Tasman’s navigation: Part 2

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LONGITUDE

latitude and  longitude

Latitude and longitude on a globe.

Longitude was the big issue for Tasman. He simply had no way of measuring how far east or west he was. There wouldn’t be a method to readily resolve longitude until Cook carried the experimental Harrison ‘K1’ instrument on his second Pacific voyage in 1772. The Harrison ‘K1’ was a clock.

The successful resolution of longitude hinges on being able to know time very accurately.

The Italian explorer Amerigo Vespucci made an insightful observation during a voyage to the America’s.

“…one night, the twenty-third of August 1499, there was a conjunction of the moon with Mars, which according to the almanac was to occur at midnight or a half hour before. I found that…at midnight Mars’s position was three and a half degrees to the east.”

Vespucci was watching a transit of the moon by mars, but it didn’t happen at the time he expected.

The earth makes a complete turn on its axis every 24 hours, and in this time the sun makes a complete revolution of the earth (to the terrestrial observer). It rises in the east, sets in the west, and then becomes invisible below the horizon until it appears again in the east. ‘Noon’ is when the sun reaches the highest point in the sky at a given location… noon is not simultaneous at all places on Earth.

The Prime Meridian at Greenwich

Standing with one foot in the east, and one in the west, at the Royal Observatory, Greenwich

Harrison K1 'one day' watch

The Harrison ‘K1’ watch carried by James Cook on his second Pacific voyage.

To a terrestrial observer, ‘noon’, when the sun is at its highest, occurs every 24 hours… precisely.

The sun moves through the sky, east to west, at 15° per hour. If I travel west then ‘noon’ occurs later, if I travel east it occurs earlier. The time that noon occurs is directly related to the distance I travel east or west.

‘Noon’, at a location 15° to the west of me, will occur exactly an hour later than at my location.

If you had an accurate clock, and set it to 12:00 ‘midday’, exactly noon at your point of departure, then you could work out your longitude anywhere in the world.

When you observe noon at your current location, and compare this to the time on the clock, then the time difference tells you your current longitude. If noon locally occurs 1 hour before noon at your departure point (which is shown by the time on your clock) then you are 15° to the east of it.

1 hour time difference between local noon time and origin noon time = 15° difference in longitude. If you know the local time at any place on the earth, then you can calculate your longitude based on the difference between local time and the time at your origin.

By the time Cook first sailed the pacific in 1769 an astronomical method had been developed for reckoning the time at Greenwich based on observations of the moon and stars. It was important to know the time at Greenwich as this was the location the British chose as the line of 0° longitude for their charts. Known as the ‘Lunar Distance’ method it involved measuring the angular distance between a star and the moon, the star’s elevation above the horizon, and the moon’s elevation above the horizon. The technique was quite accurate, but difficult. It took about four hours to perform the necessary calculations, but it yielded the time at Greenwich when the observations were made.

The difference between ‘local time’ and ‘Greenwich time’ allowed Cook to calculate his longitude, but incredibly, Cook’s ‘local time’ was still based on hour-glasses, corrected daily by his observations of the sun. On his first voyage Cook had no clock of any description.

Regardless of how tedious the process was, the ‘Lunar distance’ method produced the required result.

These days we still use Greenwich as the zero point for longitude and as the ‘normal’ point for time zones, but this convention was not universally adopted until 1884.

James Cook, using the ‘Lunar distance’ method, was able to calculate his longitude with such confidence that he no longer sailed ‘lines of latitude’… he could set a course that took him directly to his objective.

When Cook set out on his second Pacific voyage in 1772 he carried the experiment ‘K1’ watch. It was such an accurate timekeeper that he later wrote to the Admiralty… “Mr Kendall’s watch has exceeded the

expectations of its most zealous advocate…”. With this reliable timepiece Cook could determine his longitude both reliably and quickly. All he had to do was find the local noon time, by observing the sun’s height, and then read from the K1 clock how far advanced, or retarded this was from 12:00. One minute of difference in these times represented a quarter of a degree of longitude distance from Greenwich.

