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Chuck Taylor wrote:

>--- Herbert Prinz wrote:
>
>
>
>>I am wondering about Starpath's recommendation of
>>the Mark 3 as
>>
>>"... the sextant of choice for coastal piloting."
>>
>>
>...
>
>
>>What applications do they have in mind?
>>
>>
>
>I should think that they have in mind distance off by
>vertical angles (height of a lighthouse etc) and
>horizontal angles.  For those applications I would
>agree that a Davis Mark 3 would be quite adequate.
>

The main argument in support of my skepticism got snipped away: While
making their claim, Starpath admits to not expecting better accuracy
than 10' from a Mark 3. This is inconsistent. The problem is addressed
in the USPS AP course. I quote from "Advanced Piloting" 95, Rev. 0797,
USPS Advanced Grades Division, pp. SM 3-2:

"Sextants of metal, usually brass, are normally high quality instruments
and are recommended for celestial navigation. However, inexpensive, good
quality plastic sextants are available and, while they may be not as
accurate as a metal sextant, will suffice and provide the accuracy
necessary for angular measurement in coastal piloting."

I accept this more carefully formulated position. Let's go through some
math to get a feeling for the demand on accuracy. The example on p. SM
3-3, op. cit. represents a typical situation. Given: A lighthouse
charted height = 87ft, observed angle after correction is 0 deg 14'.
Required is the distance.

Bowditch Table 41, has been designed to solve this. It also conveniently
exhibits the error margins. The underlying formula is d = H / tan hs,
applying suitable unit conversions.

Table 41. Distances in nm.

Angle          85ft           90ft

  10'            4.81          [>5]
  13'            3.70          3.92
  14'            3.44          3.64                         <=
  15'            3.21          3.59
  20'            2.40          2.55

After interpolation for 87ft. between 3.44 and 3.64,  the answer is
found to be 3.52 nm. The author elaborates (p. SM 3-3):
"You may question the necessity to interpolate on the basis of 0.2 nm
difference between 85 ft and 90 ft. If your present position is not
critical and you can tolerate that much error then don't interpolate.
However, if you plan a passage through a hazardous area to save several
hours, then it would be wise to become critical, interpolate, and even
include a safety factor to avoid trouble."

The manual fails to say that in the given example an error in the
observed angle of only 1' introduces an error in the distance that
significantly exceeds that from neglecting the interpolation. The
graduation on the vernier of the Mark 3 is in steps of 2', the average
reading error therefore amounts to 1'. This alone disqualifies the Mark
3 as one of the "good quality plastic sextants" that the author of the
instruction manual may have in mind. To say nothing of the 30% to 40%
distance error that can be induced by an observed angle which is 5' off
the mark.

While I concede that plastic sextants adequate for coastal piloting are
available, Starpath's claim that the Mark 3 be one of them, indeed be
the "sextant of choice" for that purpose seems absurd.

Herbert Prinz

   

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