While passing is not an event that is a major factor in the design of four-lane highways, it is a critical component of two-lane highway design. The capacity of a two-lane roadway is greatly increased if a large percentage of the roadway's length can be used for passing. On the other hand, providing a sufficient passing sight distance over large portions of the roadway can be very expensive.

Simply put, the passing sight distance is the length of roadway that the driver of the passing vehicle must be able to see initially, in order to make a passing maneuver safely.

Our real goal is to provide most drivers with a sight distance that gives them a feeling of safety and that encourages them to pass slower vehicles. 

Calculating the passing sight distance required for a given roadway is best accomplished using a simple model. The model that is normally used incorporates three vehicles, and is based on six assumptions:

1.)  The vehicle being passed travels at a constant speed throughout the passing maneuver. 
2.)  The passing vehicle follows the slow vehicle into the passing section.
3.)  Upon entering the passing section, the passing vehicle requires some time to perceive that the opposing lane is clear and to begin accelerating.
4.)  While in the left lane, the passing vehicle travels at an average speed that is 10 mph faster than the vehicle being passed.
5.)  An opposing vehicle is coming toward the passing vehicle.
6.)  There is an adequate clearance distance between the passing vehicle and the opposing vehicle when the passing vehicle returns to the right lane.

Under these assumptions, the passing sight distance can be divided into four quantifiable portions: 

d1 -- The distance the passing vehicle travels while contemplating the passing maneuver, and while accelerating to the point of encroachment on the left lane.   
d2 -- The length of roadway that is traversed by the passing vehicle while it occupies the left lane.
d3 -- The clearance distance between the passing vehicle and the opposing vehicle when the passing vehicle returns to the right lane.
d4 -- The distance that the opposing vehicle travels during the final 2/3 of the period when the passing vehicle is in the left lane.

d2
The distance traveled during the occupancy of the left lane is also easy to understand. Since the speed of the passing vehicle was assumed to be 10 mph faster than the overtaken vehicle, all we need to know to calculate the distance d2 is the time that the passing vehicle occupies the left lane. Values for this time interval were measured for several different passing vehicle speeds. These measured values were then used to develop design values for d2.  See table 1.0.

d3
The clearance distance might not seem necessary at first, but for now let’s take it on faith that an opposing vehicle is necessary.  If this is the case, a maneuver that feels safe will require that a certain length of roadway is present between the passing vehicle and the opposing vehicle when the passing vehicle returns to the relative safety of the right lane. The clearance distance that drivers require depends on their personality. A timid driver might require several hundred feet of clearance distance, while a more aggressive driver might consider exchanging side mirrors a perfectly acceptable practice. Studies have shown that the clearance distance is normally between 100 and 300 feet.  See table 1.0.

d4
The opposing vehicle encroachment distance is the distance that seems to be the most troubling for students. Let us picture a passing section that is terminated by a sharp reduction in grade, which prevents the passing driver from seeing any vehicles beyond the end of the passing section. Let us also assume that the length of the passing section is equal to the sum of the distances d1 and d2. Our passing vehicle driver could pass the slower vehicle before leaving the passing section, but she might be flirting with destiny in doing so. Her principal problem is that she can't see if there are any opposing vehicles beyond the passing section that might conflict with her during the maneuver. 

The question now is, how much extra sight distance would she need to feel secure that an opposing vehicle would not conflict with her while she is in the left lane? If we assume that she can abort her maneuver if an opposing vehicle appears during the interval t1 or during the first third of the interval t2, we can reduce the sight distance that we need to provide. 

Let’s say that we make the passing section length equal to the passing sight distance as defined in reality (d = d1 + d2 + d3 + d4). If an opposing vehicle appears just after the first third of the interval t2 is over, the passing car can still safely pass the slower car and return to the right lane before the opposing car becomes a threat. This is because the opposing vehicle is a distance 2/3*d2 +d3 + d4 away from the passing vehicle. By the time that the passing vehicle has traveled the remaining 2/3*d2 and returned to the right lane, the opposing car will have traveled d4, and the clearance distance d3 will separate them. This is why we add the distances d3 and d4 to the passing sight distance. The distance d4 is calculated by multiplying the speed of the opposing vehicle (normally assumed to be the speed of the passing vehicle) by 2/3*t2.