A. MODEL GREENSHIELD
No. Waktu Pengamatan
Speed (S) Volume (V) Density (D)
(km/jam) (smp/jam) (smp/jam)
Yi Xi.Yi Xi
1 13.00 - 14.00 10.5 60.9 5.800 33.6402 14.00 - 15.00 11 39.2 3.564 12.700
3 15.00 - 16.00 12 70 5.833 34.028
4 16.00 - 17.00 9.5 65.8 6.926 47.9745 17.00 - 18.00 13 32.9 2.531 6.405
Total 56 268.8 24.654 134.746
634.5 ΣX = 24.654 Y = 9.333X = 4.109 ΣXY = 268.800
ΣY = 56 134.746
X2
ΣX2 =
A =
A = 134.746 . 56 - 24.654 . 268.800
6 . 134.746 - ( 24.654 ) 2
A = 4.579
B = n . ΣXY - ΣX.ΣY
B = 6 . 268.8 - 24.654 . 56.000
6 . 134.746 - ( 24.654 ) 2
B = 1.157
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sff = A = 4.579
Dj = -Sff/B = -3.9572
Dj/Sff = -0.8642
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-DS = Sff - (Sff/Dj).DS = 4.579 - ( 4.579 / -3.9572 ) . DS = 4.579 - -1.157 . D
Model Hubungan S-D
V =
V = 4.579 . D - ( 4.579 / -3.9572 ) .
V = 4.579 . D - -1.1571 .
Model Hubungan V-S
V =
V = -3.957 . S - ( -3.957 / 4.5789 ) .
V = -3.957 . S - -0.8642 .
Sff.D - (Sff/Dj).D2
D2
D2
Dj.S - (Dj/Sff).S2
S2
S2
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 268.8 - 24.654 . 56
√ 6 . 134.746 - ( 24.654 } { ( 6 . 634.5 - ( 56
=232.172936366.930859
= 0.632743
= 0.4003637158687
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinan (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/2
Vm = (Sff.Dj)/4Vm = ( 4.579 . -3.9572 ) / 4
Vm = -4.529898
Vm = -5 smp/jam
b. Untuk Kondisi S = Sff/2Vm = (Sff.Dj)/4Vm = ( 4.579 . -3.9572 ) / 4
Vm = -4.529898Vm = -5 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -5 smp/jamPada kondisi D = -3.9572 / 2
D = -1.97862 smp/jam
S = 4.579 / 2
S = 2.289428 smp/jam
B. MODEL GREENBERG
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Xi
Yi
1 10.5 60.9 5.800 1.758 3.090 18.4582 11 39.2 3.564 1.271 1.615 13.979
3 12 70 5.833 1.764 3.110 21.163
4 9.5 65.8 6.926 1.935 3.745 18.3865 13 32.9 2.531 0.929 0.862 12.071
56 268.8 24.654 7.656 12.423 84.056
15558 ΣX = 7.656 Y = 9.333X = 1.276 ΣXY = 84.056
ΣY = 56 12.423
ln D
Xi2
ΣX2 =
A =
A = 12.423 . 56 - 7.656 . 84.056
6 . 12.423 - ( 7.656 ) 2
A = 3.275
B = n . ΣXY - ΣX.ΣY
B = 6 . 84.06 - 7.656 . 56.0
6 . 12.423 - ( 7.656 ) 2
B = 4.748
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sm = - B = -4.748
A = = 3.275
A = 3.275= -0.690
Dj = 5.142E+36
= 3.275
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =S = -4.748 . 5.142E+36 / D
S = -4.748 . ( 5.142E+36 -
S = 3.275 - -4.748
Model Hubungan V-DV =V =V = -4.748 . D . ( -0.690 -V = 3.275 . D - -4.748 .
