Volume 6 Section 2
Part 6 TD 42/95 Annex 1
CALCULATION OF CAPACITY
1. The formulae for capacity calculation for 5. Right turning queues and delays in the minor
major/minor priority junctions evaluate flows, allowing road should be virtually avoided in practice by use of
for any conflict between the various traffic streams. The the 75% RFC. The loss of Net Present Value (NPV) on
computer program PICADY/3 has been developed to a typical road scheme containing major/minor priority
carry out these calculations and evaluate queues, delays junctions by using the 75% factor instead of the 85%
and, in some cases, predict accident rates. Major/minor may be relatively small in marginal cases where, for
priority junction flows, some of which are intermittent instance, the option between a ghost island and the next
turning movements, are considered to be at "capacity" upward step in the hierarchy, single lane dualling, is
when there is continuous queuing feeding a particular being investigated. Nevertheless, this sort of comparison
turning movement. Not all movements need be at should be set down in the overall framework of design.
"capacity" for the junction to be considered at
"capacity". 6. Designers should not strive to obtain a unique
value. A range of situations must be considered and the
2. The equations for the prediction of possible advantages and disadvantages of each one assessed.
minor road entry flows into a major/minor priority
junction are a function of the through flow and entry
geometry at the junction. These equations are applicable Variation
to all types of major/minor priority T-junctions,
including staggered junctions. Having developed a 7. It must be stressed that the calculated capacities,
range of Design Reference Traffic Flows, a designer queues and delays are average values of very broad
should use the equations to produce trial designs for distributions. The formulae used are based on multiple
assessment. Manual or computerised methods such as regression analyses from observations from a large
PICADY/3 may be used. However, it is not realistic to number of sites. Actual values can vary about the
calculate queue lengths and delays manually. average due to:-
Site to site variation.
Ratio of Flow to Capacity Day to day variation.
3. The ratio of flow to capacity (RFC) is an Site to site variation has been estimated, and is covered
indicator of the likely performance of a junction under by the procedures. As far as day to day variation is
design year loading. It should be calculated or computed concerned, this will manifest itself in practice as
for each trial design. Due to site to site variation, there variations in the queue lengths and delays at any given
may be a standard error of prediction of the entry time in the peak period. The formulae merely calculate
capacity by the formulae of + or - 15% for any site. the average over many days. PICADY/3 offers daily
Thus, queuing should not occur in the various turning variability calculations as well as averages.
movements in the chosen design year peak hour in 5 out
of 6 peak hour periods or sites, if a maximum RFC of
about 85% is used. Similarly, if a maximum RFC of
75% is used, queuing will theoretically be avoided in 39
out of 40 peak hour periods or sites.
4. The general use of designs with an RFC of
about 85% is likely to result in a level of provision
which will be economically justified. However, at sites
having no particular space restriction, and also where
the Design Speed may be 100kph or more, usually in
suburban and rural areas, the latter ratio, 75%, should be
used as a design yardstick. This is because the formulae
have not been derived for roads of this type. In urban
areas, the former RFC, 85%, may be appropriate.
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Volume 6 Section 2
Annex 1 Part 6 TD 42/95
Prediction of Turning Stream Capacities In each of these equations, the geometric parameters
represented by D, E and F are stream specific:-
8. The best predictive equations for turning stream
capacities, for major roads with Design Speeds of up to D = (1 + 0.094[wb-a - 3.65])(1 + 0.0009[Vrb-a - 120])(1 +
85kph, found by research to date are, with reference to 0.0006[Vlb-a - 150])
Fig A1/1:-
E = (1 + 0.094[wb-c -3.65])(1 + 0.0009[Vrb-c - 120])
qsb-a = D(627 + 14Wcr - Y[0.364qa-c + 0.144qa-b +
0.229qc-a + 0.520qc-b]) F = (1 + 0.094[wc-b - 3.65])(1 + 0.0009[Vrc-b - 120])
qsb-c = E(745 - Y[0.364qa-c + 0.144qa-b ]) Where wb-a denotes the lane width available to waiting
vehicles in the stream B-A, and Vrb-a, Vlb-a the
qsc-b = F(745 - 0.364Y[qa-c + qa-b ]) corresponding visibilities, and so on. In all cases,
capacities and flows are in pcu/hour and distances in
where Y = (1 - 0.0345W) metres. If the right hand side of any equation is negative,
the capacity is zero.
