Launching apron thickness before launching

A launching apron is laid flat at the toe of the pitching. When the bed scours, the stones slide down the scour slope and cover it. The thickness before launching follows from equality of the stone volume per metre run before and after launching.

Data

• Scour depth below original bed $= D$ (unknown, cancels out).
• Laid width of apron $= 1.8D$; scour slope $3H:1V$; launched thickness $= 1.5t$ ($t$ = thickness of pitching).

Calculation

Length of the scour slope: $\sqrt{D^2 + (3D)^2} = \sqrt{10}\,D = 3.162D$.

Volume per metre after launching: $V = 1.5t\times3.162D = 4.743\,tD$.

Volume per metre before launching: $V = T\times1.8D$, where $T$ is the thickness as laid.

$$\begin{aligned} T\times1.8D &= 1.5t\times\sqrt{10}\,D \\ T &= \frac{1.5\sqrt{10}}{1.8}\,t = 2.635\,t \end{aligned}$$

Answer: thickness of apron before launching $T \approx 2.64\,t$ (that is, about 2.6 times the pitching thickness).

Sketch

 Before launching            After launching (3H:1V)
  pitching                     pitching
 ___\____ T                   ___\
      |<--1.8D-->|                 \  1.5t thick
 bed ____apron___| river bed        \ scour slope
                                     \__ depth D

For example, if $t = 1.0$ m the laid thickness is 2.64 m.