v2.0.3

Reference Figures

Step Pool Profile View

Step Pool Section View

Slope-Plot Method Diagram

Specified-Width Method Diagram

Reference Equations

Slope-Plot Method

Name	Symbol	Equation	Topic	Ref. (NHC 2026)
Mean Wetted Width	$W_{m e a n}$	$Solved For$	Channel Geometry
D84 Steps	$D 84_{s t e p s}$	$D 84_{s t e p s} = (1.9 * S_{b e d} + 0.03) * W_{m e a n}$	Grain Size	Eq. 3.1 & 3.2
D84 Bed	$D 84_{b e d}$	$D 84_{b e d} = \frac{1}{1.25} * D 84_{s t e p s}$	Grain Size	Eq. 3.3
D50 Bed	$D 50_{b e d}$	$D 50_{b e d} = \frac{1}{2.2} * D 84_{b e d}$	Grain Size	Eq. 3.4

Specified Width Method

Name	Symbol	Equation	Topic	Ref. (NHC 2026)
D50 Bed	$D 50_{b e d}$	$Solved For$	Grain Size
D84 Bed	$D 84_{b e d}$	$D 84_{b e d} = 2.2 * D 50_{b e d}$	Grain Size	Eq. 3.4
D84 Steps	$D 84_{s t e p s}$	$D 84_{s t e p s} = 1.25 * D 84_{b e d}$	Grain Size	Eq. 3.3
Mean Wetted Width	$W_{m e a n}$	$W_{m e a n} = W_{s u r f} - W_{b a n k}$	Channel Geometry

Common to Both Methods

Name	Symbol	Equation	Topic	Ref. (NHC 2026)	Notes
Number of Step Pools	$# S P$	$# S P = (1.8 + 1.2 \log (S_{b e d})) * site length$	Frequency & Spacing	Eq. 3.16 & 3.17
Unit Discharge	$q$	$q = \frac{Q}{W_{m e a n}}$	Hydraulics	Eq. 3.5
Velocity	$v$	$v = 1.45 g^{0.23} q^{0.55} {D 84_{s t e p s}}^{- 0.33} {S_{b e d}}^{0.32}$	Hydraulics	Eq. 3.6
Mean Depth	$y$	$y = \frac{q}{v W_{m e a n}}$	Cross Sectional Dimensions	Eq. 3.7	Based on bank slope.
Residual Depth	$d_{r}$	$d_{r} = H - z$	Pool Geometry		Not changed by modifying #SP.
Pool Length	$L_{p}$	$L_{p} = (- 4.8 - 13.6 \log (S_{b e d})) * d_{r}$	Pool Geometry	Eq. 3.11 & 3.12	Not changed by modifying #SP. Represents minimum recommended value.
Step Height	$H$	$H = (0.56 - 0.5 \log (\frac{D 84_{b e d}}{W_{m e a n}})) * D 84_{b e d}$	Step Geometry	Eq. 3.14	Represents maximum recommended value.
Drop Height	$z$	$z = (0.19 - 0.44 \log (\frac{D 84_{b e d}}{W_{m e a n}})) * D 84_{b e d}$	Step Geometry	Eq. 3.13	Not changed by modifying #SP. Represents maximum recommended value.
Step Length	$L_{s}$	$\max {\begin{array}{lr} 0.27 - 2.4 \log (\frac{D 84_{b e d}}{W_{m e a n}}) - 0.035 (\frac{W_{m e a n}}{y}) \\ \min {2 * D 84_{s t e p s}, L_{s p t} - L_{p}} \end{array}}$	Step Geometry	Eq. 3.15	Represents minimum recommended value.
Step to Step Spacing	$L_{s p t}$	$L_{s p t} = \frac{site length}{# S P}$	Pool Geometry	Eq. 3.19	Represents maximum recommended value.
Tread Length	$L_{t}$	$L_{t} = L_{s p t} - (L_{s} + L_{p})$	Pool Geometry	Eq. 3.19	Represents maximum recommended value.
Step Pool Length	$L_{s p}$	$L_{s p} = L_{s} + L_{p}$	Pool Geometry	Eq. 3.20
Tread Drop	$E_{t}$	$E_{t} = \frac{(S * L)}{# S P} - z$	Pool Geometry
Total Site Drop	$\sum E_{s i t e}$	$\sum E_{s i t e} = L * S$	Reach Geometry
Total Tread Drop	$\sum E_{t r e a d s}$	$\sum E_{t r e a d s} = # S P * E_{t}$	Reach Geometry
Total Step Drop	$\sum E_{p o o l s}$	$\sum E_{p o o l s} = # S P * z$	Reach Geometry
Bank Width	$W_{b a n k}$	$W_{b a n k} = y / S_{b a n k}$	Channel Geometry	Eq. 3.21	Based on bank slope.
Bed Width	$W_{b e d}$	$W_{b e d} = W_{m e a n} - W_{b a n k}$	Channel Geometry	Eq. 3.22
Surface Width	$W_{s u r f}$	$W_{s u r f} = W_{m e a n} + W_{b a n k}$	Pool Geometry	Eq. 3.23
Hydraulic Radius	$R$	$R = \frac{Q / v}{W_{b e d} + 2 y / s i n (90 - a t a n (S_{b a n k}))}$	Channel Geometry	Eq. 3.24	Based on bank slope.
Shear Stress	$τ$	$τ = R * S_{b e d} * g * ρ_{w a t e r}$	Stability	Eq. 3.25
Shields Number	$θ_{c}$	$θ_{c} = \frac{τ}{(ρ_{s e d} - ρ_{w a t e r}) g D 50_{b e d}}$	Stability	Eq. 3.26
Shields Ratio	$θ / θ_{c}$	$θ / θ_{c} = θ / 0.045$	Stability	Eq. 3.27
Jamming Ratio	$W_{m e a n} / D 84_{s t e p s}$	$W_{m e a n} / D 84_{s t e p s} = W_{m e a n} / D 84_{s t e p s}$	Stability
Logit Instability	$g$	$g = - 5.51 + 1.92 \log (W_{m e a n} / D 84_{s t e p s}) + 9.10 \log (θ / θ_{c})$	Stability	Eq. 2.3
Probability of Instability	$P$	$P = \frac{e^{g}}{1 + e^{g}}$	Stability	Eq. 2.4

References

NHC (2026). Steep Channel Design Methodology: 2025 State of Practice. Draft Report Rev 4. Report #: 2006593.01. Prepared by Northwest Hydraulic Consultants Inc for Washington State Department of Transportation. 91 pp. January 19, 2026.