Highway Engineering

(Nandana) #1

(4.12)


This relationship is again parabolic in nature. It is illustrated in Fig. 4.3.


qku

u
j uf

=-ÊËÁ ˆ ̄ ̃


2

Basic Elements of Highway Traffic Analysis 77

Flow (veh/h) qm

um

Speed (km/h)

Figure 4.3
Illustration of speed-
flow relationship.

In order to find the speed at maximum flow, Equation 4.12 is differentiated
and put equal to zero:


since kjπ0, the term within the brackets must equal zero, therefore:


(4.13)


um, the speed at maximum flow, is thus equal to half the free-flow speed,uf. Its
location is shown in Fig. 4.3.
Combining Equations 4.10 and 4.13, the following expression for maximum
flow is derived:


therefore


(4.14)
q

uk
m
= fj
4

quk

uk
mmm
=¥= ¥fj
22

1


2


0


2


-=


=


u
u

u

u

m
f

m

f

, thus

dq
dt

k

u
j uf

=-Ê


ËÁ


ˆ


̄ ̃


1 =


2


0

Free download pdf