Metrology and Instrumentation (M602) -Module 2

References: contain a source for a nice, rather inexpensive brass clinometer that should be a pleasure to use. I have bought from this source, and can recommend it. Abney clinometers are available from surveying supply houses for considerably more money, over $100. Captain William Abney was at the School of Engineering at Chatham, England in the 19th century, and invented many ingenious surveying instruments. The Abney clinometer has a sighting tube with an angle scale reading from -90° to +90°, and a spirit level with a Vernier index that can be moved along the scale while the user looks through the sighting tube. A small mirror and lens makes the level bubble visible in the field of view. When the object is aligned with the crosshair in the sighting tube, the spirit level is rotated so that the bubble is bisected by the crosshair, as illustrated in the diagram. Then, the elevation of the line of sight can be read off on the scale. The Vernier can be read to 10 ', but it requires a magnifier to do this. The clinometer can read easily and accurately angles of elevation that would be very difficult to measure in any other simple and inexpensive way. METROLOGY AND INSTRUMENTATION (M602) -MODULE 2 A fairly common use of a clinometer is to measure the height of trees, which is easily done. A point should be marked with a stake as far from the centre of the trunk of the tree as its estimated height, so that the elevation angle is about 45°, which gives the best "geometry." This distance D is measured with a tape. The observer then stands over the stake and sights the top of the tree, finding its elevation angle θ. The height H of the tree is then H = D tan θ + HI, where HI, the height of instrument, is the height of the observer 's eye. All this is illustrated in the diagram. A useful accessory is a levelling rod, which can be home-made at little expense. Since the clinometer has no powerful telescope, the reading of the rod must be evident from a distance if you use it as a self-reading rod. Alternatively, if you have a rodperson, she can stand by the rod and move a finger or other marker up and down in response to your signals, then measure the distance with a tape. A self-reading rod can be made from a 1" x 4" x 10 ' choice pine board available at Home Depot. A bold pattern that can be estimated to a few centimetres can then be applied by stencil and matte black spray paint. Two examples are shown at the right. Colors can also be used to make distinctions. With the levelling rod, the HI can easily be obtained. Set the index at 0°, and the clinometer becomes a level. Sight the rod from close by, and read the HI. This can, of course, be done by simply making a mark on a wall just in front of your eyes, and then measuring its height. The determination of the difference in elevation of two points is called levelling, and can be carried out with the clinometer set at 0°. The place where you stand with the level is called a turning point, TP. Your rodperson holds the rod on the first point, and you make a backsight, BS, by reading the rod. The reading is the HI above the first point. Now the rod is held on the METROLOGY AND INSTRUMENTATION (M602) -MODULE 2 second point, and a foresight, FS, is taken. Foresights and backsights should be roughly equal in distance. The difference in elevation of the two points is BS - FS. This procedure is illustrated at the left. If both points cannot conveniently be viewed from one TP, a chain of turning points is used, with an intermediate elevation between each one. The difference in elevation is the sum of the backsights less the sum of the foresights. If the sights are short, such as those that are practical with the clinometer, the curvature of the earth will be taken into account automatically. The procedure for finding the height of a tree can be inverted to find the distance D when H is known. This is an application of the method of stadia. The difference in elevation angles of two points on the rod (say top and bottom) is measured, and trigonometry is used to find D in terms of this distance. If one of the points has an elevation angle of 0°, then D = H/tan θ. The clinometer is really not well-adapted to this, but it may be of use occasionally. XXXXXXXXXXXXXXX