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Re: HO 211 (Ageton) sight reduction accuracy
From: Paul Hirose
Date: 2016 Jun 18, 22:39 -0700

```On 2016-06-15 14:53, Robert VanderPol II wrote:
> You indicate that for 0.5^o tabulation, t<82^o and >98^o and dec less than
75o max error is 2.9'.  Should that read t or K?  82^o>K<98^o is what
recieves the caution in Ageton, Pepperday and Bayless as I recall.

It's not clear what you're referring to, especially since some of the
angle symbols are malformed, but one thing I said was, "if we use the
standard table, do not interpolate, exclude all sights where t is within
8° of 90, and all declinations greater than 75°, the max error decreases
to 2.9'."

Yes, I did mean t. I realize the danger zone is conventionally defined
in terms of K. But as I said in a previous message, that's inconvenient
for the navigator. I'll demonstrate. Suppose t = 83 45.7, dec = 55 07.7,
lat = 16 07.5. Take the nearest tabular values with no interpolation.

To attain the error statistic stated above, you'd normally discard the
sight because t is too close to 90. But let's use K, and interpolate
B(R) if appropriate.

1. A(R) = A(t) + B(dec) = 258 + 24279 = 24537

2. B(R) = 8470

3. A(K) = A(dec) - B(R) = 8596 - 8470 = 126

4. K = 85 38, which is in the danger zone, so recalculate starting with
step 2, and interpolate B(R) from A(R). The relevant part of the table is:

angle      A     B
34 38.0  24540  8470
38 38.5  24531  8475

2. Since 24537 is 3/9 = .3 of the way from the upper A value to the
lower, take the corresponding B(R): 8471.5.

3. A(K) = A(dec) - B(R) = 8596 - 8471.5 = 124.5

4. K = 85 40.0, which is 2 minutes different from the non-interpolated
angle.

5 K~L = 69 32.5

6. A(Hc) = B(R) + B(K~L) = 8471.5 + 45663 = 54134.

7. Hc = 16 42.5. That's only 0.1' less than the correct altitude. The
good accuracy is probably because t is not very far into the danger zone.

But note the extra work. You look up B(R), use that to compute A(K),
look up K, and observe that it's in the danger zone. Therefore, repeat
the steps, except with an interpolation from A(R) to B(R).

Time can be saved by using A(K) itself as the criterion: interpolate if
it's less than, say, 400. It's even simpler to use t instead of K, since
you know from the beginning whether or not to interpolate.

If you stipulate declination < 75 (which includes the 57 navigational
stars), and exclude sights in the danger zone, the error statistics are
practically the same whether the zone is based on t or K. So why not do
things the easy way?

If practical, the safe strategy is to not take sights in the danger
zone. Interpolation is a hassle, and it's easy to make a mistake since
the A and B values increase in opposite directions.

Of course staying out of the danger zone means some extra care planning
your shots. Still, if you can live with the limitation, an RMS altitude
error around 0.3' is sufficient for real world navigation. For special
purposes such as evaluating your sextant technique that's probably not
good enough, though.
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