Model Hubungan V-S
V =-s / -4.748
V = 5.142E+36 . S
Sm . ln Dj
ln Dj
(Pake Kalkulator tekan INV ln Dj)
Sm . ln Dj
Sm . ln Dj / Dln
ln ln D
. ln D
Sm . D. ln Dj / DSm . D. (ln Dj - ln D)
ln D )D . ln D
Dj . S . ℓ -s/sm
. ℓ
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 84.056 - 7.656 . 56
√ 6 . 12.423 - ( 7.656 } { ( 6 . 634.5 - ( 56
=75.5930783103.360239
= 0.7313555
= 0.5348808531722
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/e
Vm = Sm . (Dj/e) --> e = 2.718Vm = -4.748 . ( 5.142E+36 / 2.718 )
Vm = -8.982E+36
Vm = -9E+36 smp/jam
b. Untuk Kondisi D = Dj/e Vm = Sm . (Dj/e) --> e = 2.718Vm = -4.748 . ( 5.142E+36 / 2.718 )
Vm = -8.982E+36Vm = -9E+36 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -9E+36 smp/jamPada kondisi D = 5.1419E+36 / 2
D = 2.57E+36 smp/km
S = -4.748 Km/Jam
C. MODEL UNDERWOOD
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Yi
Xi
1 10.5 60.9 5.800 1.758 33.640 10.1962 11 39.2 3.564 1.271 12.700 4.529
3 12 70 5.833 1.764 34.028 10.288
4 9.5 65.8 6.926 1.935 47.974 13.4055 13 32.9 2.531 0.929 6.405 2.350
56 268.8 24.654 7.656 134.746 40.766
### ΣX = 24.654 Y = 1.276X = 4.109 ΣXY = 40.766
ΣY = 7.656 134.746
ln S
Xi2
ΣX2 =
A =
A = 134.746 . 7.656 - 24.654 . 40.766
6 . 134.746 - ( 24.654 ) 2
A = 0.132
B = n . ΣXY - ΣX.ΣY
B = 6 . 40.766 - 24.654 . 7.656
6 . 134.746 - ( 24.654 ) 2
B = 0.278
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Dm = - 1 / B = 3.593 = 4 smp/km
A = = 0.132
Sff = 2.3632 km/jam
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =
- D / 4
S = 2.3632 . ℓ
Model Hubungan V-D
V =- D / 4
V = 2.3632 . D
Model Hubungan V-SV =V = 4 . S . ( 2.3632 / S )
ln Sff
(Pake Kalkulator tekan INV ln Sff)
Sff . ℓ - D/Dm
Sff . D . ℓ - D/Dm
. ℓ
Dm . S . ln (Sff / s)ln
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 40.766 - 24.654 . 7.656
√ 6 . 134.746 - ( 24.654 } { ( 6 . 12.423 - ( 7.656
=55.844704356.5217009
= 0.9880224
= 0.9761881836656
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dm
Vm =
Vm = 2.3632 . 4 . ℓxp ( -4 / 4 )
Vm = 8.50752 . 0.36788Vm = 3.1297465Vm = 3.1 smp/jam
b. Untuk Kondisi S = Sff
Vm =Vm = 2.3632 . ( 4 / ℓ )
Vm = 3.1297465
Vm = 3.1 smp/jam
Jadi Volume Maksimum yang terjadi adalah : 3.1 smp/jamPada KondisiD = DmD = 4 smp/jam
S = km/jamS = km/jam
Sff . Dj . ℓxp (-D/Dm)
Sff . (Dm / ℓ )
Sff / ℓ
A. MODEL GREENSHIELD
No. Waktu Pengamatan
Speed (S) Volume (V) Density (D)
(km/jam) (smp/jam) (smp/jam)
Yi Xi.Yi Xi
1 13.00 - 14.00 35.5 1600 45.070 2031.3432 14.00 - 15.00 41 1346 32.829 1077.761
3 15.00 - 16.00 37 1481 40.027 1602.163
4 16.00 - 17.00 50 1561 31.220 974.6885 17.00 - 18.00 45 1488 33.067 1093.404
Total 208.5 7476 182.213 6779.360
8835 ΣX = 182.213 Y = 34.750X = 30.369 ΣXY = 7476.000
ΣY = 208.5 6779.360
X2
ΣX2 =
A =
A = 6779.360 . 208.5 - 182.213 . 7476.000
6 . 6779.360 - ( 182.213 ) 2
A = 6.859
B = n . ΣXY - ΣX.ΣY
B = 6 . 7476.0 - 182.213 . 208.500
6 . 6779.360 - ( 182.213 ) 2
B = 0.918
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sff = A = 6.859
Dj = -Sff/B = -7.4687
Dj/Sff = -1.0889
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-DS = Sff - (Sff/Dj).DS = 6.859 - ( 6.859 / -7.4687 ) . DS = 6.859 - -0.918 . D
Model Hubungan S-D
V =
V = 6.859 . D - ( 6.859 / -7.4687 ) .
