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EST Ai PV Hs Hm Hi Ang. V Ang. H 
COTAS SUBRASANTE 
99.80602 
E1 1.577 BM 1.654 1.566 1.500 89°19'9'' 268°55'14'' 100.000 
 
V2 1.790 1.765 1.740 89°19'45'' 200°32'28'' 99.67656 
 
V1 1.804 1.752 1.700 89°20'24'' 123°26'5'' 99.75081 
E2 1.513 BM 1.266 1.133 1.000 89°56'7'' 269°56'7'' 99.58605 
 
P1 1.727 1.533 1.300 89°36'25'' 95°57'40'' 99.70312 
 
P2 1.726 1.412 1.300 89°52'26'' 94°52'15'' 99.85897 
0+000 P3 1.726 1.513 1.300 89°50'38'' 93°44'49'' 99.78081 99.78081 
 
P4 1.728 1.513 1.300 89°50'37'' 92°38'42'' 99.70287 
 
P5 1.728 1.317 1.300 89°50'25'' 91°33'2'' 99.70536 
 
P6 1.335 1.315 1.300 94°20'16'' 130°56'19'' 99.51808 
 
P7 1.330 1.314 1.300 95°21'42'' 118°39'54'' 99.50495 
0+040 
 
P8 1.328 1.314 1.300 94°30'1'' 103°2'15'' 99.56603 100.2964 
 
P9 1.328 1.31 1.300 94°11'45'' 86°18'11'' 99.58073 
 
P10 1.331 1.463 1.300 93°34'52'' 70°49'30'' 99.58980 
E3 1.513 P10 1.755 1.463 1.171 88°58'25'' 95°14'31'' 98.49385 
 
P11 1.194 1.097 1.000 91°16'50'' 110°29'8'' 98.47641 
 
P12 1.190 1.094 1.000 91°18'11'' 108°15'17'' 98.48089 
0+080 
 
P13 1.190 1.094 1.000 91°21'58'' 105°49'24'' 98.46000 100.5291 
 
P14 1.188 1.094 1.000 91°33'20'' 103°20'46'' 98.40269 
 
P15 1.187 1.094 1.000 91°33'13'' 100°44'30'' 98.40604 
 
P16 2.820 2.710 2.600 89°17'36'' 261°15'6'' 97.56816 
 
P17 2.620 2.511 2.402 89°46'26'' 263°16'28'' 97.58188 
0+120 
 
P18 2.917 2.808 2.700 88°58'47'' 265°22'21'' 97.58518 100.7618 
 
P19 2.817 2.708 2.600 89°13'2'' 267°26'10'' 97.59528 
 
P20 2.616 2.508 2.401 89°40'49'' 269°40'32'' 97.61882 
 
P21 2.519 2.210 1.900 89°50'51'' 269°50'39'' 97.96160 
 
P22 2.517 2.209 1.900 89°50'50'' 270°34'22'' 97.96237 
0+160 
 
P23 2.038 1.705 1.419 89°51'5'' 271°21'12'' 98.46240 100.9945 
 
P24 2.113 1.806 1.500 89°46'9'' 272°7'41'' 98.44781 
 
P25 2.113 1.806 1.500 89°46'7'' 272°51'55'' 98.44841 
 
1. CÁLCULO DE DI, DH, DV y COTAS: COTA BM = 100 
 
 
E2 – P1: 
𝐷𝐷𝐷𝐷 = (1.727− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 42.7 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.7 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°36′25′′�2 
𝐷𝐷𝐷𝐷 = 42.698 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.7 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°36′25′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.2929 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃1 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸2 + 𝐶𝐶𝑠𝑠 + 𝐷𝐷𝐷𝐷 −𝐷𝐷𝑚𝑚 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃1 = 99.85897 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P2: 
𝐷𝐷𝐷𝐷 = (1.726− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 42.6 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.6 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°52′26′′�2 
𝐷𝐷𝐷𝐷 = 42.698 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.6 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°50′38′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.1161 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃2 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸2 + 𝐶𝐶𝑠𝑠 + 𝐷𝐷𝐷𝐷 −𝐷𝐷𝑚𝑚 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃2 = 99.78081𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P3: 
𝐷𝐷𝐷𝐷 = (1.726− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 42.6 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.6 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°50′38′′�2 
𝐷𝐷𝐷𝐷 = 42.5997 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.6 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°52′26′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.0938 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃3 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸2 + 𝐶𝐶𝑠𝑠 + 𝐷𝐷𝐷𝐷 −𝐷𝐷𝑚𝑚 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃3 = 99.70312 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P4: 
𝐷𝐷𝐷𝐷 = (1.728− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 42.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°50′37′′�2 
𝐷𝐷𝐷𝐷 = 42.7997 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°50′37′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.1168 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃4 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸2 + 𝐶𝐶𝑠𝑠 + 𝐷𝐷𝐷𝐷 −𝐷𝐷𝑚𝑚 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃4 = 99.70287 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
E2 – P5: 
𝐷𝐷𝐷𝐷 = (1.728− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 42.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°50′25′′�2 
𝐷𝐷𝐷𝐷 = 42.7997 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 42.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠(2 𝑥𝑥 50′25′′)
2 �
 
