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How to Calculate Saturation Flow Rate
Saturation flow rate is a fundamental concept in traffic engineering, specifically within the analysis of signalized intersections. It represents the maximum rate of flow of vehicles that can pass through an intersection approach during a single hour of continuous green signal time. Essentially, it answers the question: "If the light stayed green for an hour and there was an endless queue of cars, how many would get through?"
While the theoretical base saturation flow rate is often cited as 1,900 passenger cars per hour per lane (pc/h/ln), real-world conditions rarely match ideal scenarios. Engineers must apply adjustment factors to account for lane width, heavy vehicles, road grades, parking maneuvers, and bus blockages.
The Saturation Flow Formula
According to the Highway Capacity Manual (HCM), the formula to calculate the adjusted saturation flow rate ($S$) is:
S = S₀ × N × f_w × f_HV × f_g × f_p × …
Where:
- S₀ (Base Rate): Typically 1,900 pc/h/ln.
- N: Number of lanes in the group.
- f_w (Lane Width Factor): Adjusts for lanes narrower than 12 ft.
- f_HV (Heavy Vehicle Factor): Accounts for the slower acceleration and larger size of trucks/buses.
- f_g (Grade Factor): Accounts for the effect of gravity on acceleration (uphill vs. downhill).
- f_p (Parking Factor): Accounts for friction caused by vehicles parking or unparking.
Key Adjustment Factors Explained
Lane Width ($f_w$)
The standard lane width is 12 feet. If lanes are narrower, drivers tend to be more cautious and maintain larger headways, reducing the flow rate. The adjustment factor is calculated as:
f_w = 1 + (W – 12) / 30 (where W is lane width in feet).
Heavy Vehicles ($f_{HV}$)
Heavy vehicles (trucks, buses, RVs) take up more space and accelerate slower than passenger cars. We convert them into "Passenger Car Equivalents" (PCE). Typically, one heavy vehicle is equivalent to 2.0 passenger cars ($E_T = 2.0$).
f_HV = 100 / (100 + %HV(E_T – 1))
Road Grade ($f_g$)
The slope of the road significantly impacts how quickly vehicles can clear the intersection. Uphill grades (positive %) reduce flow, while downhill grades (negative %) may slightly increase it. The standard adjustment for uphill grades is:
f_g = 1 – (%Grade / 200)
Why is this Calculation Important?
Accurate saturation flow rate calculations are critical for:
- Signal Timing: Determining the correct green time splits for different movements.
- Capacity Analysis: Evaluating if an intersection can handle projected traffic volumes.
- Level of Service (LOS): Assessing the delay and congestion drivers will experience.
Example Calculation
Consider a single lane approach ($N=1$) with the following characteristics:
- Lane Width: 10 ft (Narrow)
- Heavy Vehicles: 5%
- Grade: 2% Uphill
- Base Rate: 1,900 pc/h/ln
Step 1: Width Adjustment ($f_w$)
$1 + (10 – 12) / 30 = 1 – 0.067 = 0.933$
Step 2: Heavy Vehicle Adjustment ($f_{HV}$)
$100 / (100 + 5(2 – 1)) = 100 / 105 = 0.952$
Step 3: Grade Adjustment ($f_g$)
$1 – (2 / 200) = 1 – 0.01 = 0.99$
Final Calculation ($S$)
$S = 1900 \times 1 \times 0.933 \times 0.952 \times 0.99 = \textbf{1,671 pc/h/g}$
This means the effective capacity of this lane is roughly 12% lower than the ideal standard due to the geometric and traffic conditions.
function calculateFlowRate() {
// Get inputs
var s0 = parseFloat(document.getElementById('baseSaturation').value);
var N = parseFloat(document.getElementById('numLanes').value);
var W = parseFloat(document.getElementById('laneWidth').value);
var HV = parseFloat(document.getElementById('heavyVehicles').value);
var G = parseFloat(document.getElementById('roadGrade').value);
var Nm = parseFloat(document.getElementById('parking').value);
// Validation
if (isNaN(s0) || isNaN(N) || isNaN(W) || isNaN(HV) || isNaN(G) || isNaN(Nm)) {
alert("Please enter valid numbers for all fields.");
return;
}
// 1. Lane Width Adjustment Factor (fw)
// Formula: fw = 1 + (W – 12) / 30
// HCM usually suggests W >= 8ft.
var fw = 1 + (W – 12) / 30;
if (fw 0, calculate reduction. If 0, factor is 1.0 (or close to it based on lanes)
// Standard Formula: fp = [N – 0.1 – (18 * Nm)/3600] / N
// This formula is complex because it depends on number of lanes N.
// If Nm is 0, fp is usually 1.0. Let's implement the specific formula.
var fp = 1.0;
if (Nm > 0) {
fp = (N – 0.1 – (18 * Nm) / 3600) / N;
if (fp < 0.05) fp = 0.05; // Prevent negative or zero flow
}
// Calculate Final Flow Rate (S)
// S = S0 * N * fw * fHV * fg * fp
var S = s0 * N * fw * fHV * fg * fp;
// Rounding
S = Math.round(S);
// Display Results
document.getElementById('resultOutput').style.display = 'block';
document.getElementById('finalFlowRate').innerText = S.toLocaleString() + " pc/h/g";
// Show breakdown
var detailsHtml = "
";
detailsHtml += "Width Factor ($f_w$): " + fw.toFixed(3) + "";
detailsHtml += "HV Factor ($f_{HV}$): " + fHV.toFixed(3) + "";
detailsHtml += "Grade Factor ($f_g$): " + fg.toFixed(3) + "";
if (Nm > 0) {
detailsHtml += "Parking Factor ($f_p$): " + fp.toFixed(3) + "";
}
document.getElementById('adjustmentFactors').innerHTML = detailsHtml;
}