aplikasi perhitungan
DESCRIPTION
pergitungan matematikaTRANSCRIPT
APLIKASI PERHITUNGAN
1. TIKUNGAN PERTAMA
X Y
P17 267480.8459 9802917.5443
P18 267722.9343 9802879.7693
P19 267889.872 9802979.6511
En = 4%
Emax = 10%
V = 40 km/jam
B = 3m
R = 50 m
LANGKAH : Desain Alinemen Horisontal
Membuat Poligon dengan cara menetapkan titik-titik Intersection Point Menghitung panjang jari-jari tikungan (R) dengan 13 rumus kemudian menetapkan tipe
tikungan yang akan dipakai Menghitung elemen-elemen tikungan seperti Ts, Ls, Lc, Es, p, k, dll Menggambar tikungan berdasarkan elemen tikungan
Menghitung A
Az1 = tan-1
x18−x17y18− y 17 = tan-1
242 .0884−37 .775 = -81,13119609 (K.II) = 98,8688
Az2 = tan-1
x19−x18y19− y18 = tan-1
166 .937799 .8818 = 59.10717 (K.1) = 59.107165
Δ = Az2-Az1 =59.107165 - 98,8688= -39.76164 = -39ᵒ45’41.8992’’
Mencari Ls ( tiga belas langkah)
V mean = 0.8 V= 0.8 x 40 km/jam = 32km/jam
Fmax = 0.270-0.002 V
= 0.19
Dmax = (c x 127)(emax+fmax)/V2
= 32.97192
D = 1432.394 / R
= 28.64788
DPI = (c x 127) emax/Vmean2
= 17.76504
HPI = {V2 x DPI / (c x 127)} – emax
= 0.05625
S1 = HPI / DPI
= 0.003166
S2 = (fmax-HPI) / (Dmax-DPI)
= 0.008795
Mo = (DPI/2Dmax)(S2-S1)(Dmax-DPI)
= 0.02306
F = Mo {(Dmax-D)/(Dmax-DPI)}2 +HPI + S2 X (D-DPI)
= 0.153833
E = V2/127R-F
= 0.098135
LS1 = 2 X 1000/ 3600 X V
= 22.2222
LS2 = 1000/3600 x V(e+en) / Ψ
= 43.85254
M = 2V + 40
= 120
LS3 = b x m (e+en)
= 49.72878
Diambil LS terbesar, yaitu LS3
Maka LS = 50m (dibulatkan ke atas)
Mencari Ts, Es, dan K
Θs =
Ls2R =0.5 rad
Δc = Δ-2θs
= -1.69397 rad
Xc = LS (1 - Θs2/10 + θs4/216 – θs6/9360 + θs8/685440)
= 48.76438 m
Yc = LS ( θs/3 – θs3/42 +θs5/1320 – θs7/75600 + θs9/6894720)
= 8.185702 m
P = Yc- R(1-cos θs)
= 2.06483 m
K = Xc-Rsinθs
= 24.79311 m
Es = (R + P) sec 1/2 Δ – R
= 5.364439 m
Ts = K + (R +P) tan 1/2 Δ
= 5.965613 m
Lc = Δc x R
= -84.6986
Tipe tikungan = Full Spiral
Maka dilakukan perhitungan sebagai berikut
Δc = 0
Δ = 0.69397 rad
Θs = Δ/2 = 0.34699 rad
LS = 2θs x R
= 34.6 m
Xc = LS (1 - Θs2/10 + θs4/216 – θs6/9360 + θs8/685440)
= 34.18807 m
Yc = LS ( θs/3 – θs3/42 +θs5/1320 – θs7/75600 + θs9/6894720)
= 3.956539 m
P = Yc- R(1-cos θs)
= 0.976414 m
K = Xc-Rsinθs
= 17.18463 m
Es = (R + P) sec 1/2 Δ – R
= 4.207127 m
