Quest to Calculate Longitude

You probably know that all you need to do to find what latitude you are at on the earth is simply measure the angle that the North Star is above the horizon.  That angle is your latitude.  But what about your longitude… thats an entirely different story and one that stumped scholars for several hundred years even after the British government offered a 20,000 Pound prize (1.5 million Pounds today or about 2 million dollars) to the person who could come up with a reliable way to determine longitude at sea.

It was basically a race between astronomers and clock makers as to who could find the solution of finding longitude at sea.  The problem is really quite simple in theory but extremely difficult in practice and the person who figured it out would be very famous and very rich and the country they were from would dominate the world both economically and militarily.

In theory all you have to do is note where the Sun is on the meridian (that is what a sextant is for). Note: The meridian is that north-south imaginary line that cuts the sky in 1/2  directly overhead.  When the Sun is on the meridian it is noon at your location.  All you need to know is the time at some other location (say Greenwich, England) and you can easily figure out how many degrees of longitude east or west of Greenwich you are since the earth rotates exactly 15 degrees every hour.

The challenge comes in knowing the exactly time in Greenwich, England, which you need to know accurately.  At 40 degrees north latitude (which is about where you are right now), you are traveling about 800 miles per hour on the rotating earth (which is about 1/4 mile per second).

The astronomers have always been the timekeepers since the years is determined by the earth’s orbit around the sun.  The month comes from the motion of the moon around the earth.  Our 24 hour day comes from the ancient Egyptians who divided daytime into 10 hours they measured with the shadow from their sundial clocks and added a twilight hour at the beginning and another one at the end of the “day-time” and did the same with the “night-time”.  The subdivision of hours and minutes into 60 comes from the Babylonians who really liked “base 60” and used it for the subdivision of the hours and minutes and even used it as a basis when they decided how to divide up a circle (360 parts or degrees).

Getting back to longitude at sea using the stars……one way the astronomers wanted to do it was to tell time with the stars or even with the moon but the calculations were very very complex.  Then they wanted to use the moons of Jupiter which were visible and predictable and easy to see when you were on solid land but very hard to accurately see on a pitching ship at sea.

The clock makers thought they had the solution and even had a very accurate clock….on dry land but when you put that clock, operated by a swinging pendulum on a pitching and rolling ship at sea the clock was very in-accurate, not to mention the humidity and temperature changes affecting the clocks operation.

Here is a detailed account of the man that solved the problem…

Between 1550 and 1650, one in five ships was lost between Portugal and India. The issue  reached a peak in the 17th century, when imperial conquest and colonialism relied on the sea trade. By the end of the century, nearly three hundred ships a year sailed between the British Isles and the West Indies to ply the Jamaica trade. Commodities and cargo, like sugar and cotton, were transported eastward across the Atlantic to meet consumer demand in Europe. The westward trade, however, was that of people who had been enslaved and forcibly transported to grow and harvest those commodities that fed the increasing European appetites [visit the National Archives website for more on this].

In 1714, merchants and sea captains banded together and brought a petition to the British Parliament to solve the longitude problem. The government paid attention and offered a hefty reward to anyone who could solve it. The Longitude Act, issued on July 8, 1714, offered up £20,000 prize  for a practical and useful method to determine longitude to an accuracy of half a degree.

Today, the motivations of the Longitude Prize are to address an intractable problem to better meet global health needs.  Although the Longitude Prize was created in another epoch its ability to attract diverse types of people to work on intractable problems is as relevant today as it was in the 18th century.

Over a period of 114 years, the board in charge of judging received countless submissions, but it wasn’t until John Harrison arrived in London in 1735 that they had a real contender. Harrison was a carpenter from Yorkshire who had taken up clock-making just a year before the prize was announced. He had no formal training. In fact, his family was of limited means, and clocks were so expensive, it’s unclear whether he’d ever seen a clock outside of pictures in books, before he created one himself.

To calculate your longitude at sea, you need to be able to compare the time on the ship to the time at a port, where longitude is known. That meant keeping accurate time for days, which was impossible with eighteenth-century clock tech. But not for Harrison.

Harrison’s clocks were remarkably innovative. They were virtually frictionless and required no lubrication, which was unheard of at the time. Without oil, a clock had a much better chance of staying accurate at sea because there were no lubricants to get thicker or thinner as the temperature changed. No one was expecting a break-through from such an unusual challenger. As Dava Sobel writes in her book Longitude: “The only thing more remarkable than the Harrison clocks’ extraordinary accuracy was the fact that such unprecedented precision had been achieved by a couple of country bumpkins working independently.”

While Harrison was never awarded the full £20,000, he won the most money of all the contenders. Over almost 50 years, he brought the Longitude board four maritime clocks. The first, H-1, was incredibly accurate, but each was better than the last, and H-4 was a masterpiece.

Lieutenant Commander Rupert Gould of the Royal Navy, who rescued and repaired Harrison’s clocks in the 1920s, summed up Harrison’s genius perfectly in a 1935 speech,  describing H-3: “It embodies several devices which are entirely unique—devices which no clock-maker has ever thought of using, and which Harrison invented as the result of tackling his mechanical problems as an engineer might, and not as a clock-maker would.” Harrison’s unique perspective, his lack of traditional expertise, gave him the ability to do something even Isaac Newton didn’t believe was possible


You are in Cleveland, Ohio and the sun is directly overhead and the time on your watch is 1:30 PM, what is your longitude?

Disregarding the “Equation of Time” which cause solar time and our clock time to vary throughout the year by as much as 14 minutes, lets do a rough calculations…

1. We know that in Greenwich, England it is 5:30 PM so that means our Time Zone is 5 hours ahead of the Greenwich England (or 1st) Time Zone.

2. We also know that each Time Zone is 15 degrees wide and 1 hour in time correction
360 degrees / 24 hours = 15 degrees per hour

So the beginning of our Time Zone is somewhere to the east of us in the /United States and is 75 degrees
15 degrees per Time Zone x 5 Time Zones = 5

It is 30 minutes pat the hour or 1/2 way past the hour so the sun is 1/2 way through our Time Zone.  If the entire Time Zone is 15 degrees wide then 1/2 way through it is 7.5 degrees

So we that the beginning of our Time Zone (75 degrees) and add how far we are into our Time Zone (7.5 degrees) and we get 82.5 degrees

The exact longitude of Cleveland, Ohio is 81.7 degrees.
Not bad for a rough calculation not taking into account the Equation of Time which, if we calculated it in, would give us our EXACT longitude.