14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)

14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)

PTOE Exam Focus: Traffic volume studies and expansion factoring are among the most heavily tested quantitative topics in Domain 5. Candidates must master the calculation of AADT from short-term sample counts using monthly ($M_i$), daily ($D_i$), and axle ($A_i$) adjustment factors, compute Design Hour Volume (DHV) and Directional Design Hour Volume (DDHV) using $K$ and $D$ factors, and compute the Peak Hour Factor ($\text{PHF} = \frac{V}{4 \cdot V_{15,\max}}$) to convert hourly volumes into peak 15-minute flow rates for HCM capacity analysis.

---

1. Traffic Volume Counting Methodologies

Traffic volume data provides the fundamental demand input for highway capacity analysis, geometric sizing, pavement design, and signal warrant evaluation. Volume studies utilize three primary counting technologies:

+-----------------------------------------------------------------------------------+
|                     TRAFFIC VOLUME DATA COLLECTION TYPOLOGIES                     |
|                                                                                   |
|  1. Automated Traffic Recorders (ATRs):                                           |
|     • Permanent continuous stations (inductive loops, piezos) operating 365 days. |
|     • Establish statewide seasonal, monthly, and day-of-week expansion factors.   |
|                                                                                   |
|  2. Portable Automatic Counts (Mid-Block):                                        |
|     • Pneumatic road tubes, radar side-fire sensors deployed for 24-48 hours.     |
|     • Measure 24-hr daily volume, speed bins, and vehicle axle classification.   |
|                                                                                   |
|  3. Manual / Video AI Turning Movement Counts (TMCs):                             |
|     • 2-hr to 4-hr intersection counts binned in 15-minute intervals.             |
|     • Tallies passenger cars, heavy vehicles, buses, bicycles, and pedestrians.   |
+-----------------------------------------------------------------------------------+

---

2. Daily Volume Definitions: ADT vs. AADT

Traffic volume exhibits significant temporal variations by hour of the day, day of the week, and month of the year. Engineering standards define two distinct daily volume metrics:

1. Average Daily Traffic (ADT)

The total volume of traffic passing a point or segment over a specified observation period of greater than 1 day and less than 1 year (typically $24\text{ to }72\text{ hours}$), divided by the number of days in that period:

$\text{ADT} = \frac{\text{Total Sample Volume}}{\text{Number of Sampling Days } (Q)} \quad (1 < Q < 365)$

2. Annual Average Daily Traffic (AADT)

The total vehicular volume passing a point or roadway segment over an entire year (365 days), divided by 365:

$\text{AADT} = \frac{\text{Total Annual Traffic Volume}}{365}$

Key Distinction: ADT is a localized sample measurement subject to seasonal and day-of-week bias, whereas AADT represents the unbiased annualized daily average used for state highway planning, HPMS reporting, crash rate calculations, and pavement structural design.

---

3. Expansion Factoring Methodology (Short-Term to AADT)

Because permanent ATR counters can only be maintained at a limited number of regional control stations, the vast majority of roadway counts are short-term counts ($24\text{ to }48\text{ hours}$) collected via pneumatic road tubes on mid-week days (Tuesday, Wednesday, Thursday). These short counts are expanded to AADT using adjustment factors derived from nearby ATR stations on functionally similar highways.

  +------------------------+
  | Raw 24-hr Tube Count   |
  | (Total Axle Strikes)   |
  +-----------+------------+
              |
              v   x Axle Correction Factor (A_i = 2 / Avg Axles)
  +-----------+------------+
  | Total Vehicles (24-hr) |
  +-----------+------------+
              |
              v   x Daily Adjustment Factor (D_i = ADT_week / Vol_day)
  +-----------+------------+
  | Weekly Adjusted Volume |
  +-----------+------------+
              |
              v   x Monthly Adjustment Factor (M_i = AADT / ADT_month)
  +-----------+------------+
  | Estimated AADT         |
  +------------------------+

1. Monthly Expansion Factor ($M_i$)

Adjusts for seasonal and monthly fluctuations:

$M_i = \frac{\text{AADT}}{\text{ADT}_{\text{month } i}}$

• In peak summer travel months (where $\text{ADT}{\text{July}} > \text{AADT}$), $M{\text{July}} < 1.0$.
• In low winter travel months (where $\text{ADT}{\text{Jan}} < \text{AADT}$), $M{\text{Jan}} > 1.0$.