V = 6.859 . D - -0.9184 .
Model Hubungan V-S
V =
V = -7.469 . S - ( -7.469 / 6.8593 ) .
V = -7.469 . S - -1.0889 .
Sff.D - (Sff/Dj).D2
D2
D2
Dj.S - (Dj/Sff).S2
S2
S2
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 7476 - 182.213 . 208.5
√ 6 . 6779.360 - ( 182.213 } { ( 6 . 8835.25 - ( 208.5
=6864.509338443.9654
= 0.8129485
= 0.660885325670593
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinan (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/2
Vm = (Sff.Dj)/4Vm = ( 6.859 . -7.4687 ) / 4
Vm = -12.807522
Vm = -13 smp/jam
b. Untuk Kondisi S = Sff/2Vm = (Sff.Dj)/4Vm = ( 6.859 . -7.4687 ) / 4
Vm = -12.807522Vm = -13 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -13 smp/jamPada kondisi D = -7.4687 / 2
D = -3.73437 smp/jam
S = 6.859 / 2
S = 3.429636 smp/jam
B. MODEL GREENBERG
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Xi
Yi
1 35.5 1600 45.070 3.808 14.503 135.1922 41 1346 32.829 3.491 12.189 143.144
3 37 1481 40.027 3.690 13.613 136.514
4 50 1561 31.220 3.441 11.841 172.0535 45 1488 33.067 3.499 12.240 157.434
208.5 7476 182.213 17.929 64.385 744.336
1E+07 ΣX = 17.929 Y = 34.750X = 2.988 ΣXY = 744.336
ΣY = 208.5 64.385
ln D
Xi2
ΣX2 =
A =
A = 64.385 . 208.5 - 17.929 . 744.336
6 . 64.385 - ( 17.929 ) 2
A = 1.223
B = n . ΣXY - ΣX.ΣY
B = 6 . 744.34 - 17.929 . 208.5
6 . 64.385 - ( 17.929 ) 2
B = 11.220
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sm = - B = -11.220
A = = 1.223
A = 1.223= -0.109
Dj = 3470.313
= 1.223
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =S = -11.220 . 3470.313 / D
S = -11.220 . ( 3470.313 -
S = 1.223 - -11.220
Model Hubungan V-DV =V =V = -11.220 . D . ( -0.109 -V = 1.223 . D - -11.220 .