𝐷𝐷𝐷𝐷 = 0.1193 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃5 = 99.70536 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P6: 
𝐷𝐷𝐷𝐷 = (1.335− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 3.5 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3.5 × �𝑠𝑠𝑠𝑠𝑠𝑠 94°20′16′′�2 
𝐷𝐷𝐷𝐷 = 3.48 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3.5 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 94°20′16′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.264 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃6 = 99.51808 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P7: 
𝐷𝐷𝐷𝐷 = (1.33− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 3 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3 × �𝑠𝑠𝑠𝑠𝑠𝑠 95°21′42′′�2 
𝐷𝐷𝐷𝐷 = 2.9738 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 95°21′42′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.2791𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃7 = 99.50495 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P8: 
𝐷𝐷𝐷𝐷 = (1.328− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 2.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 2.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 94°30′1′′�2 
𝐷𝐷𝐷𝐷 = 2.7828 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 2.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 94°30′1′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.219 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃8 = 99.56603 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
 
E2 – P9: 
𝐷𝐷𝐷𝐷 = (1.328− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 2.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 2.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 94°11′45′′�2 
𝐷𝐷𝐷𝐷 = 2.785 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 2.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 94°11′45′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.2043 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃9 = 99.58073 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E2 – P10: 
𝐷𝐷𝐷𝐷 = (1.331− 1.3) × 100 
𝐷𝐷𝐷𝐷 = 3.1 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3.1 × �𝑠𝑠𝑠𝑠𝑠𝑠 93°34′52′′�2 
𝐷𝐷𝐷𝐷 = 3.0879 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 3.1 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 93°34′52′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.1933 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃10 = 99.58980 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P10 – E3: 
𝐷𝐷𝐷𝐷 = (1.755− 1.171) × 100 
𝐷𝐷𝐷𝐷 = 58.4 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 58.4 × �𝑠𝑠𝑠𝑠𝑠𝑠 88°58′25′′�2 
𝐷𝐷𝐷𝐷 = 58.3813 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 58.4 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 88°58′25′′�
2 �
 
𝐷𝐷𝐷𝐷 = 1.0459 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸3 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 10 + 𝐷𝐷𝑚𝑚 − 𝐷𝐷𝐷𝐷 − 𝐶𝐶𝑠𝑠 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸3 = 98.49385 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P11: 
𝐷𝐷𝐷𝐷 = (1.194− 1) × 100 
𝐷𝐷𝐷𝐷 = 19.4 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 19.4 × �𝑠𝑠𝑠𝑠𝑠𝑠 91°16′50′′�2 
𝐷𝐷𝐷𝐷 = 19.3903 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 19.4 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 91°16′50′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.4334 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃11 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐸𝐸3 + 𝐶𝐶𝑠𝑠 + 𝐷𝐷𝐷𝐷 − 𝐷𝐷𝑚𝑚 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃11 = 98.47641 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
 
 
 
P12: 
𝐷𝐷𝐷𝐷 = (1.190− 1) × 100 
𝐷𝐷𝐷𝐷 = 19 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 19 × �𝑠𝑠𝑠𝑠𝑠𝑠 91°18′11′′�2 
𝐷𝐷𝐷𝐷 = 18.9902 𝑚𝑚 
 
𝐷𝐷𝐷𝐷
= 19 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 91°18′11′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.4320 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃12 = 98 48089 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P13: 
𝐷𝐷𝐷𝐷 = (1.190− 1) × 100 
𝐷𝐷𝐷𝐷 = 19 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 19 × �𝑠𝑠𝑠𝑠𝑠𝑠 91°21′58′′�2 
𝐷𝐷𝐷𝐷 = 18.9892 𝑚𝑚 
 
