SIY7.TXT Slope Distance and Clinometers 33 Chapter 7 Slope Distance and Clinometers In this chapter you will calculate the horizontal distance from the slope distance. You may construct and use a clinometer. You will need: a) Silva Ranger type 15 compass, available for $40 from CAVE Inc, 1/2 Fast Road, Ritner, KY 42639. 606/376-3137. b) These instructions, c) Semicircular protractor, string, and weight, available for $1 from CAVE Inc, 1/2 Fast Road, Ritner, KY 42639. This item is optional if your Ranger has a built-in clinometer. You will not need: a) An assistant, b) A deed. When you measured the distance on the ground from one station to another, you were measuring the slope distance. What you are supposed to be plotting on your map is the horizontal distance. If your land is flat and level, like a salt flat, then these distances are equal. Otherwise, the slope distance overstates the horizontal distance. The slope angle, or inclination, is the angle between your tape as you read it and true horizontal level. The inclination is measured with an instrument called an inclinometer, sometimes called a clinometer (without the "in" [Is that a proper preposition not to end a sentence with?]). Zero is level. The inclination is recorded in degrees, either plus (uphill), or minus (downhill). When you get around to using CAVEMAP1.BAS you will find Graph 2 there. Or you could register this disk and I'll send you the graphs. Look at Graph 2. This represents the cross section of a hill. The survey stations are named with letters. The distance to station B from station A is 300 feet. Measure this with the ruler on your compass using the scale of 100 feet per inch. SIY7.TXT Slope Distance and Clinometers 34 The inclination is 10 degrees. Measure it with the semicircular protractor. If it has been too many years since you have touched a protractor, just remember that any seventh grader can help you. Place the small hole [not the middle of the ruler] in the protractor over the starting station. Turn the protractor so that the horizontal line from the station goes thru the 0 degree mark. This is the long line where the graduations begin and end. Read the inclination on the scale where the slope line crosses it. There are two scales so that you can use either end of the protractor. To know which scale to use, think about what you are measuring. The size of the inclination angle starts at 0 when both directions are the same. Small slopes, small numbers. Be sure that you use the hole and line about a half inch back from the ruler edge of the protractor. You might have to extend some lines on your map to read the scale. Just extend as necessary. You can also use your Ranger for this purpose. The method is very similar to that of getting a compass direction from a map. Lay the compass on the drawing with the side of the base plate along the line whose slope you wish to measure. Then turn the dial until the black [or red, if you have an old Ranger] meridian lines align with the horizontal lines on your drawing. Read the slope from the dial under the index blob. If you have a reading of 300 & something, then subtract it from 360. If you have a reading near 180, then read the blob near the latch rather than the index blob. Then figure the sign of the inclination; up is positive, down is negative. Now measure the distance to station D from Station A. You can't do this in reality unless you are a miner, so be content to do it on paper. Use the ruler on the compass which is graduated in twentieths of an inch. Measure a little bit more carefully. The distance is just a little short of 300 feet. The actual horizontal distance is 295 feet. This was calculated with the help of something called the cosine, abbr. COS, pronounced "cosign". For those of you who never have had a trigonometry course [I'm one of you], the COS is simply the horizontal distance divided by the slope distance. For any given angle, the COS of that angle will always be that same number. This is not magic. It is the definition of cosine. Horizontal distance divided by slope distance equals the cosine of the inclination. The symbol for divide in computerese is "/". HDIST / TAPE = COS (INCL) Rearranged in a more useful way, HDIST = TAPE * COS (INCL) SIY7.TXT Slope Distance and Clinometers 35 That is, to calculate the horizontal distance, multiply the measured slope distance times the cosine of the measured inclination. The symbol for multiply in computerese is "*". Or you can draw a picture on a piece of graph paper and measure it there. At first all this fancy mathematics is magic. Draw yourself pictures until it isn't magic anymore. And if it ever seems like magic again, draw pictures until the magic runs out. Playing with magic is dangerous. Don't! Magic is for such as magicians and preachers. If you are interested in the vertical distance between stations B and D, you could drill a well. On paper, you can easily measure this distance with a ruler. There is also a mathematical way to calculate the vertical distance. The vertical distance equals the slope distance times the sine, abbr. SIN, pronounced "sign", of the inclination. IUP = TAPE * SIN (INCL). The calculated vertical distance is 52 feet. On the other side of the imaginary hill, measure all the distances and angles. By calculation, the slope distance is 152 feet, the horizontal distance is 143 feet, the vertical distance is minus 52 feet, and the inclination is minus 20 degrees. If you don't get these numbers, what sorts of mistakes could you have made? What sorts of mistakes could the typesetter have made? What sorts of mistakes could the printer have made? What sorts of mistakes could the draftsman have made? [Authors don't make mistakes!] Are these errors or blunders? Now calculate the run from A to B