How this calculator works
The simplified Isbash relation balances flow velocity against submerged stone stability. NCHRP Report 568 discusses coefficients 0.86 and 1.20 and the assumptions behind them. Velocity must represent the condition at the stone; local flow amplification, side slopes, gradation, filters, scour and installation details are not modelled. Bulk layer density for purchasing is separate from particle specific gravity in the stability equation.
Formula
D50 = V^2 / [2 x g x C^2 x (SG - 1)]; V = sqrt(2 x g x C^2 x (SG - 1) x D50); order volume = protected area x specified thickness x (1 + waste); mass = order volume x bulk density.
Worked example
For a mathematical check, V = sqrt(20) m/s, g = 10 m/s2, C = 1 and SG = 2 give D50 = 1 m. Separately, 10 m2 of protection at 0.5 m thick plus 10% waste is 5.5 m3.
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Frequently asked questions
Is D50 the largest stone?
No. D50 is a median stone size associated with the specified grading. Layer thickness and maximum stone size need separate design decisions.
Can I use channel average velocity directly?
Only if the selected design method establishes that it represents the relevant stone-level velocity. Local turbulence and geometry can require different values or corrections.
Does this design bridge protection?
No. Bridge piers, abutments and complex banks need the applicable hydraulic guidance and project-specific analysis, not this basic relation alone.