Traffic Engineering — Volume, Speed, Density & PCU

1. Traffic Volume — Definitions & Measures

Traffic volume is the number of vehicles passing a given point on a road during a specified time period. It is the most fundamental measure of traffic demand.

1.1 Volume Measures

1.2 Relationship Between AADT and DHV

2. Traffic Speed — Types & Relationships

2.1 Spot Speed

The speed of an individual vehicle at a specific location and instant, measured by radar gun, pneumatic tubes, or video analysis. Used for speed studies, accident analysis, and setting speed limits.

2.2 Running Speed

Distance travelled divided by running time (time while the vehicle is actually moving — stops and delays excluded). Used for level of service analysis.

2.3 Journey Speed (Overall Speed)

Distance divided by total journey time (including all delays — signals, stops, congestion). Used for O-D travel time studies.

2.4 Time Mean Speed (TMS) vs Space Mean Speed (SMS)

2.5 Free Flow Speed (u_f)

The speed vehicles travel when density is very low (near zero) — no vehicle-to-vehicle interaction. It equals the desired speed on the road. Typically 10–20% above the posted speed limit in Indian conditions.

3. Traffic Density

4. Fundamental Flow Equation: q = uk

4.1 Physical Interpretation

If 1000 vehicles occupy 10 km of road (k = 100 vehicles/km) and are moving at 80 km/h (u_s = 80), then in one hour each vehicle travels 80 km past a fixed point — the number of vehicles passing a fixed point in one hour is q = 80 × 100 = 8,000 vehicles/hour. This is exactly the flow past that fixed point.

5. Passenger Car Unit (PCU)

Indian traffic is heterogeneous — a mix of cars, motorcycles, buses, trucks, cycles, and non-motorised vehicles (bullock carts, hand-carts) all sharing the same road space. A Passenger Car Unit (PCU) converts each vehicle type to an equivalent number of passenger cars for capacity analysis purposes.

5.1 PCU Definition

5.2 PCU Values (IRC:64 and IRC:106)

6. Road Capacity — IRC:64

Road capacity is the maximum sustainable hourly traffic flow rate that can be accommodated by a road section under prevailing roadway, traffic, and control conditions.

6.1 Capacity Values (IRC:64 — PCU/hour)

6.2 Level of Service (LOS)

Level of Service classifies traffic operation from A (best) to F (worst) based on the volume-to-capacity (v/c) ratio and resulting conditions:

Design standard: roads are typically designed for LOS C (v/c ≤ 0.77) or D for urban roads.

7. Traffic Surveys

7.1 Types of Traffic Counts

7.2 Moving Observer Method

8. Spot Speed Study & 85th Percentile Speed

A spot speed study measures the speeds of individual vehicles at a specific location under free-flow conditions. Results are used to:

• Set posted speed limits (85th percentile speed rule)
• Identify accident-prone spots with abnormal speed patterns
• Evaluate geometric design adequacy
• Set signal timings for pedestrian crossings

8.1 Speed Data Analysis

8.2 Practical Speed Measurement Methods

• Radar gun (LIDAR gun): Most common; measures instantaneous speed of individual vehicles.
• Pneumatic tubes: Laid across road; records axle impacts with time stamps; speed = distance/time between tubes.
• Enoscope / stop-watch method: Observer measures time for vehicle to travel a measured base length.
• Video analysis: Vehicles tracked frame-by-frame; accurate but time-consuming.

9. Traffic Signals — Webster’s Method

9.1 Signal Terminology

9.2 Webster’s Optimal Cycle Length Formula

9.3 Green Time Allocation

9.4 Saturation Flow Rate

Saturation flow S is the maximum rate at which vehicles discharge from a stop line during the green phase under ideal conditions. IRC:106 values:

• Straight through: S = 1800 PCU/hour/lane (single lane)
• Right turn (protected): S = 1500 PCU/hour/lane
• Left turn: S = 1700 PCU/hour/lane

10. Worked Examples (GATE CE Level)

Example 1 — Time Mean Speed vs Space Mean Speed (GATE CE 2022 type)

Problem: Five vehicles are observed on a 1 km road section. Their speeds are 60, 80, 40, 100, and 50 km/h. Calculate (a) the time mean speed and (b) the space mean speed.

Answer: TMS = 66.0 km/h; SMS = 59.4 km/h. TMS > SMS as expected.

Example 2 — Fundamental Flow Equation: q = uk (GATE CE 2021 type)

Problem: A road carries traffic at a density of 40 vehicles/km and a space mean speed of 75 km/h. Find (a) the flow rate and (b) the average headway and spacing.

