SME
Transportation Engineering · Problem type
Headway and spacing
Use this for “A lane carries 2667 pc/h/ln at a density of 40 pc/km/ln. Find the mean headway, the mean spacing and the speed.”
This is an example. Type your own values to start a new problem.
h (s)
=
3600
÷
q (pc/h/ln)
s (m)
=
1000
÷
k (pc/km/ln)
q (pc/h/ln)
=
k (pc/km/ln)
×
v (km/h)
Formulas
h
=
3,600
q
1.3498
=
3,600
2,667
s
=
1,000
k
25
=
1,000
40
q
=
k
×
v
2,667 = 40 × 66.675
Assumptions
•
Headway h is the time between the fronts of two vehicles passing a point, one after the other.
•
Spacing s is the distance between the fronts of two vehicles in a row, at one moment.
•
Both are averages over one lane: 3600 s in an hour, 1000 m in a kilometre.
•
Each vehicle counts as one passenger car (pc).
Step-by-step
WE KNOW
q = 2,667 pc/h/ln, k = 40 pc/km/ln
FIND
headway (h), spacing (s), speed (v)
Step 1 · Find headway (h)
Use h = 3,600 ÷ q
An hour holds 3600 s, shared equally by the vehicles that pass in it.
h
=
3,600
2,667
h
=
1.3498
s
Step 2 · Find spacing (s)
Use s = 1,000 ÷ k
A kilometre holds 1000 m, shared equally by the vehicles on it.
s
=
1,000
40
s
=
25
m
Step 3 · Find speed (v)
Use q = k × v
Divide the flow by the density: the space-mean speed.
v
=
q
k
v
=
2,667
40
v
=
66.675
km/
h
Check
Put the numbers back in. Both sides should match.
1.3498
=
3,600
2,667
✓
25
=
1,000
40
✓
2,667 = 40 × 66.675 ✓
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