Model Hubungan V-S
V =-s / -11.220
V = 3470.313 . S
Sm . ln Dj
ln Dj
(Pake Kalkulator tekan INV ln Dj)
Sm . ln Dj
Sm . ln Dj / Dln
ln ln D
. ln D
Sm . D. ln Dj / DSm . D. (ln Dj - ln D)
ln D )D . ln D
Dj . S . ℓ -s/sm
. ℓ
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 744.336 - 17.929 . 208.5
√ 6 . 64.385 - ( 17.929 } { ( 6 . 8835.25 - ( 208.5
=727.886749786.669438
= 0.9252765
= 0.85613661130644
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/e
Vm = Sm . (Dj/e) --> e = 2.718Vm = -11.220 . ( 3470.313 / 2.718 )
Vm = -14325.595
Vm = -14326 smp/jam
b. Untuk Kondisi D = Dj/e Vm = Sm . (Dj/e) --> e = 2.718Vm = -11.220 . ( 3470.313 / 2.718 )
Vm = -14325.595Vm = -14326 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -14326 smp/jamPada kondisi D = 3470.3130 / 2
D = 1735.157 smp/km
S = -11.220 Km/Jam
C. MODEL UNDERWOOD
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Yi
Xi
1 35.5 1600 45.070 3.808 2031.343 171.6382 41 1346 32.829 3.491 1077.761 114.617
3 37 1481 40.027 3.690 1602.163 147.682
4 50 1561 31.220 3.441 974.688 107.4305 45 1488 33.067 3.499 1093.404 115.685
208.5 7476 182.213 17.929 6779.360 657.052
### ΣX = 182.213 Y = 2.988X = 30.369 ΣXY = 657.052
ΣY = 17.929 6779.360
ln S
Xi2
ΣX2 =
A =
A = 6779.360 . 17.929 - 182.213 . 657.052
6 . 6779.360 - ( 182.213 ) 2
A = 0.244
B = n . ΣXY - ΣX.ΣY
B = 6 . 657.052 - 182.213 . 17.929
6 . 6779.360 - ( 182.213 ) 2
B = 0.090
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Dm = - 1 / B = 11.066 = 11 smp/km
A = = 0.244
Sff = 11.1451 km/jam
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =
- D / 11
S = 11.1451 . ℓ
Model Hubungan V-D
V =- D / 11
V = 11.1451 . D
Model Hubungan V-SV =V = 11 . S . ( 11.1451 / S )
ln Sff
(Pake Kalkulator tekan INV ln Sff)
Sff . ℓ - D/Dm
Sff . D . ℓ - D/Dm
. ℓ
Dm . S . ln (Sff / s)ln
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 657.052 - 182.213 . 17.929
√ 6 . 6779.360 - ( 182.213 } { ( 6 . 64.385 - ( 17.93
=675.46671696.34505
= 0.9700173
= 0.940933465893338
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dm
Vm =
Vm = 11.1451 . 11 . ℓxp ( -11 / 11 )
Vm = 123.711 . 0.36788Vm = 45.510659Vm = 45.5 smp/jam
b. Untuk Kondisi S = Sff
Vm =Vm = 11.1451 . ( 11 / ℓ )
Vm = 45.510659
Vm = 45.5 smp/jam
Jadi Volume Maksimum yang terjadi adalah : 45.5 smp/jamPada KondisiD = DmD = 11 smp/jam
S = km/jamS = km/jam
Sff . Dj . ℓxp (-D/Dm)
Sff . (Dm / ℓ )
Sff / ℓ
SOAL :Data pengamatan volume lalu lintas pada simpang jalan Jend.Sudirman,Anggrek,Merdeka untuk interval 15 menitan
Waktu pengamatanMobil
Motor Becak Sepeda Pejalan KakiSedang Truck
