NavList:

   

Reply

On 2017-12-13 14:38, I wrote:
> W = arctan(tan dec / cos LHA)
>
> If LHA is between 90 and 270, replace W with its supplement: W = 180 - W

If LHA = 90 its cosine is zero and therefore the equation is undefined.
In that case, alter LHA by an insignificant amount, say .001°.

For example, lat = 50, dec = 40, LHA = 90. After you change LHA to
89.999, W = 89.99881

> If latitude and declination have same name
>      X = 90 - lat + W

X = 130 to practical accuracy

> Z = arc tan(tan LHA * cos W / cos X)

Z = arc tan(tan 89.999 * cos 89.99881 / cos 130)

At first that looks impossible on a slide rule, but tan 89.999 = 1 / tan
.001, and cos 89.99881 = sin .00119. Thus the part in parentheses is
equivalent to (sin .00119 / tan .001 / cos 130). The first quotient is
easily and accurately computed on ST: 1) align indices on slide and
body, 2) set cursor to 1.19 on ST, 3) set 1 on ST to cursor.

The quotient is on D at the C index. Its characteristic is 0 (i.e., the
value is in the range 0 - 10) if the angles are literally as set. The
actual angles are both a thousand times less, so there's no net effect
on the characteristic. The quotient is 1.19. Finish the equation: 4) set
cursor to C index, 5) set 130 (alias black 40) on S to cursor, 6) set
cursor to D index.

Z = 61.65 at the cursor on T

> Hc = arc tan(cos Z * tan X)

Hc = 29.50

The errors in Z and Hc are respectively -.6 and .08 minutes, with
respect to a solution computed for LHA exactly 90.

   

Reply