By 1772 the longitude problem was solved, but when Abel Tasman was sailing 140 years earlier, and he had to make do with far less reliable techniques.

DEAD RECKONING

Tasman had no instrument from which to directly calculate his longitude, yet in his daily journal he recorded both his latitude and his longitude… so how was this done?

What he did was estimate how far he thought he had traveled since the previous day, and in what direction. He measured his latitude at noon every day, and recorded that, and then he used his estimate of distance and direction traveled and added this variation in longitude to his previous days entry.

His estimate of longitude was cumulative, based on daily estimates of speed and direction since his departure from a known location. Thus, any deficiency in his estimate was compounded. Over the course of his 5,500 km journey across the Indian Ocean, his estimate of longitude was in error by 670 km.

He made his estimate based on two things; his speed, and the direction he was travelling. If he knew his speed, and the direction he had traveled, then he could calculate from that how far east or west he had moved since the previous day.

Measuring a vessels speed

The equipment used to measure a vessels speed

Leeway diagram

‘Leeway’ is the downwind drift of the course caused by the pressure of the wind.

Duyfken hourglass

An hourglass on the replica of the Duyfken

This technique for estimating your position without direct measurements is called ‘dead reckoning’. However, these estimates of both speed, and direction had their difficulties.

He measured his speed with a spool of thin rope, knotted at set intervals and a floating baffle. It took three sailors to measure the speed. One held the rope spool, the second dropped the float into the water, the third turned a 30 second sand glass. The second person started counting knots as they passed through his hand, and at the end of the 30 seconds the count was recorded. The number of knots that had passed was the speed of the vessel.

The direction a sailing ship travels is not the same as the course it is sailing.

The issue here is ‘leeway’; that is, the sideways drift of a ship to leeward (downwind) of the steered course. If a ship is going sideways across the wind, then as the sails propel them forward, the pressure on

the sails pushes the ship sideways across the water in the downwind direction. Their ‘course’ is the direction they’re pointing, their ‘course made’ is the direction actually traveled. The difference is their leeway.

A ship with a deep and broad keel will have a smaller sideways slippage, or leeway, than a ship with a small narrow keel.

An experienced skipper will have a good understanding of his vessel’s leeway at any sailing angle, but this is only a ‘best guess’. A more reliable way to determine ‘course made’ is to look at the wake left by the vessel, and take its bearing from the ships compass.

Tasman’s estimate of how far he had traveled each day was most determined by how accurately his measurements represented the days sailing. On any given day they would change course several times, and for each of

these tacks; speed, direction and duration were noted. ‘Duration’ was determined from the 30 minute sand glasses used to set the sailors’ watches. The sequence of course changes was plotted on a chart to determine the gross determination of course and distance for the day.

Tasman measured from this how his longitude had changed since the previous day and added thius to the previous days longitude. This is what he recorded in his log.

Every step of this process included potential error, and these errors compounded. However, even if his estimate of course and direction had been perfect, this method of ‘dead reckoning’ still contained an inherent error. The difficulty is, that the speed and direction measured is not the actual speed and actual direction… it is the speed and direction relative to the body water they are sailing on.

The observations Tasman made took no account of any movement in the ocean, and the ocean is not generally stationary, it moves in currents. If Tasman was sailing into a current then he would overestimate their actual speed, if they sailed with the current he would underestimated it. Tasman was completely oblivious to any current in the ocean body, so his estimate of longitude took no account of this movement. Tasman’s journey from the from Batavia to the Mauritius took him along the South Equatorial Current… a current flowing to the west. This is why he encountered his destination two days earlier than he expected.

Tasman's chart side by side with a 

modern map

Tasman’s chart side by side with a modern map

Tasman’s longitude estimate is only to be relied on over short time periods; otherwise, as his daily errors compound, the position indicated becomes increasingly less representative.

Given Tasman’s lack of knowledge regarding his true position, it is remarkable that his chart is even recognisable as New Zealand. Yet, despite not knowing his longitude, it bears astonishing similarity to a modern map.

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