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Rational Method for a Commercial Parking Lot — 10-yr Peak Runoff Worked Example

A first-pass drainage design for a strip-mall parking field in central Virginia. The county requires the 10-year peak discharge for inlet and pipe sizing on sites under ~10 acres where hydrograph routing is not mandated. We delineate the lot, build a composite runoff coefficient from land-cover sub-areas, estimate time of concentration with TR-55 sheet flow, pull 10-year intensity from a NOAA Atlas 14–style IDF curve, compute peak Q, and sketch grate-inlet counts. Sources: NRCS TR-55 (1986), Chow Applied Hydrology, FHWA HEC-22 (urban drainage inlet capacity), and NOAA Atlas 14 Volume 8 (Mid-Atlantic) for illustrative IDF values.

The site

A re-striping and re-drainage project for an existing 140-space lot serving a 22,000-sf retail building. Roof downspouts discharge onto the asphalt (not directly to storm drain). Survey and aerials give:

Total drainage area (A)	2.8 ac (to curb-and-gutter system)
Asphalt pavement	2.2 ac (stalls, drives, aisles)
Landscaped islands	0.4 ac (irrigated turf, flat)
Building roof	0.2 ac footprint runoff routed to pavement
Pavement cross slope	2.0% toward aisles
Longest sheet-flow path (L)	210 ft (rear stall row to aisle gutter)
Design storm	10-year, per locality drainage manual
Outlet	Combination curb opening + grate at low end of east aisle

Step 1 · Composite runoff coefficient C

Weighted by sub-area — not a single lot-wide C

From the runoff coefficient reference (Chow / typical municipal tables):

Asphalt (dense, 2% slope) ≈ C = 0.92 · 2.2 ac
Landscaped islands (grass, flat, good) ≈ C = 0.24 · 0.4 ac
Roof runoff to pavement ≈ C = 0.95 · 0.2 ac

C_composite = (0.92 · 2.2 + 0.24 · 0.4 + 0.95 · 0.2) / 2.8
C_composite = (2.024 + 0.096 + 0.190) / 2.8 = 2.310 / 2.8 = 0.825

Wrong shortcut: single C = 0.90 for “commercial paved” → 0.90 (ignores islands)
Error: 0.90 vs 0.825 = +9% on peak Q — enough to under-size inlets on a marginal lot.

Do not use one C for the whole site. Islands and roof-to-pavement routing change the weighted coefficient materially. The roof area is only 0.2 ac, but at C = 0.95 it pulls the composite up roughly 0.02–0.03 compared with asphalt-only weighting. Plan reviewers will ask for the sub-area table.

Step 2 · Time of concentration

TR-55 sheet flow over pavement

On a flat parking field, overland sheet flow to the collecting gutter dominates T_c. TR-55 segmental method (Tc methods cheat sheet) limits sheet-flow travel to 300 ft; our path is 210 ft, so sheet flow alone is appropriate — no shallow concentrated segment needed.

Sheet flow (TR-55 Eq. 2-6, T_t in hours):
  T_t = 0.007 (nL)^0.8 / (P₂^0.5 · S^0.4)

Inputs:
  n = 0.011 (smooth asphalt; TR-55 Table 3-1, paved surface)
  L = 210 ft
  S = 0.020 (2% cross slope)
  P₂ = 2.65 in (2-yr 24-hr rainfall, Atlas 14 at site — used in TR-55 sheet-flow equation)

nL = 0.011 · 210 = 2.31 → (nL)^0.8 = 1.89
P₂^0.5 = 1.628 · S^0.4 = 0.219

T_t = 0.007 · 1.89 / (1.628 · 0.219) = 0.0132 / 0.357 = 0.037 hr = 2.2 min

Local minimum T_c: jurisdiction requires T_c ≥ 5 min for developed sites.
Adopt T_c = 5 min for IDF lookup (conservative — higher intensity at shorter duration is bounded by the code floor).

Confirm with the time-of-concentration tool. If the longest path were > 300 ft via a perimeter drive, add a shallow-concentrated segment per TR-55.