𝐷𝐷𝐷𝐷
= 19 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 91°21′58′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.4528 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃13 98 4600 
 
 
 
 
 
P14: 
𝐷𝐷𝐷𝐷 = (1.188− 1) × 100 
𝐷𝐷𝐷𝐷 = 18.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 18.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 91°33′20′′�2 
𝐷𝐷𝐷𝐷 = 18.7861 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 18.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 91°33′20′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.5102 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃14 = 98.40269 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P15: 
𝐷𝐷𝐷𝐷 = (1.187− 1) × 100 
𝐷𝐷𝐷𝐷 = 18.7 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 18.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 91°33′13′′�2 
𝐷𝐷𝐷𝐷 = 18.6863 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 18.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 91°33′13′′�
2 �
 
𝐷𝐷𝐷𝐷 = −0.5068 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃15 = 98.40604 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
 
P16: 
𝐷𝐷𝐷𝐷 = (2.82− 2.6) × 100 
𝐷𝐷𝐷𝐷 = 22 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 22 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°17′36′′�2 
𝐷𝐷𝐷𝐷 = 21.9967 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 22 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°17′36′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.2713 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃16 = 97.56816 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P17: 
𝐷𝐷𝐷𝐷 = (2.62− 2.402) × 100 
𝐷𝐷𝐷𝐷 = 21.8 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.8 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°46′26′′�2 
𝐷𝐷𝐷𝐷 = 21.7997 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.8 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°46′26′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.086 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃17 = 97.58188 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P18: 
𝐷𝐷𝐷𝐷 = (2.917− 2.7) × 100 
𝐷𝐷𝐷𝐷 = 21.7 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.7 × �𝑠𝑠𝑠𝑠𝑠𝑠 88°58′47′′�2 
𝐷𝐷𝐷𝐷 = 21.6931 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.7 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2𝑥𝑥 88°58′47′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.3863 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃18 = 97.58518 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P19: 
𝐷𝐷𝐷𝐷 = (2.817− 2.6) × 100 
𝐷𝐷𝐷𝐷 = 21.70 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.7 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°13′2′′�2 
𝐷𝐷𝐷𝐷 = 21.6959 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.7 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°13′2′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.2964 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃19 = 97.59528 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
 
 
P20: 
𝐷𝐷𝐷𝐷 = (2.616− 2.401) × 100 
𝐷𝐷𝐷𝐷 = 21.5 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.5 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°40′49′′�2 
𝐷𝐷𝐷𝐷 = 21.4993 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 21.5 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°40′49′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.12 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃20 = 97.61882 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P21: 
𝐷𝐷𝐷𝐷 = (2.519− 1.9) × 100 
𝐷𝐷𝐷𝐷 = 61.9 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.9 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°50′51′′�2 
𝐷𝐷𝐷𝐷 = 61.8996 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.9 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°50′51′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.1648 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃21 = 97.96160𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P22: 
𝐷𝐷𝐷𝐷 = (2.517− 1.9) × 100 
𝐷𝐷𝐷𝐷 = 61.7 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.7 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°50′50′′�2 
𝐷𝐷𝐷𝐷 = 61.6996 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.7 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°50′50′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.1645 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃22 = 97.96237 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P23: 
𝐷𝐷𝐷𝐷 = (2.038− 1.419) × 100 
𝐷𝐷𝐷𝐷 = 61.9 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.9 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°51′5′′�2 
𝐷𝐷𝐷𝐷 = 61.8996 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.9 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°51′5′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.1606 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃23 = 98.46240 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2. CÁLCULO DE PENDIENTE Y COTAS DEL EJE DE SUBRASANTE: 
P24: 
𝐷𝐷𝐷𝐷 = (2.113− 1.5) × 100 
𝐷𝐷𝐷𝐷 = 61.3 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.3 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°46′9′′�2 
𝐷𝐷𝐷𝐷 = 61.299 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.3 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°46′9′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.247 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃24 = 98.44781 𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
P25: 
𝐷𝐷𝐷𝐷 = (2.113− 1.5) × 100 
𝐷𝐷𝐷𝐷 = 61.3 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.3 × �𝑠𝑠𝑠𝑠𝑠𝑠 89°46′7′′�2 
𝐷𝐷𝐷𝐷 = 61.299 𝑚𝑚 
 
