TR-55 calculator

Using the calculator above

The calculator opens on the worked example below: a 1.3 km² watershed of eighth-acre lots on group B soil, 125 mm of rain in 24 hours, a Type II storm, Tc of 0.75 h and no ponds. It returns 19.9 m³/s.

• Drainage area: the area draining to the point of interest, in km² or ha (mi² or acres in US units).
• Time of concentration: in hours, 0.1 to 10 h.
• Ponds and swamps: the share of the area in ponds or swamps outside the Tc flow path, 0 to 5 %.
• Curve number: type it, or choose a land use from TR-55 Table 2-2 and a hydrologic soil group. Area-weighted CN combines up to four sub-areas, each with its own land use, soil group and area.
• 24-hour rainfall and rainfall distribution: the design depth for the return period and the SCS storm type for the site.

The results give $S$, $I_a$, $I_a/P$, $Q$, $q_u$ and $q_p$, the working in TR-55’s native units, the runoff curve for the CN and the peak for each storm type. A warning shows when $I_a/P$ is outside 0.10 to 0.50 or $Q$ is under 13 mm.

How the TR-55 graphical method works

The method has two halves: the SCS curve number equation for runoff depth, then a unit peak discharge for the peak.

Runoff depth. The curve number sets the potential maximum retention S. An initial abstraction of 0.2 S is lost before runoff starts, and the rest of the rainfall is split between runoff and further retention:

In millimetres, $S = 25400/CN - 254$.

Peak discharge. TR-55 Chapter 4 gives the unit peak discharge $q_u$ as a function of $T_c$ and $I_a/P$ for each rainfall distribution. The calculator uses the polynomial fit published in TR-55 Appendix F (Table F-1), interpolating between the tabulated $I_a/P$ rows:

TR-55 works in inches, square miles and hours. SI inputs are converted, the method runs in its native units, and the peak is reported in both m³/s and cfs.

Inputs and where they come from

• Drainage area. From a map or from watershed delineation.
• Curve number. From the table below by cover type and hydrologic soil group, area-weighted for mixed land use. Soil groups come from a soil survey: the USDA Web Soil Survey in the US, national soil maps elsewhere.
• Time of concentration. TR-55 Chapter 3 builds Tc from sheet, shallow concentrated and channel flow; the time of concentration calculator runs that method and five others. Use the same Tc procedure for pre- and post-development conditions.
• 24-hour rainfall. The design depth for the return period, from NOAA Atlas 14 in the US or a national rainfall atlas elsewhere.
• Rainfall distribution. Type I, IA, II or III, by location. The design storm generator shows what each distribution looks like in time.
• Pond and swamp area. The percentage of the watershed in ponds or swamps outside the Tc flow path, 0 to 5 %.

Hydrologic soil groups, by infiltration rate when thoroughly wet:

Worked example: 1.3 km² residential watershed

A 1.3 km² (0.502 mi²) watershed of eighth-acre residential lots on group B soil drains to a road crossing. The 24-hour design rainfall is 125 mm (4.92 in), the site uses the Type II distribution, Tc is 0.75 h, and there are no ponds.

1. CN for eighth-acre lots on group B soil is 85.
2. $S = 1000/85 - 10 = 1.765$ in (44.8 mm) and $I_a = 0.353$ in (9.0 mm).
3. $Q = (4.921 - 0.353)^2 / (4.921 - 0.353 + 1.765) = 3.295$ in (83.7 mm).
4. $I_a/P = 0.072$, below the tabulated range, so the 0.10 row is used: $C_0 = 2.55323$, $C_1 = -0.61512$, $C_2 = -0.16403$.
5. $\log_{10} q_u = 2.6275$, so $q_u = 424$ csm/in.
6. $q_p = 424 \times 0.502 \times 3.295 \times 1.0 = 702$ cfs, which is 19.9 m³/s.

Changing one input at a time shows what the peak is sensitive to:

A five-point change in CN moves the peak by about 15 %, and the distribution choice moves it by a factor of 3.6. Both deserve a sentence of justification in the design report.

Curve number table (TR-55 Table 2-2, ARC II)

Studio’s lookup holds 52 rows, including contoured and terraced variants for crops, close-seeded legumes and the poor and good conditions for brush and orchards.

Limitations and when to use something else

• Peak only. The graphical method returns no hydrograph and no runoff timing. For storage design, generate a hydrograph with the unit hydrograph generator and route it with the detention pond calculator.
• One homogeneous watershed. One CN, one main stream or branches with similar Tc. Mixed watersheds with very different sub-areas need sub-area hydrographs, which this method does not produce.
• Range limits. Tc 0.1 to 10 h, CN above 40, Ia/P 0.1 to 0.5. Accuracy drops outside them, and the calculator stops when Tc or CN is out of range.
• Low runoff. Results are less reliable when Q is under 0.5 in (13 mm); the calculator warns.
• No routing. Ponds at the outlet and valley storage must be routed separately.
• Small urban sites. On a few hectares of paving, the Rational Method calculator is simpler and often what the reviewer expects.

What a free Studio account adds

• Saving to a project, with the inputs and the step-by-step working (S, Ia, Q, Ia/P, the coefficients, qu and Fp) kept in the record.
• Word and Excel reports of the calculation.
• Composite CN from up to five sub-areas, entered as areas (each in its own unit) or as percentages of the total.
• Tc from a saved time of concentration calculation, or computed in place with the six-method Tc calculator.
• Linked rainfall and area: the depth from a saved rainfall analysis, and the area from a saved watershed delineation or an uploaded catchment polygon.
• Sending results on: the peak flow to the Culvert Designer, Channel Analysis and other design tools, and the curve number to the unit hydrograph generator.