curva espiralCLCULO GEOMTRICO DE UNA CURVA ESPIRALIZADA.DATOSAzimut de la tangente de entrada37Azimut de la tangente de salida143Coordenadas del PI500N500EAbscisa del PIk2 +482,370Radio de la curva central80mCuerda unidad10mLongitud de la espiral100m

a) Elementos de las Curvas

1) parmetro de la espiral KK= (Rc*Le)

Rc80mK=89.4427191Le100m2) ngulo de deflexin de la espiral ee35.80986219571.49207759148651880.625radianes3) ngulo central de la curva circular: cSea =azimut tangente salida -azimut tangente entrada 106Entonces al tener resulta que c es igual a:

c34.38027560861.432511483693629

4) Clculo de las coordenadas cartesianas del EC (xc,yc)Xc96.1637557402myc20.2593202127m5) Coordenadas cartesianas del PC desplazado: (k,p)p=disloque5.1363697731mk49.355973905m6) Tangente de la curva espiral-circular-espiral (Te)Te162.3357525439m7) Externa de la curva espiral-circular-espiral: EeEe61.4660094845m8) Tangentes larga TL y corta de la espiral TcTL68.083704305mTc34.6255591158m9) Coordenadas cartesianas del centro de la curva circular con transiciones: (xo,yo)X0=k49.355973905mY085.1363697731m10) Cuerda larga de la espiral CLeCle98.2746558047m11) Deflexin del EC o ngulo de la cuerda larga: cc11.89682718920.495701132882015512) Longitud de la curva circular: LcGc7.16664339690.29861014153933113

Lc47.9726333576m13) Calculando las abscisas de los puntos: TE, EC, CE y ETTe=140.229Le=100Lc=35.069

kilmetro y los metros de la abscisa del PIk2+482.37Abcisa TE = Abscisa PI-Te2320.0342474561k2+320.0342474561Abscisa EC=AbscisaTE + Le2420.0342474561k2+420.0342474561Abscisa CE=Abscisa EC+Lc2468.0068808137k2+468.0068808137Abscisa ET=Abscisa CE+ Le2568.0068808137k2+568.0068808137AzPI.TE217NTE370.3529034682mETE402.3039053244mAZTE.(K2+330)37.11854997091.5466062488NK2+330378.299467265mEK2+330408.3178896478mb) Clculos de localizacin por deflexiones, por coordenadas cartesianas y por coordenadas topogrficas planas

1) espiral de entrada, desde el TE al EC:

k2+330Clculo de L (distancia desde el TE a la abscisa considerada:L9.96575254390.35565002870.0148187511953958070.006207264radianes

X9.9657141458mPara

y0.0206199622m

k2+3300.11854997090.004939582120598921

c'9.9657354781m

Clculo de las coordenadas topogrficasAzPI.TE37.1185499709NTE378.2994808731mETE408.3178767745mAZTE.(K2+330)37.11854997091.5466062487872654

