Formula Sheets: Traffic Engineering | Transportation Engineering - Civil Engineering (CE) PDF Download

 Page 1


GA TE CE 2026 F orm ula Sheet: T ra?ic Engineering
1. T ra?ic Studies on Flo w and Sp eed
• T ra?ic flo w (v olume):
q =
N
t
where:
– q : T ra?ic flo w rate (v ehicles/hour)
– N : Num b er of v ehicles observ ed
– t : Time duration (hours)
• Space mean sp eed:
v
s
=
n·L
?
t
i
where:
– v
s
: Space mean sp ee d (km/h)
– n : Num b er of v ehicles
– L : Length of road segmen t (km)
– t
i
: T ra v el time of v ehicle i (hours)
• Time mean sp eed:
v
t
=
?
v
i
n
where:
– v
t
: Time mean sp eed (km/h)
– v
i
: Sp eed of v ehicle i (km/h)
2. P e ak Hour F actor
• P eak Hour F actor (PHF):
PHF =
q
hourly
4·q
p eak 15-min
where:
– q
hourly
: Hourly tra?ic v olume (v ehicles/hour)
– q
p eak 15-min
: Maxim um 15-min ute flo w rate (v ehicles/15 min)
3. A c ciden t Study and Statistical Analysis
• A cciden t rate (p er million v ehicle-kilometers):
R =
A·10
6
V ·L
where:
– R : A cciden t rate
– A : Num b er of acciden ts
– V : T ra?ic v olume (v ehicles/da y )
– L : Length of road segmen t (km)
• Mean of tra?ic data:
¯ x =
?
x
i
n
where:
1
Page 2


GA TE CE 2026 F orm ula Sheet: T ra?ic Engineering
1. T ra?ic Studies on Flo w and Sp eed
• T ra?ic flo w (v olume):
q =
N
t
where:
– q : T ra?ic flo w rate (v ehicles/hour)
– N : Num b er of v ehicles observ ed
– t : Time duration (hours)
• Space mean sp eed:
v
s
=
n·L
?
t
i
where:
– v
s
: Space mean sp ee d (km/h)
– n : Num b er of v ehicles
– L : Length of road segmen t (km)
– t
i
: T ra v el time of v ehicle i (hours)
• Time mean sp eed:
v
t
=
?
v
i
n
where:
– v
t
: Time mean sp eed (km/h)
– v
i
: Sp eed of v ehicle i (km/h)
2. P e ak Hour F actor
• P eak Hour F actor (PHF):
PHF =
q
hourly
4·q
p eak 15-min
where:
– q
hourly
: Hourly tra?ic v olume (v ehicles/hour)
– q
p eak 15-min
: Maxim um 15-min ute flo w rate (v ehicles/15 min)
3. A c ciden t Study and Statistical Analysis
• A cciden t rate (p er million v ehicle-kilometers):
R =
A·10
6
V ·L
where:
– R : A cciden t rate
– A : Num b er of acciden ts
– V : T ra?ic v olume (v ehicles/da y )
– L : Length of road segmen t (km)
• Mean of tra?ic data:
¯ x =
?
x
i
n
where:
1
– ¯ x : Mean of data (e.g., sp eed, flo w)
– x
i
: Individual data p oin t
– n : Num b er of observ ations
• Standard deviation:
s =
v
?
(x
i
- ¯ x)
2
n
4. Microscopic and Macroscopic P arameters of T ra?ic Flo w
• Microscopic: Headw a y:
h =
3600
q
where:
– h : A v erage time headw a y (seconds)
– q : Flo w rate (v ehicles/hour)
• Microscopic: Spacing:
s =
1000·v
q
where:
– s : A v erage spacing (m)
– v : Sp eed ( km/h)
• Macroscopic: Densit y:
k =
q
v
where:
– k : T ra?ic densit y (v ehicles/km)
5. F undamen tal Relationships of T ra?ic Flo w
• Flo w-densit y-sp eed relationship:
q =k·v
• Greenshields’ linear mo del:
v =v
f
(
1-
k
k
j
)
where:
– v
f
: F ree-flo w sp eed (km/h)
– k
j
: Jam densit y (v ehicles/km)
• Maxim um flo w:
q
max
=
v
f
·k
j
4
6. T ra?ic Signs
• Minim um size of regulatory sign:
S =
v·h
k
where:
– S : Size of sign (m)
– v : Approac h sp e ed (km/h)
– h : Legibilit y distance (m)
– k : Constan t (dep ends on sign t yp e, t ypically 0.02–0.03)
2
Page 3


