Solution for Drake Circumnavigates

Solution for Drake Circumnavigates

David Berson

For this problem we have eliminated the need to find the time of Local Apparent Noon. This is because when Drake did his circumnavigation in 1537 accurate time-keeping at sea was still far in the future. It would be another 200 years before John Harrison developed the ships chronometer that revolutionized celestial navigation In Drake’s time the navigator waited until midday, and then using a three-foot cross staff, or an astrolabe, observed the highest altitude of the sun. Declinations of the sun were already recorded in an Almanac and the navigator corrected the Hs to Ho and then subtracted that from 90ï‚° to get the Zenith Distance. To the Zenith Distance the Declination of the sun was either added or subtracted in order to find the latitude. It was primitive and what is most amazing about Drake, in particular and Age of Exploration in general, is that anyone was able to find their way home.

Let’s see how this problem resolves itself. The day is December 20, and for the sake of the problem the year is 2006. The DR position of the Golden Hinde is 20ï‚°50’N by 35ï‚°15’W. The Height of Eye is 20 feet and the Hs is 87ï‚°12.2′. We are shooting the Lower Limb of the sun. For the sake of employing the modern Nautical Almanac we will say that the time of the sight was 14 hours 18 minutes GMT.

To find the HO we use the standard procedure of reducing the sight by factoring in the Dip and the 3rd correction, which includes parallax, semi-diameter and refraction:

Hs 87ï‚°12.2′

-dip 4.3′

Ha 87ï‚° 07.9′

3rd + 16.1′

Ho 87ï‚°24′

The latitude is found by the following formula: Latitude =90ï‚°- Ho =ZD +/- declination. Thus:

90ï‚°

-87ï‚°24′

ZD 2ï‚°36′. Now we have to decide whether to add or subtract the declination which we have found at 14 hours GMT in the Nautical Almanac as S 23ï‚°26.0′. A note here: there d correction is 0′ so there is no correction to the declination for the minutes of time. There are formula for this but common sense is the best way to judge whether the declination is added or subtracted. Obviously Drake knew from previous sights on earlier days if he was north or south of the equator. He knew that his DR was about 20ï‚°50’N so by elimination he knows to find his latitude that he has to subtract the ZD from the Declination. Thus:

Dec. 23ï‚°26′

– ZD 2ï‚°36′

Lat. 20ï‚° 50′

The fact that the latitude ended up as the same as the DR latitude is a fortunate accident.

For more information concerning Drake I refer the readers to “The Secret Voyage of Sir Francis Drake” by Samuel Bawlf.