Yellow change and red clearance intervals on the PE Civil Transportation exam

A change-interval problem on the Transportation exam asks how long the yellow should be, how long the all-red after it should be, or both, for a given approach speed, grade and intersection width. Both relations are in the Handbook. Its Signal Design section has an Interval Timing subsection with the ITE yellow change and red clearance formulas. The Green Book doesn't carry them. The MUTCD (Part 4) supplies the rules: durations set by engineering practices, within guidance limits.

What you actually need to own

• The yellow change interval. Y = t + v/(2a + 2Gg). t is the reaction time and a is the deceleration rate. The Handbook says to use 1 s and 10 ft/s² when the problem doesn't give values. v is the design speed in ft/s, g is gravity, and G is the grade of the approach.
• The grade term. G goes in as a decimal and is negative on a downgrade. A downgrade makes the effective deceleration smaller, so the yellow gets longer. In one practice problem, a 45-mph approach falling at 6% needs about 5.1 s. Take the same approach as level and you get about 4.3 s.
• The red clearance interval. R = (w + L)/v. w is the distance from the near-side stop line to the far-side point of clearance, and L is the vehicle length, 20 ft when the problem doesn't give one. v is the design speed in ft/s again. The Handbook describes this as an optional interval: the approach is red and no conflicting traffic is moving yet.
• The units. mph × 1.467 = ft/s. Convert before you divide.
• The MUTCD limits. Part 4 requires the yellow and the red clearance (when one is used) to be set by engineering practices. MUTCD guidance keeps the yellow between 3 s and 6 s, with the longer intervals on higher-speed approaches. It caps the red clearance at 6 s, except for a one-lane, two-way facility or an exceptionally wide intersection.
• The dilemma zone, right beside it. The same Handbook section defines the dilemma zone as the gap between the minimum safe stopping distance, X_c = 1.47V·t_stop + 1.075V²/a₂, and the maximum yellow passing distance, X₀ = 1.47V·Y − W + ½a₁(Y − t_passing)². When X_c > X₀ there is a stretch where a driver can neither stop nor clear. These two relations carry the 1.47 factor themselves, so V goes in mph.

Where people lose points

• Netting the grades. Only the approach grade enters, because it's the grade the stopping driver is on. A climb on the far side of the intersection doesn't count.
• Flipping the sign. A downgrade entered as +0.06 adds to the deceleration and gives a yellow that's too short.
• Adding a reaction time to the all-red. The red clearance has no t and no deceleration term. In one practice problem that mistake turns about 1.4 s into 2.4 s.
• Converting the wrong way. 25 mph ÷ 1.467 is not a speed in ft/s. Dividing by it makes the interval more than twice as long.
• Computing the wrong interval. The yellow formula worked on a red-clearance stem gives a convincing wrong answer.
• Mixing unit conventions between neighbours. The ITE yellow and red formulas take v in ft/s. The dilemma-zone relations take V in mph. For X₀, W is the intersection width plus the vehicle length, and the acceleration term squares (Y − t_passing), not the whole Y.

A note on standards

The exam supplies the 2009 MUTCD through March 2027 and the MUTCD 11th edition from April 2027. Take the guidance limits from the edition you'll be given. See the April 2027 change.

How to study it

Take one approach and time it at 30, 45 and 55 mph, each level, on a 4% upgrade and on a 4% downgrade. Then compute the red clearance for a narrow and a wide intersection. Write v in ft/s before every substitution. Then use the same speeds to compute X_c and X₀, in mph, and find where a dilemma zone opens up. Whether the signal belongs there at all is a signal warrant question.

Part of the Traffic Signals area of the PE Civil Transportation exam. → Start practicing free — the whole practice bank, free with an account.