# USCG Exam Solutions: Compass Error by Azimuth

After the last post about solving for compass error by amplitude, the only logical place to go is onward and upward to the other type of celestial problem you are likely to encounter on a near coastal exam. Compass Error by Azimuth.

### What is Azimuth?

Azimuth is a word that we inherited from the Arabic language, and it literally means direction. When we calculate the azimuth, we are simply finding the direction of an object, this time in relation to North or South. Now, the coast guard let us off easy (okay, maybe not really) with amplitude, only giving us questions about the sun during sunset or sunrise. With Azimuth, the questions will have us look up the computed angle for what could be the sun, a star or a planet. The celestial body in question will also not be on the horizon, which means that we will need more information to compare where it is in the celestial sphere. Namely we will be adding the local hour angle to our declination and latitude.

### Local Hour what?

You should recognize declination from the amplitude problem, but we never talked about what it was. Now that we are getting a little further into celestial navigation, it is time to talk about just what declination is, and hour angles as well. Whenever we think of where we are on the globe, we think of our LAT / LONG position, right? The meridian that tells where we are East or West is the Longitude. It is in relation to Greenwich, England, home of the royal observatory where a lot of these celestial navigation problems were first solved. Yeah, we get it, Greenwich, jolly old England, what about it? Well, if we look at a celestial body in the sky, and draw a line from the center of the earth to that point in the sky, the point where that line goes through the surface of the earth is what we are going to use to calculate everything. When we talk about declination, local hour angle or greenwich hour angle here as we solve these problems, you can think of them as ways of measuring the LAT / LONG of that point on the globe. The hour angle is the angle between a fixed point of reference and a point on the globe, measured East or West. Our longitude is the greenwich hour angle of our location. The local hour angle is how far something is from us, instead of Greenwich. The declination is how far above or below the equator something is. Our latitude is basically our declination. The following illustration should help clear it up a bit.

### Wait, but isn’t declination what you said was the amplitude?!?

Amplitude is the angular measure of how far North or South something is from the *direction* True East or West from our location, the *parallel* of the equator from our point on earth. Declination is how far North or South from the *actual* Equator something is. That’s why we only need our latitude and the objects declination to solve the amplitude of an object on the horizon. In fact, if you go back to the proper equation at the end of that post, it is actually known as the altitude-azimuth formula. It yields the cosine of the azimuth, but because amplitude and azimuth are complimentary and their co-functions are equal we can use it to get the sine of the amplitude. We could use it for the azimuth if these problems were on the horizon as well. But, I digress, and try not to worry about any of that, we just need to pass a test here, let’s keep it simple.

### Organization is key

So, putting it all together, we will have a lot of items to keep track of. Once again, organization is key. Take a look at how I lay out my azimuth problems below, look familiar? Keep your layout as close to the amplitude as you can, no need to reinvent the wheel.

### Solving for Local Hour Angle

Depending on whether we are solving for the azimuth of a planet, star or the sun, we will need to correct the Greenwich hour angle to get our local hour angle. Sun sights simply require us to adjust for the minutes and seconds of the actual sighting, which we find in the yellow pages at the back of the Nautical Almanac. Planetary sights require us to apply a correction for the sidereal hour angle, which is listed as SHA. (It’s simply the adjustment between our star and Aires, which we look up in the table to start) We look up the GHA for Aires on the left column first, correct for the minutes and seconds and then add the SHA which is listed beside our stars name on the right hand column. The declination will also be listed there and requires no adjusting in this case. When correcting for a planet, we will see a v value listed at the bottom of the page, right beside the d value for the declination. When we correct for the minutes and seconds in the yellow pages at the back of the book, we will look up the d correction for the declination and the v correction for the GHA in the column for our object. We will cover this in the video, but it can be a bit confusing so simply know that the SHA is only for stars, and the v and v correction are only for planets. After we have corrected our GHA, we add or subtract the longitude. This is the * OPPOSITE *of at weddings (add West). Because we are working from Greenwich to local, not local to Greenwich, we

**subtract West.**If we end up with an answer over 360°, simply subtract 360° to get your local hour angle (LHA).

### The Problem

#01451 On 11 December 1981, your 1816 zone time DR position is LAT 26° 30.0′ N, LONG 140° 35.0 E. At that time, you observe Venus bearing 230° pgc. The chronometer reads 09h 14m 52s and the chronometer error is 01m 02s slow. The Variation is 3.5° E. What is the gyro error?

- A- 2.2° E
- B- 3.3° E
- C- 3.2° W
- D- 4.2° W

## The meat and potatoes, the video how to

First, get your resources together:

- Nautical Almanac
- The Sight Reduction Tables (Pub. 229 Vol. 2)
- Scratch paper
- Calculator
- Patience

Then follow along below

Part 2.

## In closing

That is a lot to digest, so let’s just break down the steps again real quick:

- Write Down the Date and Time
- Write down the LAT / LONG
- Find Zone Description
- Correct the chronometer
- Apply Zone Description to see if we need to adjust chronometer to get GMT
- Enter the Nautical almanac using GMT and LAT
- Determine what celestial body we are looking up
- Get the Greenwich hour angle
- Get the declination
- Get the d value to look up DEC correction
- Get the v value for a planet, or SHA for a star
- Look up the d correction, v correction in the yellow pages at the back of the almanac
- Look up the GHA adjustment for minutes and seconds in the yellow pages
- Apply corrections to get corrected GHA
- Add or subtract LONG, remember working
*from*Greenwich we -W and +E - Write down DEC and LHA computed in step 15
- Write down whether DEC and LAT are contrary or the same
- Enter the sight reduction tables with LHA, DEC and LAT, contrary or same
- Write down base values
- For each argument, add 1 and keep all other arguments the same, write down new Z value below base Z value for the argument that is plus 1
- Find the differences between the base and plus 1 values
- Multiply the difference by the minutes of the argument
- Divide by 60 to get adjustment
- Sum the three adjustments and apply to the base Z value
- Look up whether Zn is equal to Z, 360- Z or 180-Z
- Get Zn by applying adjustment
- Enter Zn as True Bearing
- Solve using TEG, TVMDC +W
- Find Deviation which is our answer.

## Whew, That is all there is to it.

Good luck on your exams, thanks for checking this out!

Not since Susan Howell’s wonderful book “Practical Celestial Navigation” has someone laid out the problem solving in such a logical way. Nice work on this blog, keep it up! Capt. Voss

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