What is the critical storm duration?

The storm duration that makes inflow volume minus outflow volume largest for a fixed release rate. That largest difference is the storage estimate. Source: NYC DEP Criteria for Detention Facility Design (2012) pp. 3 to 4; UDFCD DCM Vol. 2 (2007) p. SO-11.

What average outflow does the method assume?

NYC DEP takes 2/3 of the maximum release for an orifice under rising head and 95% for a pump. UDFCD uses m = ½(1 + Tc/T), between 0.5 and 1. Source: NYC DEP (2012) pp. 3 to 4; UDFCD eq. SO-7.

Does it work for multi-stage outlets?

No. It sizes one level of peak control only. Source: UDFCD DCM Vol. 2 (2007) p. SO-10.

How accurate is the TR-55 storage chart by comparison?

TR-55 says not to use its Figure 6-1 for final design if a 25% storage error cannot be tolerated. Source: TR-55 (1986) p. 6-3.

Detention volume calculator

Storage needed to hold post-development runoff to an allowable release rate, by the modified rational critical-duration method.

PRELIMINARYReference tables are still being checked against their printed sources. How results are checked

11,069cf

0.254 ac-ft of storage, at a critical duration of 120.0 min. Preliminary estimate.

Critical duration: 120.0 min
Intensity at that duration: 1.04 in/hr
Inflow Cf · C · i · A: 1.70 cfs
Average outflow ratio k: 0.67
Storage: 0.254 ac-ft

Show the table

Storage at each duration. The largest is the estimate.
Duration (min)	i (in/hr)	Inflow (cfs)	Storage (cf)
5.0	7.00	11.50	3,401
10.0	5.60	9.20	5,421
15.0	4.67	7.67	6,751
30.0	3.11	5.11	8,902
60.0	1.87	3.07	10,442
120.0	1.04	1.70	11,069
180.0	0.72	1.18	10,941
360.0	0.37	0.61	9,651
720.0	0.19	0.31	6,321
1,440.0	0.10	0.16	0

The link carries these inputs, not the answer.

Worked example

The default inputs above are a published example: NYC DEP 2012 Example 1A (Bronx, orifice): C 0.768, 93,200 sqft, 0.25 cfs, with NYC's 10-yr IDF i = 140/(t + 15) at the NOAA durations. NYC prints 10,895 cf from its rounded closed form (0.19 for 0.19284); the exact form is about 1.5 percent higher..

Outflow assumption: NYC DEP Criteria for Detention Facility Design (2012) § I p. 3: k = 2/3
Critical duration t = 120.0 min, i = 1.04 in/hr
Inflow = C × i × A = 0.768 × 1.04 in/hr × 93,200 sf = 1.70 cfs
V = 60 × 120.0 × (1.70 − 0.67 × 0.25) = 11,069 cf (0.254 ac-ft)

The formula

V(t) = 60 t · (Cf · C · i(t) · A − k · Qo); V = max over t ≥ Tc

NYC DEP Criteria for Detention Facility Design (2012) pp. 1 to 4; UDFCD Drainage Criteria Manual Vol. 2 (2007) eq. SO-6 to SO-10. A preliminary estimate, not a NYSDEC method.

V(t): storage needed for a storm of duration t, cf
t: storm duration, searched from Tc upward, min
i(t): rainfall intensity for that duration, in/hr
C: runoff coefficient (Cf · C when a frequency factor applies)
A: drainage area, ac
Qo: allowable release rate, cfs
k: average outflow over the storm as a share of Qo

A preliminary estimate, not a NYSDEC method

The critical-duration method sizes one level of peak control for one release rate. It does not route a hydrograph through an outlet, and it cannot represent a multi-stage riser. NYC DEP uses it for on-site detention to the city sewer. The New York design manual names TR-55 and TR-20 for the peak rates its criteria check, and no NYSDEC statement on this method was found either way. Use it to get a first pond size, then route the design storm.

The three outflow assumptions

NYC DEP 2012 § I p. 3: k = 2/3, orifice under rising head
NYC DEP 2012 § II p. 4: k = 0.95, near-constant outflow
UDFCD 2007 eq. SO-7: m = ½(1 + Tc/T), 0.5 to 1

Questions about this calculation

What is the critical storm duration?: The storm duration that makes inflow volume minus outflow volume largest for a fixed release rate. That largest difference is the storage estimate.; NYC DEP Criteria for Detention Facility Design (2012) pp. 3 to 4; UDFCD DCM Vol. 2 (2007) p. SO-11
What average outflow does the method assume?: NYC DEP takes 2/3 of the maximum release for an orifice under rising head and 95% for a pump. UDFCD uses m = ½(1 + Tc/T), between 0.5 and 1.; NYC DEP (2012) pp. 3 to 4; UDFCD eq. SO-7
Does it work for multi-stage outlets?: No. It sizes one level of peak control only.; UDFCD DCM Vol. 2 (2007) p. SO-10
Does NYSDEC accept the modified rational method?: No NYSDEC statement was found either way. The design manual names TR-55 and TR-20 for the peak rates behind its criteria.; NYSDEC DM2024 § 4.6
How accurate is the TR-55 storage chart by comparison?: TR-55 says not to use its Figure 6-1 for final design if a 25% storage error cannot be tolerated.; TR-55 (1986) p. 6-3

The other calculators

Curve number and runoff. Composite CN from cover type and hydrologic soil group, then TR-55 runoff depth for a 24-hr rainfall.
Time of concentration. TR-55 Tc from a sheet flow, a shallow concentrated flow and a channel flow segment, in hours and minutes.
Rational method peak flow. Peak runoff Q = Cf·C·i·A from the runoff coefficient, rainfall intensity and drainage area, with the frequency factor for the storm.
NY water quality volume. WQv = P·Rv·A/12 from the 90th percentile rainfall, impervious cover and contributing area, per the NYSDEC design manual.

How results are checked Pricing for the full app

The full app runs the whole site: Atlas 14 rainfall frozen for the project, pre and post hydrographs, and the pond routed through its outlets. Then the NYSDEC checks you select, and a PDF report with the SWMM file a reviewer can rerun.

Start trial

14-day trial, every feature, no card.