GA TE CE 2026 F orm ula Sheet: T ra?ic Engineering
1. T ra?ic Studies on Flo w and Sp eed
• T ra?ic flo w (v olume):
q =
N
t
where:
– q : T ra?ic flo w rate (v ehicles/hour)
– N : Num b er of v ehicles observ ed
– t : Time duration (hours)
• Space mean sp eed:
v
s
=
n·L
?
t
i
where:
– v
s
: Space mean sp ee d (km/h)
– n : Num b er of v ehicles
– L : Length of road segmen t (km)
– t
i
: T ra v el time of v ehicle i (hours)
• Time mean sp eed:
v
t
=
?
v
i
n
where:
– v
t
: Time mean sp eed (km/h)
– v
i
: Sp eed of v ehicle i (km/h)
2. P e ak Hour F actor
• P eak Hour F actor (PHF):
PHF =
q
hourly
4·q
p eak 15-min
where:
– q
hourly
: Hourly tra?ic v olume (v ehicles/hour)
– q
p eak 15-min
: Maxim um 15-min ute flo w rate (v ehicles/15 min)
3. A c ciden t Study and Statistical Analysis
• A cciden t rate (p er million v ehicle-kilometers):
R =
A·10
6
V ·L
where:
– R : A cciden t rate
– A : Num b er of acciden ts
– V : T ra?ic v olume (v ehicles/da y )
– L : Length of road segmen t (km)
• Mean of tra?ic data:
¯ x =
?
x
i
n
where:
1
– ¯ x : Mean of data (e.g., sp eed, flo w)
– x
i
: Individual data p oin t
– n : Num b er of observ ations
• Standard deviation:
s =
v
?
(x
i
- ¯ x)
2
n
4. Microscopic and Macroscopic P arameters of T ra?ic Flo w
• Microscopic: Headw a y:
h =
3600
q
where:
– h : A v erage time headw a y (seconds)
– q : Flo w rate (v ehicles/hour)
• Microscopic: Spacing:
s =
1000·v
q
where:
– s : A v erage spacing (m)
– v : Sp eed ( km/h)
• Macroscopic: Densit y:
k =
q
v
where:
– k : T ra?ic densit y (v ehicles/km)
5. F undamen tal Relationships of T ra?ic Flo w
• Flo w-densit y-sp eed relationship:
q =k·v
• Greenshields’ linear mo del:
v =v
f
(
1-
k
k
j
)
where:
– v
f
: F ree-flo w sp eed (km/h)
– k
j
: Jam densit y (v ehicles/km)
• Maxim um flo w:
q
max
=
v
f
·k
j
4
6. T ra?ic Signs
• Minim um size of regulatory sign:
S =
v·h
k
where:
– S : Size of sign (m)
– v : Approac h sp e ed (km/h)
– h : Legibilit y distance (m)
– k : Constan t (dep ends on sign t yp e, t ypically 0.02–0.03)
2
7. Signal Design b y W ebster’s Metho d
• Cycle length:
C =
1.5L+5
1-Y
where:
– C : Optim um cycle length (seconds)
– L : T otal lost time p er cycle (seconds)
– Y : Sum of critical flo w ratios, Y =
?
qi
si
– q
i
: Flo w rate for phase i (v ehicles/hour)
– s
i
: Saturation flo w rate for phase i (v ehicles/hour)
• Effectiv e green time for phase i :
g
i
=
y
i
Y
(C-L)
where:
– g
i
: Effectiv e green time for phase i (seconds)
– y
i
: Flo w ratio for phase i , y
i
=
qi
si
• Lost time p er cycle:
L =
?
(t
L
+t
a
)
where:
– t
L
: Start-up lost time (t ypically 2–3 se conds/phase)
– t
a
: Am b er time (t ypically 3–5 seconds)
8. T yp es of In tersections
• Channelization island area (appro ximate):
A
i
=k·W
2
lane
where:
– A
i
: Area of island (m²)
– W
lane
: Lane width (m)
– k : Constan t (dep ends on in tersection t yp e, t ypically 2–5)
9. High w a y Capacit y
• Lev el of Service (LOS) based on densit y:
k =
q
v
where:
– LOS A: k= 7 v ehicles/km/lane
– LOS F: k= 42 v ehicles/km/lane (HCM standards)
• Capacit y of high w a y:
C =s·N ·f
w
·f
HV
·f
p
where:
– C : High w a y capacit y (v ehicles/hour)
– s : Saturation flo w rate (t ypically 1800–2000 v ehicles/hour/lane)
– N : Num b er of lanes
– f
w
: Lane width adjustmen t factor
3
Page 4