NK2+330386.2460446699mEK2+330414.3318610979mPara k2+ 340 k2+340Clculo de L (destancia desde el TE a la abscisa considerada:L19.96575254391.42749310120.059478879216495020.0249144547X19.9645132453mPara k2+340y0.1658045939mk0+340c'19.9652017341mPara k0+340k2+3300.47582853330.019826188886251223Clculo de las coordenadas topogrficasAzPI.TE180AZTE.(K2+330)37.47582853331.561492855552918NK2+330386.1979261193mEK2+330414.4512667617mPara k2+ 350 tenemos quk2+350Clculo de L (destancia desde el TE a la abscisa considerada:L29.96575254393.21553341760.133980559067324560.0561216453X29.9563157896mPara k2+350y0.5604496765mk0+350c'29.961558029mPara k0+350k2+3301.07181589110.04465899546310928Clculo de las coordenadas topogrficasAzPI.TE217AZTE.(K2+330)38.07181589111.586325662129776NK2+330393.9430960563mEK2+330420.779661218mPara k2+ 360 tenemos quk2+360Clculo de L (destancia desde el TE a la abscisa considerada:L39.96575254395.71977097790.238323790747884570.099828836X39.9259418603mPara k2+360y1.3289651317mk0+360c'39.9480535415mPara k0+360k2+3301.90642943490.07943455978544613Clculo de las coordenadas topogrficasAzPI.TE180AZTE.(K2+330)38.90642943491.6211012264521127NK2+330401.4531601085mEK2+330427.3932956952mPara k2+ 370 tenemos quk2+370Clculo de L (destancia desde el TE a la abscisa considerada:L49.96575254398.94020578220.372508574258174850.1560360267X49.8442367674mPara k2+370y2.5943030918mk0+370c'49.9117055154mPara k0+370k2+3302.97945400020.12414391667661638Clculo de las coordenadas topogrficasAzPI.TE180AZTE.(K2+330)39.97945400021.6658105833432832NK2+330408.6404052276mEK2+330434.3728184015mPara k2+ 380 tenemos quk2+380Clculo de L (destancia desde el TE a la abscisa considerada:L59.965752543912.87683783040.53653490959819560.2247432174X59.6635758833mPara k2+380y4.4761173741mk0+380c'59.8312452981mPara k0+380k2+3304.29044171890.1787684049553793Clculo de las coordenadas topogrficasAzPI.TE360AZTE.(K2+330)41.29044171891.720435071622046NK2+330415.4096244216mEK2+330441.785127908mPara k2+ 390 tenemos quk2+390Clculo de L (destancia desde el TE a la abscisa considerada:L69.965752543917.52966712240.73040279676794680.3059504081X69.313665577mPara k2+390y7.0877847104mk0+390c'69.6751098156mPara k0+390k2+3305.83858188740.24327424530970246Clculo de las coordenadas topogrficasAzPI.TE397AZTE.(K2+330)42.83858188741.784940911976369NK2+330421.6568430356mEK2+330449.6784671356mPara k2+ 400 tenemos quk2+400Clculo de L (destancia desde el TE a la abscisa considerada:L79.965752543922.89869365840.95411223576742810.3996575987X78.6979001948mPara k2+400y10.5320530358mk0+400c'79.3995191183mPara k0+400k2+3307.62253919940.3176057999747775Clculo de las coordenadas topogrficasAzPI.TE360AZTE.(K2+330)44.62253919941.8592724666414442NK2+330427.2685099019mEK2+330458.0767555002mPara k2+ 410 tenemos quk2+410Clculo de L (destancia desde el TE a la abscisa considerada:L89.965752543928.98391743831.207663226596640.5058647894X87.6906499804mPara k2+410y14.8951485268mk0+410c'88.9467005774mPara k0+410k2+3309.64025838280.4016774326178943Clculo de las coordenadas topogrficasAzPI.TE360AZTE.(K2+330)46.64025838281.943344099284561NK2+330432.1213037445mEK2+330466.9732504134mPara k2+ 420 tenemos quk2+420Clculo de L (destancia desde el TE a la abscisa considerada:L99.965752543935.78533846211.49105576925558240.6245719801X96.1359780483mPara k2+420y20.2392875606mk0+420c'98.2433460152mPara k0+420k2+33011.88873467640.49536394485060176Clculo de las coordenadas topogrficasAzPI.TE180AZTE.(K2+330)48.88873467642.0370306115172685NK2+330436.0827246096mEK2+330476.3237949232mPara k2+ 420,035 tenemos quk2+420.035Clculo de L (destancia desde el TE a la abscisa considerada:L100.000752543935.81040116761.49210004865009640.6250094068X96.1643660231mPara k2+420.035y20.2597605381mk0+420.035c'98.2753437525mPara k0+420.035k2+33011.89700504160.4957085434004757Clculo de las coordenadas topogrficasAzPI.TE180AZTE.(K2+330)48.89700504162.0373752100671423NK2+330436.094861709mEK2+330476.3572296797mCurva circular, desde el EC al CEPunto inicio430Deflexin por cuerda unidad3.58332169850.14930507076966557Punto final CE468.008Cuerda final CE460Deflexin por metro0.35833216980.014930507076966559/mDeflexin subcuerda lado del EC3.57078007250.14878250302197138Deflexin subcuerda del CE2.86952401610.11956350067234793De manera que obtenemos las deflexiones de la curva cmo sigue:DeflexinDeflexin acumuladaDeflexin K2+420.0350.00.0Deflexin K2+4300.148782503021971380.14878250302197138Deflexin K2+4400.2980875737916370.44687007681360835Deflexin K2+4500.447392644561302570.8942627213749109Deflexin K2+4600.59669771533096821.490960436705879Deflexin K2+468.0080.7162612160033162.2072216527091952Las coordenadas topogrficas de los puntos ubicadas en la curva circular vienen dados por:EC.0=Rc80mAZPLe.ec72.80986219573.033744258153186AzEC.O162.80986219576.7837442581531855N0359.6685219056ME0500.0007189369MK2+430AzO.(K2+430)349.951422340714.58130926419713NK2+430438.4413357605mEK2+430486.0420729644mK2+440AzO.(K2+430)357.092982485814.87887427024107NK2+430439.5655741564mEK2+430495.943498011mK2+450AzO.(K2+430)364.234542630815.176439276285015NK2+430439.4501332611mEK2+430505.9078747262mK2+460AzO.(K2+430)371.376102775915.474004282328957NK2+430438.0968042508mEK2+430515.7805962615mK2+460AzO.(K2+430)378.51766292115.771569288372902NK2+430435.5265853213mEK2+430525.4084778861mEspiral de salida, desde ET al CE:Para la espiral de salida las deflexiones y las coordenadas cartesianas de la espiral de salida se calculan tomando como origen el ET y punto final el CE.K2+560Abscisa ET568.0068808137mL8.0068808137m0.22957752920.009565730382506040.0040068838radianesXk2+5608.0068679586mYk2+5600.0106942013mk2+5600.07652583270.0031885763607888257c'8.0068751003mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+5608.0068751003mAzTE.PI323AzET.(K2+560)322.923474167313.455144756972544NK2+560376.7410366131mEK2+560592.8689004808m

