# Mass Injection

The amount of mass injected into the airbag needs to be defined with respect to time. This is required as a function.

The specific heat, ${c}_{p}$ , along with a function defining the change in temperature with time is required.

The data can be obtained by two methods:

- Possibly from the airbag manufacturer
- From a tank experiment

A diagram of a tank experiment can be seen in Figure 1.

The mass versus time curve can be derived from the pressure curve if ${T}_{in}$ is known:

$$\dot{m}=\frac{\dot{P}VM}{\gamma R{T}_{in}}$$

Where, $M$ is the molecular weight of the injected gas. $R$ is the perfect gas constant: $\frac{R}{M}={c}_{p}-{c}_{v}$ ; $\gamma =\frac{{c}_{p}}{{c}_{v}}$ .

The average estimate for temperature of injection is:

$${T}_{in}=\frac{\text{\Delta}P}{\text{\Delta}m}\frac{VM}{\gamma R}$$

Where,

- $\text{\Delta}P$
- Total pressure variation during the experiment
- $\text{\Delta}m$
- Total injected mass, which can be derived from the mass of propellant in the pyrotechnic inflator and the chemical reaction; 40% is a typical value for the ratio of the produced mass of gas to the solid propellant mass.