𝐷𝐷𝐷𝐷 = 61.3 × �
𝑠𝑠𝑠𝑠𝑠𝑠�2 𝑥𝑥 89°46′7′′�
2 �
 
𝐷𝐷𝐷𝐷 = 0.2476 𝑚𝑚 
 
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑃𝑃25 = 98.44841𝑚𝑚𝑠𝑠𝑠𝑠𝑚𝑚 
 
 
 
 
 
E1 
V1 V2 
a 
b 
c 
α 
De la imagen anterior nos apoyaremos en encontrar la distancia horizontal que existe entre V2 
y V1, mediante la Ley de Cosenos: 
 
 
 
 
 
 
 
 
Ahora se calculará la diferencia de cotas que hay entre V2 y V1, con el objetivo de obtener el 
desnivel entre estos dos: 
 
 
 
 
Ahora se calculará la pendiente porcentual que hay entre V2 y V1: 
 
 
 
 
 
Esta pendiente se aplicará a lo largo de la vía, por lo que a continuación se calculará las cotas 
de la subrasante en cada progresiva: 
 
 
 
 
 
 
 
 
𝑎𝑎 = 4.9993 𝑚𝑚 ;𝑏𝑏 = 10.3986 𝑚𝑚 
𝛼𝛼 = 𝐶𝐶𝐴𝐴𝐸𝐸1−𝑉𝑉1 − 𝐶𝐶𝐴𝐴𝐸𝐸1−𝑉𝑉2 
𝛼𝛼 = 200°32′28′′ − 123°26′5′′ 
𝛼𝛼 = 77°6′23′′ 
 
 𝑐𝑐 = �4.99932 + 10.39862 − 2(4 ⋅ 9993)(10.3986) 𝑐𝑐𝑐𝑐𝑠𝑠(77°6′23′′) 
𝐷𝐷𝐷𝐷𝑉𝑉2−𝑉𝑉1 = 10.4844 𝑚𝑚 
 
𝐷𝐷𝐷𝐷𝑉𝑉2−𝑉𝑉1 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐷𝐷1− 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐷𝐷2 
𝐷𝐷𝐷𝐷𝑉𝑉2−𝑉𝑉1 = 99.75081− 99.67656 
𝐷𝐷𝐷𝐷𝑉𝑉2−𝑉𝑉1 = 0.07425 𝑚𝑚 
 
𝑝𝑝% =
𝐷𝐷𝐷𝐷
𝐷𝐷𝐷𝐷
× 100 
𝑝𝑝% =
0.07425
10.4844
× 100 
𝑝𝑝% = 0.7082% 
 
 
0+000: 99.70312 
0+040: 99.70312 + 0.28328 = 99.9864 
0+080: 99.9864+ 0.28328 = 100.26968 
0+120: 100.26968 + 0.28328= 100.55296 
0+160: 100.55296 + 0.28328 = 100.83624 
 
DS cada 40 metros: 
0.7082
100
=
𝐷𝐷𝐷𝐷
40
 
𝐷𝐷𝐷𝐷 = 0.28328 
 
3. NIVELACIÓN DEL EJE (CORTE LONGITUDINAL): 
ESTACIÓN PUNTO COTA SUBRASANTE 
E2 0+000 99.70312 99.70312 
 0+040 99.56603 99.9864 
E3 0+080 98.46000 100.26968 
 0+120 97.58518 100.55296 
 0+160 98.46240 100.83624 
 
4. NIVELACIÓN DE PERFILES TRANSVERSALES (CORTES TRANSVERSALES): 
 IZQUIERDA EJE DERECHA 
ESTACIÓN PUNTO -1.65 -0.825 0 0.825 1.65 
E2 
0+000 99.85897 99.78081 99.70312 99.70287 99.70536 
SUBRASANTE 99.69352 99.69832 99.70312 99.70792 99.71272 
0+040 99.51808 99.50495 99.56603 99.58073 99.58980 
SUBRASANTE 99.97680 99.98160 99.98640 99.99120 99.99600 
E3 
0+080 98.47641 98.48089 98.46000 98.40269 98.40604 
SUBRASANTE 100.26008 100.26488 100.26968 100.27448 100.27928 
0+120 97.56816 97.58188 97.58518 97.59528 97.61882 
SUBRASANTE 100.54336 100.54816 100.55296 100.55776 100.56256 
0+160 97.96160 97.96237 98.46240 98.44781 98.44841 
SUBRASANTE 100.82664 100.83144 100.83624 100.84104 100.84584 
 