K2+550Abscisa ET568.0068808137mL18.0068808137m1.16112674820.048380281176982890.0202654848radianesXk2+56018.0061413034mYk2+5600.1216358215mk2+5600.38704090380.01612670432322173c'18.0065521383mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56018.0065521383mAzTE.PI323AzET.(K2+560)322.612959096213.44220662901011NK2+560384.6603061969mEK2+560586.7623860735mK2+540Abscisa ET568.0068808137mL28.0068808137m2.80887321120.11703638380119010.0490240858radianesXk2+56028.0001504982mYk2+5600.4575920144mk2+5600.93627201960.03901133415010071c'28.0038893436mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56028.0038893436mAzTE.PI323AzET.(K2+560)322.063727980413.419321999183232NK2+560392.4417915515mEK2+560580.4778951138mK2+530Abscisa ET568.0068808137mL38.0068808137m5.17281691810.215534038255127740.0902826868radianesXk2+56037.975913234mYk2+5601.1431220187mk2+5601.72415330280.07183972094874867c'37.9931140328mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56037.9931140328mAzTE.PI323AzET.(K2+560)321.275846697213.386493612384584NK2+560400.0046086841mEK2+560573.92006963mK2+520Abscisa ET568.0068808137mL48.0068808137m8.25295786890.34387324453879570.1440412878radianesXk2+56047.9073723278mYk2+5602.3015772562mk2+5602.75050251960.11460427164943081c'47.9626269216mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56047.9626269216mAzTE.PI323AzET.(K2+560)320.249497480413.343729061683902NK2+560407.2623324278mEK2+560566.9982990001mK2+510Abscisa ET568.0068808137mL58.0068808137m12.04929606370.50205400265219410.2102998889radianesXk2+56057.7508646009mYk2+5604.0534528942mk2+5604.01492664420.1672886101741361c'57.8929429423mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56057.8929429423mAzTE.PI323AzET.(K2+560)318.985073355813.291044723159198NK2+560414.1213363534mEK2+560559.6287529704mK2+500Abscisa ET568.0068808137mL68.0068808137m16.56183150230.69007631259532280.2890584899radianesXk2+56067.4408486819mYk2+5606.5136519816mk2+5605.51669752580.2298623969077566c'67.7546731456mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56067.7546731456mAzTE.PI323AzET.(K2+560)317.483302474213.228470936425575NK2+560420.4794437691mEK2+560551.7367017786mK2+490Abscisa ET568.0068808137mL78.0068808137m21.79056418480.90794017436818180.3803170909radianesXk2+56076.886136278mYk2+5609.7874185817mk2+5607.25459549850.302274812437397c'77.5065901343mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56077.5065901343mAzTE.PI323AzET.(K2+560)315.745404501513.156058520895938NK2+560426.2250177746mEK2+560543.2591559556mK2+480Abscisa ET568.0068808137mL88.0068808137m27.73549411131.15564558797077120.4840756919radianesXk2+56085.9669945269mYk2+56013.9647553945mk2+5609.22671665040.38444652710141686c'87.0938490436mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56087.0938490436mAzTE.PI323AzET.(K2+560)313.773283349613.073886806231917NK2+560431.2366397541mEK2+560534.1478317063mK2+470Abscisa ET568.0068808137mL98.0068808137m34.39662128171.43319255340309140.6003342929radianesXk2+56094.5336357384mYk2+56019.1132448614mk2+56011.43023567620.47625981984043014c'96.4464847211mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56096.4464847211mAzTE.PI323AzET.(K2+560)311.569764323812.982073513492905NK2+560435.3835559209mEK2+560524.3724086772mK2+468.008Abscisa ET568.0068808137mL99.9988808137m35.8090606421.49204419341704940.6249860102radianesXk2+56096.1634848266mYk2+56020.2586653697mk2+56011.89648616470.4956869235280255c'98.2742557161mClculo de las coordenadas topogrficasNET370.3529034682mEET597.6960946756mET.(K2+560)=c'K2+56098.2742557161mAzTE.PI323AzET.(K2+560)311.103513835312.962646409805307NK2+560436.0943136001mEK2+560522.3446304705mTabla 1: Cartera de localizacin de la curva espiral-circular-espiralAbscisasLongitud desde el TE y ET espiralesDeflexiones desde el TE, EC Y ETCoordenadas cartesianas desde el TE y ETCoordenadas topogrficasLXYNETE=K2+320,03503309.965752543934019.965752543935029.965752543936039.965752543937049.965752543938059.965752543939069.965752543940079.965752543941089.965752543942099.9657525439EC=K2+420,035100EC=K2+420,035-430-440-450-460-CE=K2+468,008-CE=K2+468,00899.998880813747098.006880813748088.006880813749078.006880813750068.006880813751058.006880813752048.006880813753038.006880813754028.006880813755018.00688081375608.0068808137ET=K2+568,0080