2. Daily Expansion Factor ($D_i$)

Adjusts for day-of-the-week fluctuations:

$D_i = \frac{\text{Average Weekday Daily Traffic (AWDT)}}{\text{Volume on Specific Day } i}$

3. Axle Correction Factor ($A_i$)

Pneumatic road tubes record one count for every two axle strikes (1 pulse = 2 axles). Because multi-axle commercial trucks (3-axle, 4-axle, 5-axle semi-trailers) register multiple pulses for a single vehicle, raw tube counts overestimate vehicle volumes. The axle correction factor compensates for this stream composition:

$A_i = \frac{\text{Actual Vehicles}}{\text{Recorded Pulses}} = \frac{2}{\bar{n}_{\text{axles}}}$

Where $\bar{n}_{\text{axles}}$ is the weighted average number of axles per vehicle in the traffic stream.

Master AADT Expansion Equation:

$\text{AADT} = \text{Vol}_{\text{raw 24hr}} \times A_i \times D_i \times M_i$

---

4. Design Hour Volume (DHV) & The $K$-Factor

Designing a highway to accommodate the single highest hourly volume of the year is economically wasteful, as that capacity would sit idle for $8,759\text{ hours}$. Conversely, designing for the average hourly volume would result in severe oversaturation and gridlock during daily commute hours.

The 30th Highest Hourly Volume ($30\text{HV}$)

Standard engineering practice establishes the Design Hour Volume (DHV) as the 30th highest hourly volume of the year ($30\text{HV}$). On a curve of hourly volumes ranked from highest to lowest (1 to 8760), the slope transitions from very steep to relatively flat near the 30th hour, providing the optimal economic balance between construction capital and operational congestion.

The $K$-Factor Formulation

The $K$-factor is the ratio of the Design Hour Volume to the Annual Average Daily Traffic:

$K = \frac{\text{DHV}}{\text{AADT}} = \frac{30\text{HV}}{\text{AADT}} \implies \text{DHV} = \text{AADT} \times K$

Typical $K$-Factor Ranges:

• Urban Arterials / Freeways: $K = 0.08\text{ to }0.12$ ($8%\text{ to }12%$). Urban corridors experience peak spreading and constrained capacity, leading to lower $K$-values.
• Rural / Recreational Highways: $K = 0.12\text{ to }0.18+$ ($12%\text{ to }18%$). Rural and tourist routes experience sharp, highly concentrated weekend and seasonal peaks.

---

5. Directional Distribution ($D$-Factor) & DDHV

Traffic during peak hours is rarely distributed equally between travel directions. The Directional Distribution Factor ($D$) represents the proportion of total peak hour bidirectional traffic traveling in the dominant (peak) direction:

$D = \frac{V_{\text{peak-direction}}}{\text{DHV}}$

Directional Design Hour Volume (DDHV)

To determine the required number of travel lanes for a specific approach or direction, highway capacity analyses use the Directional Design Hour Volume (DDHV):

$\text{DDHV} = \text{AADT} \times K \times D$

Typical $D$-Factor Ranges:

• Radial Suburban Commuter Corridors: $D = 0.60\text{ to }0.70$ ($60%\text{ to }70%$ inbound AM / outbound PM).
• Urban Downtown Grid / Circumferential Belts: $D = 0.50\text{ to }0.55$ (balanced two-way demand).

---

6. Peak Hour Factor (PHF) & Sub-Hourly Flow Rates

Within the peak hour, vehicle arrivals are not uniformly distributed. Flow surges occurring within localized $15\text{-minute}$ intervals can cause temporary breakdown even if the total hourly volume is within nominal capacity.