 
 
 
 
 
 
 
 
 
 
𝐶𝐶𝐶𝐶1 𝐶𝐶𝑅𝑅1 
𝐶𝐶𝑅𝑅2 𝐶𝐶𝑅𝑅3 
𝐶𝐶1 𝐶𝐶2 
Primero se calculará las áreas de relleno y corte de las secciones S1 y S2: 
SECCIÓN 1: 
 
SECCIÓN 2: 
 
 
 
 
 
 
 
 
 
 
 
 
𝐶𝐶𝐶𝐶1 =
𝐵𝐵 × ℎ
2
 
𝐵𝐵 = 99.859− 99.694 = 0.1654 
ℎ = 1.65 
𝐶𝐶𝐶𝐶1 =
0.1654 × 1.65
2
 
𝐶𝐶𝐶𝐶1 = 0.1365 𝑚𝑚2 
 
 
 
 
𝐶𝐶𝑅𝑅1 =
𝐵𝐵 × ℎ
2
 
𝐵𝐵 = 99.713− 99.705 = 0.0074 
ℎ = 1.65 
𝐶𝐶𝑅𝑅1 =
0.0074 × 1.65
2
 
𝐶𝐶𝑅𝑅1 = 0.0061𝑚𝑚2 
 
 
 
 
𝐶𝐶1 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 99.982 − 99.505 = 0.4767 
𝑏𝑏 = 99.977− 99.518 = 0.4587 
ℎ = 0.825 
𝐶𝐶1 =
0.4767 + 0.4587
2
× 0.825 
𝐶𝐶1 = 0.3858 𝑚𝑚2 
 
 
 
 
𝐶𝐶2 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 99.982 − 99.505 = 0.4767 
𝑏𝑏 = 99.986− 99.566 = 0.4204 
ℎ = 0.825 
𝐶𝐶2 =
0.4767 + 0.4204
2
× 0.825 
𝐶𝐶2 = 0.3700 𝑚𝑚2 
 
 
 
 
𝐶𝐶𝑅𝑅3 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 99.986− 99.566 = 0.4204 
𝑏𝑏 = 99.996 − 99.590 = 0.4062 
ℎ = 1.65 
𝐶𝐶𝑅𝑅3 =
0.4204 + 0.4062
2
× 1.65 
𝐶𝐶𝑅𝑅3 = 0.6819 𝑚𝑚2 
 
 
 
 
𝑨𝑨𝑹𝑹𝑹𝑹 = 𝑨𝑨𝟏𝟏 + 𝑨𝑨𝑹𝑹 = 𝟎𝟎.𝟕𝟕𝟕𝟕𝟕𝟕𝟕𝟕 𝒎𝒎𝑹𝑹 
𝑨𝑨𝑹𝑹𝑹𝑹 = 𝟎𝟎.𝟔𝟔𝟕𝟕𝟏𝟏𝟔𝟔 𝒎𝒎𝑹𝑹 
 
Ahora se calculará tanto el Volumen de relleno y de corte entre las secciones S1 y S2: 
Volumen de Relleno: 
 
 
 
 
 
 
 
 
Volumen de Corte: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
𝐷𝐷𝑅𝑅2−𝐶𝐶1 =
𝑑𝑑
2 �
𝐶𝐶𝑅𝑅22
𝐶𝐶𝐶𝐶1 + 𝐶𝐶𝑅𝑅2
� 
𝐷𝐷𝑅𝑅1−𝐶𝐶1 =
40
2 �
0.75582
0.1365 + 0.7558�
 
𝐷𝐷𝑅𝑅1−𝐶𝐶1 = 12.8093 𝑚𝑚3 
 
𝐷𝐷𝑅𝑅3−𝑅𝑅1 =
40
2
(0.6819 + 0.0061) 
𝐷𝐷𝑅𝑅3−𝑅𝑅1 = 13.76 𝑚𝑚3 
 
𝑽𝑽𝑹𝑹𝑺𝑺𝟏𝟏−𝑺𝑺𝑹𝑹 = 𝑹𝑹𝟔𝟔.𝟕𝟕𝟔𝟔𝟔𝟔𝑹𝑹 𝐦𝐦𝑹𝑹 
𝐷𝐷𝐶𝐶1−𝑅𝑅2 =
𝑑𝑑
2 �
𝐶𝐶𝐶𝐶12
𝐶𝐶𝐶𝐶1 + 𝐶𝐶𝑅𝑅2
� 
𝐷𝐷𝐶𝐶1−𝑅𝑅1 =
40
2 �
0.13652
0.1365 + 0.7558�
 
