

MtMan-List: Re: Celestial Navigation

I'm going to turn the reply to this one over to my husband. Jeff responds:

"Pat Quilter" <pat_quilter@qscaudio.com> wrote:

> one's latitude (north or south position on the
>earth) is relatively easy to obtain, by measuring the angle of the north 
star to
>the horizon.

Curiously enough, using the pole star to find latitude was not done 200 
years ago due to the necessity of knowing the exact time. This is because 
the pole star is not right at the celestial pole, but about 1/2 a degree 
away. Failure to compensate for this would result in an error of position of 
up to 30 nautical miles. The problem was, unlike today, knowing the exact 
time was difficult (see below).

> Since the sun travels a predicable path in the sky (even though the
>apparent height varies with season) with the use of tables and a "noon 
>(measuring the sun several times around estimated noon and determining its
>highest position) you could establish your latitude, using a sextant (an 
>to measure the angle between an object and the horizon). 

Acually, the observer simply adjusts the sextant one way until the sun 
appears to ascend no higher. At this point the observer knows that transit 
has occured and should be able to compute a latitude to an accuracy of about 
1.5 nautical miles even 200 years ago. (As David Thompson did).
Note that Latitude can also be obtained with a "common" (ie. accurate to 
within 10 seconds or so per hour) watch using a technique called the "double 
altitude" method. This was used by Thompson (and others) when solar transits 
were not convenient. For a full explanation of the method see my articles in 
Northwest Journal Volume IX. (For more information on Northwest Journal see 
www.telusplanet.net/public/gottfred/nwj.html, or write me)

>Actual practices
>involved more tricks (such as the artificial horizon noted) to compensate for
>inability to see the true "flat" horizon.

An artifical horizon (called "Parallel Glasses" 200 years ago) was essential 
for accurate results. (Dip short technniques using lake and river horizons 
were used but the error in estimating the distance to the far shore yielded 
poor results). Note that on land the navigator does not have to contend with 
many of the problems that plague the ocean navigator. This allows consistent 
and accurate results that would be impossible or very difficult at sea. I 
don't know what other 'tricks' you are referring to.

> Determining your longitude (how far
>east or west we are) would be simple IF we knew what time it was at a 
standard reference
>longitude (normally taken to be the Royal Observatory at Greenwich, 
England). We
>need only measure the difference in time between high noon at Greenwich and our
>local noon (using the same repeated noon sightings taken above) to 
determine how
>many time zones around the earth we are. 

Local apparent noon can not be determined to the necessary accuaracy by 
observing the time of tranist. The technique used was to compute one's 
latitude using either a transit or a double altitude followed by a 'time 
shot' in which the height of sun above the horizon is measured, and a 
spherical triangle solved to determine the local hour angle at the instant 
of the observation. This arc can be converted to time at the rate of fifteen 
degrees per hour, and the result is the sun's apparent time ante or post 
meridian. (As an interesting historical note, converting local apparent 
solar time to local mean time (using the equation of time) was not required 
as the lunar distance tables of the day used local apparent time.)

>Of course, before radio time signals,
>there were very limited ways to determine the time at Greenwich while
>travelling. The ultimate method, of course, required accurate chronometers; a
>good 1815 British Navy captain sailed with three of them and kept accurate
>records of their relative drift, and noted their offset upon returning to
>Greenwich. Lewis and Clark did not succeed in keeping a chronometer going 
>while travelling, but, "Undaunted Courage" describes Lewis's process of taking
>"lunars" to determine the true time. 

Quite so. L & C had "pocket chronometers" made by Arnold, presuambly using a 
detent escapement, but even so the accuracy over weeks would not be 
sufficient for computing longitude directly. David Thompson only posessed 
"common" watches - highly inaccurate things useless for computing longitude 

>The moon is constantly eclipsing various
>stars, which events are regular and can be put in tables. When the moon passes
>in front of star x, the Greenwich time is exactly ___. If you set even an
>average-quality watch to this time, it will still be close enough for a noon
>sighting the next day. The positions of Jupiter's four moons was another
>celestial clock. All of these events, of course, occur at inconvenient
>intervals, and cloud cover was the bane of surveyors.

It was not necessary to wait for the moon to eclipse a star (hardly ever 
happens for stars listed in the Nautical Almanac of the day). The observer 
simply chose a navigational star close to the ecliptic, and measured the 
distance from the limb of the moon to the star. He then "cleared the 
distance" of the effects of refraction using one of several techniques, and 
compared the result to the published distances as listed in the Nautical 
Almanac. David Thompson usually used the sun as the second object (as do I). 
Any given lunar distance will only yield a result accurate to about 20' 
(minutes) of longitude. So to get a position narrowed down to tolerable 
limits (say, within 5' longitude) one must make a dozen observations and 
average the results. For a complete explaination of these techniques see the 
cited Northwest Journal articles. 
By the time the 1800's rolled around, Jupiter's moons were no longer used 
for finding Greenwich time as the lunar distance method was far more 
convienient and yielded far more accurate results.

>Using these methods, I believe
>most of Lewis and Clark's positions were within 30 miles of their true 
>but as noted, this could be a deadly degree of error for a sailing ship.     

I stood at the Giant Springs of the Missouri River near Great Falls and 
measured their latitude as did Lewis. I was stunned to find that Lewis' 
latitude observation was in error by some 17 nautical miles. Even by the 
standards of his time this was a lousy observation. (David Thompson would 
have gotten it to within 1.5 Nautical Miles, I got it to under a kilometer) 
Perhaps Meriwether was having an especially bad day....

Pat, read my articles and give these techniques a try! I assume from your 
comments that you are an ocean navigator. Being land-locked, I developed an 
interest in studying how David Thompson was able to build such accurate 
maps. I have completely re-constructed his techniques, and, using my Astra 
IIIb sextant can nearly obtain the accuracy that he did with his Dollond. 
Doing this stuff will open up a whole new vista of fun (and humbling!) 
things you can do with your sextant. I would be happy to answer any 
questions you might have regarding the special problems of land navigation. 
Also- I have tables for f factors for altitudes above sea level &c. that you 
might be interested in...