Ts = K + (R +P) tan 1/2 Δ
= 35.61878 m
Lc = Δc x R
= 0
TIKUNGAN KEDUA
X Y
P18 267722.9343 9802879.7693
P19 267889.872 9802979.6511
P20 267970.6815 9802949.8344
En = 4%
Emax = 10%
V = 40 km/jam
B = 3m
R = 50 m
LANGKAH : Desain Alinemen Horisontal
Membuat Poligon dengan cara menetapkan titik-titik Intersection Point Menghitung panjang jari-jari tikungan (R) dengan 13 rumus kemudian menetapkan tipe
tikungan yang akan dipakai Menghitung elemen-elemen tikungan seperti Ts, Ls, Lc, Es, p, k, dll Menggambar tikungan berdasarkan elemen tikungan
Menghitung A
Az1 = tan-1
x19−x18y19− y18 = tan-1
166 .937799 .8818 = 59.10717 (K.1) = 59.107165
Az2 = tan-1
x20−x19y20− y 19 = tan-1
80 .8095−29 .8167 = -69,74719073 (K.II) = 110.25281
Δ = Az2-Az1 =110.25281 - 59.107165 = 51.145644= 51ᵒ8’44.3185’’
Mencari Ls ( tiga belas langkah)
V mean = 0.8 V= 0.8 x 40 km/jam = 32km/jam
Fmax = 0.270-0.002 V
= 0.19
Dmax = (c x 127)(emax+fmax)/V2
= 32.97192
D = 1432.394 / R
= 28.64788
DPI = (c x 127) emax/Vmean2
= 17.76504
HPI = {V2 x DPI / (c x 127)} – emax
= 0.05625
S1 = HPI / DPI
= 0.003166
S2 = (fmax-HPI) / (Dmax-DPI)
= 0.008795
Mo = (DPI/2Dmax)(S2-S1)(Dmax-DPI)
= 0.02306
F = Mo {(Dmax-D)/(Dmax-DPI)}2 +HPI + S2 X (D-DPI)
= 0.153833
E = V2/127R-F
= 0.098135
LS1 = 2 X 1000/ 3600 X V
= 22.2222
LS2 = 1000/3600 x V(e+en) / Ψ
= 43.85254
M = 2V + 40
= 120
LS3 = b x m (e+en)
= 49.72878
Diambil LS terbesar, yaitu LS3
Maka LS = 50m (dibulatkan ke atas)
Mencari Ts, Es, dan K
Θs =
Ls2R =0.5 rad
Δc = Δ-2θs
= -0.10734 rad
Xc = LS (1 - Θs2/10 + θs4/216 – θs6/9360 + θs8/685440)
= 48.76438 m
Yc = LS ( θs/3 – θs3/42 +θs5/1320 – θs7/75600 + θs9/6894720)
= 8.185702 m
P = Yc- R(1-cos θs)
= 2.06483 m
K = Xc-Rsinθs
= 24.79311 m
Es = (R + P) sec 1/2 Δ – R
= 7.719149 m
Ts = K + (R +P) tan 1/2 Δ
= 49.70804 m
Lc = Δc x R
= -5.36701
Tipe tikungan = Full Spiral
Maka dilakukan perhitungan sebagai berikut
Δc = 0
Δ = 0.89266 rad
Θs = Δ/2 = 0.44633 rad
LS = 2θs x R
= 44.6 m
Xc = LS (1 - Θs2/10 + θs4/216 – θs6/9360 + θs8/685440)
= 43.72097 m
Yc = LS ( θs/3 – θs3/42 +θs5/1320 – θs7/75600 + θs9/6894720)
= 6.536919 m
P = Yc- R(1-cos θs)
= 1.645907m
K = Xc-Rsinθs
= 22.15295 m
Es = (R + P) sec 1/2 Δ – R
= 7.25473 m
Ts = K + (R +P) tan 1/2 Δ
= 46.86741 m
Lc = Δc x R
= 0