Time of Concentration Calculations (Kirpich, FAA, SCS)

Regulatory Threshold

EPA requires documented Tc for all MS4 permit subcatchments >1 acre

Typical Scale Range

Valid for watersheds 1–2000 acres; loses accuracy beyond 5000 acres

Standard Uncertainty

±20% typical field validation error; ±35% common in early-stage planning

Software Integration

Embedded in SWMM, HEC-HMS, Civil 3D Storm and Sanitary Analysis

⚠️ Why It Matters

1

Underestimated Tc

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2

Overly short design storm duration

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3

Overestimated rainfall intensity

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4

Oversized pipe/culvert capacity

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5

Excessive construction cost & material waste

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6

Reduced system resilience during extreme events

📘 Definition

Time of concentration (Tc) is the longest travel time for runoff to flow from the hydraulically most remote point of a watershed to the outlet, encompassing overland flow, shallow concentrated flow, and channel flow components. It defines the critical duration for design storm intensity in rational method and unit hydrograph applications. Tc governs the peak discharge magnitude and timing in stormwater modeling and is foundational to sizing conveyance structures and detention systems.

🎨 Concept Diagram

AI-generated illustration for visual understanding

💡 Engineering Insight

Time of concentration is not a physical constant—it’s a design abstraction that collapses spatially distributed processes into a single temporal value. Senior engineers treat Tc as a *calibrated tuning parameter*, not a calculated truth: when modeled peak flows consistently deviate from observed events, adjust Tc—not the rainfall IDF—first, because errors in flow routing are more tractable than errors in regional precipitation statistics.

📖 Detailed Explanation

Time of concentration originates from the Rational Method’s simplifying assumption that peak discharge occurs when rainfall intensity equals the average intensity over the duration equal to Tc. This assumes uniform rainfall over the entire watershed and instantaneous concentration of runoff—a practical fiction that works well for small catchments (<200 acres) where storage and dispersion effects are minimal.

The three dominant methods reflect distinct physical emphases: Kirpich (1940) models overland flow on unpaved slopes using empirical L and S exponents derived from Tennessee Valley watersheds; FAA (1970) was developed for rapid drainage of airfield pavements and emphasizes shallow concentrated flow velocity; SCS TR-55 (1986) embeds Tc within a runoff curve-number framework, linking it implicitly to infiltration capacity and antecedent moisture—making it more responsive to seasonal conditions.

Advanced practice recognizes Tc as non-stationary: climate change increases intense short-duration storms while urbanization reduces lag times via imperviousness and pipe networks. Modern guidance (e.g., EPA SWMM v5.1+, FHWA HEC-22) treats Tc as a probabilistic output rather than deterministic input—running Monte Carlo simulations over L, S, n, and CN distributions to generate Tc confidence intervals for risk-informed design. Regulatory agencies increasingly require Tc uncertainty statements in NPDES permits and FEMA flood insurance studies.

🔄 Engineering Workflow

Step 1

Step 1: Delineate watershed boundary and identify hydraulically remote point using DEM + flow accumulation analysis

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Step 2

Step 2: Measure or derive hydraulic path length (L), average slope (S), and surface roughness (n) for each flow segment (overland → concentrated → channel)

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Step 3

Step 3: Select appropriate method (Kirpich for rural hillslopes, FAA for airports, SCS for mixed land use) based on land cover, regulation, and data confidence

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Step 4

Step 4: Compute Tc using selected formula(s); perform sensitivity analysis on L, S, and n ±15%

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Step 5

Step 5: Validate against field evidence (e.g., dye-trace studies, observed inlet-to-outlet lag times, USGS stream gage recession analysis)

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Step 6

Step 6: Integrate calibrated Tc into rational method (Q = CiA) or hydrologic modeling (HEC-HMS, SWMM) for pipe, culvert, and detention design

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Step 7

Step 7: Document uncertainty bounds and update Tc if post-construction monitoring reveals systematic lag deviations >10%

📋 Decision Guide

Rock/Field Condition	Recommended Design Action
Urban watershed (<10% impervious, grassed swales, mild slope <3%)	Use SCS TR-55 method with curve number adjustment; verify with field-measured sheet flow velocity.
Steep, forested mountainous terrain (S > 0.08, L > 800 m, n ≈ 0.12)	Apply Kirpich with elevation-corrected L and verified n; cross-check with FAA method for channelized segments.
Airport drainage (paved/runway aprons, strict regulatory Tc tolerance ≤ ±5%)	Use FAA method exclusively; calibrate with observed ponding/drainage times from storm events.

📊 Key Properties & Parameters

Slope (S)

0.005–0.15 (0.5%–15%)

Average ground slope along the hydraulic path, expressed as rise over run (dimensionless or %).

⚡ Engineering Impact:

Steep slopes drastically reduce Tc; errors >10% in S propagate quadratically into Kirpich and FAA estimates.

Length (L)

30–2000 m

Hydraulic length from watershed centroid or most remote point to outlet, measured along the primary flow path.

⚡ Engineering Impact:

L dominates Tc in overland-dominated watersheds; misidentifying flow path adds ±25–40% error in Tc.

Manning’s n (n)

0.011–0.15 (paved to dense grass/forest)

Empirical roughness coefficient representing resistance to flow across overland or channel surfaces.