Answer: q = 3000 vehicles/hour; spacing = 25 m; headway = 1.2 seconds

Example 3 — PCU Conversion and Volume in PCU (GATE CE type)

Problem: A traffic count over one hour on a two-lane highway records: 800 passenger cars, 200 buses/trucks (PCU = 2.2), 400 two-wheelers (PCU = 0.5), and 100 cycle rickshaws (PCU = 2.0). Find the total flow in PCU/hour and determine the LOS if road capacity is 1500 PCU/hour.

Answer: Q = 1640 PCU/hour; v/c = 1.09 → LOS F (over capacity)

Example 4 — Webster’s Optimal Cycle Length (GATE CE 2020 type)

Problem: A two-phase signalised intersection has the following data: Phase 1 — critical flow 600 PCU/hour, saturation flow 1800 PCU/hour; Phase 2 — critical flow 400 PCU/hour, saturation flow 1800 PCU/hour. Lost time per phase = 2 s. Find (a) the optimal cycle length, (b) the effective green time for each phase.

Answer: C₀ = 25 s; g₁ = 13 s (Phase 1); g₂ = 8 s (Phase 2)

Example 5 — Moving Observer Method (GATE CE type)

Problem: In a moving observer study on a 1 km road section, the test vehicle runs with traffic and records m_a = 15 (vehicles overtaken – vehicles that overtook the test car). Running against traffic, m_w = 80 vehicles are counted. Travel time with traffic t_a = 2 min; against traffic t_w = 1.5 min. Find (a) the flow q, (b) the journey time t̄, and (c) space mean speed u_s.

Answer: q = 1629 vehicles/hour; t̄ = 1.45 min; u_s = 41.5 km/h

Example 6 — Peak Hour Factor and Design Flow (GATE CE type)

Problem: The peak hour volume on an approach to an intersection is 900 PCU/hour. Within the peak hour, the maximum 15-minute volume is 280 PCU. Find (a) the PHF and (b) the design flow rate.

Answer: PHF = 0.804; Design flow rate = 1119 PCU/hour

11. Common Mistakes

Mistake 1 — Using TMS Instead of SMS in the Flow Equation q = uk

Error: Substituting Time Mean Speed (arithmetic average) into q = uk instead of Space Mean Speed (harmonic mean).
Root Cause: TMS is easier to compute (simple average) and is often the first “mean speed” students calculate. But the fundamental equation q = uk is derived from the definition of density and flow — it requires the space mean speed (average speed over a section of road).
Fix: When a GATE problem gives individual vehicle speeds, compute SMS = n/Σ(1/u_i) = harmonic mean, and use that in q = uk. TMS > SMS always — using TMS overestimates the flow for a given density.

Mistake 2 — Using Actual Vehicle Count Instead of PCU Flow for Capacity Comparison

Error: Comparing the actual number of vehicles per hour (e.g., 1500 vehicles/hour) directly against the capacity in PCU (e.g., 1500 PCU/hour), concluding the road is exactly at capacity.
Root Cause: PCU capacity and actual vehicle count are in different units. Indian traffic with buses, trucks, and NMVs has PCU values much larger than 1.0 for many vehicle types, so 1500 actual vehicles can easily exceed 2000 PCU/hour on an Indian road.
Fix: Convert all vehicle counts to PCU first: Q_PCU = Σ(n_i × PCU_i). Then compare Q_PCU against the IRC:64 road capacity (which is in PCU/hour).

Mistake 3 — Forgetting the Lost Time in Webster’s Cycle Length Formula

Error: Writing C₀ = 5/(1–Y) instead of C₀ = (1.5L + 5)/(1–Y), omitting the 1.5L term.
Root Cause: The constant 5 in the numerator is the minimum cycle length when L = 0 (hypothetical); the 1.5L term accounts for lost time. When L is small (2–4 s), 1.5L = 3–6 s and the numerator changes significantly.
Fix: Webster’s formula is C₀ = (1.5L + 5)/(1–Y). Always compute L first: L = number of phases × lost time per phase. For a 2-phase signal with l = 2 s/phase: L = 4 s; C₀ = (1.5 × 4 + 5)/(1–Y) = 11/(1–Y).

Mistake 4 — Confusing ADT with AADT

Error: Treating Average Daily Traffic (ADT) computed from a short count (e.g., 3-day summer survey) as the Annual Average Daily Traffic (AADT).
Root Cause: ADT and AADT are both in vehicles/day but are not the same — ADT from a short count at one season may not represent the annual average. AADT requires either a full year of counts or correction of the short-period ADT using seasonal and day-of-week factors from nearby permanent counting stations.
Fix: AADT requires annual data or correction factors. ADT from a spot count is only a sample. For pavement design and road planning, always use AADT (or confirm the design CVPD is based on AADT projections).