13.00 - 13.15 86 0 449 20 5 1813.15 - 13.30 70 0 427 26 10 3813.30 - 13.45 82 0 312 23 2 013.45 - 14.00 114 1 412 18 2 014.00 - 14.15 82 0 364 15 1 014.15 - 14.30 89 1 358 18 1 114.30 - 14.45 63 1 269 14 2 314.45 - 15.00 54 3 355 9 4 515.00 - 15.15 92 2 369 20 0 415.15 - 15.30 71 1 309 15 12 315.30 - 15.45 98 0 333 32 1 015.45 - 16.00 119 0 470 33 0 316.00 - 16.15 110 0 464 35 2 216.15 - 16.30 76 4 367 15 8 516.30 - 16.45 67 1 332 15 0 716.45 - 17.00 82 0 398 29 11 1417.00 - 17.15 77 0 389 13 7 417.15 - 17.30 63 5 368 6 3 617.30 - 17.45 66 0 394 14 0 317.45 - 18.00 79 1 337 14 4 8
Mobil
Waktu PengamatanSpeed (S) Volume (V) Density (D)(km/jam) (smp/jam) (smp/jam)
13.00 - 14.00 60 353 5.88314.00 - 15.00 61 293 4.80315.00 - 16.00 70 383 5.47116.00 - 17.00 75 340 4.53317.00 - 18.00 68 291 4.279
Total 334 1660 24.971
Motor
Waktu PengamatanSpeed (S) Volume (V) Density (D)(km/jam) (smp/jam) (smp/jam)
13.00 - 14.00 35.5 1600 45.07014.00 - 15.00 41 1346 32.82915.00 - 16.00 37 1481 40.02716.00 - 17.00 50 1561 31.22017.00 - 18.00 45 1488 33.067
Total 208.5 7476 182.213
Becak
Waktu PengamatanSpeed (S) Volume (V) Density (D)(km/jam) (smp/jam) (smp/jam)
13.00 - 14.00 10.5 60.9 5.80014.00 - 15.00 11 39.2 3.56415.00 - 16.00 12 70 5.83316.00 - 17.00 9.5 65.8 6.92617.00 - 18.00 13 32.9 2.531
Total 56 268.8 24.654
Mobil Truck
Waktu PengamatanSpeed (S) Volume (V) Density (D)(km/jam) (smp/jam) (smp/jam)
13.00 - 14.00 10.5 68.6 6.53314.00 - 15.00 11 43.4 3.94515.00 - 16.00 12 9.8 0.81716.00 - 17.00 9.5 0 0.00017.00 - 18.00 13 0 0.000
Total 56 121.8 11.295
A. MODEL GREENSHIELD
No. Waktu Pengamatan
Speed (S) Volume (V) Density (D)
(km/jam) (smp/jam) (smp/jam)
Yi Xi.Yi Xi
1 13.00 - 14.00 60 353 5.883 34.6142 14.00 - 15.00 61 293 4.803 23.071
3 15.00 - 16.00 70 383 5.471 29.937
4 16.00 - 17.00 75 340 4.533 20.5515 17.00 - 18.00 68 291 4.279 18.313
Total 334 1660 24.971 126.486
22470 ΣX = 24.971 Y = 55.667X = 4.162 ΣXY = 1660.000
ΣY = 334 126.486
X2
ΣX2 =
A =
A = 126.486 . 334 - 24.971 . 1660.000
6 . 126.486 - ( 24.971 ) 2
A = 5.871
B = n . ΣXY - ΣX.ΣY
B = 6 . 1660.0 - 24.971 . 334.000
6 . 126.486 - ( 24.971 ) 2
B = 11.965
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sff = A = 5.871
Dj = -Sff/B = -0.4907
Dj/Sff = -0.0836
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-DS = Sff - (Sff/Dj).DS = 5.871 - ( 5.871 / -0.4907 ) . DS = 5.871 - -11.965 . D
Model Hubungan S-D
V =
V = 5.871 . D - ( 5.871 / -0.4907 ) .
V = 5.871 . D - -11.9648 .
Model Hubungan V-S
V =
V = -0.491 . S - ( -0.491 / 5.8714 ) .
V = -0.491 . S - -0.0836 .
