# What are discharge coefficients?

Aircraft decompression analysis performed using thermodynamics relies on a model made of a network of *volumes* connected by *vents*.

In this acceptation, a vent provides a way for the air to move from one volume to another one. Its main characteristic is thus its *area*; the bigger it is, the easier it will be for the air to move on.

However, the gross area need to be reduced by a *discharge coefficient*. Those coefficients reduce the *Actual area* to an *Effective area*.

Discharge coefficients depend on:

- pressure ratio (NACA TN1947
^{1}) - Aspect ratio (NACA TN3466
^{2}) - Hole geometry (sharp or smooth)

The dependence to pressure ratio implies that Discharge coefficients will change with respect to the time and **should thus be dynamically computed**. It is however admitted to fix them once for all.

## Cabin to Ambient Discharge Coefficient

This Discharge Coefficient is treated separately due to highest flow speed going through the explosion hole.

**The flow is very often supersonic at the beginning of the
process and CD is thus reduced**.

From FAA AC25-20, §8f:

“In calculating the cabin altitude decompression profile, unless a different value can be established by a rational analysis acceptable to the FAA, an orifice discharge coefficient of \(Cd = 0.75\) for loss of a window and \(Cd = 0.5\) for a hole resulting from fuselage damage should be assumed”

We can assume that the high Discharge Coefficient used for the loss of window is due to the *clean* way it opens for the air, by opposition to the hole resulting of fuselage damage.

## Cabin internal Discharge Coefficients

Internal discharge coefficients are not determined by regulations, but should be reasonably chosen based on geometries.

A good starting point is:

- \(Cd=0.8\): Wide ways (like artificial division between big volumes).
- \(Cd=0.6\): Large, clean ways like doors.
- \(Cd=0.4\) to \(0.45\): exotic width/height ratios, or grids, dado panels,
*etc.*.

For more exotic geometries or situations, a CFD analysis can be performed to determine the Discharge Coefficient.