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$ BEGIN METADATA
$ ====================================================================
$ DESCRIPTION:
$ iPOGO batch command file to compute B&O railroad H.O.T. points
$ as posted By Steve G on 9/1/2000 on rpls.com message board.
$ Computed by Stan Thompson, PLS 9/2/00.
$ All lines beginning with $ are comments.
$ ====================================================================
$ COMPUTING PROCEDURES:
$ 1) Assign beginning N,E to point 1
$ 2) Then compute points 2 thru 10 using
$ valuation map bearings and station distances.
$ 3) Compute spirals on new curve alignment
$ 4) Plot the linework and print the stationing
$ ====================================================================
$CONCLUSIONS:
$ Per review of the following comps:
$ Using strictly val map data, the length of curve
$ is 0.1 foot short.
$ The delta angle should be 2° 51' 07.7"
$ or the degree of curve (chd def)
$ should be 0°44'59.29" 7641.501213
$ ====================================================================
$SPECIAL FORMULAS:
$ Given Ls=200, Dc=0.75, Total Delta=2°51'
$ 1) Radius of simple curve
$ Rc = 50 / sin(Dc/2) = 7639.49181 feet
$ 2) total spiral delta
$ SD = (LS*Dc) / 200 = 0.75°
$ 3) length along original tangent to offset at end of spiral
$ X = Ls - (Ls^3 / 40 * Rc^2) = 199.996573 feet
$ 4) perpendicular offset from original tangent to end of spiral
$ Y = Ls^2 / (6 * Rc) = 0.872658 feet
$ 5) throw distance from original curve to end of spiral
$ O = Y - (Rc * (1 - cos(SD))) = 0.21816 feet
$ 6) distance from OFFSET T.C. to T.S.
$ Xo = X - (Rc * Sin(SD)) = 99.998715 feet
$ 7) tangent length of original curve
$ Tc = Rc * Tan(TotalDelta/2) = 190.04054 feet
$ 8) tangent length from original PI to TS
$ Ts = Xo + Tc + (O * Tan(TotalDelta/2)) = 290.0447 feet
$ 9) tangent length from original TC to TS
$ TcTs = Xo + (O * Tan(TotalDelta/2)) = 100.0041 feet
$ 10) spiral chord length
$ Sc = (X^2 + Y^2)^0.5 = 199.998477 feet
$ 11) rate of change in radius
$ a = 100 * (Dc / Ls) = 0.375° per 100 feet
$ ====================================================================
$ END METADATA
$ COMPUTATIONS
$ ====================================================================
$ original alignment computation per valuation map
0 1 10000 10000 ; $ 1 = 463+69 CT
1 2 1 sw 73 10 0 3079.4 $ 2 = 494+48.4 H.O.T. - 19'Rt defl
sw 73 29 0 62.6 $ 3 = 495+11.0 H.O.T. - 23'Lt defl
sw 73 06 0 1589.0 $ 4 = 511+00.0 H.O.T. - 04'Rt defl
sw 73 10 0 939.7 $ 5 = 520+39.7 H.O.T. - 02'Rt defl
sw 73 12 0 860.3 $ 6 = 529+00.0 H.O.T. - 10'Rt defl
sw 73 22 0 352.7 $ 7 = 532+52.7 T.C.
9e9 7639.49181 $ 8 = R.P. of 0°45' curve Chd def
8e8 2 51 0 7639.49181 $ 9 = 536+32.8 C.T.
9e9 1467.2 0 ; $ 10 = 551+00.00 - 04'Lt
$ set new spiral T.S. at distance TcTs from old T.C.
1 20 7 7 6 100.0041 ;
$ set new S.C. at spiral station 2+00 by using plus and offset of X and Y
1.1 30 20 7 0 199.996573 0.872658 ;
$ set PI of spiral tangents by intersection using 2/3 delta from sharp end
3 31 20 20 7 30 8e8 0 30 0 30 20 ;
$ Compute points 21 - 29 on 10 chord spiral using
$ the -2 command and right angles.
