Why a drainage calculation asks how long something takes
The rational method computes a peak flow as Q = C i A, and the term that trips people up is i, the rainfall intensity in inches per hour. Rainfall frequency data does not hand you a single intensity for a storm — it hands you a table with duration down one axis. A five-minute burst in a 10-year storm might be several times as intense as the hourly average of the same storm. So which row do you read?
The convention is the time of concentration: the travel time from the hydraulically most distant point in the drainage area to the point where you want the flow. The reasoning is that the whole area is only contributing at once when the storm has lasted at least that long, and that is the moment the peak occurs. Shorter storms are more intense but never engage the whole area; longer storms engage everything but at a lower intensity. The maximum sits at the crossover, and the crossover is Tc.
Three kinds of moving water, three different speeds
Water leaving a hilltop does not travel at one speed. The standard treatment splits the path into segments and adds their travel times.
Sheet flow is a thin unconcentrated film across a surface, and it is slow — often the majority of the total time even though it covers the shortest distance. Its travel time comes from a kinematic wave solution simplified to Tt = 0.007 (n L)0.8 / (P20.5 s0.4), with Tt in hours, L in feet and s in feet per foot. The roughness n here is an overland-flow value, not a channel value: dense grass carries an n around 0.24 where the same manual gives a grassed ditch about 0.05. That is not an inconsistency, it is a different physical situation — the film is shallow enough that individual grass blades matter.
The P2 term is the two-year 24-hour rainfall for your location, and it is in the equation because the depth of the film depends on the rain falling on it. It is a specific published statistic, not the design storm, and it is looked up by coordinates.
Shallow concentrated flow begins where the sheet has gathered into rills and shallow swales. Velocity here is treated as a simple function of slope: about 16.13 times the square root of the slope on unpaved ground, 20.33 on paved. At a two percent grade that is 2.28 and 2.88 feet per second respectively.
Channel flow takes over once there is a defined ditch, gutter or pipe, and velocity comes from Manning: V = (1.49 / n) R2/3 s1/2. A grassed swale at n = 0.05, hydraulic radius 0.6 feet and half a percent grade moves at about 1.5 feet per second.
| Segment | Typical share of the path | Typical share of the time |
|---|---|---|
| Sheet flow | Up to 100 ft | Often more than half |
| Shallow concentrated | Hundreds of feet | A small fraction |
| Channel | The rest | Depends entirely on the grade |
The lesson in that table is where to spend your effort. A hundred feet of sheet flow can account for well over half the total travel time, so getting the sheet flow roughness roughly right matters far more than refining the channel hydraulic radius.
The cap on sheet flow length is not a formality
The method limits sheet flow to about 100 feet, and some manuals cut that to 50 or less. The limit exists because unconcentrated sheet flow is physically unstable — across any real ground it finds a wheel rut, a mower line, an old furrow or a slight hollow within a fairly short distance and concentrates, at which point it speeds up and stops obeying the sheet equation.
Ignoring the cap is not a conservative simplification. Because the sheet term dominates, stretching it to 300 feet inflates the time of concentration substantially, which sends you to a longer duration on the intensity table, which gives a lower intensity and a lower design flow. The error runs in the direction of undersizing.
What happens to Tc when a lot gets developed
This is the part worth understanding even if you never run the calculation again. Development almost always shortens the time of concentration. The overland path gets smoother, the length gets shorter because water is intercepted by a driveway or a gutter partway down, and grades often get steeper at the edges of graded areas.
A shorter Tc means you read the intensity at a shorter duration, and short-duration intensities are much higher. So the peak flow leaving a developed lot rises for two separate reasons: a larger fraction of the rain runs off, and the rain is counted at a higher rate. People who only think about the runoff coefficient see half the change.
It also explains a real-world observation — that a neighbourhood can start flooding at the bottom of a hill after upstream development even though the total rainfall never changed. The same water arrives sooner and more of it arrives together.
Where this stops
The output is a duration, not a design. Once you have it, the intensity lookup is on you, the runoff coefficients are on you, and the flow calculation itself is on the culvert and swale flow calculator. If you want a volume rather than a rate, the curve number runoff calculator is the other approach entirely. Where the water finishes up — a rain garden, a dry well, a basin — is a storage problem rather than a timing one.
Questions people ask
What is the two-year 24-hour rainfall and why does the sheet flow equation want it?
It is a published statistic for your specific location: the 24-hour rainfall depth with a two-year return interval, available from NOAA Atlas 14 point precipitation frequency estimates by latitude and longitude. It appears in the sheet flow equation because the travel time of a thin film depends on how deep that film is, and the film depth depends on rainfall rate. The two-year 24-hour value was chosen as a convenient index of the local rainfall climate rather than because your design storm is a two-year event. It is not the storm you are designing for and the two numbers are usually different.
My sheet flow segment is most of the total time. Is that right?
Usually, yes. A hundred feet of dense grass at two percent takes roughly fifteen minutes; four hundred feet of shallow concentrated flow on the same grade takes about three. Unconcentrated flow across a rough surface is genuinely slow, and once the water gathers into a defined path it accelerates enormously. This is why the sheet flow roughness value is the input most worth getting right, and why stretching sheet flow past its length limit distorts the answer more than any other single mistake.
What roughness should I use for sheet flow?
Take it from the sheet flow roughness table in your drainage manual, which is a different table from the channel roughness one and gives much larger numbers. The values reflect what a film of water a fraction of an inch deep actually encounters: smooth pavement at the low end, cultivated soil and short grass in the middle, dense grass and woodland with litter at the high end. Using a channel value here, which is a mistake that looks reasonable, will cut the sheet travel time by a factor of several and inflate the design flow.
Does a minimum time of concentration exist?
Many drainage manuals set one, and the calculator has a field for whatever yours says, but the value is a local rule rather than a physical constant and this page states none. The reason floors exist is that intensity-duration-frequency curves become unreliable at very short durations, and small computed times of concentration on small sites can produce intensities the data does not really support. If your computed number comes out very low, that is worth a question to whoever reviews the design rather than an assumption in either direction.
Can I use this for a whole subdivision or a stream watershed?
The segment method itself scales up reasonably, but the rational method it usually feeds does not. The rational method is a small-watershed tool that assumes rainfall is uniform across the area and that the storm lasts at least as long as the time of concentration, and it degrades as the area grows — where the threshold sits is set locally, often somewhere in the low tens of acres. Above that, different methods apply and the choice is not yours to make casually. For anything beyond a few lots, this is a number to hand to an engineer rather than to build from.