𝐷𝐷𝐶𝐶1−𝑅𝑅1 = 0.4178 𝑚𝑚3 
 
𝑽𝑽𝑽𝑽𝑺𝑺𝟏𝟏−𝑺𝑺𝑹𝑹 = 𝟎𝟎.𝟒𝟒𝟏𝟏𝟕𝟕𝟕𝟕 𝒎𝒎𝑹𝑹 
 
 
 
 
 
 
 
 
 
𝐶𝐶𝑅𝑅2 𝐶𝐶𝑅𝑅3 
𝐶𝐶𝑅𝑅4 𝐶𝐶𝑅𝑅5 
Primero se calculará las áreas de relleno de las secciones S2 y S3: 
SECCIÓN 2: 
 
 
 
SECCIÓN 3: 
 
 
 
 
 
 
 
𝑨𝑨𝑹𝑹𝑹𝑹 = 𝑨𝑨𝟏𝟏 + 𝑨𝑨𝑹𝑹 = 𝟎𝟎.𝟕𝟕𝟕𝟕𝟕𝟕𝟕𝟕 𝒎𝒎𝑹𝑹 
𝑨𝑨𝑹𝑹𝑹𝑹 = 𝟎𝟎.𝟔𝟔𝟕𝟕𝟏𝟏𝟔𝟔 𝒎𝒎𝑹𝑹 
 
 
 
 
 
𝐶𝐶1 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 100.260− 98.476 = 1.7837 
𝑏𝑏 = 100.265 − 98.481 = 1.784 
ℎ = 0.825 
𝐶𝐶1 =
1.7837 + 1.784
2
× 0.825 
𝐶𝐶1 = 1.4716 𝑚𝑚2 
 
 
 
 
𝐶𝐶2 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 100.270− 98.460 = 1.8097 
𝑏𝑏 = 100.265 − 98.481 = 1.784 
ℎ = 0.825 
𝐶𝐶2 =
1.8097 + 1.784
2
× 0.825 
𝐶𝐶2 = 1.4824 𝑚𝑚2 
 
 
 
 
𝐶𝐶3 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 100.274− 98.403 = 1.8718 
𝑏𝑏 = 100.270 − 98.460 = 1.8097 
ℎ = 0.825 
𝐶𝐶3 =
1.8718 + 1.8097
2
× 0.825 
𝐶𝐶3 = 1.5186 𝑚𝑚2 
 
 
 
 
𝐶𝐶4 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 100.279− 98.406 = 1.8732 
𝑏𝑏 = 100.274 − 98.403 = 1.8718 
ℎ = 0.825 
𝐶𝐶4 =
1.8732 + 1.8718
2
× 0.825 
𝐶𝐶4 = 1.5448 𝑚𝑚2 
 
 
 
 
𝑨𝑨𝑹𝑹𝟒𝟒 = 𝑹𝑹.𝟔𝟔𝟕𝟕𝟒𝟒 𝒎𝒎𝑹𝑹 
𝑨𝑨𝑹𝑹𝟕𝟕 = 𝑹𝑹.𝟎𝟎𝟔𝟔𝑹𝑹𝟒𝟒 𝒎𝒎𝑹𝑹 
 
 
 
Ahora se calculará el Volumen de relleno entre las secciones S2 y S3: 
Volumen de Relleno: 
 
 
 
 
 
 
 
𝐷𝐷𝑉𝑉𝑆𝑆2−𝑆𝑆3 =
𝑑𝑑
2
(𝐶𝐶𝑉𝑉𝑆𝑆2 + 𝐶𝐶𝑉𝑉𝑆𝑆3) 
𝐷𝐷𝑉𝑉𝑆𝑆2−𝑆𝑆3 =
40
2
(1.4377 + 6.0174) 
𝐕𝐕𝐕𝐕𝐒𝐒𝑹𝑹−𝐒𝐒𝑹𝑹 = 𝟏𝟏𝟒𝟒𝟔𝟔.𝟏𝟏𝟎𝟎𝑹𝑹 𝐦𝐦𝑹𝑹 
 
 
Primero se calculará las áreas de relleno y corte de las seccionesS3 y S4: 
SECCIÓN 3: 
 
