Time of Concentration Calculator - Kirpich Scs

Time of concentration is the travel time from the hydraulically most remote point of a catchment to its outlet, and it matters because it sets the storm duration that produces the largest peak flow. Rain lasting less than Tc never engages the whole basin at once; rain lasting longer than Tc engages all of it but at a lower average intensity, since intensity-duration-frequency curves fall as duration grows. The maximum peak therefore occurs at a duration equal to Tc, which is why this single parameter drives the intensity selected in the Rational Method and the shape of a synthetic unit hydrograph. The two formulas here reach that number by different routes. Kirpich uses only geometry, Tc = 0.0078 L^0.77 S^-0.385 with L in feet, so its negative 0.385 exponent on slope encodes the observation that a fourfold steepening cuts travel time to roughly 58 percent of its original value. The SCS lag equation adds land condition through the retention term S = 1000/CN - 10, then converts lag to Tc by dividing by 0.6, reflecting the empirical finding that lag is about 60 percent of time of concentration for a standard hydrograph shape. Expect disagreement between the two; Kirpich was fitted to steep bare agricultural channels and tends to run short, and common practice multiplies it by about 2 for overland flow across grass and by roughly 0.4 for concrete-lined channels. The SCS lag method is formally restricted to basins under about 8 square kilometers with fairly homogeneous cover, and neither method handles storm sewers or urban conveyance explicitly.

Both equations grew from the small-watershed monitoring the US Department of Agriculture began in the 1920s and 1930s. Charles Ramser, an agricultural engineer, instrumented a set of small terraced farm channels near Jackson, Tennessee, and published measurements of runoff travel time from them in 1927. Z. P. Kirpich fitted a regression to that Tennessee data and published the resulting formula in 1940 in the journal Civil Engineering. The calibration basins were tiny, generally well under a square kilometer, steep, and largely bare, which explains both the equation's durability as a quick estimate and its known bias when applied to flatter or vegetated terrain. The SCS lag equation emerged from the same agency's broader hydrology program, the work associated with Victor Mockus that also produced the Curve Number procedure, and was documented in Section 4 of the National Engineering Handbook. Tying lag to the Curve Number let a single land use and soil assessment serve both the runoff volume calculation and the timing calculation, a considerable practical economy for field conservationists. Publication of Technical Release 55 in 1975, and its 1986 revision, carried both the lag method and a segmented velocity method into urban drainage practice, where the velocity approach of summing sheet flow, shallow concentrated flow, and channel travel times is now often preferred for developed catchments. Reviews by hydrologists including Richard McCuen have since documented how widely competing Tc formulas diverge on identical basins, reinforcing the practice of computing several and judging the spread.