Hello. We will go over the second part of the exercise after having seen the grid azimuth calculation, we're interested in the station's orientation. As can be seen on the right image, a station, so a theodolite, is positioned on a fixed point and it's horizontal circle is oriented arbitrarily, there's no reference to a preferential direction. We'll recall here what the station's direction is, which consists of determining the orientation unknown or omega (<i>ω</i>), that's to say the grid azimuth which gives the direction of the theodolite's zero with respect to the map's North. To determine this orientation unknown, two fixed points are required. Here on this example we have the points S and M, so we have our vector which allows calculating a grid azimuth here, and then when I will come with my theodolite, I will place, here, my theodolite on the station S. For example, like this one. And then I have, here, a zero direction, which is arbitrary, which is my origin 0.00. And what interests me here, the orientation unknown, well, it's the <i>ω</i> with respect to the map's North. From my zero zero, clearly, I will take my readings. For example, here, the r, the horizontal direction, towards the point M. I will take the same figure here with these calculated and measured elements. Initially, I can calculate or, on my figure here, measure my <i>ΦSM.</i> I measure here, and it's 70 gon. Coming with my theodolite, I will place myself here arbitrarily with my direction, here, of zero. And here I'd have a value for the direction rM, so measured in the terrain in this case, which is 125 gon here. The <i>ω</i>, if I measure it on my figure, well, here I have 345 gon. And via calculation, I know that <i>ω</i>, is equal to my <i>ΦSM</i> minus my direction rM, in this case 70 minus 125, which is equal to negative 55 gon. And takes us to in-between zero and 400, with <i>ω</i> which is equal to negative 55 plus 400, which is equal to 345 gon. Let's take a small numerical exmaple here with the coordinates of a station S and of a point M. I can trace the vector here which links these two points. Likewise, I give the direction, here, X, of the map's North. And I know that I read a value here of 53,485 gon, which I can reconstruct on my canvas by setting this value to 53 or 54 gon, if I round up or down with my protractor. I find the direction of my circle here when doing the field measurement So I can now trace this direction here from zero, and I effectively have, with respect to the map's North, I have my <i>ωS</i> which I can draw here and likewise I can read the value with my protractor, which is approximately 11 gon. The <i>ω</i>, if I also know my <i>Φ</i>, here, <i>SM,</i> I can take the reading or I can calculate it, it's 65 gon. So graphically, the <i>ω</i> it's my 65 minus the direction, 53,5 gon, which I rounded up, and I obtain my 11,5 gon, which verifies my reading well here on this graphic. We'll now move on to the part of actual calculations with a repetition of the calculation of the grid azimuth of <i>ΦSM</i>. Earlier I calculated a <i>ΔY</i> which was 33,03, a <i>ΔX</i>, which is equal to 20,49. The <i>ΦSM</i> is the arc tangent of 33,03 over 20,49, which is equal to 64,652 gon. We are in the first quadrant, so we can keep this value as it is. The <i>ωS</i> is my grid azimuth, so 64,652 minus the reading of the horizontal direction towards the orientation point, so 53,485, which is equal to 11,167 gon. Comparing this to the graphical value, we can say the check is ok with respect to the graphical value. This shows that it's important to make a graphic, to have a estimated value for the orientation unknown in order to check the calculation. In topography, a measurement isn't enough. One needs to be able to check it. This is also valid for the orientation. A single point isn't enough. We cannot detect a measuring error. We'll take a small example here to show that at least two points are required to check the orientation. So I have my X axis here, my Y axis. I take my station S again with a point M and a second orientation point N. We can consider my vectors here, towards the orientation points N and M. If I come with my theodolite, I will place it here, at the station clearly with a direction of zero, here, arbitrarily, and i have, from this zero, a direction value towards the point M and a direction value towards the point N. So I have two direction measurements and I have two orientation points. So I can determine a <i>ω1</i>, starting with the measured direction towards the point M, a <i>ω2</i> with the direction towards the point M, and so I have a check, even if the two measurements aren't coherent, in this moment the operation should be repeated or possibly be applied to a third point. If there are several points the average is taken of the orientation unknowns. As can be seen here with a set of measurements that are coherent because we can see that the results are coherent, so in this case, there are no errors and we can take the average of these determinations, which is given here to have the orientation unknown of this station.
