How did the navigators calculate their star sights?

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Tim Zukas

Member
It seems Titanic's navigators didn't do celestial navigation the way we think of it nowadays, the Marcq St Hilaire method of assuming a lat-lon and shifting it as needed to match the measured star altitudes. Instead they would do a couple of star sights to get their latitude, and a couple more to get their longitude. How much do we know about the details? How did they do the calculations, converting star altitude to latitude and star altitude to longitude?

That Titanic book says the ship carried the expected Nautical Almanac, chronometer and sextant, and the only other thing it mentions is Burwood, presumably meaning Burdwood's tables. Hathitrust has that book; turns out it gives you the star's azimuth to an arc minute, if you tell it your latitude (to a whole degree) and the star's declination (to a whole degree) and the star's LHA (to a whole degree). It doesn't give you the star's altitude -- of course you can eventually calculate that, given the azimuth, declination and LHA, but there must have been a better way. Another problem: the star's declination couldn't exceed 23 degrees north or south.

One possible alternative for longitude was Martelli -- Hathitrust has that too. If you know your latitude and the star's declination and altitude, it tells you its LHA.

Another alternative was to just use a regular table of logarithms of trig functions -- Hathitrust has the Bowditch book of tables that came out in 1911 and includes all the necessary five-place logs, and the formulas don't look prohibitively lengthy.

Related question: how much did navigators rely on Polaris? Was the sky usually clear enough, or often clear enough, to get a good sight on a second-magnitude star while the horizon was still visible? No other way to get an accurate latitude, which they need to get an accurate longitude.

Another question: Boxhall said they would get longitude by shooting a star to the east and another to the west. Did the eastern horizon remain distinct for a while after sunset, long enough for a bright star to appear above it?



 
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Doug Criner

Doug Criner

Member
Latitude is easy - just measure the altitude of Polaris with a sextant. Longitude is determined by measuring the altiude of several stars and reduce the sights using the exact GMT and the current nautical almanac - each star sight will allow plotting a line of postion, and the fix is where the lines of postion intersect. A noon sun sight will also allow determining longetude. Star sights are best taken in twilight when the horizon is sharp.
 
Samuel Halpern

Samuel Halpern

Member
Dave Gittins wrote an interesting article some years ago about navigational methods in 1912.
I was able to access it here:
then click on Titanic Navigation link in the top left side of the box.
 
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Tim Zukas

Member
Thanks for the link. Turns out Hathitrust has the 1890 edition of Norie's tables; he gives the logarithms of trig functions needed to calculate the longitude, given a star's altitude, the assumed latitude and Greenwich time. He doesn't give any easier method to calculate longitude.

Say they're doing star sights at 2233 GMT on 14 April 1912, with the ship at 41.85 N 47.92 W. If they want two star shots for latitude, the two stars closest to the meridian are Polaris and Alphard, the latter being a second-mag star at altitude 39 degrees, azimuth 170 degrees. So its LHA is 352 degrees, which is far enough from the meridian that reduction to the meridian gives less accuracy. (In the 1911 Bowditch tables, the reduction table doesn't extend that far from the meridian.) So the question is, would they settle for less accuracy, or would they work with logarithms to get the right answer?

For longitude they'll use Aldebaran (altitude 29 deg, azimuth 266 deg) and maybe Arcturus (alt 20 deg, azi 81 deg) or maybe Saturn (alt 14 deg, azi 279 deg). No bright star is better than those. But maybe it's not that important to get their longitude, if they got a good sight of the sun when it was directly west of them that afternoon?

If they do want longitude from the Aldebaran sight, the calculation could go like this:

Add p (Aldebaran's polar distance), latitude 41.85 deg, and h, the corrected observed altitude; divide the total by 2 to get S. Then the logarithm of the haversine of Aldebaran's LHA is

log of the cosine of S, plus
log of the sine of (S - h), plus
log of the secant of 41.85 deg, plus
log of the cosecant of p.

Still have to calculate Greenwich sidereal time to get Aldebaran's GHA, but they have to do that whatever method they're using.

Maybe now they could use Burdwood -- the interpolation isn't easy, but they can get a rough idea of Aldebaran's azimuth, allowing them to draw a line of position thru 41.85 N at the calculated longitude. The alternative is to add up the logarithms again, but assuming latitude 41 degrees instead of 41.85 -- then they'd have two points on the almost-north-south line of position.
 
Tony Francombe

Tony Francombe

Member
What I found curious about the star sight position fixing on the night of the Titanic's accident was the number of different officers involved. Lightowler took the sights about 7 pm , passed them on to Boxall to do the calculations, and then Captain Smith put the position on the chart about 10 pm. This seems a true recipe for errors. At least in post World War 2 times the normal practice was for just one officer to do the whole task. For those navigators who used star sights regularly (sometimes twice a day on long ocean passages), the whole job could be under in about 30 minutes. Tony Francombe
 
Doug Criner

Doug Criner

Member
What I found curious about the star sight position fixing on the night of the Titanic's accident was the number of different officers involved. Lightowler took the sights about 7 pm , passed them on to Boxall to do the calculations, and then Captain Smith put the position on the chart about 10 pm. This seems a true recipe for errors. At least in post World War 2 times the normal practice was for just one officer to do the whole task. For those navigators who used star sights regularly (sometimes twice a day on long ocean passages), the whole job could be under in about 30 minutes. Tony Francombe
My experience in the U.S. Navy was during the period when celestial navigation was still widely used. Even on my small destroyer, the navigator was essentially one officer's full-time job. The navigator stood no regular bridge watches - since he was occupied with morning and evening star stights, reducing the sights, plotting positions, planning which stars to use for the next round of sights, and was continually on call. The navigator was assisted by an enlisted quartermaster. Typically, the navigator handled the sextant, and the quartermaster assisted by punching the clock when the naviagor called, e.g., "Betelguese, mark!" The navigator would then read the altitude off the sextant's vernier, and the quartermaster would record it.

