20 July 2010

More Corrections

Last time, we calculated Apparent Altitude by correcting Hs for both Index Error and Dip Error. If you are like most people, you've already forgotten what these words mean, so it would be a good idea to go back and review what we did last time, before continuing on.

I'll wait...

Everything clear? Okay. There are 3 more errors we need to correct for. Again, I'll just touch them briefly, but they'll give you a good feeling for how a sextant works in the real world.

Refraction Correction:  Ever notice how a straw seems to bend when you immerse half of it in water?

Refraction of light as it transitions from air to water
photo wikimedia commons

The same thing happens when the light from the Sun enters the atmosphere from space. The light bends, or is refracted, causing the sun to look higher than it is. Therefore, we must correct this error by subtracting an equal amount. How much? I will discuss this in a moment.

Parallax Correction: All the tables in the Nautical Almanac are calculated from the center of celestial bodies. For example, from the center of the Earth to the center of the Sun. However, I took my measurements about 4,000 miles from the center of the Earth. This causes the sun to look lower than it is and we must correct this error by adding an equal amount. Again, I'll discuss how to find the correction in a moment.

Semidiameter Correction: Finally, when I measured the height of the sun over the horizon with my sextant, I aligned the horizon with the bottom of the sun, not with the center of the sun, because it's easier to see when the bottom of the sun is lined up. That means the center of the Sun was actually higher than I measured. Quite a bit higher, in fact... about 16'. So we definitly need to correct for that error.

Lucky for us celestial navigators, the Nautical Almanac takes care of all three errors with one look-up table.

Altitude Correction Table
Nautical Almanac

To find the correction, look at the left-hand column labeled 'Sun'. The Sun column is divide in two sub-columns, one for Oct-Mar, the other Apr-Sep. Our sights were taken in July, so we use the Apr-Sep side of the table.

The sub-columns are further divided into 'Lower Limb' and 'Upper Limb'. 'Limb' is CN-speak for half-circle. Since we measured to the bottom of the Sun, we will use the Lower Limb value.

We look for our Apparent Altitude of 70° 59.0' and don't find it. But way down at the bottom of the table, we find 67° 15' and 73° 14'. The correction for all altitudes between these two angles is +15.6'.

Again, +15.6' is the total of the three corrections described above. It is labled + so we know it must be added to the Apparent Altitude.

Apparent Altitude:70° 59.0'
Altitude Correction:+15.6'
Ho:71° 14.6'

What we end up with is called Ho, or the 'observed' height of the Sun above the horizon. This is the real deal. The actual height of the Sun over the ideal horizon, with all errors corrected for.

Except for human error, of course! That's not possible to calculate. We just have to hope it's small.

So, I promised back in the beginning that if we could find the exact height of the Sun above the horizon, we could use that to find our latitude. How do we do that?

Easy-peasy. And that will be our discussion next time!

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>>> Next Episode: Finding Our Latitude (finally!)

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  1. Does being in the southern hemisphere change things? I'm thinking not.

  2. Stewart: Your location doesn't factor into any of the measurements or corrections we've discussed so far.


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