GA TE CE 2026 F orm ula Sheet: T ra?ic Engineering
1. T ra?ic Studies on Flo w and Sp eed
• T ra?ic flo w (v olume):
q =
N
t
where:
– q : T ra?ic flo w rate (v ehicles/hour)
– N : Num b er of v ehicles observ ed
– t : Time duration (hours)
• Space mean sp eed:
v
s
=
n·L
?
t
i
where:
– v
s
: Space mean sp ee d (km/h)
– n : Num b er of v ehicles
– L : Length of road segmen t (km)
– t
i
: T ra v el time of v ehicle i (hours)
• Time mean sp eed:
v
t
=
?
v
i
n
where:
– v
t
: Time mean sp eed (km/h)
– v
i
: Sp eed of v ehicle i (km/h)
2. P e ak Hour F actor
• P eak Hour F actor (PHF):
PHF =
q
hourly
4·q
p eak 15-min
where:
– q
hourly
: Hourly tra?ic v olume (v ehicles/hour)
– q
p eak 15-min
: Maxim um 15-min ute flo w rate (v ehicles/15 min)
3. A c ciden t Study and Statistical Analysis
• A cciden t rate (p er million v ehicle-kilometers):
R =
A·10
6
V ·L
where:
– R : A cciden t rate
– A : Num b er of acciden ts
– V : T ra?ic v olume (v ehicles/da y )
– L : Length of road segmen t (km)
• Mean of tra?ic data:
¯ x =
?
x
i
n
where:
1
– ¯ x : Mean of data (e.g., sp eed, flo w)
– x
i
: Individual data p oin t
– n : Num b er of observ ations
• Standard deviation:
s =
v
?
(x
i
- ¯ x)
2
n
4. Microscopic and Macroscopic P arameters of T ra?ic Flo w
• Microscopic: Headw a y:
h =
3600
q
where:
– h : A v erage time headw a y (seconds)
– q : Flo w rate (v ehicles/hour)
• Microscopic: Spacing:
s =
1000·v
q
where:
– s : A v erage spacing (m)
– v : Sp eed ( km/h)
• Macroscopic: Densit y:
k =
q
v
where:
– k : T ra?ic densit y (v ehicles/km)
5. F undamen tal Relationships of T ra?ic Flo w
• Flo w-densit y-sp eed relationship:
q =k·v
• Greenshields’ linear mo del:
v =v
f
(
1-
k
k
j
)
where:
– v
f
: F ree-flo w sp eed (km/h)
– k
j
: Jam densit y (v ehicles/km)
• Maxim um flo w:
q
max
=
v
f
·k
j
4
6. T ra?ic Signs
• Minim um size of regulatory sign:
S =
v·h
k
where:
– S : Size of sign (m)
– v : Approac h sp e ed (km/h)
– h : Legibilit y distance (m)
– k : Constan t (dep ends on sign t yp e, t ypically 0.02–0.03)
2
7. Signal Design b y W ebster’s Metho d
• Cycle length:
C =
1.5L+5
1-Y
where:
– C : Optim um cycle length (seconds)
– L : T otal lost time p er cycle (seconds)
– Y : Sum of critical flo w ratios, Y =
?
qi
si
– q
i
: Flo w rate for phase i (v ehicles/hour)
– s
i
: Saturation flo w rate for phase i (v ehicles/hour)
• Effectiv e green time for phase i :
g
i
=
y
i
Y
(C-L)
where:
– g
i
: Effectiv e green time for phase i (seconds)
– y
i
: Flo w ratio for phase i , y
i
=
qi
si
• Lost time p er cycle:
L =
?
(t
L
+t
a
)
where:
– t
L
: Start-up lost time (t ypically 2–3 se conds/phase)
– t
a
: Am b er time (t ypically 3–5 seconds)
8. T yp es of In tersections
• Channelization island area (appro ximate):
A
i
=k·W
2
lane
where:
– A
i
: Area of island (m²)
– W
lane
: Lane width (m)
– k : Constan t (dep ends on in tersection t yp e, t ypically 2–5)
9. High w a y Capacit y
• Lev el of Service (LOS) based on densit y:
k =
q
v
where:
– LOS A: k= 7 v ehicles/km/lane
– LOS F: k= 42 v ehicles/km/lane (HCM standards)
• Capacit y of high w a y:
C =s·N ·f
w
·f
HV
·f
p
where:
– C : High w a y capacit y (v ehicles/hour)
– s : Saturation flo w rate (t ypically 1800–2000 v ehicles/hour/lane)
– N : Num b er of lanes
– f
w
: Lane width adjustmen t factor
3
– f
HV
: Hea vy v ehicle adjustmen t factor
– f
p
: Driv er p opulation factor
• Hea vy v ehicle adjustmen t factor:
f
HV
=
1
1+P
T
(E
T
-1)+P
B
(E
B
-1)
where:
– P
T
, P
B
: Prop ortion of truc ks and buses
– E
T
, E
B
: P assenger car equiv alen ts for truc ks and buses
4