NavList:

Alex wrote:

> I just returned from my short sailing trip,
> from Kiel to Danish islands,
> and report my observations with the new
> pocket sextant (XIX century Troughton and Simms).
>
> June 18, Sun, boat under motor, good conditions.
> Local time 10 Average of 5 obs. error +0.6' (sigma=0.6')
> Local time 12 Average of 5 obs. error 0.0' (sigma=1.5')
> Local time 12:40 Average of 6,  error 0.0' (sigma=1.0')
> Local time 14:30 Average of 3, error -0.5'

Alex

I'm impressed (and a bit jealous) of your results.  I spent June 22-27 on
Lake Michigan.  Boat--Catalina 350.

The first day I was able to make some cel nav observations (after working on
compass variation and autopilot calibration). 1-3 ft immature seas,
otherwise very good conditions.  I made 7 observations, but
miscommunications between my helper and myself made the first 4 useless.  I
chose the time of sights to coincide with the sun being approx. 270d so I
could also play with time sights.

Averaging time, position and Ho I was -0d 1.4' (-1.5' if I consider sun
velocity of 14d 59' 52").  Translating into 1.04 nm off at 41d 46!25 N.

Separate observations:

21:53:00 GMT  -1.5' error
21:54:57 GMT  -2.0' error
21:56:47 GMT  -1.0' error
Average       -1.5' error
SD             0.5'

The time sight was off by 0d 01!95 (east of GPS location) or 1.44 nm. Hmm,
back to the drawing board?

Saturday was a beautiful day in Chicago , but I spent most of the day at the
planetarium admiring their collection of sundials, astrolabes etc. (As the
harbor master remarked, "If it was this beautiful all the time we couldn't
afford to live here.")

The other days were 10-15kt and 3-5ft seas, usually building to 15-20 kt and
4-6 (or better) seas, mostly overcast, so we had our hands full and I did
not run for the sextant when the sun popped out briefly.

I did have some fun with coastal piloting techniques on the way back.  I did
three position checks (against GPS coordinates) using the angle between the
Sears and John Hancock buildings.  We were about 4 nm out, angle around 16d.

2:53 EDT
Compass (hockey puck) bearings of 303M  Sears and 319M JH
Off by < 0.2nm (on course line but further out than GPS coordinated)

2:58 EDT
Sears Bearing by compass   300d
Sextant angle              16d 25!4 corrected for IC
Course approx. 42 Mag
Off 0.15 nm along bearing to Sears, too close to Sears

3:03 EDT

Sears bearing
   GPS            285T
   Compass        288M = <285T
   Sextant angle  16d 33!8
   Course approx. 42 Mag
   Spot on

Later on did some calculations on distance vs height above horizon using the
Bowditch Table 15 formula.  In all cases I used GPS distance and location as
the standard, and both compass and GPS bearings for plotting in 2 of the 3
Chicago calculations. The compass was spot the first plot, 1d off GPS the
second observation, <1.5 off GPS the third observation.  Oddly, the compass
beat the GPS in nailing the GPS location the third observation.

Distance from GPS location varied by no more than 0.3 nm in any case.  Some
were too close to differentiate on the plot.

Now we get to the interesting and finite part. I have long contended that
the Bowditch refraction constants for T15 placed one too close to the
object, and derived new constants based on Frank's suggestions on
terrestrial refraction as well as from a web page he pointed us to many
moons ago.


THE NUMBERS

H Sears, 1485 ft above water level
He 6 ft
1d 05!2 Sextant angle, corrected for IC and dip
12.04 nm   Distance GPS
11.92 nm   Distance calculated Bowditch constants
12.06 nm   Distance calculated / my constants
12.04 nm   Distance calculated / Frank's constants


H Sears, 1485 ft above water level
He 6 ft
0d 057!2 Sextant angle, corrected for IC and dip
13.52 nm   Distance GPS
13.33 nm   Distance calculated Bowditch constants
15.52 nm   Distance calculated / my constants
13.50 nm   Distance calculated / Frank's constants

H AON, 1163.5 ft above water level
He 6 ft
0d 031!9 Sextant angle, corrected for IC and dip
17.28 nm   Distance GPS
16.83 nm   Distance calculated Bowditch constants
17.30 nm   Distance calculated / my constants
17.25 nm   Distance calculated / Frank's constants


Coming into Michigan City, the results were not as good for the cooling
tower.

H Light house, light 55 ft above water level (used 60 ft to top)
He 7 ft
0d 04!0 Sextant angle, corrected for IC and dip
5.15 nm   Distance GPS
4.95 nm   Distance calculated Bowditch constants
5.19 nm   Distance calculated / my constants
5.16 nm   Distance calculated / Frank's constants

H Cooling tower, 381  ft above water level (361 ft + 20? ft) level (use 381)
He 7 ft
1d 04!6 Sextant angle, corrected for IC and dip
3.40 nm   Distance GPS
3.21 nm   Distance calculated Bowditch constants
3.22 nm   Distance calculated / my constants
3.22 nm   Distance calculated / Frank's constants
Smells like pilot error <G>

If interested, following are the constants I derived and used in the T15
equation for the calculations:

Bowditch:  0.0002419 & 0.7349
Bill:      0.0002001 & 0.6079
Frank:     0.0002039 & 0.6196

Summing it up, there is not a lot of data and a pretty wild platform, but
based on my observations and Frank's beach shots I would tend to favor the
constants derived from Frank over those derived from the web page, and both
over the Bowditch constants.  I would love to learn the results if anyone
experiments with the proposed constants.

Bill
===================================

SECOND PART

Bill Wrote

"H Cooling tower, 381 ft above water level (361 ft + 20? ft) level (use 381)
He 7 ft
1d 04!6 Sextant angle, corrected for IC and dip
3.40 nm   Distance GPS
3.21 nm   Distance calculated Bowditch constants
3.22 nm   Distance calculated / my constants
3.22 nm   Distance calculated / Frank's constants
Smells like pilot error <G>"

A possible reprieve. <G>  On the water I had real trouble telling the
difference between my helper's 0 & 6's, and 4 & 7's.  The cooling tower was
my last observation before going wing-on-wing, rigging a preventer and
taking the helm into harbor.  Then I cooked dinner for the boys, packed and
hit the road home.  So I did the lighthouse and cooling tower calculations a
day later.  Now that I look at the original, I have no idea if it Hs was 1d
07!6 or 1d 04!6.  If the latter I am about on the money.  Won't know until I
can wave the original past my helper's eyes.

Another interesting exercise:

5:48 PM EDT we were watching a southbound lake freighter closing off our
port bow. I did compass bearings at approx. 5 minute intervals to determine
if we would pass safely astern. She gained about a degree a minute, so no
problems.  At 6:03 it dawned on me I might try to determine distance to the
ship using the sextant.  Bow to stern 5d give or take a few tenths.

at 600 feet LOA  1.13 nm
at 700 feet LOA  1.32 nm
at 800 feet LOA  1.50 nm

Then I did a Distance = Time * Speed calculation when we passed astern at
6:19.

16 minutes * 5.12kt SOG = 1.36 nm.

Not rocket science, but a fun sanity check.

Bill    




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