Mistake 5 — Applying the IRC:64 Two-Lane Road Capacity (1500 PCU/hour) per Direction Instead of Both Directions

Error: Using 1500 PCU/hour as the one-directional capacity of a two-lane undivided road, then doubling it to get 3000 PCU/hour total.
Root Cause: IRC:64 specifies 1500 PCU/hour as the total two-way (both directions combined) capacity of a two-lane undivided road. On such a road, vehicles in both directions share the same two lanes — overtaking and passing use the opposing lane, limiting total combined capacity.
Fix: Two-lane undivided: 1500 PCU/hour total (both directions). For divided roads (separate carriageways), the capacity per direction is approximately 2000 PCU/hour (four-lane) — per lane ≈ 1000 PCU/hour.

12. Frequently Asked Questions

Q1. Why is space mean speed always less than or equal to time mean speed?

This follows from a fundamental mathematical inequality: the harmonic mean of any set of positive numbers is always less than or equal to their arithmetic mean (and equals the arithmetic mean only when all values are identical). Space mean speed is the harmonic mean of individual vehicle speeds; time mean speed is the arithmetic mean. The intuitive explanation is that fast vehicles spend less time on a road section (time-based sampling underweights them), while slow vehicles spend more time (overweighting them in a time-based sample). Space-based sampling, by contrast, counts all vehicles present at a given instant — fast and slow alike. A slow truck (say 20 km/h) spends 3 minutes on a 1 km section; a fast car (60 km/h) spends 1 minute. If you count all vehicles at a point over 3 minutes, you see the truck 3 times longer than you see the fast car — biasing the time mean speed upward relative to the true spatial average. This bias matters for traffic flow calculations: the fundamental equation q = uk correctly uses SMS (the unbiased spatial average), not TMS.

Q2. What is the PCU concept’s main limitation, and how does IRC:64 address it?

The main limitation of PCU is that it is not a fixed property of a vehicle type — it varies with traffic speed, road geometry (grade, lane width, curve), traffic composition, and the vehicle’s own performance characteristics (power-to-weight ratio for trucks on grades). A bus on a flat urban road might have PCU = 2.2, but the same bus on a 6% grade in mountainous terrain might have PCU = 5.0 or more because its power-to-weight ratio limits speed significantly, and following vehicles are forced to slow down across a much longer queue. IRC:64 partially addresses this by providing separate PCU tables for plain/rolling terrain and hilly/mountainous terrain (see Section 5.2), but even these two categories cannot capture the full complexity of terrain effects. For critical design decisions (intersection capacity analysis, expressway planning), more sophisticated microsimulation models (VISSIM, CORSIM, SimTraffic) are used where each vehicle type’s individual performance characteristics (acceleration, deceleration, maximum speed, reaction time) are modelled, and the PCU concept is bypassed entirely.

Q3. How is the 85th percentile speed used in practice for Indian highways?

The 85th percentile speed (V₈₅) from a spot speed study represents the speed below which 85% of free-flowing vehicles travel — by convention, it represents the speed that “most” drivers voluntarily choose as safe and reasonable for the road conditions. In Indian highway practice, V₈₅ is used for three key purposes. First, it helps set advisory speed limits: if the posted limit is significantly lower than V₈₅, drivers routinely violate it and the limit lacks credibility. Conversely, if V₈₅ is much higher than the design speed for the geometric elements, the road has a hidden safety deficiency (drivers are travelling faster than the geometry safely permits). Second, V₈₅ is used in road safety audits to identify geometric deficiencies at curves, crests, and intersections where the actual operating speed exceeds the design speed. Third, for new roads, V₈₅ is predicted from design speed and used to check that the geometric design (superelevation, sight distance) is adequate at the operating speed, not just the nominal design speed. IRC recently published guidelines on setting speed limits using V₈₅ as part of the National Road Safety Policy (NRSP) implementation.

Q4. What is the saturation flow rate, and why does it matter for signal design?

Saturation flow rate S is the maximum rate at which vehicles can discharge through a stop line when given a continuous green signal, under prevailing traffic, geometry, and lane conditions — typically 1800 PCU/hour/lane for a straight-through movement on an urban arterial. It represents the capacity of the approach when the signal is always green. The flow ratio y = q/S for a phase represents the fraction of the green time that approach needs to pass all its vehicles — a phase with y = 0.5 needs 50% of the green time. When Y = Σy_i (sum over all critical phases) approaches 1.0, the intersection is operating at theoretical capacity and any additional traffic will cause the intersection to fail (LOS F, with ever-growing queues). Webster’s formula gives the cycle length that minimises average delay for Y < 1.0 — for Y close to 1.0, the optimal cycle approaches infinity (very long cycles are needed to accommodate high flow ratios). In practice, signal designers limit Y ≤ 0.85–0.90 (leaving a 10–15% reserve capacity) and cap cycle lengths at 120 seconds for driver compliance and pedestrian safety.