# ITE Journal - March 2020 - 37

```Therefore, the minimum time to traverse the minimum
stopping distance (by definition, the minimum yellow change
interval, Ymin) for a vehicle that decelerates within the critical
distance to negotiate a turn is given by:
v
(v0 -vE_) _____
+ E
Ymin = tPR+ _____
amax
2amax

(11)

Algebraic simplification of the Järlström's extended kinematic
model shown in Equation 11 yields:
v0 -½v_E
Ymin = tPR+ _____
amax

Where (v0 ≥ vE > 0):
Ymin = Minimum yellow change interval (s)
v0 = Maximum uniform initial/approach velocity, (ft./s or m/s)
vE = Maximum intersection entry velocity, (ft./s or m/s)
tPR= Maximum allocated driver-vehicle perception-reaction time, (s)
amax = Maximum uniform safe and comfortable deceleration, (ft./s2
or m/s2)
Figure 4 illustrates the extended kinematic model compared
to GHM's STOP or GO solutions across the critical distance (xC)
referenced to time.
The validity of Järlström's Extended Kinematic Equation is
established in the following manner:
When vE = v0 (constant velocity), the protocol yields the ITE
Kinematic Equation applicable for through movements (Equation 3).
When vE = 0 (zero end velocity), the protocol yields the equation
to calculate the minimum time to come to a complete stop:

Figure 3. Zones of driver-vehicle motion while decelerating to
negotiate a turn.
Since the length of the Deceleration Zone (xDec) equals the
vehicle's time to traverse the Deceleration Zone (tDec) multiplied by
the vehicle's average velocity (vav):
2
2
(v - v ) v0 - v E
(v0 + v E) _______
* 0 E =_______
xDec = vavtDec = _______
2
amax
2amax

(12)

tStop = tPR+

v
amax

(13)

0	 _
____

(7)

And, from the last term of Equation 1, the braking distance is:
xBr =

2

v
2amax

0
_____

(8)

The length of the Go Zone is:
2
2
2
2
v - v E _______
vE
v0
- _0______
=
xGo = xBr-xDec = ______
2amax
2amax
2amax

(9)

The time to traverse the Go Zone (tgo) equals the length of the
Go Zone (xgo) divided by the vehicle's velocity across this distance
(the driver's target entry velocity (vE)):
vE2
____

xGo _2a
vE
max
___
____
_____
=
(10)
tGo = =
vE
vE
2amax

Figure 4. Time model including vehicle deceleration traversing the
minimum stopping distance.
w w w .i t e.or g

M a rch 2020

37

```
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# ITE Journal - March 2020

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