$ Deflection angles computed by (ls/Ls)^2*(SpiralDelta/3)
$ Chords computed from tangent offset calculations of X and Y
$ (See Excel spreadsheet)
-2 21 20 20 7 00 00 09 20.0000 $ 21 = 0+20 flat to sharp stakeout
00 00 36 40.0000 $ 22 = 0+40
00 01 21 60.0000 $ 23 = 0+60
00 02 24 79.9999 $ 24 = 0+80
00 03 45 99.9998 $ 25 = 1+00
00 05 24 119.9997 $ 26 = 1+20
00 07 21 139.9995 $ 27 = 1+40
00 09 36 159.9992 $ 28 = 1+60
00 12 09 179.9989 ; $ 29 = 1+80
$ the following is basically duplicated from the above spiral comps
$ set new spiral S.T. at distance TcTs from old C.T.
1 40 9 9 10 100.0041 ;
$ set new C.S. using plus and offset of X and Y
1.1 50 40 9 0 199.996573 -0.872658 ;
$ set PI of spiral tangents by intersection using 2/3 delta from sharp end
3 51 40 40 9 50 8e8 -0 -30 0 50 40 ;
$ compute points 41 - 49 on 10 chord spiral using
$ the -2 command and left angles
-2 41 40 40 9 -00 -00 -09 20.0000 $ 41 = 0+20 flat to sharp stakeout
-00 -00 -36 40.0000 $ 42 = 0+40
-00 -01 -21 60.0000 $ 43 = 0+60
-00 -02 -24 79.9999 $ 44 = 0+80
-00 -03 -45 99.9998 $ 45 = 1+00
-00 -05 -24 119.9997 $ 46 = 1+20
-00 -07 -21 139.9995 $ 47 = 1+40
-00 -09 -36 159.9992 $ 48 = 1+60
-00 -12 -09 179.9989 ; $ 49 = 1+80
$ compute new radius point of simple curve at right angles
$ to spiral tangents at sharp end
3 100 30 9e9 31 30 50 9e9 50 51 ;
$ PRINT/PLOT RESULTS
$ ====================================================================
15.1 CLRw CLRw 1; $ define FeatureCode, LayerName and Color
15.1 CLTrack CLTrack 3;
91; $ activate plotting
15 CLRw;
100 Original Centerline Right of Way Points on Val Map; $ text label for output
7 1 1 -7 8.1 9 10; $ inverse the centerline
76 c; $ activate chord definition for output
15 CLTrack; $ activate the featureCode
100 Centerline Track Stations for New Alignment; $ text label for output
77 1 46369 1 -6 20 -30 100.1 50 -40 10; $ inverse the centerline
-91; $ deactivate plotting
END; $ stop batch file computing
iPOGO COMPUTED OUTPUT:
=======================================================================================
Begin Batch Processing <03-Sep-00> <12:17:03 PM>
Original Centerline Right of Way Points on Val Map
1 10000.0000 10000.0000 0.0000 1
2 S 73° 10' 00" W 3079.400 9108.2406 7052.5486 0.0000 2
3 S 73° 29' 00" W 62.600 9090.4438 6992.5317 0.0000 3
4 S 73° 06' 00" W 1589.000 8628.5180 5472.1549 0.0000 4
5 S 73° 10' 00" W 939.700 8356.3915 4572.7200 0.0000 5
6 S 73° 12' 00" W 860.300 8107.7374 3749.1380 0.0000 6
7 S 73° 22' 00" W 352.700 8006.7785 3411.1963 0.0000 7
9 S 74° 47' 30" W 379.964 7907.1029 3044.5397 0.0000 9
10 S 76° 13' 00" W 1467.200 7557.5410 1619.5897 0.0000 10
