Hello. This part of the lesson on survey by ray and distance and orientation is dedicated to fundamental orientation problems. To illustrated this problematic a little we can ask ourselves some questions. How to define a direction in space? I'll take a little example here with this map, with a road here, near Wabern, and I have a river here that flows through the area. I can express a relationship between the river's orientation and the road. In this case here, the two axes are almost parallel, I have a notion of relative orientation here. Even so, if I desire to create a map or a topographic survey, I need to have an absolut reference, namely a north, in this case the map's north. In this case, I'll be interested in the direction that defines for example my road here, with the North and I will talk about the grid azimuth here, that's to say the direction that defines the road with regards to the map's north. What are the different norths? We have the map's north, the geographical North, and also the magnetic North. Everyone has used a compass once, it's also a method to define orientation. Summarized we describe the magnetic North here. Effectively, in surveying the compass is barely used as an orientation method, it's not precise enough for our works. We have a map here with magnetic declinations, namely the differences between the directions of the geographical north and the direction of the magnetic North. We see the different lines here that represent these values that can represent several dozens of degrees. We see a green line on Europe that represents the zero, that is to say the difference is zero for the year of 2010 represented here. For orientation questions we have two possible references. The map's north or the geographical North. Regarding the geographic North, we can define the azimuth as being the orientation of a direction with regards to this North. And on the map we'll talk about the grid azimuth here with regards the map's north. We'll recall the definition of the Swiss projection here with the convergence of the meridian as being the difference between the direction of these two norths. As an example we'll take Lausanne with a convergence of the meridian under 0.7 gon, so here we effectively have a grid azimuth that's bigger than the azimuth. We'll recall several values here. If we find ourselves in the western region of Switzerland, in Geneva, the convergence will be approximately minus 1 degree and if we find ourselves all the way east, in Grison, it'll be approximately plus 2 degrees. To be more concrete with this notion of orientation I'll take up my example of a building survey. I've modeled my building here with its base print... so I've drawn it here with the four points of it's base. To attach this to a coordinate system,... defined here by my little red triangles. So here I have a set of fixed points that will serve to define an orientation. If I take a first point P here, whose coordinates I know, and if I consider the vector towards a point Q here, with regards to my map's north I have a grid azimuth here, big phi (i>Φ</i>), between the point P and the point Q. So here I've defined a spatial vector that gives me an absolute orientation with regards to the map's north. Now I can associate this system with let's say polar measurements, namely the angles and distances that allow to determine the coordinates of the my building's base in the national coordinate system. If the coordinates of some points in space are known the grid azimuth can be calculated. The calculation of the grid azimuth will be done by the coordinate differences and the arc tangent function. What should be known is that angles in topometry are measured between zero and 400 gon. If I have the map's north here, I have a first direction towards a point, a second direction towards another point. For example here I have the center point, which is the point P, I have a point Q1 here,... here a point Q2. From the map's north I have a first grid azimuth towards this point Q1, which I can call Φ1 here, and a second grid azimuth here, Φ2, between the map's north and the point Q2. Let's recall that the grid azimuth Φ are comprised between zero and 400 gon. We recall that the arc tangent function will give us values between minus 100 gon and plus 100 gon. So if I consider my quadrants, in topometry I will have values here comprised between zero and 100 gon, here between 100 and 200 gon, here between 200 and 300 gon, and finally, here between 300 and 400 gon. So we need to think clearly about which quadrant we are dealing with, for this we can do tests on the signs of ΔX, ΔY, as you can see here on this table. Depending on the quadrant in which we find ourselves, for example here in the quadrant II, we'll have to add 200 gon here to the value <i>Φ'</i> that results from the arc tangent function. We'll illustrate this orientation principle by using a protractor. I'll place my protractor here on a fixed terrain point, in this case the point P,... and I'll use an orientation point, here, orientation, the point Q. I'll trace a vector here between my point P and my point Q which defines a spatial vector with regards to the direction here of the map's north in this case the axis X, and so, I have my grid azimuth here, <i>Φ</i>, between P and Q. The protractor was arbitrarily placed on the ground. It's zero is in an unknown direction but it will serve as a reference to mesure the direction. In this case, I will measure the direction of r between P and Q here. So I have this horizontal direction, rPQ. I'll still have to determine the unknown orientation from my spatial vector, here. With my rQ measurement I will be able to calculate the direction of my zero, namely this unknown orientation. Transposed on the terrain this orientation principle presents itself in the following way : I have my measuring device here, the theodolite, which is placed on a station point, the fixed point, and I will use a known point here, for example a bell tower, to have this spatial vector which will serve the orientation. Here we'll recall that the origin of the circle here is nondescript and it's necessary to measure the direction towards the bell tower to determine the unknown orientation. To summarize this part about orientation, we have seen the different definitions of norths, the usage the map's north in topometry, the definition of the azimuth, which is the direction with regards to the geographical North, the grid azimuth being the direction with regards to the map's north, and the utilisation of fixed points of the coordinate system for orientation when making topometric measurements.