The navigator was also responsible for calculating tides, currents, checking chronometers, following weather reports, maintaining the dead reconning plot, and knowing instantly when sun and moon rises/settings would occur.

I tend to agree with Tony - having a parade of people involved in celestial fixes and other navigational chores, seems to suggest the old adage: too many cooks spoils the broth.
 
Georges Guay

Georges Guay

Member
Regrettably for Captain Thomas Hubbard Sumner, Captain Adolphe Laurent Anatole Marcq de Blond de Saint-Hilaire (Marcq Saint-Hilaire) born in 1832, published in the Maritime Review in 1873, a first memoir which he entitled «Note on the determination of the point» where he resumed the Sumner method, without naming it. Two years later in 1875, he published in the same review a second dissertation entitled «Calculation of the observed point - Method of estimated heights» where he considerably simplified the calculations and which is considered as the «birth certificate» of the Intercept Method of calculating a celestial fix position from an estimated position and ever since, universally practiced. However, it must be noted that even the Intercept Method was initially described in 1875; the method did not really begin to be generally practiced on ship’s bridges before 1900.

In 1912, they could certainly solve a:

  • Stellar Celestial Fix from Marcq St. Hilaire Intercept method at nautical dawn,
  • Latitude from Polaris,
  • Magnetic Compass check at sunrise by the Amplitude method,
  • Longitude at Prime Meridian Passage, lat. and dec. agreeing,
  • Sun line in mid-morning,
  • Latitude, Longitude and Chrono error check at sun Meridian Passage,
  • Longitude by Chronometer with a Sun line running fix,
  • Sun line in mid-afternoon,
  • another Longitude at Prime Meridian Passage, lat. and dec. agreeing,
  • another compass check at sunset by the Amplitude method,
  • Latitude from Polaris,
  • Stellar Celestial Fix from Marcq St. Hilaire Intercept method at nautical twilight,
…without forgetting the Longitude and Chrono check by Lunar Distance Method!

All the calculations could be computed using the Nautical Almanac or Ephemeris and the Norie’s Table. The Intercept was outlined on large scale plotting chart, most probably easily made on board. For a Stellar Celestial Fix, the easiest method was to sight a celestial body dead ahead, one visible on the stern quarter and one on each beam so to minimize inaccuracy during the LOPs’ Run.

For example, on April 14 1912 at 7:38pm (22h38m GMT), Aldebaran was dead ahead, Polaris on the Stb’d beam, Arcturus on the stern and Alphard on the port beam, all at proper altitudes to minimize refraction. Capella, Kochab, Regulus were fine as well...
 

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Tim Zukas

Member
All the calculations could be computed using the Nautical Almanac or Ephemeris and the Norie’s Table..

Looking thru Norie's book


it seems the only way to use it to convert a star's altitude to a position line on the chart is logarithms. He gives logarithm tables, but far as I can see he gives nothing simpler than that. So my question is: did Titanic's officers use logarithms for their sight reduction, for lack of a better method? Or did they use Martelli's tables to get their longitude, and logarithms just for their latitude?

By the way: they probably knew better than to try to get their longitude at noon. On 14 April the sun reached its maximum altitude (seen from Titanic) when its azimuth was 181 degrees.
 
Georges Guay

Georges Guay

Member
This is what I believe to be the Stellar technique used for the 7.40pm celestial fix. I don’t see any other method than that.

1656277656972
 
Georges Guay

Georges Guay

Member
In 1912, to execute a (multiple stars) Stellar you needed:

  • Navigational Star Chart (Nautical Ephemeris)
  • Sextant (corrected for the instrumental errors)
  • Chronometer set on GMT (Chronometer Error & Rate Book)
  • Nautical Ephemeris (Greenwich Hour Angle (GP long) & Declination (GP lat) of heavenly bodies)
  • Norie’s Table (Sextant Altitudes Corrections, Haversine, Natural Functions of Angles & ABC Azimuth Tables)
  • Large scale plotting chart, parallel rules and divider

... and hours of unforgiving tables inspections, interpolations and calculations to hopefully obtain a celestial fix within a precision of approx 5 nautical miles, better than 20 miles off ! ;)
 
Georges Guay

Georges Guay

Member
Here is an example of table’s inspections, interpolations and calculations they had to do for every single heavenly body sighted!
(see the attachments for the details)

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T

Tim Zukas

Member
So you think Titanic's navigators did use Marcq St Hilaire? I thought someone testified that they would do a couple of stars for latitude and a couple of other stars for longitude.

The 1890 edition of Norie's (the one at Hathitrust) doesn't show haversines or logarithms of haversines (or natural tangent/cotangents). Did those appear in a pre-1912 edition of Norie's? If not, the 1911 Bowditch tables would do the job (tho they were only five-place tables -- I haven't tried to figure out whether that matters).

Far as anyone knows, no one did sight reduction without logarithms in 1912? They might use different formulas, but all the formulas used logarithms?
 
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Bill West

Member
Hi Tim. The first "Admiralty Manual of Navigation" was published in 1914, I found a copy in an old bookstore. It was a bit of a struggle for me to follow as I know none of the abbreviations but I did find that the examples used logs and haversines. There was no mention of more direct tables for that step of the examples.

I have 1900 and 1907 copies of Norie's and they both have log haversines in table XXXI.

Bill
 
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