# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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.