Mathematical Formulation

The Peak Hour Factor (PHF) quantifies the relationship between total hourly volume and the maximum flow rate within that hour:

$\text{PHF} = \frac{V}{4 \times V_{15,\max}}$

Where:

• $V$ = Total hourly volume (vehicles per hour, veh/h)
• $V_{15,\max}$ = Maximum volume recorded during any single $15\text{-minute}$ interval within the peak hour
• $4$ = Number of $15\text{-minute}$ periods in one hour

Peak 15-Minute Equivalent Flow Rate ($v$)

In Highway Capacity Manual (HCM) analyses, all demand volumes are converted to equivalent peak $15\text{-minute}$ hourly flow rates ($v$):

$v = \frac{V}{\text{PHF}} = 4 \times V_{15,\max}$

Key PHF Properties:

• Range: $0.25 \le \text{PHF} \le 1.00$
  • $\text{PHF} = 1.00$: Perfectly uniform flow ($V_{15}$ is identical in all four quarters).
  • $\text{PHF} = 0.25$: Extreme peaking (all hourly volume arrives in a single 15-minute window).
• Typical Field Values:
  • Dense urban networks / congested freeways: $\text{PHF} = 0.92\text{ to }0.98$
  • Suburban arterials: $\text{PHF} = 0.85\text{ to }0.92$
  • Rural or low-volume roads: $\text{PHF} = 0.70\text{ to }0.85$

Traffic Volume Factoring Parameters & Typical Design Ranges

7. Worked Calculation Examples

Example 1: Full AADT Expansion from 24-Hour Tube Counts

Problem: A 24-hour pneumatic tube count conducted on a Wednesday in April records $22,400\text{ total axle pulses}$ (where 1 pulse = 2 axles). Classification data indicates the average number of axles per vehicle on this corridor is $\bar{n}_{\text{axles}} = 2.15$. The state DOT ATR group factors for this highway classification are:

• Monthly Factor ($M_{\text{April}}$): $1.08$
• Day-of-Week Factor ($D_{\text{Wednesday}}$): $0.96$

Calculate the estimated Annual Average Daily Traffic (AADT).

Step-by-Step Solution:

1. Axle Correction Factor ($A_i$): $A_i = \frac{2}{\bar{n}_{\text{axles}}} = \frac{2}{2.15} = 0.9302$

2. Actual 24-Hour Vehicle Count ($\text{Vol}_{24\text{hr}}$): $\text{Vol}_{24\text{hr}} = 22,400 \times 0.9302 = 20,836.5\text{ vehicles}$

3. Compute AADT using Master Expansion Formula: $\text{AADT} = \text{Vol}_{24\text{hr}} \times D_{\text{Wed}} \times M_{\text{April}}$ $\text{AADT} = 20,836.5 \times 0.96 \times 1.08 = 20,003.04 \times 1.08 = 21,603.3 \approx 21,603\text{ veh/day}$

---

Example 2: DDHV and Peak 15-Minute Flow Rate Calculation

Problem: A planned 4-lane suburban divided highway has an estimated AADT of $32,000\text{ veh/day}$. Traffic engineering studies establish the following design parameters:

• Design Hour Factor: $K = 0.11$
• Directional Split: $D = 0.65$
• Peak Hour Factor: $\text{PHF} = 0.88$

Compute the Directional Design Hour Volume (DDHV) and the peak $15\text{-minute}$ equivalent hourly flow rate ($v$).

Step-by-Step Solution:

1. Compute Directional Design Hour Volume (DDHV): $\text{DDHV} = \text{AADT} \times K \times D$ $\text{DDHV} = 32,000 \times 0.11 \times 0.65 = 3,520 \times 0.65 = 2,288\text{ veh/h}$

2. Compute Peak 15-Minute Equivalent Flow Rate ($v$): $v = \frac{\text{DDHV}}{\text{PHF}} = \frac{2,288\text{ veh/h}}{0.88} = 2,600\text{ veh/h}$

Capacity Implication: If lane capacity is $1,900\text{ veh/h/ln}$, two directional lanes provide $3,800\text{ veh/h}$ capacity, comfortably accommodating the $2,600\text{ veh/h}$ peak flow rate ($v/c = 0.68$, Level of Service C).