** CURVE DATA **
CNTR PC PT RADIUS DELTA ARC TANGENT CHORD
8 7 9 7639.492 2° 51' 00" 380.003 190.041 379.964
Centerline Track Stations for New Alignment
----------------------------------------------------------------------------------------
1 = 463 + 69.000 10000.0000 10000.0000 0.0000
S 73° 10' 00" W 3079.400
2 = 494 + 48.400 9108.2406 7052.5486 0.0000
S 73° 29' 00" W 62.600
3 = 495 + 11.000 9090.4438 6992.5317 0.0000
S 73° 06' 00" W 1589.000
4 = 511 + 00.000 8628.5180 5472.1549 0.0000
S 73° 10' 00" W 939.700
5 = 520 + 39.700 8356.3915 4572.7200 0.0000
S 73° 12' 00" W 860.300
6 = 529 + 00.000 8107.7374 3749.1380 0.0000
S 73° 22' 00" W 252.696
20 = 531 + 52.696 8035.4043 3507.0158 0.0000
S 73° 22' 09" W 20.000
21 = 531 + 72.696 8029.6802 3487.8525 0.0000
S 73° 23' 03" W 20.000
22 = 531 + 92.696 8023.9611 3468.6876 0.0000
S 73° 24' 51" W 20.000
23 = 532 + 12.696 8018.2521 3449.5197 0.0000
S 73° 27' 33" W 20.000
24 = 532 + 32.696 8012.5581 3430.3475 0.0000
S 73° 31' 09" W 20.000
25 = 532 + 52.696 8006.8843 3411.1692 0.0000
S 73° 35' 39" W 20.000
26 = 532 + 72.696 8001.2355 3391.9836 0.0000
S 73° 41' 03" W 20.000
27 = 532 + 92.696 7995.6169 3372.7891 0.0000
S 73° 47' 21" W 20.000
28 = 533 + 12.696 7990.0334 3353.5843 0.0000
S 73° 54' 33" W 20.000
29 = 533 + 32.696 7984.4902 3334.3678 0.0000
S 74° 02' 39" W 20.000
30 = 533 + 52.696 7978.9922 3315.1381 0.0000
Curve Center = 100 15326.8209 1224.3648 0.0000
Radius = 7639.497
Len = 180.000 (chord def)
Delta = 1° 21' 00"
Tangent = 90.005
Chord = S 74° 47' 30" W 179.997
50 = 535 + 32.696 7931.7737 3141.4448 0.0000
S 75° 32' 21" W 20.000
49 = 535 + 52.696 7926.7793 3122.0783 0.0000
S 75° 40' 27" W 20.000
48 = 535 + 72.696 7921.8305 3102.7001 0.0000
S 75° 47' 39" W 20.000
47 = 535 + 92.696 7916.9224 3083.3118 0.0000
S 75° 53' 57" W 20.000
46 = 536 + 12.696 7912.0499 3063.9145 0.0000
S 75° 59' 21" W 20.000
45 = 536 + 32.696 7907.2078 3044.5095 0.0000
S 76° 03' 51" W 20.000
44 = 536 + 52.696 7902.3911 3025.0982 0.0000
S 76° 07' 27" W 20.000
43 = 536 + 72.696 7897.5947 3005.6820 0.0000
S 76° 10' 09" W 20.000
42 = 536 + 92.696 7892.8136 2986.2618 0.0000
S 76° 11' 57" W 20.000
41 = 537 + 12.696 7888.0426 2966.8392 0.0000
S 76° 12' 51" W 20.000
40 = 537 + 32.696 7883.2768 2947.4154 0.0000
S 76° 13' 00" W 1367.196
10 = 550 + 99.892 7557.5410 1619.5897 0.0000
----------------------------------------------------------------------------------------
PROGRAM STOPPED BY THE END STATEMENT AT LINE 103.
End Batch Processing <03-Sep-00> <12:17:03 PM>
The total execution time is - 0.06 seconds
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