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    Re: Allowing for current
    From: George Huxtable
    Date: 2009 Oct 2, 01:14 +0100

    Douglas Denny asked -
    
    My final question to you has to be:  have you tried your method by sailing 
    across the English Channel?
    
    Yes, invariably; in both directions. I have never even attempted to follow a 
    straight ground-track in those circumstances. And most years, between 1970 
    and 2005, I've made that round trip; in some years, twice.
    
    ========================
    
    Asked for for the reason why the "straight ground-track" gives him a better 
    result, he replied-
    
    "It is my claim.  And the explanation has already been given: I have already 
    experienced the variabilities that there are 'out there' in the Eng.Ch. and 
    I know correct coastal navigation can only be done with a methodical 
    approach, not the haphazard method you propound."
    
    No such explanation has yet appeared. It can't be that it's made necessary 
    by the "variabilities" in the English Channel, because he has already told 
    us that he would use the same procedure in a simpler environment in which 
    all those "variabilities" had been swept away.
    
    Let's look at some numbers in the example I provided. Assume that a tide 
    runs for six hours between turnings, though in reality it's usually a bit 
    longer.
    
    Douglas and I, each in a craft that does 4 knots through the water, set off 
    at 6 am, across that idealised stretch of water running East-West, 48 miles 
    wide, to a harbour due South of us, just as the Eastgoing stream starts.
    
    If the tide is going to sweep through 11 miles between turnings, that's a 
    maximum rate of 2.9 knots. It will be running Eastwards at that rate at 9am, 
    then slack water at noon, 2.9 knots Westerly at 3pm, and slack again at 6pm.
    
    I will keep to a constant heading of 180�, due South, so each hour I will 
    make 4 miles of Southing. Douglas, however, will keep to a straight 
    ground-track, steering so as to offset the tide as necessary.
    After the first hour, the tide will be running Easterly at 1.4 knots, and he 
    will have to head off from a Southerly course by 21�, to steer 201, to keep 
    to his track. As a result, the Southerly component of his speed will fall to 
    3.7 knots.
    By 8am, the current has increased to 2.5 knots, and he must now steer 219�, 
    so his rate of Southing drops to 3.1 knots.
    By 9am, the current has reached its maximum of 2.9 knots, and Douglas has to 
    counter it by heading 226�, and he is then making no more than 2,8 knots 
    towards his Southerly goal. However, he has kept perfectly on track. His 
    Southing, over that 3-hour period, adds up to 10.25 miles.
    On the other hand, at my steady 4 knots, I have made 12 miles Southwards in 
    the same 3 hours, though by now I am away to the West by 5.5 miles.
    
    Over the next 3 hours, to noon, the current will gradually slacken, and 
    Douglas will slowly be able to head back towards his intended Southerly 
    course. In that period, he should make exactly the same Southing as in the 
    previous 3 hours, 10.25 miles, so 20.5 miles Southing altogether. And still 
    exactly on track. While I make an additional 12 miles of Southing, or 24 
    atogether. Now I'm halfway across, but way over, by 11 miles, to the East.
    Then, the tide turns, and follows the same pattern Westerly for the next six 
    hours during which Douglas will be having to steer increasingly away from 
    his destination, towards the NE, then back toward South at 6pm, by which 
    time his total Southing will have become 41 miles. Still on track, but still 
    with another 7 miles to go of the 48 mile crossing. By this time, at my 
    steady 4 knots, I have just got to the other side, and what's more, the tide 
    has just brought me nicely to the intended destination.
    
    Now, there's nothing hypothetical or theoretical about this. It's simply an 
    inevitable result of forcing a straight track over the ground, when there's 
    no reason to do so. And I would like to discover what advantage Douglas 
    finds, in taking the track he does, when in this example it has set him back 
    7 miles in a 48 mile passage.
    
    Douglas seems to think my own procedure is "haphazard", but it isn't. I 
    expect that in my own crossings, I've made just as many DR plots, and taken 
    as many bearings of various sorts, as he has. And as a result of any 
    evidence that comes up, the passage details may well get reassessed, and 
    corrective action taken. That's what navigation is about.
    
    It is just a convenient accident that in the case I described, a boat speed 
    and a crossing distance correspond to two tides' worth, so they cancel out, 
    and that's why I chose it as a simple example. For a faster craft, that 
    would not be the case, but the principle would be the same. Estimate the 
    passage time, sum up the overall tidal displacement that would occur during 
    that period (now non-zero), make the appropriate offset from the course to 
    destination by a simple vector diagram, and then steer that course, without 
    bothering about any "cross-track error" that may arise. And certainly, plot 
    the positions that result, at regular intervals.
    
    George
    
    contact George Huxtable, at  george{at}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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