Excerpts

Excerpt 1-
Using `Heavenly Bodies for Navigation.

So far, our investigations have considered only terrestrial objects and phenomena such as lighthouses, cliff tops and the horizon. How can the techniques and knowledge which we have discovered be adapted to aid the navigator who is out of sight of land?

To answer this question, let us consider how astronomical objects (or `heavenly bodies') can be used for navigation.

Let us begin by considering the Pole Star (Polaris). Assume that the Pole Star is exactly in line with the Earth's axis produced, as shown in diagram 17.

To an observer O on the Equator (lat. 0°) the Pole Star will be in line with the horizon (i.e. it will have an angle of elevation or altitude of 0°).

• Note. 1. The Pole Star is slightly offset from the Earth's axis but for the purposes of this exercise, we can assume that it is in line without any great loss of accuracy.
• 2. Because of the great distance of the Pole Star from the Earth, we can also assume reasonably that the horizon corresponds to the Earth's axis.

If the observer (O) were to move 60 nautical miles due north from the Equator to a latitude of 1°N, then the altitude of the Pole Star will obviously increase to 1° (i.e. it will now be 1° above the horizon) as shown in diagram 18.

From this, we can see that, in the northern hemisphere, the altitude of the Pole Star corresponds to the latitude of the observer. So, if a navigator measures the altitude of the Pole Star and finds it to be 45°, then he can conclude that he is at latitude 45°N.

To arrive at this conclusion, he would simply have to employ the technique of measuring angles of elevation (altitude) and combine this with a knowledge of the relationship between latitude and the astronomical position of the Pole Star.

In the next chapter we will look more closely at the concept of latitude as well as exploring the concepts of small circles, great circles and longitude.

Excerpt 2
Time difference between meridians of longitude.

We know that the Earth revolves about its axis once every 24 hours. In other words, the Sun completes its apparent revolution of 360° in 24 hours. This means that the Sun crosses each of the 360 meridians of longitude once every 24 hours. So, in 1 hour, the Sun appears to move 15°, in 4 minutes, it appears to move 1°, in 1 minute it appears to move 15', in 4 seconds it appears to move 1'.

From this, it becomes obvious that there is a direct relationship between arc and time such that 1 minute of time equals 15 minutes of arc.

If we have two accurate clocks, one calibrated to GMT and the other calibrated to local time, then it is an easy matter to calculate our longitude from the difference between the two times. In fact, we can manage with just one clock because we know that noon, local time is when the Sun is at its highest altitude. For example, if the difference between GMT and local time is three hours, then the difference in longitude must be 3 x 15°. If local time is ahead of GMT then the local longitude must be east of the Greenwich Meridian and if local time is behind GMT the longitude must be west. (See diagram 19 if you are not sure about this).

Example: If it is 18.00 GMT when it is 09.20 local time, then local time must be 8 hours and 40 minutes behind GMT.

Therefore: longitude =
- [8 x 15°] + [(40 ¸ 60) x 15°] = -[120° + 10°] = 130° west

However, if we had no way of knowing the time in GMT, we would be in the same situation as mariners were before John Harrison invented the chronometer in the 18th. Century. They had to navigate the oceans without a reliable method of calculating their longitude.

Excerpt 3
Calculating Lat. & Long. In A Survival Situation.

The aim of this appendix is to provide a simple method that could be used in a survival situation to establish a vessel's position assuming that automated navigation systems are not available.

The method takes into account that in such a situation, charts and drawing instruments may not be available and that in any case, it is not likely that conditions will be suitable to use such materials for chart work. …………………..

Introduction to the method. ·

• The purpose of the method is to establish the survivors' position in terms of latitude and longitude.
• Latitude is found by using the formulae developed in this book for calculating the Sun's declination. Note. declination could be read directly from a nautical almanac but these are usually quite cumbersome and are also likely to get wet and soggy in an open boat. Furthermore the method described here can be used for any year whereas a nautical almanac has to be updated each year. So, for these reasons, we will assume that a nautical almanac is not available in this demonstration.
• Longitude is found by calculating the difference between local time (noon) and GMT. ……………………………..

Scenario.

A ship is en-route from Yokohama to Hawaii. On the 12th. June, the ship is struck by a severe tropical storm and sinks. The survivors are in an inflatable life-raft which has a survival bag containing the equipment listed above onboard. The last known position of the ship before it sank was approximately 30o North 162o East.

At noon, the survivors calculate the position of the life-raft using the following method …………………