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Peter Fogg
>
> Bill wrote:
> (average them on the fly then do a plot against
> the actual Hc slope later).
>
> How is this averaging on the fly achieved, Bill?

Texas Instrument TI-30XA calculator (about $12 US now).

Using the statistics mode (converting input to decimal), enter the Ho's and
find the mean.  Do the same with the times of observations.  (One could just
add them up and divide by n.) This gives you and average time and Ho to
reduce.  As you have noted, averaging this way has its pitfalls, but it is
down and dirty.
>
> From an approx. 11 meter sailcraft under
> good conditions I would expect individual intercepts to be +/- 1.6 nm or
> better 66% of the time, with an average intercept (plot fitted to Hc line as
> per David Burch) better than 01.5 nm.
>
> Sounds pretty good to me, given those somewhat trying conditions.  Its
> interesting that, if I have understood correctly, your actual sights have been
> improved via some sort of comparison with slope technique.  And yes, please
> send me that PDF of the Burch article.

Not a statistics maven, but it strikes me averaging data with a normal
distribution (or not) by any means will help to establish central tendency.
With the Burch method we gain an advantage lab-rat observers don't have by
comparing to a known.
>
> My worst set (first on-the-water experience) was using a kit cardboard
> sextant against sand dunes with a hazy horizon and confused 8-10ft seas on a
> 34' fin-keel sailboat.  My intercepts were about 5-7 nm off, all in the same
> direction.
>
> Still rather good for cardboard.  I'll have to lift my game.

No matter what what Celestaire advertises (what the manufacturer claims,
accurate to 8 arc minutes) that bad boy can be good to 2 minutes of an arc
in ideal conditions if you take care in assembling it (frame flat, index and
horizon mirrors perpendicular to the frame) and calibrating it for IE (which
only changes with humidity ;-)  The $8 bubble attachment is a godsend as
opposed to their $60 "real sextant" practice bubble horizon.  Limiting marks
to assist in centering the bubble and easily lighted from above for taking
elevations of stars for star-to-star sextant checks. A bit prone to flapping
in the wind and and not waterproof.

As to your game, check out the numbers in the Starpath article on using
plastic sextants. A wealth of information applicable to the OCD metal
sextant user and a target to shoot at.
>
> My second worst (using Astra) was a day with 4 ft seas but with the
> totally-obscured horizon mentioned above.  I looked at distance boats'
> waterlines, and adjusted with dip short to guess about where above the
> bottom and below the top of the mess the horizon might be.  The range of
> intercepts was approx. plus/minus 6'.  Using the Hc slope method the
> "averaged" outcome was almost spot on. Better lucky than good. 
>
> Lucky or an endorsement of the slope technique?

Lucky I think.  If I caught a bullet in the dark with my teeth the first
time out, I wouldn't go around bragging how good I was ;-)  I expected
better given my "scientific" approach. Mathematically averaging as outlined
above (given the range and standard deviation of Hc vs Ho for individual
sights) was not significantly off the Burch method.
>
> In my last on-the-water attempt (July 2008) clouds rolled in just as I was
> ready to shoot.  I got off 2 observations shooting through the cloud before
> the sun was obscured. 3 ft seas and a usable although not crisp horizon.  I
> had to shoot through sails/rigging so I was not able to fully rock the
> sextant to my satisfaction.  My intercepts,  0!7 and 1!9 (average 1!3) were
> both larger than the Hc. That suggests to me the sextant was not plumb.
>
> As to fixes, I cheat and do not follow established procedure. I factor
> leeway into DR and use my EP as AP. I would agree that any running fix (5
> hours) greater than 3 nm off my GPS position under average conditions would
> have me looking for a reason why.
>
> I don't think this is cheating.  Sounds more like common sense.

There is the purist in me. If I understand the texts and discussions on the
list, DR is derived from heading, speed, and time.  Nothing more.  This may
work well in blue water.

I take note that some texts go to the trouble of publishing leeway tables
based on course related to true wind (point of sail), true wind velocity,
power vs. sail and keel type. Even wind-driven current formulas.

The bulk of my salt-water sailing has been on Rhode Island's Naragansette
Bay and Connecticut's Long Island Sound. Their tide-induced currents merit
special attention.

Somehow using DR I am supposed to extract current (set and drift),
wind-induced surface current, and leeway after the fact from the
statistically-probable distance my fix is off from my DR position?

Why the heck do the texts and tidal charts give you information to help you
estimate position and keep off the rocks if you are intent on using DR for
your AP?  What is the cry from the crow's nest? "Island dead ahead, but DR
says we are not here, ignore it." 

Bill B





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