Single Proportion Example T26S, R12W, W.M. S W ch.

Transcription

1 Single Proportion Example T26S, R12W, W.M.? S W ch.

2 Reduce record and retraced to cardinal equivalents. Sec. 23 Total W-E ompare apples to apples eliminate the influence of hard skew bearings. W Sec. 26 E Then proportion. Finally, shift the proportioned corner position in a cardinal direction until it falls on line between the nearest controlling corners.

3 Reduce record and retraced to cardinal equivalents. Sec. 23 Total W-E Record W-> (lat W, dep W ) E -> (lat E, dep E ) Retraced Total W-E -> (lat W-E, dep W-E ) W Sec. 26 E dep W-E dep W + dep E dep W dep W From the cor. of secs. 22, 23, 26, and 27 cardinal east dep W dep W-E dep E Then cardinal north or south to true line (or reverse) dep E dep W + dep E dep E (Proportion latitudes for N-S lines.) dep W

4 Record W-> (lat=d W cosb, dep=d W sinb) W-> ( , ) E-> (lat=d E cosb, dep=d E sinb) E -> ( , ) S W ch ch ch. S W ft. Retraced Total W-E -> (lat=d W-E cosb, dep=d W-E sinb ) Total W-E -> ( , ) W E Then proportion: dep W dep E dep W = dep E = dep W + dep E = = = Total W-E

5 Then calculate the distance along the true bearing. bearing dep for N-S lines: lat cos(bearing) From the cor. of secs. 23, 24, 25, and 26 dist W + dist E = Total W-E? dep E dep W (or reverse)

6 Simple Version Sec. 19 Record Retraced Total W-E W E dist W dist E Sec. 30 Single proportion Total W-E dist W dist E Better? dist W + dist E dist W dist E This only works when the corners are on a common bearing.

7 Simple Version S W ch. Record Retraced ch ch. S W ft. W E dist W dist E dist W = dist E = By golly, it s the same numbers as the long way!

8 N 0 04 W ch. N 0 04 W ch. Double Proportion Example T30S, R10W, W.M. S W ch.? N W ch.

9 S N Reduce record and retraced to cardinal equivalents. Sec. 9 Total N-S Sec. 10 Total W-E Proportion north-south and east-west. W Sec. 16 Sec. 15 E Remember this is NOT any kind of bearing-bearing or distance-distance intersection! Finally, shift the proportioned corner position to the intersection of cardinal directions from the north-south and east-west proportioned positions.

10 S N Reduce record and retraced to cardinal equivalents. Sec. 9 Total N-S Sec. 10 Record N-> (lat N, dep N ) S -> (lat S, dep S ) W-> (lat W, dep W ) E -> (lat E, dep E ) Retraced Total N-S -> (lat N-S, dep N-S ) Total W-E -> (lat E-W, dep E-W ) W Total W-E E Sec. 16 Sec. 15 From the ¼ cor. bet. secs. 15 and 16: cardinal north lat S From the ¼ cor. bet. secs. 9 and 16: cardinal east dep W lat N-S lat N lat S lat N + lat S dep W-E dep W + dep E lat N dep W dep W lat S dep E dep E lat S Then cardinal to true dep W

11 N E ft. S N N 0 04 W ch. N 0 04 W ch. Record N-> ( , ) S -> ( , ) W-> ( , ) E -> (0.4220, ) Sec. 9 Sec. 10 S W N W ch ch. Sec. 16 Sec. 15 Retraced Total N-S -> ( , ) Total W-E -> ( , ) Sec. 9 Sec. 10 S W ft. W E Sec. 16 Sec. 15

12 S N Record N-> ( , ) S -> ( , ) W-> ( , ) Sec. 9 Total N-S Sec. 10 E -> (0.4220, ) Retraced Total N-S -> ( , ) Total W-E W E Sec. 16 Sec. 15 Total W-E -> ( , ) lat N lat S lat N = lat S = dep W dep E dep W = dep E =

13 lat N = lat S = dep W = dep E = Then cardinal to true cor. From the ¼ cor. bet. secs. 15 and 16 cardinal north lat S From the ¼ cor. bet. secs. 9 and 16 cardinal east dep W But what are the cardinal moves to the true corner? (or reverse)

14 Using a coordinate system as shown, the coordinates for the true corner position are (lat S, dep W ). I also determined the intersection coordinates Move Move Intersection Int. -> True: -> True: lat M = lat T - lat I = dep M = dep T - dep I = N E True orner Position: ( , ) I can now calculate a move from the intersection point to the true corner. (0, 0) Intersection: ( , )

15 One-Point ontrol Example T22S, R8W, W.M.?

16 There is nothing to proportion and nothing to compare using cardinal equivalents. Sec. 28 Sec. 33 E Simply replace the corner at the record bearing and distance being sure to use true bearing.

