#41




Sorry, guys. My brain gets soft after 10 PM. I had to take that graphic down as my post had a fatal error. Please disregard my last post. I will try to get a correction up soon.
It is a real challenge to work these problems without using trig and limiting the transit use to not having to read the vernier. 
#42




OK, Let me try this again, This is a case where you need to stake a curve between points A & B. Only this time you don't know the radius.
All that is known about this curve is that the straight line between start and end is 44 ft and it bows outward 4 ft in the center. The radius length must be determined. Begin by setting the transit at point A pointed at B. Measure half the distance (22 ft) and set a stake at X. Most of you know how to lay out a triangle with sides of a multiple of 3,4, and 5 to form aright triangle. Do so for the area shaded green using the transit to keep point Y on the line between A and B as shown. Use two tapes to set point Z. Stretch a string line between X and Z. Then measure down the string line and set point C. Next you have to get the transit pointed at where D is. The angle CAD is the same as angle CAB. But it will be an oddball angle. If you have an electronic transit with a digital display or know how to read the vernier on an analog transit, you can zero on point B and then turn to C, read the angle, double it, and then turn the doubled amount to be pointed at D. There is another way to get the transit pointed at D without reading angles. A transit has lower motion lock knob and adjustment knob. There is also an upper motion lock knob and adjustment knob. When the lower motion is released the rotation of the transit does not change the angle reading. When the lower motion is locked and the upper motion is released, the angle reading changes as the transit is rotated. Ordinarily the upper motion is set to zero and locked. The lower motion is then used to point the transit at a target object and then locked. The upper motion is then released and the transit is turned to another object and the angle is then read. In this case withe the transit at A, zero and point at C, lock the lower motion. Release the upper motion and turn to B and lock the upper motion. Leave the upper motion on its reading and release the lower motion. Turn back to look at C with the transit not set to zero but the untouched angle that was made to B. Lock the lower motion, release the upper motion and turn the transit left until it reads zero. You are now pointed at point D. With the zero end at point X, stretch a tape along the string line toward Z. Look through the transit scope and read the tape distance directly to get the measurement X to D. In this particular case the distance will be 8.27 ft. Next you need the distance from A to D. If you have set a stake at D you can measure the distance (make sure you check for an equal distance from D to B) Or you can compute the distance by squaring the distance from A to X, add to the square of the distance X to D, then take the square root of the sum to get the distance A to D. In this particular case the distance will be 23.50. With all sides of the shaded triangle known, it's time to computer the radius. Divide line AX by line XD (22/8.27= 2.6602....), then multiply by the line AD (2.6602 * 23.50=62.5) to get the radius. With the radius known, use the method I described earlier to stake out the curve I know it looks complicated, but that's only because I explained it in detail. This will not be of much interest for those carrying a laptop with autocad loaded .... unless your battery runs out. 
#43




That last process was a bit too much. I'll drop back to something simple.
When I talk of setting a stake, I often mean something more accurate than a location of a wooden stake. For most curve work, a nail, tack, or some other mark should be used in a stake to more precisely mark the location. Someone mentioned the use of string lines to mark curves. They were probably thinking of the process of laying out an oval shape. But there is a way to use string lines for some circular curves. The good part is that you don't need a transit or even a hand calculator to do it. A curve can be staked with string lines from a point A to point B if all of the following are true: 1. The distance from A to B is less than the radius. 2. The radius is 25 ft or more, but not much more than 80 ft 3. There is open space past one or both points to swing the string lines around the outside of the curve. Suppose you have stakes A and B that are 21 ft apart and you need to stake a 50 radius curve between them. Decide what distance you want between your curve stakes, in this case every 4 ft would give you about 5 or 6 points along the curve (22 divided by 4). Go to a place that is reasonably flat to do your string set up. Set a radius point. Measure the radius distance to set a point. Set a second point to the side as shown above with the distance between the two equal to half the distance you want between the stakes you will later set on your curve. Attach string lines to the radius and stretch them past the points you set. Attach the string lines to a stick and adjust them on the stick to match the distance between the two points. With the stick held perpendicular to the radius points the string lines should lay exactly over the staked points with about the same line tension on both strings. Both in set up and use. the stick should be held perpendicular to the radius point or point where the strings are attached. Next, take your string setup to the curve site and attach the strings to one of the curve end points (A or B). Using the stick, stretch the strings past the other point (B) so that one string passes over the point and the other string passes over where you will set a curve point. Measure the staking distance to a point under the string line. What you are doing is using the string lines to replace the transit for staking angles as I earlier described. As each point gets set, move the string lines over to repeat the process. You can stake the curve from one point and then check it by restaking from the other end. Where space is limited you may have to stake part of the curve from one end, then move your string line to the other point to complete the staking. 
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