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6.2 DESIGN PRINCIPLES
6.2.1 Determination of saturation flow, S
The capacity of a traffic-signal controlled intersection is limited by the capacities of the individual approaches to the intersection. This capac-ity of an approach is measured independently of traffic and other controlling factors and is expressed as the saturation flow.
Saturation flow is defined as the maximum flow, expressed as equiva-lent passenger cars, that can cross the stop line of the approach where there is a continuous green signal indication and a continuous queue of vehicles on the approach.
Basic saturation flow (S) expressed in passenger car units per hour with no parked vehicles is given by
i) where effective approach width W > 5.5 m S = 525 W p.c.u./hr
ii) and where W < 5,5 m, see Table 6-1.
Where there are parked vehicles, effective approach width is to be reduced by LW where
LW = 14 - 0.9 ( Z-7.6 ) / k
Where Z (>7.6 m) is the clear distance of the nearest parked car from the stop line (m) and k is the green time (sees).
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If the whole expression becomes negative, the effective lose should be taken as zero. The affective loss should be increased by 50 percent for a parked lorry or wide van.
Note : The British formula, assuming m green time of 30 seconds, infers that there is no effect on the approach capacity if parking is approximately 61 m (20O ft) or more away from the stop line.
This basic saturation flow is then has to be corrected for the effect of gradient, turming radium, and the proportion of turning traffic.
Table 6-l
Relationship between effective lane width and saturation flow
a) Gradient
See table below
w ( m ) 3.0 3.25 3.5 3.75 4.0 4.25 4.5 4.75 5.0 5.25
s ( pcu/h )
1845 1860 1885 1915 1965 2075 2210 2375 2560 2760
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Table 6-2
Correction factor for the effect of gradient
b) Turning radium
Saturation flows for approaches with exclusive turning traffic need to be corrected with factor that takes into consideration the magnitude of the turning radius, R. See table below.
Table 6-3
Correction Factor for the effect of turning radius
Correction Factor, Fg Description
0.85 0.88 0.91 0.94 0.97 1.00 1.03 1.06 1.09 1.12 1.15
for upward slope of 5%
for upward slope of 4%
for upward slope of 3%
for upward slope of 2%
for upward slope of 1%
for level grade for downward slope of 1%
for downward slope of 2%
for downward slope of 3%
for downward slope of 4%
for downward slope of 5%
Correction Factor, Ft Description
0.85 0.90 0.96
for turning radius R < 10 m
for turning radius where 10 m < R < 15 m for turning radius where 15 m < R < 30 m
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c) Turning traffic
When u lane comprises straight-on and turning traffic, the pro-portion of turning traffic is one of the factors determining the saturation flow, S.
Table 6-4 specifies correction factors for various percentages of turning traffic over the total traffic on the approach lane.
Table 6-4
Correction factors for turning traffic
Note :
1. If a lane comprises both right and left turning traffic, the total factor will be Fr x Fl
2. In cases where total saturation flow of the exits is lower than of the approaches, the lower value has to be taken into account.
% turning traffic Factor for right-turn, Fr
Factor for left-turn, F1
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6.2.2 Determination of Y value Y = q/S
where y = ratio of flow to saturation flow
q = actual flow on a traffic-signal approach converted in pcu/hr ( See Table 6-5 for conversion )
S = saturation flow for the approach in pcu/hr.
The y value for a phase is the highest y value from the approaches within that phase.
n For the whole junction, Y = E yi
where n = number of phase
yi = highest y value from the approach within that phase i.
This Y value is a measure for the accupancy of the intersection.
Y should preferably not be higher than 0.65. If the value found is higher than 0.85, it is recommended that the geometrics of the inter-section be upgraded to increase the capacity.
Table 6-5
Conversion factors to pcu's
Vehicle Type Equipment pcu value
Passenger cars Motor cycles
Light vans Medium lorries
Heavy lorries Buses
1.00 0.33 1.75 1.75 2.25 2.25
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6.2.3 Determination of total lost time percycle, L
From Webster and Cobbe, the total lost time per cycle is n n
L = E ( I - a ) + E1
I=1 I=1
where I = the intergreen time between the phases a the amber time, usually taken as 3
seconds.
a = the amber time, usually taken as 3 seconds.
1 = drivers reaction time at begin of green per phase. In practise, this time is set to 2 seconds but 0 - 7 seconds can also be used.
