• Author / Uploaded
• Luis Enoc Espitia Fontalvo

Citation preview

1. Calcular el parametro de la espiral o longitud de la espiral dependiendo e

DATOS Le Rc Az TE Az ET C Abscisa PI NTE ETE

100 m 80 m 37 0.645772 143 2.495821 10 m 2482.37 500 500 180 3.141593

𝐾=√𝑅𝑐𝐿𝑒 Radianes Radianes

K

89.44272

2. Calcular angulo de deflexion de la espiral.

𝜃𝑒=(90°)/𝜋 (𝐿𝑒/𝑅𝑐) Radianes 𝜃𝑒

35.80986 35°48'35.50" 0.625

3. Calcular el angulo central de la curva circular.

∆𝑐=∆−2𝜃𝑒 ∆ ∆𝑐

106 106°0'0.00" 34.38028 34°22'48.99"

4. Coordenadas cartesianas del EC (Xc, yc) Xc Yc

96.16376 20.25922

5. Calcular las coordenadas cartesianas del PC desplazado (k,p)

p

5.136271

6. Tangente de la espiral - curva - espiral

k

Te

162.33562176

7. Externa de la espiral - curva - espiral.

Ee

8. Calcular las tangentes larga y corta de la espiral

TL

68.0838409021

Tc

34.6253906778

de la espiral dependiendo el caso.

8. Calcular coordenadas cartesianas del centro de la curva circular. Xo yo

49.35597 85.13627

9. Cuerda larga de la espiral Cle Cle

98.27464

Rad 10. Deflexion del EC 𝜑

0.207638 11.89677 11°53'48.38"

1.850049 0.600049 11. Longitud de la curva circular

Gc

esplazado (k,p)

0.12508152 Rad 7.1666434 7°9'59.92"

Lc

12. Calcular las abscisas de los puntos: TE, EC, CE Y ET. Abscisa TE

49.35597 Abscisa TE Abscisa EC

2320.034

47.97263

m

Abscisa EC

2420.034

Abscisa CE

2520.034

Abscisa ET

2620.034

Abscisa CE

61.46585 Abscisa ET

13. Calculos de localizacion por deflexiones por coordenadas cartesianas y por coordenadas topograficas planas.

rva circular. Abscisa 2320.035 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420

11°53'48.38"

Li 9.965 19.965 29.965 39.965 49.965 59.965 69.965 79.965 89.965 99.965

𝜃 Decimal °'" Radianes 0.355596 0°21'20.15"0.006206 1.427385 1°25'38.59"0.024913 3.215372 3°12'55.34"0.056119 5.719556 5°43'10.40"0.099825 8.939936 8°56'23.77"0.156031 12.8765112°52'35.45"0.224738 17.5292917°31'45.44"0.305944 22.8982622°53'53.75"0.39965 28.98343 28°59'0.36"0.505856 35.7848 35°47'5.28"0.624563

Coord. Cartesianas X Y 9.964962 0.020615 19.96376 0.165786 29.95556 0.560407 39.92519 1.32889 49.84349 2.594186 59.66284 4.47595 69.31295 7.087558 78.69721 10.53176 87.68999 14.89476 96.13537 20.23875

𝜑 Radianes 0.002069 0.008304 0.018706 0.033272 0.052 0.07488 0.1019 0.133036 0.168251 0.207493

Decimal 0.118532 0.475793 1.071762 1.906358 2.979364 4.290334 5.838456 7.622394 9.640085 11.8885

enadas topograficas planas.

NTE 370.353 Cli

°'" 0°7'6.72" 9.964983 0°28'32.85" 19.96445 1°4'18.34" 29.96081 1°54'22.89" 39.9473 2°58'45.71" 49.91096 4°17'25.20" 59.8305 5°50'18.44" 69.67437 7°37'20.62" 79.39879 9°38'24.31" 88.94599 11°53'18.60"98.24264

Decimal 37.11853 37.47579 38.07176 38.90636 39.97936 41.29033 42.83846 44.62239 46.64009 48.8885

ETE 402.304 Azimut Radianes °'" 0.647841 37°7'6.72" 0.654076 37°28'32.85" 0.664478 38°4'18.34" 0.679044 38°54'22.89" 0.697772 39°58'45.71" 0.720652 41°17'25.20" 0.747672 42°50'18.44" 0.778808 44°37'20.62" 0.814023 46°38'24.31" 0.853265 48°53'18.60"

Coord. Planas N E 378.299 408.3175 386.197 414.4509 393.9393 420.7793 401.4389 427.3929 408.5986 434.3724 415.3082 441.7846 421.4434 449.6779 426.8652 458.0762 431.4215 466.9726 434.9501 476.3231

Punto EC

CE

Deflexion por unidad de acuerda Abscisa EC Abscisa i Abscisa CE Abscisa i Abscisa 𝜑 Abscisa 2420.035 2430.035 2440.035 2450.035 2460.035 2468.008

2420.035 2430 2468.008 2460

Decimal °'" 0 0°0'0.00" 3.5707800725 3°34'14.81" 7.154101771 7°9'14.77" 10.737423469 10°44'14.72" 14.320745168 14°19'14.68" 17.190269184 17°11'24.97"