 
 
 
SECCIÓN 4: 
 
 
 
 
 
 
 
Ahora se calculará tanto el Volumen de relleno y de corte entre las secciones S3 y S4: 
Volumen de Relleno: 
 
 
 
 
 
 
 
 
 
 
 
 
𝐶𝐶𝐶𝐶4 
𝑨𝑨𝑹𝑹𝟒𝟒 = 𝑹𝑹.𝟔𝟔𝟕𝟕𝟒𝟒 𝒎𝒎𝑹𝑹 
𝑨𝑨𝑹𝑹𝟕𝟕 = 𝑹𝑹.𝟎𝟎𝟔𝟔𝑹𝑹𝟒𝟒 𝒎𝒎𝑹𝑹 
𝑨𝑨𝑹𝑹𝑺𝑺𝑹𝑹 = 𝟔𝟔.𝟎𝟎𝟏𝟏𝟕𝟕𝟒𝟒 𝒎𝒎𝑹𝑹 
 
 
 
 
𝐶𝐶1 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐵𝐵 = 100.543− 97.568 = 2.9752 
𝑏𝑏 = 100.563 − 97.619 = 2.9437 
ℎ = 3.30 
𝐶𝐶1 =
2.9752 + 2.9437
2
× 3.30 
𝐶𝐶1 = 9.7661 𝑚𝑚2 
 
 
 
 
𝑨𝑨𝑹𝑹𝑺𝑺𝟒𝟒 = 𝟔𝟔.𝟕𝟕𝟔𝟔𝟔𝟔𝟏𝟏 𝒎𝒎𝑹𝑹 
 
𝐷𝐷𝑉𝑉𝑆𝑆3−𝑆𝑆4 =
𝑑𝑑
2
(𝐶𝐶𝑉𝑉𝑆𝑆3 + 𝐶𝐶𝑉𝑉𝑆𝑆4) 
𝐷𝐷𝑉𝑉𝑆𝑆3−𝑆𝑆4 =
40
2
(6.0174 + 9.7661) 
𝐕𝐕𝐕𝐕𝐒𝐒𝑹𝑹−𝐒𝐒𝟒𝟒 = 𝑹𝑹𝟏𝟏𝟕𝟕.𝟔𝟔𝟕𝟕 𝐦𝐦𝑹𝑹 
 
 
 
 
 
 
 
 
 
 
Ahora se calculará las áreas de relleno y corte de las secciones S4 y S5: 
SECCIÓN 4: 
 
 
SECCIÓN 5: 
 
 
 
 
 
 
 
 
 
 
Ahora se calculará tanto el Volumen de relleno y de corte entre las secciones S3 y S4: 
Volumen de Relleno: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
𝐶𝐶1 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐶𝐶1 =
2.8650 + 2.9678
2
× 1.65 
𝐶𝐶1 = 4.81𝒎𝒎𝑹𝑹 
 
 
 
 
𝐶𝐶2 =
𝐵𝐵 + 𝑏𝑏
2
× ℎ 
𝐶𝐶2 =
2.9678 + 2.9437
2
× 1.65 
𝐶𝐶2 = 4.87𝒎𝒎𝑹𝑹 
 
 
 
 
𝑨𝑨𝑹𝑹𝑺𝑺𝟒𝟒 = 𝟔𝟔.𝟕𝟕𝟔𝟔𝟔𝟔𝟏𝟏 𝒎𝒎𝑹𝑹 
 
𝐷𝐷𝑉𝑉𝑆𝑆4−𝑆𝑆5 =
𝑑𝑑
2
(𝐶𝐶𝑉𝑉𝑆𝑆4 + 𝐶𝐶𝑉𝑉𝑆𝑆5) 
𝐷𝐷𝑉𝑉𝑆𝑆4−𝑆𝑆5 =
40
2
(9.7661 + 9.68) 
𝐕𝐕𝐕𝐕𝐒𝐒𝟒𝟒−𝐒𝐒𝟕𝟕 = 𝑹𝑹𝟕𝟕𝟕𝟕.𝟔𝟔𝑹𝑹𝑹𝑹 𝐦𝐦𝑹𝑹