Finding your Latitude

Even without elaborate navigational instruments, the wayfinder can still locate his destination island. One strategy is to use latitude sailing. Basically the wayfinder, utilizing the upwind, sails to the latitude of the island. Then he begins searching for the island along that latitude. For this method to work, the navigator must be able to tell when he is at the latitude of the island.

Using the North Star

In the northern hemisphere, the altitude of our relatively fixed North Star is approximately equal to the latitude of the observer. Thus,

At Hawaii (20 N latitude), Hokupa'a (Hawaiian name for the North Star) is about 20 above the horizon.
At Satawal (7 N latitude), Fuesemagut (Satawalese for the North Star) is about 7 above the horizon.
At Tahiti (18 S latitude), the North Star is always invisible.

It becomes harder to estimate the altitude at higher latitude as small errors add up. More so without instruments.But how do you find out the altitude?

Using latitude hook

Using your arm and hand

The hand held at arm's length can give you an estimate for the various angles. Most people either have long arms/big hands or short arms/small hands, so the arm/hand ratio is relatively fixed. A good test is to measure the angle from horizon to the zenith using a closed fist. Stacking their fists on top of each other, most people will reach the zenith at the 9th fist. Since one fist is roughly 10 degrees, 9 fists will give you 90 degrees, which is the angular distance of the zenith from the horizon. This is a very handy method for estimating the altitude of a star and is taught to the beginner stargazer nowadays.

1 degree 2 degrees 5 degrees
10 degrees 15 degrees 20 degrees



Meridian Pairs

A star will always cross the meridian at a certain altitude for a given latitude. Thus, if the navigator knows the altitude of the meridian crossing of a star at particular latitude, he can, by measuring the altitude, get estimation for his latitude. To know whether the star is crossing the meridian, he uses stars that cross the meridian together (meridian pairs). When the pair is perpendicular to the horizon, they are crossing the meridian. Meridian pairs are also pointers to direction. Meridian pairs in the northern sky point north, pairs in the southern sky point south. Interestingly this was the solution Nainoa Thompson arrived at one night to his navigational problem. According to the plan, he was to sail, using dead reckoning, to the latitude of Hawaii, then turn west to look for the Hawaiian Islands. But when should he turn? He couldn't use the North Star as it was too high up (20 degrees). Then he realized he could have used the Southern Cross. Read his account on Solving a Navigation Problem.

Meridian Pointers to the North
Alpheratz + Caph
Alpha Trianguli + Segin
Theta Aurigae + Menkalinan
Procyon + Castor & Pollux
Merak + Dubhe
Cor Caroli + Alioth
Ed Asich + Pherkad
Gienah + Deneb
Markab + Scheat

Meridian Pointers to the South
Mirzim + Canopus
Suhail + Star in the False Cross
Cross Dividers: Mu Velorum + Unnamed star cluster
Gacrux + Acrux
Menkent + Beta Centauri
Alpha Lupi + Alpha Centauri
Dschubba + Pi Scorpii
Epsilon Scorpii + Mu2 Scorpii + Zeta Scorpii
Shaula + Sargas


Using Southern Cross to determine latitude

Kaulia and Ka Mole Honua are Gacrux and Acrux respectively in western astronomy. At the equator, the altitude of a meridian-crossing star is equal to 90 minus the star's declination. The declination of Kaulia is 57 S and Ka Mole Honua 63 S. Thus, at the equator, Kaulia crosses the meridian 33 above the horizon due south (90-57=33) and Ka Mole Honua crosses the meridian 27 above the horizon due south (90-63=27).

As the wayfinder sails north of the equator, these two stars will cross the meridian at lower and lower altitudes above the south. To get the new altitude, he subtracts his destination latitude from the altitude of the meridian-crossing star at the equator. Therefore, if his destination latitude is 10 N, the new altitude of Kaulia will be 23 (33-10=23). Similarly the new altitude of Ka Mole Honua will be 17 (27-10=17). Thus, the wayfinder knows he has reached his destination latitude (10 N) when he finds Kaulia is 23 and Ka Mole Honua 17 above the south when they cross the meridian (that is when they are pointing upright).

Conversely, as the wayfinder sails south of the equator, the two stars will cross the meridian at higher and higher altitudes above the south. To get the new altitude, he adds the destination latitude to the altitude of the star at the equator when it is crossing the meridian. Thus at 10 S, Kaulia will be 43 (33+10) and Ka Mole Honua 37 (27+10) from the southern horizon when they cross the meridian.

The interesting thing here is that at 21 N (about mid-latitude of Hawaii), Kaulia crosses the meridian 12 above the southern horizon (33-21=12) and Ka Mole Honua 6 above the southern horizon (27-21=6). Here the distance between Kaulia and Ka Mole Honua is equal (6 ). This is a clue that the wayfinder has reached the latitude of Hawaii. This was the solution to Nainoa Thompson's problem!

Cross @ Hawaii
Clue that you have reached latitude of Hawaii


Latitude-Rising and Setting Pairs

Sometimes pairs of stars rise and set together and they only do so at specific latitudes. A rising or setting pair can give the navigator a clue about his latitude. For instance, at Tahiti 17 S, the pair Sirius and Pollux will set (and rise) together. They will not do so at the equator. It is easier to observe a setting pair than a rising pair since the setting pair will be sinking to the horizon but you have to anticipate the appearance of a rising pair.

Setting Sirius at Tahiti
Setting Sirius at Tahiti

Setting Sirius at the equator
Setting Sirius at the equator


Zenith Stars

At a latitude, certain stars will pass through the zenith. These stars will not pass through the zenith of other latitudes. The zenith star of a latitude is just the brightest star of the group of stars that pass through the zenith. The zenith star of Hawaii is Hokule'a (Arcturus) and the one for Tahiti is Sirius. The declination of the zenith star tells you the latitude of that place and vice versa. For example, Sirius, being the zenith star of Tahiti, has declination 17 S and the latitude of Tahiti is 17 S.

During a journey, the navigator will check for the stars overhead. He can estimate his latitude, as he would have known the various overhead stars for a given latitude. In reality this method is more inaccurate than the others since the navigator has to deal with a canoe that's more or less rolling on the ocean.

References:
1. Polynesian Voyaging Society: How the Wayfinder Determines Latitude
2. Night Sky: Measuring Angles