0.06254076 Radianes 3.5833217 Decimal 3°34'59.96" Deflexion EC a C 3.57078007 3°34'14.81"

EC.O 80 80 80 80 80 80

Azo.i Decimal Radianes 342.8098622 5.983161 349.9765056 6.108242 357.143149 6.233324 364.3097924 6.358405 371.4764358 6.483487 377.2154838 6.583652

Deflexion por metro

Deflexion CE a C 2.869524 2°52'10.29"

Coord. Planas N E 434.9501 476.323076 437.3027 486.042407 438.4244 495.979302 438.2976 505.978498 436.9243 515.883758 434.9397 523.643862

0.006254076 Radianes 0.35833217 Decimal 0°21'30.00" /m

NO EO Az Pie.EC Az CEO 72.80986 1.270772 162.8099 2.841568

358.5238 499.9666

𝜃Abscisa 2568.008 2560 2550 2540 2530 2520 2510 2500 2490 2480 2470

Li 8.008 18.008 28.008 38.008 48.008 58.008 68.008 78.008 88.008 98.008

𝜑

Coord. Cartesianas Decimal °'" Radianes X Y 0.23 0°13'48.00" 0.00401 8.008 0.011 1.161 1°9'39.60" 0.02026 18.007 0.122 2.809 2°48'32.40" 0.04903 28.001 0.458 5.173 5°10'22.80" 0.09029 37.977 1.143 8.253 8°15'10.80" 0.14404 47.908 2.302 12.05 12°3'0.00" 0.21031 57.752 4.054 16.562 16°33'43.20" 0.28906 67.442 6.514 21.791 21°47'27.60" 0.38032 76.887 9.788 27.736 27°44'9.60" 0.48408 85.968 13.965 34.397 34°23'49.20" 0.60034 94.534 19.114

Radianes Decimal 0.001374 0.0787 0.006775 0.3882 0.016355 0.9371 0.030088 1.7239 0.048014 2.751 0.070082 4.0154 0.096288 5.5169 0.126623 7.2549 0.161038 9.2268 0.199502 11.4306

°'" 0°4'43.32" 0°23'17.52" 0°56'13.56" 1°43'26.04" 2°45'3.60" 4°0'55.44" 5°31'0.84" 7°15'17.64" 9°13'36.48" 11°25'50.16"

Cli 8.008 18.007 28.005 37.994 47.963 57.894 67.756 77.508 87.095 96.447

NTE 370.353

ETE 597.696

Decimal 322.9213 322.6118 322.0629 321.2761 320.249 318.9846 317.4831 315.7451 313.7732 311.5694

Azimut Coord. Planas Radianes °'" N E 5.63604322°55'16.68"376.7419 592.8679 5.630638322°36'42.48"384.6603 586.7619 5.621058322°3'46.44"392.4402 580.4787 5.607326321°16'33.96"399.9948 573.9282 5.589399320°14'56.40"407.2284 567.026 5.567332318°59'4.56"414.036 559.7024 5.541125317°28'59.16"420.2945 551.906 5.510792315°44'42.36"425.8675 543.6069 5.476375313°46'23.52"430.6058 534.8061 5.437912311°34'9.84"434.3482 525.5389

Est. X Pto nuevo PI Pto viejo

Y 25000 25700 26100

Le1 Le2 Rc e a b

29000 28500 27000

80 m 60 m 260 8% 3.6 m 2%

Y 29500

29000

28500

28000

27500

27000

26500

26000 24800

25000

25200

25400

25600

25800

26000

26200

1. Calcular la tangente de entrada

1.1 Calcular el angulo de deflexion de la espiral

𝜃𝑒=(90°)/𝜋 (𝐿𝑒/𝑅𝑐) 𝜃𝑒1 𝜃𝑒2

8.814735 8°48'53.05 0.153846 6.611051 6°36'39.79 0.115385

1.5 Calcular el disloque de la espiral ∆R1, p ∆R2, p

1.024774 0.576649

XM1, k1 XM2, k2

39.96846 29.98669 Te1

26000

26200

1.2 Calcular el angulo de deflexion principal

Azimut 1 Azimut 2 2.88099

2. Calcular la tangente de salida

0.620249 125.5377 125°32'15.64" 1.310194 165.0686 165°4'6.90" 75.06858 39.53091 39°31'51.26" ∆ 0.689944 radianes

Te2

3. Calcular las abscisas de los puntos TE 1.3 Angulo de deflexion curva circular.

∆𝑐=∆−(𝜃𝑒1+𝜃𝑒2)

Distancia API Abscisa TE

∆𝑐

24.10512 24°6'18.43" 0.420714 Radianes 1.4 Coordenadas cartesianas Xc1, Xc2 o Xe1, Xe2.

Abscisa EC

Xc1, Xe1 Xc2, Xe2

79.81086 59.92017

Yc1,Ye1 Yc2, Ye2

4.095633 2.305499

Abscisa CE

Calcular la longitud de curva Lc 109.3856 Abscisa ET

el disloque de la espiral

d

0.704053

133.06136

a tangente de salida

124.326664

as abscisas de los puntos TE, EC, CE, ET y el punto de pueblo viejo. 860.2375

Distancia PIB Abscisa PV

Abscisa TE

727.1761

Abscisa EC

807.1761

4. Coordenadas (X,Y) de los puntos ET y TE 1552.417

XTE YTE

25591.73 28577.34

XET YET

25732.03 28379.87

2404.652

Abscisa CE

916.5617

ongitud de curva

Abscisa ET

976.5617

de los puntos ET y TE