17 Sec. 28 Record E -> well, record E Sec. 33 From the cor. of secs. 27, 28, 33, and 34 record true bearing and distance E Remember to use true bearing.

18 Two-Point ontrol Example T22S, R8W, W.M.?

19 N Reduce record and retraced to cardinal equivalents. Sec. 18 Sec. 17 There is nothing to proportion north-south or east-west. Use the cardinal equivalents. Sec. 19 E Shift the proportioned corner position to the intersection of cardinal directions from the north-south and east-west positions determined from the cardinal equivalents.

20 Reduce record to cardinal equivalents. N Sec. 18 E Sec. 17 Record Sec. 19 N-> (lat N, dep N ) E -> (lat E, dep E ) From the cor. of secs. 7, 8, 17, and 18 cardinal south record lat N From the ¼ cor. bet. secs. 18 and 19 lat N cardinal east record dep E Then cardinal to true corner dep E

21 Three-Point ontrol Example T22S, R8W, W.M.?

22 unsurveyed N Reduce record and retraced to cardinal equivalents. S Total N-S Sec. 23 E Single proportion in one direction. Use the suitable cardinal equivalent in the other. Sec. 26 Shift the proportioned corner position to the intersection of cardinal directions from the proportioned position and the position determined from the cardinal equivalent.

23 Reduce record and retraced to cardinal equivalents. Record Retraced N-> (lat N, dep N ) unsurveyed N Total N-S S Sec. 23 E Total N-S -> Sec. 26 S-> (lat S, dep S ) (lat N-S, dep N-S ) E -> (lat E, dep E ) Single proportion N-S lat N-S lat N lat N From the cor. of secs. 23, 24, 25, and 26 cardinal west record dep E lat N + lat S lat N lat N-S lat N + lat S lat S lat S lat S dep E Then cardinal to true corner

24 Meander Line Adjustment Example T22S, R8W, W.M.??? (a.k.a. ompass Rule Adjustment)

25 Reduce record and tie to cardinal equivalents. Proportion the error (tie) through each individual segment of record line. tie from record position to found corner Use the distance of each segment divided by the distance of the entire line. Multiply by the latitude or departure of the tie, then add the latitude or departure of the segment. It is especially important to keep track of signs!

26 Reduce record and tie to cardinal equivalents. Record rec 1 -> (lat 1, dep 1 ) rec 2 -> (lat 2, dep 2 ) rec 3 -> (lat 3, dep 3 ) Retraced T -> (lat T, dep T ) tie from record position to found corner Also: (lat 1, dep 1 ) -> new 1 : brg. dist t = dist 1 + dist 2 + dist 3 dist 1 dist t lat T lat 1 lat 1 dist 1 dist t dep T dep 1 dep 1

27 Grant Boundary Adjustment Example T22S, R8W, W.M.???

28 Ignore cardinal equivalents! Determine the record and measured bearing and distance of the tie between the found original corners. rec 4 rec 1 rec 3 rec 2 Rotate the bearing of each segment by the difference between measured and record bearings of the tie. Then proportion the distance of each segment, using the ratio of measured and record distances of the tie. Note that this method holds fixed the angles at each corner it fixes the shape of the parcel.

29 First rotate the parcel to match the measured bearing. rec 4 rec 3 az T az T θ rec 1 rec 2 az 1 θ az 1 az 2 θ az 2 Record Retraced az 3 θ az 3 az 4 θ az 4 Then shrink or expand the parcel (proportionately). Watch your signs! dist T dist 1 dist T dist 1 dist 2 dist 2 dist 3 dist 3 dist 4 dist 4

30 Irregular Boundary Adjustment Example? T26S, R12W, W.M. Remember this one?

31 In 1976, a resurvey reestablished the ¼ corner at midpoint. In 2009, I found the 1976 ¼ corner: 3.62 ft. S 16½ E of the true position 3.55 ft. S 11½ E of the midpoint position We accepted the 1976 ¼ corner as a technically incorrect but good-faith reestablishment of the original.

32 Suppose you resurvey the line a decade later and fail to find the 1976 ¼ corner? How do you put it back? Toto, the corner s not at midpoint anymore...

33 Reduce record and retraced to cardinal equivalents. Sec. 23 Single proportion in the obvious direction (in this case, east-west). Sec. 26 In the opposite direction (in this case, north-south), determine the difference between the measured and record latitude (in this case) and divide by the total record length of the whole line. Then multiply this by the record distance of each segment and add the measured latitude (in this case) of that segment.