Note :
i ) The shortest total lost time is the most economic one because the greater part of the cycle can be used by traffic flows.
ii ) Intergreen, I = R + a (in seconds) where R = all red interval iii ) To check for adequacy of amber time, a
a = V + W + L
---
---2 A V
where
a = amber time ( sec )
2 A = acceleration ( taken as 4.58 m/S ) V = approach speed ( m/s )
W = width of intersection crossed ( m ) L = length of vehicle ( suggested 5.5 m )
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6.2.4 Determination of optimum cycle time, Co
An expression for the optimum cycle time, Co,is given in Road Research Technical Paper No. 56 as
Co = 1.5L + 5 ( in seconds )
---I - Y
This optimum cycle time, Co, gives the minimum average delay for the intersection. But this delay is not greatly increased if the cycle time varies within the range of 0.75 to 1.50 of the calculated Co.
For practical purposes, cycle time should be between 45 seconds to 120 seconds, although an absolute minimum of 25 seconds can be used.
8.2.5 Determination of signal settings
Effective green time is the green time plus the change interval minus the lost time for a designated phase.
The total effective green time = cycle time minus total lost time.
g + g + ... + g = Co - L
1 2 n
where n denotes the number of phases and gn is the effective green time of phase n.
For optimum conditions
g = y ( for a 2 phase cycle )
1 1
--
--g y
2 2
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With the above ratio, the following formulas apply to each individual phase.
g = Yn (Co - L) ( in seconds )
n
----Y
where g = effective green time of the n
n signal phase
Yn = calculated Y-value of the same signal phase.
For a 2 phase cycle
9 = Yl ( Co L )
1
---Y
and g = Y (Co L)
2 2
---Y
The actual green time, G = 9 + I + R
The controller setting time, K = G - a - R
= g + 1 - a Therefore for a two-phase example
K = g + 1 - a
1 1
and K = g + I - a
2 2
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6.2.6 Determination of Capacity a) Practical capacity, Y prac
The maximum possible value of Y which can be accommodat-ed is
Y max = 1 - L
---CM
where L = total lost time ( sec )
C = maximum cycle time (sec) m
*
For practical purposes, Cm = 120 seconds than Y = 0.9 - 0.0075 L
prac
For design purposes Co is used rather than C m.
b) Reserve Capacity, RC
This reserve capacity is the difference between the capacity and the actual flow. As a percentage of the present flow, RC is given by
RC = 0.9 ( 1 - L/C max ) - Y x 100%
---Y
or more conveniently
RC = Y - Y
prac
--- x 100%
Y
Y is the actual value at the junction.
A useful mean of calculating RC is by using the Reserve Capacity Diagram in Figure 6-1
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c) Design Life of Junction, n n = log ( Q1 /Qo )
---log ( I + GR )
where n = number of years
Q1 = 90% of ultimate capacity Q0 = present flow
MGR = growth rate
This design life is calculated when C = 120 secs. Therefore all the green times should be adjusted to suit this condition.
6.2.7 Determination of delays and queues
a) Average delay per vehicle on a particular intersection arm is given by
2 2
d = 9 [ C ( I - ~ ) + x ]
--- --- ---10 [ 2 ( l - ~x ) 2q ( l - x ) ]
where d = average delay per vehicle c = cycle time
~ = proportion of the cycle that is effec-tively green for the phase under consideration ( i.e.g/C )
q = flow
x = degree of saturation, which is the ratio of actual flow to the maximum flow that can pass through the approach ( i.e. q/,.S )
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To enable the delay to be calculted more easily, the equation is rewritten as.
d = CA + B/q - K 2
where A = ( 1 - ~ )
--- tabulated in fable 6 - 6 2 ( 1- ~x )
2
B = X
--- tabulated in Table 6 - 7 2 ( 1 - x )
and K = correction factor tabulated in Table 6 - 8.
