Drop Spillway Calculator
Straight-drop principal spillway and grade-control structure per NRCS NEH-11 and Rand (1955). Computes discharge over the crest, impinging-jet geometry from the drop number, conjugate depth required at the apron, and total stilling-basin length. Use this for screening sizing of small embankment-dam principal spillways.
Rand 1955 / NRCS NEH-11 power-law fits for straight-drop geometry. End sill, blocks, and rip-rap downstream are sized separately. Apply at d < ~8 ft for principal spillways; for larger drops use a Type II/III stilling basin.
How to use this calculator
Enter the crest length L, head over crest H during the design event, and drop height d. The calculator computes free-fall discharge over the crest using the chosen weir formula, then applies Rand's drop-number relations to size the stilling basin downstream. The stilling-basin length Lbasin is the minimum apron required to contain the impinging jet plus the hydraulic jump that follows it. Confirm tailwater depth in the receiving channel exceeds y2 — if it doesn't, the jump will sweep out and the basin won't function. Add an end sill at Lbasin sized at 0.07·d (NRCS NEH-11 detail).
Drop-number scaling
| DN | xa/d | y2/d | Lbasin/d |
|---|---|---|---|
| 0.001 | 1.04 | 0.30 | 2.8 |
| 0.005 | 1.51 | 0.42 | 4.0 |
| 0.01 | 1.82 | 0.49 | 4.7 |
| 0.05 | 2.66 | 0.68 | 6.7 |
| 0.10 | 3.21 | 0.79 | 7.9 |
| 0.50 | 4.71 | 1.10 | 11.3 |
| 1.00 | 5.68 | 1.28 | 13.4 |
Computed from xa/d = 4.30·DN0.27, y2/d = 1.00·DN0.22, Lbasin = xa + 6·y2. Source: Rand, W. (1955) Flow Geometry at Straight Drop Spillways, ASCE Paper 791. NRCS NEH-11 (Drop Spillways).
Worked example
Example — small NRCS sediment-dam principal spillway
References: Rand, W. (1955). Flow Geometry at Straight Drop Spillways. ASCE Proceedings 81 (Paper 791). USDA NRCS, NEH-11 (Drop Spillways). Chow, V.T. (1959), Open-Channel Hydraulics, §15-9.
Related tools
- Hydraulic jump & stilling basin — for chute spillways and Type II/III basins
- Sharp-crested weir — pick the correct Cd
- Broad-crested weir — auxiliary spillway alternative
- Riprap sizing — downstream channel armor