q c-a
q c-b
Arm C Arm A
(Major) (Major)
q a-c
q a-b
q b-a
q b-c
Arm B
(Minor)
Notes
q c-a = the flow of vehicles for the stream c-a
q b-a = the flow of vehicles for the stream b-a
and so on
Superscript s (eg q b-a) denotes the flow from a saturated
s
stream, ie one in which there is stable queueing
Figure A1/1 : Definition of Turning Stream Capacities
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Volume 6 Section 2
Part 6 TD 42/95 Annex 1
9. Visibilities are measured as detailed in Chapter Wn = ½ (W2 + W4) and Wf = ½ (W1 + W3 )
7 of the main document. W, Wcr and w are measured as
follows:- b. At dual carriageway sites with a kerbed central
reserve, the width of the central reserve, Wcr is
a. The major road width, W, has two main
components, the "nearside" width, Wn, and the "farside" Wcr = ½ (W5 + W6)
width, Wf, which are added together to give the total
carriageway width. With reference to Fig A1/2,
W1 W3
W2 W4
W1
W3
°° °°
W2 W4
W1 W3
W2 W4
Ghost islands
W1 W3
W6 W5
W2 W4
Kerbed islands
Figure A1/2 : Lane Width Measurement for Major Road
c. The lane width for non-priority streams, w, is reference should be made to Fig A1/3, and the lane width
measured directly where there are clear lane markings. calculated according to:-
The average of measurements taken at 5m intervals over a
distance of 20m upstream from the Give way line is used. w = ¹ª5 (a + b + c + d + e)
Any measurement exceeding 5m is reduced to 5m before
the average is taken.
Where lane markings are either unclear or absent,
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Volume 6 Section 2
Annex 1 Part 6 TD 42/95
MAJOR ROAD
a 0m
b
5m
c a, b, c, d, e are equal to
10m
½ (approach width to
d nearside of median line)
15m
Each<5m
e
20m
MINOR ROAD
Diagram (a) Lane width measurements for the right-turning minor road stream
MAJOR ROAD
a 0m
b
5m
c a, b, c, d, e are equal to
10m ½ (approach width to
d nearside of median line)
15m Each<5m
e
20m
MINOR ROAD
Diagram (b) Lane width measurements for the left-turning minor road stream
20m 15m 10m 5m 0m
e d c b a
(Minimum = 2.1m)
a, b, c, d, e are equal to the lane width
where there is explicit provision for
right turners (each<5m), and equal
2.1m otherwise
Diagram (c) Lane width measurements for the right-turning major road stream
Figure A1/3 : Lane Width Measurements for Non-Priority Streams
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Volume 6 Section 2
Part 6 TD 42/95 Annex 1
Manual Calculation Ranges of Factors
10. Using the formulae the RFCs of the various 12. For the purpose of manual or computerised
turning movements should be examined. The Design calculation of turning stream capacities, the practical
Reference Flows should be multiplied by 1.125 to allow ranges of the geometric parameters defined above are
for short term variations in traffic flows. Short term given in Table A1/1.
variation is included in PICADY/3. The standard error
of capacity prediction due to variation between sites is The maximum values used for central reservation width
13%. and visibilities should be 10m and 250m respectively,
even if it is proposed to provide physically greater
values when the junction is constructed.
Computerised Calculation
13. An example of a typical calculation follows.
11. A computer program such as PICADY/3 should
be used. The appraisal should normally be based on an
RFC of about 85% in urban areas or 75% in rural areas.
In calculating this, a time segment length of not less than
5 minutes should be used to build up the flow pattern
during the peak. The program prints out the RFC
(labelled Demand/Capacity in the output), queue lengths
and delays for each turning movement, for each time
segment.
Parameter Practical Range
w lane width for non-priority streams 2.05 - 4.70m
Vr visibility to the right 17.0 - 250.0m
Vl visibility to the left 22.0 - 250.0m
Wcr width of central reserve 1.2 - 9.0m
(dual carriageway sites only)
W major road width 6.4 - 20.0m
Table A1/1: Range of Parameters for Capacity Formula
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