Step 3 · Rainfall intensity (10-yr / 5-min)

NOAA Atlas 14–style IDF

The Rational Method requires rainfall intensity at a duration equal to T_c. From NOAA Atlas 14 Volume 8 (precipitation-frequency atlas for the Ohio River Basin and surrounding states, applicable to central VA), illustrative 10-year partial-duration frequencies at the project coordinates:

i_{10, 5-min} = 8.14 in/hr
i_{10, 10-min} = 6.42 in/hr
i_{10, 15-min} = 5.28 in/hr

At T_c = 5 min: i = 8.14 in/hr

Always pull IDF from the official Atlas 14 point precipitation-frequency estimator for your coordinates — the values above are representative, not a permit substitute.

Step 4 · Frequency factor and peak Q

Q = C_f · C · i · A

Runoff coefficients in standard tables are calibrated to ~10-year conditions. For a 10-year design storm, the frequency factor C_f ≈ 1.0 (Chow; many state manuals omit C_f at 10-yr). For 25-year designs, C_f ≈ 1.10 is common.

C_f = 1.0 (10-yr design — no adjustment)
C_design = 0.825 · 1.0 = 0.825

Q₁₀ = C · i · A = 0.825 · 8.14 in/hr · 2.8 ac
Q₁₀ = 18.8 cfs

Sensitivity: single C = 0.90 → Q = 20.5 cfs (+9%)
Sensitivity: if C_f = 1.10 were wrongly applied at 10-yr → Q = 20.7 cfs (+10%)

Do not double-apply the frequency factor. Applying C_f = 1.10 to a 10-year design when your C values already represent developed urban cover is a common spreadsheet error. Reserve C_f > 1.0 for storms above the coefficient's basis (e.g., 25-yr, 100-yr) per your state's drainage manual.

Verify in the Rational Method calculator.

Step 5 · Inlet sizing — first pass

Grate + curb opening at the low aisle (HEC-22 simplified)

Total lot discharge must be intercepted before gutter spread exceeds the allowable width (typically 8–10 ft from the curb for pedestrian safety). A first-pass allocation without full HEC-22 gutter spread iteration:

Design peak: Q_total = 18.8 cfs

Grate inlet (Type R, 2 ft × 4 ft, no depression, on-grade):
  HEC-22 Chart 4B, V_gutter ≈ 1.0 ft/s, S_x = 0.020:
  Intercept capacity ≈ 4.2 cfs per grate (first-order; confirm with full spread calc)

Curb opening (12 ft length, depression 0.5 in):
  Capacity ≈ 5.8 cfs at same gutter conditions

Proposed layout:
  Low end east aisle: 1 × combination (curb + grate) ≈ 5.8 + 4.2 overlap → use 7.5 cfs effective
  Mid-lot: 2 × grate inlets @ 4.2 cfs = 8.4 cfs
  Total intercepted ≈ 7.5 + 8.4 = 15.9 cfs — short of 18.8 cfs

Add 1 grate at northwest low corner (+4.2 cfs) → 20.1 cfs capacity ✓
Recommend: 1 combination inlet + 3 grate inlets; verify spread < 8 ft in HEC-22 before permit.

First-pass inlet counts are not a permit package. HEC-22 requires iterative gutter spread, bypass flow to downstream inlets, and clogging factor (typically 50% reduction on grates). The numbers above are order-of-magnitude — they tell you that two inlets are not enough, not that four is final.

Step 6 · What we did NOT do, and when you would

Limits of Rational on parking lots

No hydrograph or storage routing. Rational gives peak only. If the lot drains through a detention basin with 10-minute storage, peak outlet Q is lower than 18.8 cfs — route the hydrograph.
No NRCS CN check. For water-quality volume (first-flush, VA VSMP), compute runoff depth with NRCS curve number separately; Rational Q does not give volume.
No pipe hydraulic grade line. After inlets, size the 18-inch trunk with Manning's and check HGL for surcharge at the low corner.
No climate non-stationarity. Atlas 14 PFDS are being revised in some regions; confirm the adopted curve in the jurisdiction's current manual amendment.

Full parking-lot drainage with inlet optimization and sealed calcs: HydroComplete.

Tools used in this example

Reproduce each step in PE-Calc: Rational Method · time of concentration · Manning's equation (downstream pipe). Reference values from runoff coefficients and Tc methods.

Buying the lot? Check the drainage before you buy.

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