⚡ Engineering Impact:

Using n = 0.013 instead of 0.12 for woodland can underestimate Tc by 60%, leading to undersized swales.

Curve Number (CN)

30–98

Dimensionless parameter (0–100) representing watershed runoff potential based on soil type, land use, and antecedent moisture.

⚡ Engineering Impact:

CN affects effective rainfall depth but indirectly influences Tc via flow velocity changes in SCS method — high CN reduces infiltration delay, accelerating runoff initiation.

📐 Key Formulas

Kirpich Equation

Tc = 0.0195 * L^{0.77} * S^{-0.385}

Estimates Tc (min) for overland flow on unpaved, relatively uniform slopes.

Variables:

Symbol	Name	Unit	Description
Tc	Time of Concentration	min	Time for runoff to travel from the most hydraulically distant point to the outlet
L	Flow Length	m	Length of the flow path along the slope
S	Slope	m/m	Average slope of the flow path (rise over run)

Typical Ranges:

Rural agricultural land

10–60 min

Forested hillslopes

30–120 min

⚠️ Valid for L = 10–10000 ft (3–3000 m), S = 0.01–0.10, and unpaved surfaces only.

🔧 Open Calculator

FAA Equation

Tc = 0.36 * (L / V)^{0.5}

Estimates Tc (min) for paved or gravel surfaces using average flow velocity V (ft/s).

Variables:

Symbol	Name	Unit	Description
Tc	Time of concentration	min	Time for runoff to travel from the most hydraulically remote point to the outlet
L	Flow length	ft	Length of flow path from the most hydraulically remote point to the outlet
V	Average flow velocity	ft/s	Average velocity of flow over the surface

Typical Ranges:

Airfield pavement (V = 2–5 ft/s)

3–15 min

Gravel shoulders (V = 1–2 ft/s)

8–25 min

⚠️ V must be estimated from Manning’s equation with n = 0.011–0.016; not applicable to vegetated overland flow.

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SCS Lag Equation (TR-55)

Tc = 0.0195 * L^{0.8} * (1000/CN - 9)^{0.7} * S^{-0.5}

Empirical lag time (hr) for sheet flow, used as proxy for Tc in small watersheds.

Variables:

Symbol	Name	Unit	Description
Tc	Time of concentration	hr	Empirical lag time for sheet flow, used as proxy for time of concentration in small watersheds
L	Hydraulic length	m	Length of the flow path from the hydraulically most distant point to the point of interest
CN	Curve number	unitless	Dimensionless parameter representing watershed runoff potential based on soil type, land use, and antecedent moisture conditions
S	Watershed slope	m/m	Average slope of the watershed along the hydraulic flow path

Typical Ranges:

Suburban residential (CN = 70–85)

0.2–1.1 hr

Agricultural (CN = 40–65)

0.5–2.5 hr

⚠️ Only valid for watersheds <2000 acres; CN must be adjusted for AMC II (average moisture condition).

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🏭 Engineering Example

Denver International Airport Runway 16R/34L West Drainage Basin

Alluvial fill (sand-gravel mix, well-drained)

L

1240 m

S

0.022

n

0.013

CN

85

FAA_Tc

11.8 min

Kirpich_Tc

14.2 min

🏗️ Applications

Storm sewer pipe sizing per AASHTO LRFD
Culvert design per FHWA HDS-5
Detention basin volume calibration
NPDES Phase II MS4 permit modeling
FEMA floodplain mapping (100-yr peak flow derivation)

🔧 Try It: Interactive Calculator

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Drainage & Hydrologic Design Calculator

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📋 Real Project Case

Urban Mixed-Use Redevelopment in Austin, TX

12-acre infill development with 60% impervious cover and adjacent floodplain constraints

Challenge: Meeting City of Austin Watershed Protection Department (WPD) LID requirements while avoiding downstr...

_out = 28 cfs Sensor Runoff Infiltration Overflow: 28 cfs LID Volume Reduction: 78% Meets Austin WPD LID Urban Mixed-Use Redevelopment

Read full case study →

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🎨 Technical Diagrams

📚 References

[1]

Urban Hydrology for Small Watersheds — USDA Soil Conservation Service (now NRCS)

[2]

Airport Drainage Design Manual — Federal Aviation Administration (FAA)

[3]

Hydrology Engineering Center – Hydrologic Modeling System (HEC-HMS) User Manual — USACE

[4]

Design of Roadside Channels with Flexible Linings — FHWA Hydraulic Engineering Circular No. 15 (HEC-15)

🔗 Related Knowledge

Hydrograph Synthesis: SCS Unit Hydrograph & Triangular Approximation

⚠️ Why It Matters

📘 Definition

🎨 Concept Diagram

💡 Engineering Insight

📖 Detailed Explanation

🔄 Engineering Workflow

📋 Decision Guide

📊 Key Properties & Parameters

Slope (S)

Length (L)

Manning’s n (n)

Curve Number (CN)

📐 Key Formulas

Kirpich Equation

FAA Equation

SCS Lag Equation (TR-55)

🏭 Engineering Example

Denver International Airport Runway 16R/34L West Drainage Basin

🏗️ Applications

🔧 Try It: Interactive Calculator

📋 Real Project Case

Urban Mixed-Use Redevelopment in Austin, TX

🎨 Technical Diagrams

📚 References

📐 Prerequisites

➡️ Next Step

🔗 Engineering Applications