34 Reduce record and retraced to cardinal equivalents. Sec. 23 Record W-> (lat W, dep W ) E -> (lat E, dep E ) Retraced Total W-E -> (lat W-E, dep W-E ) Sec. 26 dep W-E Single proportion. dep W dep E dep W + dep E dep W dep E hange dep to lat for N-S lines.

35 Adjust for break in bearing. Sec. 23 Record W-> (lat W, dep W ) E -> (lat E, dep E ) Retraced Total W-E -> (lat W-E, dep W-E ) Sec. 26 Also: dist t = dist W + dist E lat W-E lat W-E lat W + lat E dist t lat W + lat E dist t dist W lat W lat W dist E lat E lat E hange lat to dep for N-S lines.

36 heck your work. Sec. 23 dep W-E = dep W + dep E lat W-E = lat W + lat E Sec. 26 Finish. (lat W, dep W ) -> new W : brg. (lat E, dep E ) -> new E : brg.

37 Single Proportion Unusual Situations? Example T27S, R9W, W.M. Where does the north ¼ corner go?

38 GLO, as corrected and accepted in 1901 given parenthetical ch. sec ch. S E ch. sec ch ch.

39 private surveyor, as filed in 1992 original corner corrected original found (BLM 1975) calculated and set Note: corrected by BLM in 1975 N E sec ft. N E ft ft. N E ft ft. N E ft. Note: corrected by BLM in 1983 sec. 6

40 1901 sec ch ch ch ch. S E ch ch ch. sec. 6 calculated 1992 Note: found and corrected by BLM in 1975 N E sec ft. N E ft ft ft. N E ft ft. N E ft. Note: found and corrected by BLM in 1983 sec dist dist

41 Which corners control alignment? sec. 31 sec. 6 Which corners control proportioning? Note that it is important to use the original closing corners for proportioning!

42 1992 Note: found and corrected by BLM in 1975 N E sec ft. N E ft ft ft. N E ft ft. N E ft. Note: found and corrected by BLM in 1983 sec Note: found and corrected by BLM in 1975 S W sec ft. N W ft ft. S W S W ft. Note: found and corrected by BLM in 1983 sec. 6 about 0 03 rotational difference distance differences are negligible

43 1901 sec ch ch ch. S E ch ch ch ch. sec S W sec ft. N W ft ft. S W S W ft. To original : N W, 8.58 ft. sec. 6 To original : N E, 8.75 ft. The line is not straight; therefore, I must reduce the parts to cardinal equivalents.

44 1901 sec. 31 L = D = L = D = sec L = D = L = sec. 31 D = L = D = sec. 6 L = D = L = D = from one original to the other L = D = L = D = dep dep

45 dep dep To original : N W, 8.58 ft. S W sec ft. N W ft ft ft. sec ft. S W ft. S W ft. To original : N E, 8.75 ft. plat dep =

46 1992 N E sec ft. N E ft ft. N E ft. N E ft ft. sec ft S W sec ft. N W ft ft. S W ft. S W ft ft ft. sec. 6 ¼ corner moved 4 ft. West 1/16 corner moved 16 ft. West

47 Single Proportion Unusual Situations Another Example T27S, R9W, W.M.? What about the west ¼ corner?

48 39.73 ch ch. N orth ch. North ch. GLO, as corrected and accepted in 1901 North 7.60 ch. sec. 6 given parenthetical So the west ¼ cor. of sec. 6 is 0.27 ch. N of the east ¼ cor. of sec right? sec. 1

49 39.73 ch ch. N E ft. North ch. North ch. N W ft North 7.60 ch. sec N W ft. sec. 6 To original : N W, 8.58 ft. Note: found and corrected by BLM in 1975 reduce to cardinal equivalents sec. 1 sec. 1

50 L = D = L= D = L = D = L = D = L = D = L = D = L = D = sec L = D = sec. 6 L = D = sec. 1 sec. 1

51 ontrolling corners? sec. 6 NE sec. 1 E1/4 sec lat lat lat S1/ sec. 1

52 ontrolling corners? sec. 6 NE sec. 1 E1/4 sec. 1 NE sec. 1 SE sec ft. S! lat S1/ lat S1/ lat S1/ sec. 1

53 Original! ontrolling corners? sec. 6 NE sec. 1 E1/4 sec. 1 NE sec. 1 SE sec. 1 NW sec. 6 SW sec. 6 = SE sec. 1 another 5 ft. S! lat S1/ lat S1/ lat S1/ lat S1/ sec. 1 Nearly 40 ft. S of obvious position 20 ft. S of the E1/4 sec. 1!

54 N E ft ft ft. N W ft ft ft N W ft. sec. 6 lat S1/ To original : N W, 8.58 ft. lat S1/ N E ft. plat.lat = sec. 1