[silent marshal]

How to find your own position – Part 1.

With the ANM-Algoritmus you will have three output options to find your position with graphically methods as tools provide at the nav-map:

(a) Find your position as in real life by drawing two „Standlinien“. It is the most complex option for the user because you have to draw a lot of angles, distances etc. You also have to consider transformations from WGS to UTM_120 (the coordinate system of SH5). You also have to be careful when using the algebraic signs. You will see, this is an option for the sophisticated navigators among us .
(b) Let the „Navigationsrechner“ do all the algebraic stuff for you and find your position with horizontal and vertical distances (cartesian coordinates). This is the arcade version…
Method (c) has the same background as (b) but for those who like using the triangle, the position can be found with polar coordinates.


Now I will show you how it all works when you are at sea. I will not show any interim results which will go beyond the scope of that post.

You are somwhere in the atlantic sea, approximately 200km NW of Ireland, but you don’t know exactly. It is the 5th of October 1938, 10:12:00 UT1. You fix your assumed position (G1) at 56°N / 11°W. Now take your Sextant and shoot the sun!

Input values 1st measurement
Date: 05.10.1938
Time (T1): 10:12:00
G1: 56,0°N / 11,0°W
Angle of sun h_b: 22,898° (in this example, we use precise values).

From SH5 we read our exact position: 56,5°N / -10,0°W. Now we have all we need for the calculation. Start the Navigationsrechner!

Results of 1st measurement: (take a look at the three options mentioned above)
(a) Azimut A: 141°; Radialversatz u: -5,8km
(b) W: ---,-km; V: ---,-km
(c) Azimut epsilon: ---°; Distance D: ---,-km

What’s that? No values for (b) and (c)? These values are a result of the whole procedure so you have to make another measurement at afternoon.

But in the meantime we can draw our first „Standlinie“ with the results of (a). We start with drawing the Radialversatz u with the circle.



Now we draw the Azimut A:



What you can see here ist that A is always positiv from north heading clockwise. Attention: Parameter u is negative so you have to draw the Standlinie diagonally opposite of A! The Standlinie is tangential to A. Don’t be lax at this point. Your position will be terrible wrong! Here we go:



Well done!

For our first example, we loiter around at G1, not changing our position (phi…course and s…distance). Time has come to shoot the sun a second time:

Input values 2nd measurement
Time (T2): 14:25:00
h_b: 24,423°
s: 000,0km (!)
phi: 000,0°

Results of 2nd measurement:
(a) A: 211°; u: -79,64km; Horizontalversatz w: 57,85km (NEW!); Vertikalversatz v: 4,49km (NEW!)
(b) W: 118,9km; V: 63,6km
(c) epsilon: 63°; D: 133,5km

Ok, lets start with (a):

Draw u and A like done above. Because the triangle of SH5 only reaches from 0° to 180° we have to draw 360°-211°=149°:



Now we extend the two Standlinien so that they intersect:



The intersection point (“Markierung 1”) is your true position. But beware: this is your position at WGS relativ to G1. You have to transform (stretch) the intersection point to UTM_120. That’s what the Horizontal- (w) and Vertikalversatz (v) is good for.



Vola! Our true position ("Markierung 2") is 56,505°N, 10,01°W. The error is about 0,3km. But consider that all input values are exact ones. If you use your sextant manually and additionally the Nautical Yearbook, the error is expected to be greater.

That’s a lot of drawing we have to do and it’s getting more complex if you change your position from T1 to T2. With (b) and (c) you can minimize your work load:

Using (b) - cartesian coordinates W (horizontal) and V (vertical) in UTM_120:



Even better! The often you use the default drawing tools the greater the error will be. You can also use (b) and (c) to check if your drawings are ok.

Using (c), things are more elegant (in my opinion):



Now let‘s compare our results:
Exact position from SH5: 56,5°N / 10,0°W
Position calculated with the ANM-algorithm: 56,5049°N / 10,0089°W
Using (a): 56,505°N / 10,01°W. The results with (b) and (c) are nearly the same, the variance is in a range of 100-200m.

The display of results summarizes the output values:
Red…(a), blue…(b), green…(c). The yellow marking shows the calculated variance from the exact position.



The true distance from G1 to our exact position was about 85km. The greater this distance is, the greater the variance will be. This is caused by the curvature of the earth and the plane geometry of the ANM-algorithm.

The results of the graphically methods will depend on your screen resolution. For this example I have used 1920x1080.

That’s all for this time, the next time I will show you how to consider position changes during the two measurements at T1 and T2 („Versegeln der Standlinie“).


Hope you like the results!