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First things first - I'd like to introduce myself.  I'm Martin Gardner, but
not _the_ Martin Gardner.  That should save some correspondence.

I've been lurking with interest for a few weeks.

A couple days ago, I was fooling around putting some formulas on my Palm.
One of them was the formula to compute table 9 in Bowditch.

To review: Table 9 is "Distance by Vertical Angle Measured between Sea
Horizon and Top of Object Beyond Sea Horizon".
"Angle" runs from -4 minutes (a puzzle in itself) to +30 degrees;
"Difference in feet between height of object and height of eye of observer"
runs from 25 feet to 2000 feet

The formula given in my 1981 Bowditch is

Distance = sqrt (
       ((tan A)/0.0002419)**2
   +  (H-h)/0.7349
    -  (tan A)/0.002419
)

I plugged this into my calculator and got hopelessly wrong results.
Naturally I figured I'd keyed wrong, and checked and checked. (Maybe I did
key wrong......but damned if I can find it)

Then I looked more closely:

(1) I do match table 9 for A=0 - so I keyed the middle of the three terms
correctly.

(2) An Ocean Navigator reference page on navigation repeats this formula,
but in their case both of the ...2419  constants have three leading zeros,
contrary to my Bowditch.

(3) The current online Bowditch  leaves the third term outside the sqrt -
probably a typesetting error.

I tried these variations of the formula without success.

More serious: as I read the formula, we are taking the sqrt of three terms
of the form

A**2 + B - A

Which will get larger with increasing A (if A is > 1 - which is true for
angles over 1 minute)

So the formula, as I understand it, is going the wrong way - producing
larger distances for increasing angles....

Please help me find  my error or  -- gasp -- an error in Bowditch.

Thanks,

Martin Gardner
Venice CA

   

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