# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Sign conventions and units.**

**From:**George Huxtable

**Date:**2001 Apr 21, 4:08 PM

MUSINGS about sign conventions and units used in navigation. >From the earliest days of their art, navigators have been reluctant to give a mathematical sign (plus or minus) to the various quantities involved. Instead, "Names" have been used (North or South, East or West). And a complex series of rules-of-thumb has evolved for handling these Names, such as "take the difference between A and B if the Names are the same, add them if Names differ". In the days when logs were used, trig functions of angles were expressed as Versines, which never go negative. Not surprising, really, when many mariners were unlearned, and got their results by rote rather than understanding. The manipulations of signed arithmetic, such as subtracting -5 from -2, and getting the right answer (+3) could have them out of the depth. Nowadays, every schoolchild is taught how to handle such problems (even if some of them may fail to learn successfully). LATITUDE Anyone who has tried writing a program for astro-nav computation quickly meets the problem that the mathematics handles quantities with signs rather than names. The first thing he has to do is to convert from the names, such as North or South, into a sign, plus or minus, and then perhaps convert back at the end. Or he can ask the user to fall in with a simple sign convention when inputting data, such as North = Positive, South = Negative. That convention, for Latitude, is one that everyone can accept. Everyone draws maps with North upwards, even Australians. So, for Latitude, there's no argument. LONGITUDE. Not so for Longitude, however. There isn't one accepted convention, but two! The worst possible state of affairs. There are good reasons for choosing the West-is-positive convention. The Geographical positions of all heavenly bodies travel Westwards as the Earth turns, so it's convenient to have the longitudes of those positions increase with time: therefore GHA of Aries and star are measured Westwards. And in practice, many instruments and programs originate from the US, who have found it convenient to presume a positive longitude for their own waters. However, there are equally valid reasons for measuring longitude positively to the East. It fits in with the conventional way that we draw a graph, with the X-axis increasing to the right, and the Y-axis increasing upwards. It fits in with the way astronomers have always measured celestial positions, in terms of the sidereal time at which a star will cross the Greenwich meridian, and is measured in hours, increasing in an Easterly direction. Certainly some instruments, such as certain Decca Navigators, presumed that East was positive. If the navigators of this mailing list were in a position to choose their preferred direction for a convention for positive longitude for the world to adopt, which would it be, East or West? I wonder. Of course, whichever direction was adopted as positive, longitudes could be measured either 0 to 360 degrees from Greenwich in that direction, or as 0 to +180 in that direction and 0 to -180 in the other, with no ambiguity. AZIMUTHS. There's a similar difficulty when specifying azimuths and courses. Navigators finally broke clear of the complex and non-numerical "points" system of "NE by N three-quarters N" (and so on), and it's rarer to see azimuths measured quadrantally, 0 to 90 degrees E or W of N or S. Instead me now use (mostly) the simple convention, 0 to 360 measured clockwise from N, as marked on modern compasses. Surely there's no argument about that, one might hope. But indeed there is!. Jean Meeus, in his invaluable book "Astronomical Algorithms", chooses to define azimuths as measured clockwise from the South, not from the North. He claims that this is a convention commonly used by astronomers, but accepts that there's a choice. So again we have the worst possible situation, tmo contradictory standards. If the world could settle on one, which should it be? And would the astronomers agree? UNITS OF ANGLE. Angles such as lat or long are measured in degrees, we all accept. But what about subdivisions of the degree? Do we prefer to use decimal parts of a degree? Or minutes? And if minutes, should we state parts of a minute as decimal minutes, or as seconds? Instruments, and charts, are calibrated in many different ways. Do we navigators know what we would prefer to be the standard for the future? UNITS OF DISTANCE. We are accustomed to using nautical miles, which fits in (almost) to the length of a minute of latitude. But this is an awkward unit in that it's incompatible with the length of the mile as used on land, and with the kilometer. As the kilometer is becoming the standard of length measurement over much of the world, excluding the US, are we willing to accept a change to the kilometer as a unit of navigational length, with its implications. ================================ The text above is a serious suggestion that we navigators should think about, and decide, what conventions we wish to see adopted. What follows is rather more frivolous. RADICAL CHANGE IN UNITS. Much of the calculation in navigation stems from converting quantities from one awkward and incompatible unit to another. The revolutionary French had a good shot at reforming the system of measurements, but from a navigator's point of view they left much of this work undone, or made unsatisfactory choices. Wouldn't a navigator's work become simple if we could make the following changes? I know it's only a pipe-dream, but just think about it. 1. Measure angles, not in degrees, but in Turns, corresponding to one complete rotation. 1000 milliTurns would bring you back to where you started. A right-angle would be 250 mT. For many calculations, one could simply cast off whole integer turns, and use the fractional part. 2. Measure time in Days and milliDays, so that time in milliDays and longitude in milliTurns become instantly interchangeable (rather than 15 degrees per hour). Breakfast would be around 200mD and midday at 500mD. If dates were registered by counting up whole days from the year start, 0 to 364 or 365, ignoring months altogether, then time intervals between two events become a simple subtraction process, except over a year-end. 3. Measure distances, not in miles or in kilometres, but in units equal to the Earth's circumference (the Circ?), so that one milliCirc corresponds (almost) to a milliTurn of latitude. The French approached this idea by making the kilometer one 10,000th of the distance between equator and pole, but they really got it wrong. So one Circ would correspond to 40,000 km, and a microCirc would be worth 40 metres. One would need to coin a name for a smaller decimal subdivision of this unit. You will be aware that I have ignored all the practical implications and difficulties of making such far-reaching changes, such as recalibrating the World's clocks and chronometers, sextants, compasses, logs, charts. That's because these suggestions are really.nothing more than an exercise in wishing. But wouldn't it be nice if the French had done the right thing in the 18th century? George Huxtable. ------------------------------ george---.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------