CE 2710 Transportation Engineering
Homework 7 Solution
1. Given s = 0.30 / (60 - u), derive the relationships u-k, u-q, and q-k. Estimate the
capacity (i.e., qmax ) of the roadway. Note: s - spacing in miles, u - speed in miles
per hour (mph)
hrvehq
mivehk
kdk
dq
setqfindTo
kkuuukq
ku
uk
u
kHence
k
sEqtoAccording
m
/3000
/100
060.060
:0,
30.06033.3200
30.060
33.3200 30.0
60
,
1
,1.3.3.
max
max
22
=
=
=−
=
−=−==
−=
−=
−
=
=
2. The table below contains speed and concentration observations for different times
on a rural road. Plot this data and use a trial-and-error approach to fit an equation
of the form (or a line fitting program like excel),
u = a k + c
where u - speed, k - concentration, a and c are constants. Draw the u-k, u-q, and q-
k plots showing both the fitted line (using the equations) and the actually data
points. Estimate from the fitted line maximum flow, velocity and concentration at
maximum flow, the jam concentration (this is concentration when q=o).
Solution u = -0.53k + 62.6 from plot
qmax = 2070 veh/hr
@ qmax , u = 34.5 mph and k = 53 veh/mi
kj = 125 veh/mi
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