Note : User shall use this equation with caution at high degrees of saturation (i.e. x approaches 1) as it will greatly overestimate delay. When x = 1, d = "
b) Maximum queue occurs at the start of green and has an average value of
N = q x r
or whichever is greater
N = q ( r/2 + d )
where N = number of vehicles q = flow ( veh/sec )
d = average delay per vehicle for a particular arm ( seconds )
r = C - g = effective red time (seconds)
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To calculate 'Reserve Capacity' use the left hand diagram to obtain a point corresponding to the 'Lost time' and the maximum cycle time suitable for the junction, extend a line horizontally from this point to the right hand diagram to meet a vertical line corresponding with the Y value - the Reserve Capacity ( RC ) may be read at the point of intersection. Example : Lost Time 10 seconds; Cycle time 75 seconds; Y value 6; Reserve Capacity 30%.
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TABLE 6 - 6
Tabulation of A = ( l - ~2 ) ---2 ( l - ~x )
---x 0.1 0.2 0.3 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.80 0.90 ---O.l 0.409 O.337 0.253 0.319 0.188 O.158 0.132 0.107 0.085 0.066 0.048 0.032 0.005 0.2 0.413 0.383 0.261 0.227 0.196 0.166 0.138 0.114 0.091 0.070 0.052 0.024 0.006 0.3 0.418 0.340 0.269 0.236 0.205 0.175 0.147 0.121 0.088 0.076 0.067 0.026 0.007 0.4 0.422 0.348 0.378 0.246 0.314 0.184 0.156 0.130 0.109 0.003 0.063 0.039 0.008 0.5 0.426 0.356 0.288 0.256 0.325 0,195 0.167 0.140 0.114 0.091 0.089 0.033 0.009 0.55 0.423 0.360 0.393 0.362 0.231 0.201 0.172 0.145 0.119 0.095 0.073 0.036 0.010 0.60 0.431 0.364 0.299 0.267 0.237 0,207 0.179 0.151 0.125 0.100 0.078 0.038 0.011 0,65 0.433 0.368 0.304 0.273 0.243 0.214 0.185 0.150 0.131 0.106 0.083 0.042 0.012 0.70 0.435 0.372 0.310 0.280 0.250 0.331 0.192 0.165 0.138 0.113 0.088 0.045 0.014 0.75 0.438 0.376 0.316 0,286 0.257 0.228 0.200 0.172 0.145 0.120 0.095 0.050 0.015 0.80 0.440 0.381 0.322 0.293 0.265 0.236 0.208 0.181 0.154 0.128 0.102 0.056 0.018 0.85 0.443 0.386 0.329 0.301 0.373 0.245 0.217 0.190 8.163 0.137 0.111 0.063 0.021 0.90 0.445 0,390 0.336 0.300 0.281 0.354 0.227 0.200 0.174 0.148 0.123 0.071 0.026 0.92 0.446 0.392 0.388 0.312 8.205 0.258 0.231 0.205 0.179 0.152 0.126 0.076 0.028 0.94 0.447 0.394 0.341 0.315 0.280 0.262 0.236 0.210 0.183 0,157 0.133 0.081 0.032 0.96 0.448 0.396 0.344 0.318 0.292 0,266 0.240 0.215 0.189 0.163 0.137 0.086 0.037 0.98 0.449 0.398 0.347 0.322 0.296 0.271 0.245 0.220 0.194 0.168 0.143 0.083 0.042
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TABLE 6 - 7
2
Tabulation of B = x
---2 ( l - u )
---x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ---0.l 0.006 0.007 0.008 0.0l0 0.0Il 0.013 0.0l5 0.0l7 0.020 0.022 0.2 0.225 0.028 0.031 0.034 0.038 0.042 0.046 0.050 0.054 0.059 0.3 0.064 0.070 0.075 0.081 0.088 0.094 0.101 0.109 0.116 0.125 0.4 0.133 0.I42 0.152 0.162 0.173 0.184 0.l96 0.208 0.222 0.235 0.5 0.350 0.265 0.282 0.299 0.317 0.336 0.356 0.378 0.400 0.425 0.6 0.450 0.477 0.586 0.536 0.569 0.604 0.641 0.680 0.723 0.768 0.7 0.817 0.869 0.926 0.987 1.05 1.13 1.20 1.29 1.38 1.49 0.8 0.60 1.73 1.87 2.03 2.21 2.41 2.64 2.91 3.23 3.60 0.9 4.05 4.60 5.28 6.18 7.36 9.03 11.5 15.7 24.0 49.0
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TABLE 6 - 8 Correction term of equation d = cA + B - K as a percentage of the first
---two terms q
x
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6.3 GUIDING PRINCIPLES