is big enough, but it is generally better to use the larger and less sophisticated versions intended for marine navigation.

Compasses and Measuring direction at sea

Direction at sea is measured using a compass – essentially an instrument which points north, and goes on pointing north regardless of the movement of the boat around it. In practice most yachts carry at least two compasses. One, steering compasses are relatively large, fixed to the boat, and used to measure heading. The other is usually smaller, portable and is used to measure the direction of distant objects, so it is called a hand bearing compass. Sometimes one compass can do both jobs: on many ships and a few large yachts an attachment called a pelorus allows the steering compass to be used for taking bearings, while on very small craft, a hand bearing compass clipped into a bracket can serve as a steering compass.

There are many ways of making an instrument that will stay pointing in one Direction, including gyroscopes, and what are called ‘ring laser gyros’, but although these have their advantages, they are much too sophisticated, and therefore expensive, to be of practical interest for yachts. The Overwhelming majority of yacht compasses Depend on magnetism, and in that respect can be seen as direct developments from instruments that were probably in use several thousand years ago. Compasses make use of the fact that the earth has a magnetic field, which is very much as though a huge bar magnet were embedded in its core and aligned with its North-South axis.

Any magnet that is free to swing tends to line itself up with the earth’s magnetic field. This effect is particularly obvious in the small, flat compasses used for orienteering and rambling on land, in which a single straight needle-like magnet gives a direct Indication of north. In marine compasses, several such magnets, or a single magnet in the shape of a ring, are mounted underneath a circular ‘card’, with a scale of degrees or compass points marked on it. The whole thing is suspended in a bowl filled with a mixture of water and alcohol, which slows Down the movement of the card, to reduce the swinging that would otherwise be caused by the pitching and rolling of the boat.

Compasses intended for fast motor boats are much more heavily damped than those intended for sailing craft; the rapid slamming of a planing boat can be enough to make the card of a sailboat compass rotate continuously.

Steering compasses

On a steering compass the fore-and-aft line of the boat is marked by a line or pointer on the compass bowl, called the lubber line, against which the boat’s current heading can be read from the card, so it is obviously important for the compass to be installed so that the lubber line is accurately aligned with, or parallel to, the centre line of the boat. Many compasses have supplementary lubber lines offset by 45° and 90° on each side, intended mainly for use in situations such as tiller-steered boats where the helmsman is likely to be looking at the compass from one side or the other.

Of course, there are variations intended to suit particular applications. On many small and medium sized sailing yachts, where cockpit space is at a premium, the compass is set into the aft bulkhead of the superstructure, so that the rear edge of the card is visible, rather than its upper surface. A compass intended for this type of mounting has an aft lubber line and a scale of degrees marked on the down-turned rim of the card. An even more extreme variation is occasionally found in compasses intended for steel craft, whose structure effectively masks the compass from the earth’s magnetic field. This problem can be reduced by mounting the compass as high above the hull as possible, so compasses have been produced that can be mounted on the wheelhouse roof, with mirrors or prisms arranged so that the helmsman effectively looks upwards at the bottom of the compass card.

Grid compasses

Grid compasses, intended primarily for aircraft navigation, enjoyed a surge of popularity after the Second World War, when many boats were fitted out from Army surplus stores! The claim that they were easier to steer by maintained their popularity for at least 20 years and several marinized versions were produced. A grid compass has a card with a particularly prominent north set in a flat-topped bowl. On top of the bowl is a transparent cover, marked with a grid of parallel lines and with a scale of degrees es around its edge. The required course is set by rotating the cover, and the helmsman then steers so as to keep the –. mark on the card lined up with the grid.

Hand bearing compasses

A hand bearing compass is basically a small, portable version of a steering compass, fitted with some form of sighting arrangement that allows it to be accurately lined up on a distant object. They can be subdivided into two groups: those intended to be used at arm’s length, which are usually fitted with a handle; and those intended to be held close to the eye, which are usually supplied with a neck strap. Which kind is best is very much a matter of personal preference, but anyone who uses spectacles or a hearing aid is well advised to go for an arm’s-length compass because even small pieces of ferrous metal such as the hinges of spectacles can cause compass errors if they are only inches away.

Sighting arrangements vary. The classic Sestrel Radiant, for instance, has a prism mounted above the bowl, with a V-shaped notch on top. When the compass is held up at arm’s length and eye level the lubber line and compass card can be seen in the prism. To take a bearing of a distant object, you line up the ‘target’ with the notch, rotate the compass until the lubber line appears in the prism immediately below the target, and then read off the bearing. Another common arrangement has two sights on top of the bowl, like the fore sight and back sight of a gun, and an edge-reading compass card. Close-to-the-eye compasses do not have such obvious sighting arrangements: instead they have a small prism mounted on top, whose optics are arranged in such a way that when you look at a landmark across the top of the compass, its bearing appears in the prism immediately below.

Fluxgate compasses

A new type of compass is rapidly gaining in popularity. Unlike a conventional ‘swinging card’ compass, a fluxgate compass has no moving parts, but instead uses electronics to detect the earth’s magnetic field and present that information on some kind of display. A fluxgate depends on the phenomenon of electromagnetic induction – as used in transformers and the ignition coil of a petrol engine. If you pass an electric current through a coil of wire wound around a suitable metal core, the core becomes a magnet. Which end is the north pole, and which the south, depends on the direction of the current flow in the wire, so if you apply an alternating current to the wire, the north and south poles of the core change places each time the current reverses. If you have a second coil of wire wound around this whole assembly the constantly-reversing magnetic field induces an electric current in the secondary winding.

In a fluxgate there are two cores side by side, with their primary windings receiving alternating current from the same source, but wound in opposite directions. This means that in a magnetically ‘clean’ environment (with no external magnetic influences) the induced magnetism in the two cores would be equal and opposite, so they would cancel each other out and produce no current at all in the secondary winding that surrounds both of them. The presence of an external magnetic field upsets the balance, causing a short surge of electricity in the secondary winding each time the primary current reverses. This effect is most pronounced if the two cores are parallel to the external magnetic field. In a practical fluxgate compass, several fluxgates are arranged in a circle. By comparing the voltages induced in the various secondary windings it is possible to deduce where north is relative to the ring of flux-gates.

At present, the most common use of this technology is to provide heading information for other electronic equipment such as autopilots or radars, but it can also be used to provide a steering display for the helmsman or as the heart of an electronic hand bearing compass. Apart from the ease with which fluxgate compasses can be connected to other navigational electronics, their big advantages are that they can be fitted with an automatic correction facility, and that because the sensor and display are usually separate from each other, the sensor can be mounted anywhere on board and well away from distorting magnetic Influences. Fluxgate hand bearing compasses also have the facility to ‘store’ headings, to save the navigator having to memorize them.

Their main disadvantage is that very large errors can occur if the fluxgate ring is not kept perfectly horizontal. There are electronic solutions to this problem, but the fact remains that the compass without moving parts actually requires more sophisticated gimbal arrangements than its swinging card counterparts.

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