The properties of a circle for what I think you are doing is this: x^2 + y^2 = r^2
In other words, the radius (r) is 770, the x is, if you draw this out on paper like a picture of a Bow and Arrow where the arrow is the 770 radius and the lot stakes are the tips of the bow, the side to side orientation (remember the cartesian coordinate system, X,Y graphs, etc). If you are on the arrow, in other words you have not gone up or down toward the lot stakes, your y value is still 0, so you plug that in to your equation above; x^2 + 0^2 = 770^2 and you get that x^2 =770^2 or x=770.
If you move upward toward the tips in 8′ increments, you then put 8^2 in your equation for the y value, then 16, then 24 until you get to 60(.5). each time then, you will solve for the x value by doing the subtraction of the y^2 value from the r^2 value then taking the square root of the difference. You will also need to know how far out from the Bow string that the tip of the arrow extends, which you will get by finding the value of x at the tip of the bow (when y=60.5). Then for every x value you find as you move up or down the bow, you will subtract the x value of the string.
Example at the center (or along the arrow): r^2 =592900; x^2 + y^2 = 592900, y=0 so x^2 + 0 = 592900. x^2=592900; x = square root of 592900 or 770. Tthe tip of the arrow is some distance from the bow string. The bow string is located as a straight line fropm the bow tips which is a vertical line on this diagram. Therefore the y value is 60.5 and you then solve for the x value; x^2 + 60.5^2 = 592900 or x^2 + 3660.5 =592900. x^2 = 592900-3660.5 or x^2 = 589239.5 so x = square root of 589239.5 or 767.62 which means the property line is only 770-767.62 (2.38 feet) off from the straight line between the stakes.
In practical terms then, if you were to locate your fence at the tip of the arrow (on the property line, and then basically make it straight toward each of the property stakes, you will not be off from the property line by more than a few inches and with a fence, that is probably good enough.
Sorry for the odd explanation, but I did not know an easy way to explain this without the luxury of drawings. Hopefully, if I misunderstood your explanation of your property, you can still sketch it out and use the basic equation.
Good luck
Replies
Starting from the mid-point of the chord (middle post of the fence), offsets are
2.38', 2.34', 2.21', 2.00', 1.72', 1.34', 0.88', and 0.34'. I'll leave it to you to convert to whatever other units you prefer.
Be advised that you will have about a 4 1/2 ft fence section at each end (4.56', by my estimation). Be further advised that I am not a land surveyor, so you're on your own with your neighbors.
Be seeing you...
Thanks for your quick reply... greatly appreciated! If there's anything I can help you in the way of commercial construction, please ask!
Mark
Many thanks for your help... greatly appreciated! If there's anything I can help you in the way of commercial construction, please ask!
Mark
Great problem, though you might want to consider building the fence on your side of the property line and not on the line itself. If so the 770' should be reduced some. Because the length of the arc is 1-1/2" longer then the cord it is not evenly divisable by 8'. If you want evenly spaced sections try 7'-6 27/32"
Why are you relocating this fence?
You are quite right about the 1 1/2" length difference. The offsets I gave were based on a quick CAD drawing I made as follows. After establishing a 770' radius and 121' chord, and starting in the middle of the arc, I simply drew an 8' radius circle centered on the mid point of the arc. Another 8' radius circle centered on the intersection of the first with the arc, and so on. The 8' radius circles represent the set of all points where the fence post could be for an 8' fence panel with one end position defined (think of an 8' door swinging), and the intersection with the arc is where you want it to be. I then measured the distance from each intersection point to the perpendicular on the chord (well, I asked the computer to measure). So the small difference between arc and chord length is taken into account already. But, since the location of each post is based upon the previous, there is the potential for cumulative error. markjrogers has to locate each post 8' from the last, offset from the chord by the amount tabulated. A piece of string with a pin at each end, 8' apart, and a tape measure should make for a fast layout. Another string between property corners will establish the chord.
I'm sitting here designing machine parts on AutoCAD anyway, so it only took a couple of minutes. Took way longer to describe it than do it.
Be seeing you...
The city built a new street behind my property , and gave me the new lot dimentions, after eminate domain, the fence if all but falling down anyway, so I get the privilage of building a new one now. Thanks for your quick response.....Mark
Mark,
Having 30 years experience as a surveyor, here's the way I'd do it.
Use a transit or a string line between both corners, if you can see'em. Put a nail or stake on this line 60.5' from either corner.
From this stake, place nails or stakes every eight feet both ways, till you end up near the corners. The last distance will be 4.5'.
From the center stake, at 90 deg to your line, pull over 2.38'. From the next, 2.34, then 2.21, 2.00, 1.72, 1.34, 0.88, and finally 0.34. These distances will be used the other direction too.
On a curve like this it would be a good idea to set the property line, then back off half a foot or so to make sure that you aren't encroaching on the other tract with the thickness of the fence material.
You may want to check the curve data on your plat to verify that what we're using is correct.
I=9-00-46, Arc=121.12, T=60.69
Hey...thanks for the help. The current fence is all but falling down, the city built a new street behind the current fence and gave me the new eminate domane dimentions for my property.. so...now I get the privilage of building a new fence.... Mark
Mark,
To save some later headaches, check the bearngs and distances on the city's ROW (Right of Way) information. Request a hard copy signed by the appropriate officials. Sometimes the surveys made for street ROW don't agree with your plat or the calls on your deed.
If you notice a descrepancy, build the fence to the city ROW, not your information, even though it will be a senior survey.
Also check the city's ROW info for PUE's (public utility easements) as these may require a further setback than the ROW indicates.
If the street hasn't been built yet, check for temporary construction easements that would require a fence to be removed.