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Wndsn Quadrant Telemeter Tutorials

Making the most out of our graphical telemetry computers.

Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses.


Measuring the Depth of a Well

We are looking for the depth of a well and, equivalent, the length of a tunnel or the height of a column; all objects with parallel characteristics, i.e. they are as wide (or tall) at the near end as at the far end.

To determine the depth of a well, working on the assumption that the walls are parallel, we measure the width at the top and the angular size of the bottom or any sightable feature we are interested in. The same concept can be applied to tunnels, chimneys, as well as partial dimensions of natural or man-made structures.

There are two ways to determine the angular size

Angular size via Quadrant

We aim at the opposite edge of the water level with the quadrant, and make sure that our plumb line is aligned directly with the edge on our side.

Measuring the depth of a well.

Measuring the depth of a well. Note that the measurement starts at the vertex of the instrument.

Angular size via Telemeter

We sight with the Telemeter across the well at the widest point of the water level, and make sure that the zero mark is aligned with the opposite edge.

Measuring the depth of a well.

Measuring the depth of a well. Note that the measurement starts at eye of the observer.

Example

  1. Width at the top: 3 ft
  2. Angular width at the base: 6°
  3. Using the Telemeter nomograph, we have 6° as input on the α scale; and 3 ft on the S scale for a result of ≈ 28 ft depth of the well

To consider

In both cases does the measurement not necessarily start at the edge of the well, but at the vertex of the Quadrant and respectively at the end of the string for the Telemeter. These extra lengths are subtracted for the real depth of the well.

Another application of the technique

A variation of the depth-of-a-well problem is determining the height of a structure we are located right in front of, or the length of a straight tunnel.

Measuring a parallel structure.

Measuring a parallel structure.

The method (with the Telemeter only) is to measure, with a tape, the part of the structure that is right in front of us -- this works with any structure that is made of parallel lines, columns, the well, etc. Now, knowing the absolute width, we can use the Telemeter to determine the angular width at the far end (compare the graphic, and note that the Telemeter can measure in any plane in space) and use the nomogram to calculate the height (in this case) of the building. (Rotating the graphic by 90° shows even more applications.)

Example

  1. Measured width: 1 m at the bottom (and hence at the top)
  2. Angular width at the top: 1.8°
  3. The nomogram returns a height of 32 m

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