The following are the suppositions used to determine the values of d1, d2, and d3 (m):

• Until there is a chance for a safe overtaking operation, the overtaking vehicle A is compelled to slow down from its design speed of v (m/sec) to Vb (m/sec) of the slow vehicle B and move behind it, leaving a spacing of s (m).
• The vehicle A goes at a speed of vb (m/sec) via a distance of d1 from position A1 to A2 when the driver of vehicle A detects a sufficient clear gap ahead and decides within a response time t (sec) to accelerate and pass the vehicle B.
• In the time T (sec) between positions A2 and A3, the vehicle A accelerates and passes the slower vehicle B within a distance d2. The distance d2 is divided into three pieces.

• The distance travelled by the slow vehicle B between B1 and B2 during the overtaking manoeuvre of A;
•  The spacing, s (m), between A2 and B1 The vehicle C approaching from the opposite direction moves over a distance of d3 from position C1 to C2 during this overtaking period T (sec).
• Spacing (m) between B2 and A3.

Determination of the components of OSD

• From point A1 to A2, the distance, d1, travelled by vehicle A after passing it at a slower speed, vb, during the reaction time, t, is equal to vb t. (m). The IRC advises that as the driver’s primary goal is to locate an opportunity to overtake, the reaction time t may be considered as an average value of 2.0 sec. As a result, d1 = 2vb.
• In position A3, ahead of B, vehicle A accelerates from position A2, moves to the next lane, passes vehicle B, and then returns to its original lane during the overtaking time, T. (sec). The straight line between positions A2 and A3 is calculated as d2 (m), which is then divided into three components, d2 = (s + b + s).
• The minimal separation s (m) between the two vehicles while driving at the speed vb (m/sec) may be determined as the minimum distance between positions A2 and B1. The empirical formula s = (0.7 vb + 6) determines the minimal distance between vehicles in relation to their speed.
• The time T now depends on the speed of the overtaking vehicle B and its average acceleration (m/sec2), a. By applying the basic formula for the distance travelled by a uniformly accelerating body with beginning speed vb m/sec and an is the average acceleration during overtaking in m/sec2, d2 = (vb T + 2s), it is possible to compute the overtaking time T (sec).
• When vehicle A is being overtaken, or during time T (sec), the distance travelled by vehicle C driving at design speed v (m/sec) equals the distance d2 (m) between positions C1 and C2.Thus, d3 = v T. (m)In units of m/sec.

OSD = (d1 + d2 + d3) = (vb t + vb T + 2s + vT)

Here, vb = initial speed of overtaking vehicle, m/s

t = reaction time of driver = 2 sec

V = speed of overtaking vehicle or design speed, kmph

T = √4s/A

s = spacing of vehicles = (0.7 vb + 6)

a= average acceleration during overtaking, m/sec.

In kmph units

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Over Taking Requirement and Factors governing the distance:

Theoretically, there shouldn’t need to be any overtaking if every vehicle travels down a road at the intended pace. Each driver is free to travel at lesser speeds, therefore all vehicles actually don’t move at the planned speed. This is especially true when there is mixed traffic. Fast moving traffic must be passed or overtaken in order to proceed. The Minimum Overtaking Sight Distance (OSD) or Safe Passing Sight Distance is the shortest distance that the driver of a vehicle must see in order to safely pass a slow-moving vehicle in front of them.

The OSD is the distance measured along the centre line of the road which a driver with his eye level at 1.2m above the road surface can see the top of an object 1.2m above the road surface.

Factors Affecting OSD:

• The velocities of the vehicles being passed, being passed, and the vehicles coming from the opposite direction
• The distance between vehicles that are being passed and those that are being overtaken; the minimum distance depends on the speeds Road gradient, overtaking vehicle’s rate of acceleration, and the driver’s skill and reaction time.

Analysis of OSD on a Two – Way Road:

Simple overtaking process on a 2 – lane highway with 2 – way traffic movement

Vehicle A wants to pass another slow-moving vehicle B going at a speed of vb m/sec or Vb kmph while travelling at its design speed of v m/sec or V kmph. Before oncoming vehicle C approaches the overtaking stretch, vehicle A must speed, change to the adjacent right-side lane, complete the overtaking manoeuvre, and then return to the left lane.

The overtaking manoeuvre may be split up into 3 operations, thus dividing OSD into 3 parts d1, d2and d3.

• d1 is the distance (m) travelled by the overtaking vehicle A during the reaction time, t (secs) of the driver from position A1 to A2 before starting to overtake the slow vehicle B
• d2 is the distance travelled (m) travelled by the vehicle A during the actual overtaking operation during T (secs) from position A2 to A3
• d3 is the distance (m) travelled by oncoming vehicle C during the actual overtaking operation of A during T (secs) from position C1 to C2. Thus, on a 2-lane road with 2-way traffic the OSD = d1 + d2 + d3 in meters

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