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    Re: Wartime (WW2) navigation
    From: Jeremy C
    Date: 2010 Jan 31, 23:34 EST
    I cannot speak for navigation in the 40's or on British ships, but typically aboard today's US merchant ships, great circle tracks are laid out as a series of rhumb lines based on a fairly constant interval of longitude (usually 5 degrees such as 85, 90, 95 100, etc).  This is done because a relatively easy formula is available to calculate latitude at a given longitude along a GC track line.  These waypoints give a good approximation of the great circle track, while making it easy to keep a constant course for a reasonable span of time.  To change course based on a time interval would complicate this calculation needlessly.
    Engine revs give a reasonable account for speed if the assumed slip of the propeller is well known and accurate.  Usually slip is calculated by comparing engine distance from the revs to the noon fixed based on LOP's, but there if there were no observations available, this might be a good check for any log device available.  Whether this was done or not I cannot say.
    In a message dated 1/31/2010 9:05:40 A.M. Eastern Standard Time, george@hux.me.uk writes:
    Trevor Bell wrote-

    "I am researching the sinking of the RMS Rangitane in WW2 300 miles off New
    Zealand on her way to the UK via Panama. I have established that she was
    about 50nm off a whole circle course after about 45 hours having sailed
    420nm of the 1500nm to her first pre-arranged waypoint. I am trying to
    establish whether being off course could have been the result of normal
    navigation error.

    I know that the weather at the time was not good - overcast skies and rain
    for much of the time. I have learnt a little bit about old fashioned
    (pre-GPS) navigation and would like to test out some conclusions on you
    learned guys.

    1. I have been advised that under normal wartime conditions of radio silence
    and out of sight of land an accuracy of about 2 arc minutes or 2 nm was
    routinely achievable with celestial navigation on a large ship. But with
    constant cloud cover, I assume that a position could only be estimated from
    bearing, log, knowledge of currents and leeway.
    2. Compass error could be as much as one degree - about 7nm in 420nm from
    poor steering and calibration.
    3. Errors from a poorly calibrated log could be as much as 5% - 23nm after
    45 hours.
    4. Errors from a mid ocean 1kt current could be as much as 42nm but I
    understand that this would have been automatically compensated for by the
    5. I do not know how much windage would have affected a 16,000 ton ship.

    If all these factors were cumulative then I assume that 50nm deviation after
    45 hours might have been possible, yet many people have told me that it is
    highly unlikely. But I need to explore one further possibility but my maths
    isn't up to it:
    I understand that there are two fundamental ways to navigate between two
    points - whole circle and Mercator and I think I understand the relative
    benefits. But how do I calculate the difference in track after 45 hours
    using the two different methods? Can anybody point me to some software which
    might help?"


    Those error assessments sound to me as if they have been made by an
    experienced navigator. The only thing that doesn't ring true is the phrase
    "whole circle", which no navigator would use; "great circle" is what is
    meant. I wonder, then, whether that information has been badly translated
    from a document that was written in another language- German, perhaps?

    Compass error of "one degree - about 7nm in 420nm" sounds about right to me.
    I can't see how Irv Haworth makes it 4 nm.

    I would question the estimate of 5% inaccuracy in a ship's log. Ships of
    that era would normally tow a taffrail log, and I would put that at about
    2%. As Irv has stated, counting propellor revs will also give distance
    travelled, and except in extreme conditions, I would expect that to be
    within 2%. But on this list there's Henry Halboth, with direct experience
    aboard vessels of that era, who can contribute with authority; and I hope he

    Ocean current in this area is weak. The November pilot chart, that Gary has
    pointed to, gives it as going southeasterly at 5 to 10 miles per day. Your
    limit of 42 miles seems too high to me. But what information did navigators
    have in 1941, I wonder? Wikipedia on "Ocean currents" shows an American
    global chart for 1943, to which information the navigator might have had
    access in 1941. That also shows a southeast-going current, indicated as
    rather weak, but without numbers for its speed.

    Overall, I would say that the navigator of such a well-found ocean liner
    would be able to assess his dead-reckoning position, after such an interval,
    within a radius of 25 miles, rather than Trevor Bell's estimate of 50.

    I agree with Irv, that except in extreme conditions, windage doesn't need to
    be considered.


    All I know about the fate of the Rangitane is from a quick scan of-
    http://www.btinternet.com/~thebells/rangitane/story.htm , a well-written
    account which has been put together by our enquirer, Trevor Bell.

    This makes it clear that Rangitane left her berth in Auckland at 1 pm on
    Sunday 24th November, 1940, anchored overnight below Rangitoto Island,
    raised anchor at 5am, and "cleared the swept channel by noon on the 24th
    November". Presumably, this is an error, and 25th November was intended. I
    don't know how far that swept channel would extend, but 7 hours sailing at
    16 knots would take her past Cape Colville and Cuvier Island (36º 27'S, 175º
    46'E), which would be a likely landmark for her to "take her departure".
    From then on, she would be relying on dead reckoning, if the sky was cloudy.

    A German raider was sighted at 3.35 am on Wednesday 27th, and the liner had
    been boarded, and was in flames, by dawn. So that's an elapsed interval,
    since the previous sight of land, of less than 40 hours, not 45 hours (I'm
    nit-picking here), for which dead-reckoning was required. If she had been
    doing 16 knots, that would put her some 632 miles west of her
    departure-point, which we can take to have been somewhere within sight of
    Cuvier. Trevor states above "after about 45 hours having sailed 420nm  of
    the 1500 nm ..." Why would she have been going so slowly, at less than 10
    knots, which would only increase the danger of interception?

    In normal times no mariner would deviate significantly from a great-circle
    course to such a distant landmark, which would have been the Columbian
    island of Malpelo, on the approach to Panama. That would have been a course,
    from Cuvier, starting off at about 93º, which is slightly South of due East,
    and a distance of 6152 miles. Each day, the vessel would steer a rhumb-line
    course for the day, with constant compass bearing. At intervals, probably
    daily, the great-circle course, from the position reached, would be
    recalculated, and sailed as a rhumbline for a time. But to keep to such a
    predictable track would invite interception, by the German raiders which
    were by then known to be at work in the South Pacific. Trevor Bell tells us
    that a prearranged waypoint had been established, 1500 miles along the path,
    though he doesn't state the coordinates.  They would be useful for us to
    know, if he has them. It was likely to have been deliberately somewhat away
    from that great-circle.

    However, to get from the latitude of, say, Cuvier, to a waypoint exactly
    1500 miles West, at the same latitude (for example), there's damn-all to be
    gained by sailing a great circle, starting at a heading of 99.4º, rather
    than a directly due-East rhumb-line, keeping to a constant due-East of 90º.
    The difference is no more that 7 miles or so. So a navigator might choose to
    sail a great circle, or might just as well not bother. There is, however, a
    significant difference in the midpoint track, which would go some 40 miles
    further South, for the great circle, than for the rhumbline.

    But I should make it clear that I don't have practical experience of ocean
    passages or big-ship navigation, my experience being entirely in small craft
    near continents. Others on this list do have that experience.


    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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