>
> The main effect is the change in the height scale factor. The change in that, to a good approximation, in a rise of 2500 ft. is going to be:
>
> [(2500 + 20,905,000)/20,905,000] - 1 = 0.000120 = 120ppm
>
> If you compute an average Combined Grid Factor for the line based upon the mean elevation, then that height scale factor will differ by about 60ppm from that at either end.
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> If the midpoint is 1250 ft. higher than the lower end, then the average height scale factor (averaging the scale factors at the endpoints) for each half mile will be 30ppm smaller or 30ppm larger than the mean for the mile, depending upon whether the average elevation of the half-miles is less or greater than the average for the mile.
That is exactly right......however, if you measure in one direction then the other, you will reduce that difference in half, I believe. ie: if you could see a direct line between section corners, and measure directly, you would turn your zenith angles, and reduce the measurements, once from point A to point B then from point B back to point A. One direction would appear be 120ppm longer than the other. If you took the mean of the forward and reverse direction you would have 240ppm if I am not mistaken.
The same if you measured at half-way (and/or each direction to the half-way point). I may have not thought through this thoroughly through yet.....but that is where I was going with it.
I am thinking the same would be true if you broke chain or traversed in shorter-segment distances....you would be taking each measurement at a slightly-changed elevation.
> That is exactly right......however, if you measure in one direction then the other, you will reduce that difference in half, I believe. ie: if you could see a direct line between section corners, and measure directly, you would turn your zenith angles, and reduce the measurements, once from point A to point B then from point B back to point A. One direction would appear be 120ppm longer than the other. If you took the mean of the forward and reverse direction you would have 240ppm if I am not mistaken.
No, you ought not to have a greater difference than about 120ppm in the forward and back distance measurements from endpoints differing in height by 2500 ft. if you did the reductions to horizontal correctly.
> The same if you measured at half-way (and/or each direction to the half-way point). I may have not thought through this thoroughly through yet.....but that is where I was going with it.
The only thing really different about the forward and back measurements is the height of the tilting axis of the instrument relative to the target at the other point. A correct reduction to horizontal will take into account the fact that the verticals at both stations are not parallel.
> The only thing really different about the forward and back measurements is the height of the tilting axis of the instrument relative to the target at the other point. A correct reduction to horizontal will take into account the fact that the verticals at both stations are not parallel.
No Kent, you're wrong. (Uh, oh...I shouldn't have said that).
The reduction to horizontal at 2,500 feet is a longer horizontal than the reduction at 0.00 feet. You are reducing to horizontal at the elevation you are at.
If you are running horizontal lines at 2,500 feet of elevation, you will have distances that are shorter if you reduced them to 0' elevation. However, you don't do that, you use horizontal distances at the elevation you are at (not at sea level).
If you work your way up a high hill, you will get a different different state-plane horizontal distance reduction ratio at ever segment of the line.
If you shot the measurement from one end of the section corner at 0' elev. and shot from the other end at 2,500 feet, then did a mean of the two sets of zenith angles, it is averaging the difference....and getting a zenith angle (which would be the equivalent of the slope at the midpoint of the line). You need to get your ppm based on half-way up your hill, or at 1,250' elevation.
Okay...did I convince you or am I about to get pummeled. Don't worry, I will know. (You will either come back and slam me or you won't respond if you think I am right)
😉
> > The only thing really different about the forward and back measurements is the height of the tilting axis of the instrument relative to the target at the other point. A correct reduction to horizontal will take into account the fact that the verticals at both stations are not parallel.
>
> No Kent, you're wrong. (Uh, oh...I shouldn't have said that).
>
> The reduction to horizontal at 2,500 feet is a longer horizontal than the reduction at 0.00 feet. You are reducing to horizontal at the elevation you are at.
Uh, yes, of course. Was that ever in doubt? The reduction to horizontal at a particular elevation does take into account the geometric situation that the verticals (plumb lines) at the instrument and target stations aren't parallel.
The difference in scale of the back and forward distances on that mile-long line with endpoints differing in height by about 2,500 ft. is *obviously* the result of the verticals not being parallel. That's why the difference can't be more than about 120ppm unless there is some large geoid undulation.
> Uh, yes, of course. Was that ever in doubt? The reduction to horizontal at a particular elevation does take into account the geometric situation that the verticals (plumb lines) at the instrument and target stations aren't parallel.
>
> The difference in scale of the back and forward distances on that mile-long line with endpoints differing in height by about 2,500 ft. is *obviously* the result of the verticals not being parallel. That's why the difference can't be more than about 120ppm unless there is some large geoid undulation.
Okay, I thought you were disagreeing with me that the difference would be about half of 120ppm (or 240ppm). Apparently we were agreeing and I just took it the wrong way. I agree that the different would not be any more than 120ppm.....and am adding that it would more likely be closer to 240ppm.
> I agree that the different would not be any more than 120ppm.....and am adding that it would more likely be closer to 240ppm.
On a line only about a mile long with endpoints differing in height by 2,500 ft., how in the world do you get a difference in scale of back and forward measurements (reduced to horizontal at the elevation of the instrument) of 240ppm? That difference in height amounts to a scale difference of about 120ppm, as I demonstrated above.
> Is this a joke?
What, my post or the OP?
Mine, only a little bit. There wasn't enough info in the OP to know whether he looked for the original or had some definite record that the original had either been lost or never set.
Without such a record, proportional measure shouldn't even be considered until after a thorough search for the original corner monument and/or any potential indication of its original position.
Without further info, I stand by the advice of going back out and looking. I'm not ready to recognize it as a math problem at this point.
> On a line only about a mile long with endpoints differing in height by 2,500 ft., how in the world do you get a difference in scale of back and forward measurements (reduced to horizontal at the elevation of the instrument) of 240ppm? That difference in height amounts to a scale difference of about 120ppm, as I demonstrated above.
Probably a simpler way to put is this: on two plumb lines, the distance between points on each line at the same height will increase by about 1ppm for every 20.9 ft. that the heights of the points increases. So, distance between two points at 2020.9 ft. will increase by about 1ppm over that between two points on the same plumb line at an ellipsoid height of 2,000 ft.
2,500 ft./20.9 ft. x 1ppm = 120ppm