Sff.D - (Sff/Dj).D2
D2
D2
Dj.S - (Dj/Sff).S2
S2
S2
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 1660 - 24.971 . 334
√ 6 . 126.486 - ( 24.971 } { ( 6 . 22470 - ( 334
=1619.757581774.65449
= 0.9127171
= 0.8330525819272
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinan (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/2
Vm = (Sff.Dj)/4Vm = ( 5.871 . -0.4907 ) / 4
Vm = -0.7203143
Vm = -1 smp/jam
b. Untuk Kondisi S = Sff/2Vm = (Sff.Dj)/4Vm = ( 5.871 . -0.4907 ) / 4
Vm = -0.7203143Vm = -1 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -1 smp/jamPada kondisi D = -0.4907 / 2
D = -0.2454 smp/jam
S = 5.871 / 2
S = 2.93572 smp/jam
B. MODEL GREENBERG
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Xi
Yi
1 60 353 5.883 1.772 3.140 106.3272 61 293 4.803 1.569 2.463 95.727
3 70 383 5.471 1.700 2.888 118.968
4 75 340 4.533 1.511 2.285 113.3595 68 291 4.279 1.454 2.114 98.859
334 1660 24.971 8.006 12.890 533.241
6E+05 ΣX = 8.006 Y = 55.667X = 1.334 ΣXY = 533.241
ΣY = 334 12.890
ln D
Xi2
ΣX2 =
A =
A = 12.890 . 334 - 8.006 . 533.241
6 . 12.890 - ( 8.006 ) 2
A = 2.711
B = n . ΣXY - ΣX.ΣY
B = 6 . 533.24 - 8.006 . 334.0
6 . 12.890 - ( 8.006 ) 2
B = 39.686
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Sm = - B = -39.686
A = = 2.711
A = 2.711= -0.068
Dj = 1513.227
= 2.711
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =S = -39.686 . 1513.227 / D
S = -39.686 . ( 1513.227 -
S = 2.711 - -39.686
Model Hubungan V-DV =V =V = -39.686 . D . ( -0.068 -V = 2.711 . D - -39.686 .
Model Hubungan V-S
V =-s / -39.686
V = 1513.227 . S
Sm . ln Dj
ln Dj
(Pake Kalkulator tekan INV ln Dj)
Sm . ln Dj
Sm . ln Dj / Dln
ln ln D
. ln D
Sm . D. ln Dj / DSm . D. (ln Dj - ln D)
ln D )D . ln D
Dj . S . ℓ -s/sm
. ℓ
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 533.241 - 8.006 . 334
√ 6 . 12.890 - ( 8.006 } { ( 6 . 22470 - ( 334
=525.364611554.950122
= 0.946688
= 0.8962181358406
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2 })
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dj/e
Vm = Sm . (Dj/e) --> e = 2.718Vm = -39.686 . ( 1513.227 / 2.718 )
Vm = -22094.894
Vm = -22095 smp/jam
b. Untuk Kondisi D = Dj/e Vm = Sm . (Dj/e) --> e = 2.718Vm = -39.686 . ( 1513.227 / 2.718 )
Vm = -22094.894Vm = -22095 smp/jam
Jadi volume maksimum yang terjadi adalah :
Vm = -22095 smp/jamPada kondisi D = 1513.2270 / 2
D = 756.614 smp/km
S = -39.686 Km/Jam
C. MODEL UNDERWOOD
No.
