A double-acting cylinder consumes air on both strokes. The forward (cap-end) stroke acts on the full bore area; the return (rod-end) stroke acts on the annular area between the bore and the piston rod. The net result is obtained by summing the two swept volumes:

\begin{equation}\label{eq:pneumatic-air-requirement-double-acting-volume} Q_{cyl} = \frac{\frac{\pi}{4} \cdot (2 D^2 - d_r^2) \cdot L \cdot n}{k_{in^3}} \end{equation}

This is equivalent to computing the single-acting volume for the bore alone and then adding the single-acting volume for the annular rod side:

\begin{equation}\label{eq:pneumatic-air-requirement-double-acting-expanded} Q_{cyl} = \frac{2 \cdot k_{in^3} \cdot Q_{sa} - \frac{\pi}{4} \cdot d_r^2 \cdot L \cdot n}{k_{in^3}} \end{equation}

where \(Q_{sa}\) is the single-acting intake volume for the same bore, stroke, and cycle rate.

Symbols

\(Q_{cyl}\)	Combined cylinder air intake per minute \([\unit{ \cubicFoot\per\minute}]\)
\(Q_{sa}\)	Single-acting intake volume for the full bore \([\unit{ \cubicFoot\per\minute}]\)
\(D\)	Inner bore diameter of the cylinder \([\unit{ \inch}]\)
\(d_r\)	Piston rod diameter \([\unit{ \inch}]\)
\(L\)	Piston stroke length \([\unit{ \inch}]\)
\(n\)	Number of complete cycles per minute \([\unit{ \per\minute}]\)
\(k_{in^3}\)	Cubic inches per cubic foot (1728) \([\unit{ \inch\cubed\per\cubicFoot}]\)

Note

The factor \((2D^2 - d_r^2)\) reflects the combined piston areas: the forward stroke sweeps \(D^2 \cdot \pi/4\) and the return stroke sweeps \((D^2 - d_r^2) \cdot \pi/4\). Their sum is \((2D^2 - d_r^2) \cdot \pi/4\). For a cylinder with no rod (or a very small rod relative to the bore), the double-acting consumption approaches twice the single-acting value.