Trigonometric leveling is a fast method to spread elevations across a large area of varied topography. If you use an electronic total station you can achieve quite good accuracy. It’s important that the instrument be in good alignment and that you prepare by doing a vertical index test.

Set up and level precisely. Sight a distinct unmovable object at about 20° below the zenith (20° below vertical). Note the vertical angle reading, say 71° 49’ 30". Invert the telescope and sight the object in the exact same location. Note the vertical angle reading, say 288° 10’ 00". In a perfect world the two readings should add up to 360°. If your instrument is perfectly level, that 30" bias is due to its technical misalignment. Do this test at least twice to get a good idea of what your average technical misalignment actually is. Half of that bias will always be factored into the computed reduction from the slope distance measured by the instrument to the horizontal distance and the vertical difference.

In most cases the bias applied to horizontal reductions will be slight if you work in fairly flat terrain. In computing the vertical difference for trig leveling, this bias is a more important factor and needs to be taken into account depending on your needed accuracy. Follow the instruction manual of your instrument to make the necessary adjustment to your vertical bias. Sometimes this can be done automatically by the instrument or by small internal adjustments. If your bias is severe, over 1’ 30", you should consider having a bench technician service it. Regular checks are advisable in any event.

Once ready to measure, keep notes of your HI (height of instrument) and ROD (height to mirror center) at every setup. You can combine your leveling with a traverse run without any extra effort, just by extra note keeping. You must always close back with a measurement to your starting point to achieve any confidence in your results, and you must keep a careful record of the vertical difference (D V) as a plus or minus value.

To reduce your notes, begin with a diagram of each setup. Draw a profile view, showing the relationship of the rod above or below the HI, keeping in mind the minus and plus values of the D V. Begin with the known elevation, add the ROD, add a minus D V and subtract a plus D V from the backsight point. Now you have the elevation of the telescope. Subtract the HI to set the ground elevation of the point of occupation. Return to the value of the elevation of the telescope and subtract a minus D V or add a plus D V and subtract the ROD to obtain the ground elevation of the foresight point. In this manner you can leapfrog point to point setting elevations ahead until you return to the first point sighted.

The difference in the beginning and ending elevation on the same point is the error of closure and, if it does not reveal a blunder, must be distributed systematically among all the points occupied. In differential leveling, this is done by distributing the error to every turning point on the theory that no reading is more suspect than is another. With trig levels, the concept is a bit more complicated, since the steepness of the slope and the distance of the shot are added factors to take into account. Having said that, we can ignore that complexity for our purposes and make the same adjustment, by distributing the error evenly: an 0.18’ error over 6 setups means 0.03’ added or subtracted at each setup cumulatively. The first setup receives 0.03’, the second 0.06’ and so on, so that the relationship between consecutive setups is maintained.