Speed (S) Volume (V) Density (D)
Xi.Yi(km/jam) (smp/jam) (smp/jam) Yi
Xi
1 60 353 5.883 1.772 34.614 10.4262 61 293 4.803 1.569 23.071 7.538
3 70 383 5.471 1.700 29.937 9.299
4 75 340 4.533 1.511 20.551 6.8525 68 291 4.279 1.454 18.313 6.221
334 1660 24.971 8.006 126.486 40.336
### ΣX = 24.971 Y = 1.334X = 4.162 ΣXY = 40.336
ΣY = 8.006 126.486
ln S
Xi2
ΣX2 =
A =
A = 126.486 . 8.006 - 24.971 . 40.336
6 . 126.486 - ( 24.971 ) 2
A = 0.040
B = n . ΣXY - ΣX.ΣY
B = 6 . 40.336 - 24.971 . 8.006
6 . 126.486 - ( 24.971 ) 2
B = 0.311
ΣX2 . ΣY - ΣX . ΣXY
n . ΣX2 - (ΣX)2
n . ΣX2 - (ΣX)2
Dm = - 1 / B = 3.216 = 3 smp/km
A = = 0.040
Sff = 0.9094 km/jam
Menentukan hubungan S-D, V-D dan V-S
Model Hubungan S-D
S =
- D / 3
S = 0.9094 . ℓ
Model Hubungan V-D
V =- D / 3
V = 0.9094 . D
Model Hubungan V-SV =V = 3 . S . ( 0.9094 / S )
ln Sff
(Pake Kalkulator tekan INV ln Sff)
Sff . ℓ - D/Dm
Sff . D . ℓ - D/Dm
. ℓ
Dm . S . ln (Sff / s)ln
Perhitungan Nilai Koefisien Korelasi ( r )
r =n . ΣXiYi . ΣY - ΣXi . ΣYi
=6 . 40.336 - 24.971 . 8.006
√ 6 . 126.486 - ( 24.971 } { ( 6 . 12.890 - ( 8.006
=42.094613642.3334219
= 0.9943589
= 0.9887495616289
√({n . ΣXi2 - (ΣXi)2} {n . ΣYi2 - (ΣYi)2}
({ )2 )2
Perhitungan Koefisien Determinasi (r2)
r2
Menentukan Volume Maksimum
a. Untuk Kondisi D = Dm
Vm =
Vm = 0.9094 . 3 . ℓxp ( -3 / 3 )
Vm = 2.91008 . 0.36788Vm = 1.0705602Vm = 1.1 smp/jam
b. Untuk Kondisi S = Sff
Vm =Vm = 0.9094 . ( 3 / ℓ )
Vm = 1.0705602
Vm = 1.1 smp/jam
Jadi Volume Maksimum yang terjadi adalah : 1.1 smp/jamPada KondisiD = DmD = 3 smp/jam
S = km/jamS = km/jam
Sff . Dj . ℓxp (-D/Dm)
Sff . (Dm / ℓ )
Sff / ℓ
Kesimpulan :Menentukan model yang terbaik :1. Model yang terbaik untuk hubungan S - D adalah Model Underwood dengan
Mobil : 0.98875Motor : 0.940933Becak : 0.976188
2. Model yang terbaik untuk hubungan V - D adalah Model Underwood dengan
Mobil : 0.98875Motor : 0.940933Becak : 0.976188
3. Tidak ada model yang terbaik untuk hubungan V - S, akan tetapi model Underwoodmemberikan bias / tingkat kesalahan yang lebih kecil
koefisien Determinasi r2 :
koefisien Determinasi r2 :
SOAL : andikaData pengamatan volume lalu lintas pada simpang jalan Jend. Sudirman - Binturu untuk interval 15 menitan
Waktu pengamatanMobil
Motor Becak Sepeda Pejalan KakiSedang Truck