&"AR BERKLEY,Normal"UAC Carrera Profesional de Ingenieria Civil &"-,Normal"&"AR BLANCA,Normal"CAMINOS

Caminos Elvin Quispe Marcavillaca

Cuadro Gral.

ELEMENTOS DE LAS CURVASAcimut de entrada=37Gc=0.29861014153933113Te=162.3357525439mAcimut de salida=143e=1.4920775914865188Ee=61.4660094845mAbscisa de PI=k2 +482,370mc=1.432511483693629Tl=68.083704305m=106c=0.4957011328820155Tc=34.6255591158mRc=80mXc=96.1637557402mX0=49.355973905mC=10mYc=20.2593202127mY0=85.1363697731mLe=100mp=5.1363697731mCle=98.2746558047mK=89.4427191mK=49.355973905mLc=47.9726333576m

ABSCISASLONGITUD DESDE TE y ET ESPIRALDEFLEXIONES DESDE EL TE, EC y ETCOORDENADAS CARTESIANAS DESDE EL TE y ETCOORDENADAS TOPOGRFICAS PLANASLXYNETE=K2+320.0350000370.3529034682402.30390532443309.96575254390.00493958219.96571414580.0206199622378.2994808731408.317876774534019.96575254390.019826188919.96451324530.1658045939386.1979261193414.451266761735029.96575254390.044658995529.95631578960.5604496765393.9430960563420.77966121836039.96575254390.079434559839.92594186031.3289651317401.4531601085427.393295695237049.96575254390.124143916749.84423676742.5943030918408.6404052276434.372818401538059.96575254390.17876840559.66357588334.4761173741415.4096244216441.78512790839069.96575254390.243274245369.3136655777.0877847104421.6568430356449.678467135640079.96575254390.317605878.697900194810.5320530358427.2685099019458.076755500241089.96575254390.401677432687.690649980414.8951485268432.1213037445466.973250413442099.96575254390.495363944996.135978048320.2392875606436.0827246096476.3237949232EC=K2+420.035100.00075254390.495708543496.164366023120.2597605381436.094861709476.3572296797EC=K2+420.0350436.094861709476.35722967974300.148782503438.4413357605486.04207296444400.2980875738439.5655741564495.9434980114500.4473926446439.4501332611505.90787472624600.5966977153438.0968042508515.7805962615CE=K2+468.0080.716261216435.5265853213525.4084778861CE=K2+468.00899.99888081370.495686923596.163484826620.2586653697435.5265853213525.408477886147098.00688081370.476259819894.533635738419.1132448614435.3835559209524.372408677248088.00688081370.384446527185.966994526913.9647553945431.2366397541534.147831706349078.00688081370.302274812476.8861362789.7874185817426.2250177746543.259155955650068.00688081370.229862396967.44084868196.5136519816420.4794437691551.736701778651058.00688081370.167288610257.75086460094.0534528942414.1213363534559.628752970452048.00688081370.114604271647.90737232782.3015772562407.2623324278566.998299000153038.00688081370.071839720937.9759132341.1431220187400.0046086841573.9200696354028.00688081370.039011334228.00015049820.4575920144392.4417915515580.477895113855018.00688081370.016126704318.00614130340.1216358215384.6603061969586.76238607355608.00688081370.00318857648.00686795860.0106942013376.7410366131592.8689004808ET=K2+568.0080000370.3529034682597.6960946756

Hoja3