to C. And the run from A to D to C. What is the difference in going over the hill rather than going thru it? Is this enuf error to be a problem to you? The sine and cosine can be easily obtained with a fancy scientific calculator. Just enter the angle and push the button labeled SIN or COS. Or just stick with graph paper. SIY7.TXT Slope Distance and Clinometers 36 Sine Table Angle SIN COS Angle SIN COS Angle SIN COS 0 0.000 1.000 15 0.256 0.966 30 0.500 0.866 1 0.017 1.000 16 0.276 0.961 31 0.515 0.857 2 0.035 0.999 17 0.292 0.956 32 0.530 0.848 3 0.052 0.999 18 0.309 0.951 33 0.545 0.839 4 0.070 0.998 19 0.326 0.946 34 0.559 0.829 5 0.087 0.996 20 0.342 0.940 35 0.574 0.819 6 0.104 0.995 21 0.358 0.934 36 0.588 0.809 7 0.122 0.993 22 0.375 0.927 37 0.602 0.799 8 0.139 0.990 23 0.391 0.921 38 0.616 0.788 9 0.156 0.988 24 0.407 0.914 39 0.629 0.777 10 0.174 0.985 25 0.423 0.906 40 0.643 0.766 11 0.191 0.982 26 0.438 0.899 41 0.656 0.755 12 0.208 0.978 27 0.454 0.891 42 0.669 0.743 13 0.225 0.974 28 0.470 0.883 43 0.682 0.731 14 0.242 0.970 29 0.485 0.875 44 0.695 0.719 45 0.707 0.707 How much error are you willing to tolerate so that you don't have to fiddle with the clinometer and the arithmetic? If you are making a pace map, don't even bother thinking about the clinometer error. The change in your pace length is more than the error which you would produce by ignoring the clinometer. And if it is too steep to walk comfortably, it is too steep to pace. SIY7.TXT Slope Distance and Clinometers 37 Silva made a Ranger type 15TCL with a built-in clinometer. Except for measuring strike and dip while mapping geologic structure, I personally dislike the clinometer Ranger. For surveying, I would rather use my homemade clinometer than the built-in Silva Ranger clinometer. The new Ranger type 15CL comes with a much improved clinometer. It is just as inconvenient to use, but the new and improved clinometer doesn't get in the way like the old one. To use the clinometer on a Ranger compass for surveying, set the compass reading to either 90 or 270 (due East or due West). Open the sighting mirror to about 45 degrees. Flop the Ranger on its side so that the base plate is vertical. Tilt it front to back and sight your target along the top, which is really the side of the base plate. Look in the mirror and read your inclination. Note that you must read the clinometer while you are sighting it and that the base plate must be vertical so that the clinometer pointer swings freely. Unlike the compass reading, the clinometer reading is not preserved. An alternate method is to very carefully rotate the Ranger flat while still sighting along the edge of the base plate towards your target. Now you can read the clinometer scale more easily. The clinometer reading is preserved until you jiggle or bump the compass. If it is worth using the clinometer, it is worth reading twice so that you know that you have not bumped the reading. An alternative alternate method is to open the mirror all the way and hold the Ranger vertical and crosswise in front of you. This method cannot be used to determine the inclination from station A to station B. It can tell you the slope of a far away hillside in profile, or the dip in a roadcut. Actually, you are reading apparent slope or apparent dip. Play around with it until you see the difference between dip and apparent dip. Or maybe you couldn't give a dip about strike and dip. I use an Abney level for my surveying work. An Abney level costs about $75. I doubt that most of you would need it even if it were already in your pocket. But do build the protractor clinometer and/or experiment with the clinometer on the Ranger. Use it when the land is steep enuf or valuable enuf to be worth the effort. You decide. If nothing else, you can use it to determine the height of standing trees. Same trigonometry. The homemade protractor clinometer consists of three parts: the protractor, the weight, and the string. Tie one end of the string thru the small hole and around the ruler edge of the protractor, so that the string pivots from the small hole. Tie the weight on the other end of the string. The string should be long enuf so that the weight clears the curved edge of the protractor. SIY7.TXT Slope Distance and Clinometers 38 To read an inclination with your new instrument, hold the protractor with the curved side down out in front of you at arm's length. Sight along the top edge to your target. Tilt the protractor a little so that the string swings free of the scale. Get a good sight and tilt the protractor straight again. Hold the string against the scale with a finger until you read it. Unfortunately, this is not the inclination. Level, 0 degrees inclination, reads 90 on the protractor scale. The inclination which you want is the scale reading minus 90. Uphill is plus, downhill is minus. I know this indirect reading is a hassle. Hopefully your land is level enuf so that you can leave the clinometer in your pocket. Anyone knowing a source of cheap semicircular protractors with 0 in the center of the scale, please let me know. Usually the inclination can be safely ignored in all but the more accurate surveying or on steep ground. But only usually. You must be alert to this error. And this is a systematic error. The error is all the same way; the horizontal distance is always shorter than the measured slope distance. But don't get carried away when following a previous surveyor who didn't even know that there is a difference between the slope distance and the true horizontal distance. As one of the local realtors here in backwoods Kentucky sez, "The Good Lord put the land here on the sides of the hills so's that He could fit more acres in here." Dave Beiter CAVE Inc 1/2 Fast Road Ritner, KY 42639. 606/376-3137