13.00 - 13.15 30 0 155 5 0 613.15 - 13.30 27 0 130 7 6 1413.30 - 13.45 37 0 121 11 1 013.45 - 14.00 41 0 140 7 1 014.00 - 14.15 27 0 135 7 0 014.15 - 14.30 30 0 120 5 0 014.30 - 14.45 22 1 100 7 1 014.45 - 15.00 15 0 150 4 0 115.00 - 15.15 35 1 141 7 0 215.15 - 15.30 26 1 114 4 6 115.30 - 15.45 32 0 120 19 0 015.45 - 16.00 46 0 178 11 0 016.00 - 16.15 33 0 162 12 1 116.15 - 16.30 29 2 142 7 2 316.30 - 16.45 28 0 120 7 0 116.45 - 17.00 30 0 140 12 7 1117.00 - 17.15 32 0 130 5 4 217.15 - 17.30 26 2 135 3 3 317.30 - 17.45 24 0 125 6 0 317.45 - 18.00 28 0 115 5 2 6
SOAL : esthiData pengamatan volume lalu lintas pada simpang jalan Merdeka - Anggrek untuk interval 15 menitan
Waktu pengamatanMobil
Motor Becak Sepeda Pejalan KakiSedang Truck
13.00 - 13.15 16 0 96 6 4 413.15 - 13.30 11 0 122 14 4 2413.30 - 13.45 9 0 42 9 0 013.45 - 14.00 14 0 80 7 1 014.00 - 14.15 22 0 57 3 1 014.15 - 14.30 13 1 71 9 0 114.30 - 14.45 7 0 42 3 1 014.45 - 15.00 8 1 29 4 0 015.00 - 15.15 11 1 54 6 0 215.15 - 15.30 11 0 41 6 6 115.30 - 15.45 16 0 62 8 0 015.45 - 16.00 9 0 65 9 0 016.00 - 16.15 18 0 97 12 1 116.15 - 16.30 18 1 66 6 1 216.30 - 16.45 11 0 71 4 0 116.45 - 17.00 18 0 95 12 4 217.00 - 17.15 11 0 91 5 3 217.15 - 17.30 2 2 62 3 0 317.30 - 17.45 12 0 96 6 0 017.45 - 18.00 18 0 65 5 2 1
SOAL : niniData pengamatan volume lalu lintas pada simpang jalan Binturu - Jend. Sudirman untuk interval 15 menitan
Waktu pengamatanMobil
Motor Becak Sepeda Pejalan KakiSedang Truck
13.00 - 13.15 35 0 165 7 1 213.15 - 13.30 29 0 145 2 0 013.30 - 13.45 34 0 123 2 1 013.45 - 14.00 51 0 153 2 0 014.00 - 14.15 29 0 150 3 0 014.15 - 14.30 39 0 145 4 1 014.30 - 14.45 31 0 111 3 0 314.45 - 15.00 28 1 157 0 2 415.00 - 15.15 42 0 151 6 0 015.15 - 15.30 29 0 124 1 0 115.30 - 15.45 46 0 124 2 1 015.45 - 16.00 62 0 197 7 0 316.00 - 16.15 44 0 173 5 0 016.15 - 16.30 26 1 139 1 4 016.30 - 16.45 25 1 123 2 0 516.45 - 17.00 30 0 140 2 0 117.00 - 17.15 32 0 137 1 0 017.15 - 17.30 28 1 145 0 0 017.30 - 17.45 25 0 140 0 0 017.45 - 18.00 29 1 135 1 0 1
SOAL : emilData pengamatan volume lalu lintas pada simpang jalan Anggrek - Merdeka untuk interval 15 menitan
Waktu pengamatanMobil
Motor Becak Sepeda Pejalan KakiSedang Truck
13.00 - 13.15 5 0 33 2 0 613.15 - 13.30 3 0 30 3 0 013.30 - 13.45 2 0 26 1 0 013.45 - 14.00 8 1 39 2 0 014.00 - 14.15 4 0 22 2 0 014.15 - 14.30 7 0 22 0 0 014.30 - 14.45 3 0 16 1 0 014.45 - 15.00 3 1 19 1 2 015.00 - 15.15 4 0 23 1 0 015.15 - 15.30 5 0 30 4 0 015.30 - 15.45 4 0 27 3 0 015.45 - 16.00 2 0 30 6 0 016.00 - 16.15 15 0 32 6 0 016.15 - 16.30 3 0 20 1 1 016.30 - 16.45 3 0 18 2 0 016.45 - 17.00 4 0 23 3 0 017.00 - 17.15 2 0 31 2 0 017.15 - 17.30 7 0 26 0 0 017.30 - 17.45 5 0 33 2 0 017.45 - 18.00 4 0 22 3 0 0
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