1 The variables

• Hammer spring
  • length
  • wire diameter
• Hammer
  • mass
  • travel
• Valve
  • opening surface area
• Valve return spring
  • spring constant
  • proload
• Plenum
  • volume
  • regulated pressure
• Regulator
  • recovery rate

2 The firing process and physics

2.1 Cocked hammer

The amount of energy stored has to do with spring rating and the length of compression. This energy has nothing to do with the mass of the hammer.

The spring constant \(k\) is measured in force per distance. The SI unit is \(\mathrm{N}\mathrm{m}^-1\). The potential energy stored in a spring compressed by a displacement of \(x\) is \(\frac{kx^2}{2}\).

For a spring that is uniform, the length of the spring does not affect \(k\).

The cocking mechanism of most PCPs dictate a maximum \(x\). If the hammer is allowed to “free-flight”, the actual compression displacement can be less than this maximum.

2.2 Upon hammer valve stem impact

After the firing mechanism launches the hammer, the compressed spring decompresses and the stored energy is then converted to kinetic energy in the hammer in flight.

Upon the hammer impacting the valve stem, conversations of momentum and energy are both in play. The impact decelerates (rather quickly) the hammer. Due to the conversations of momentum, two components have movements.

The action of the airgun is often much more massive than the hammer. As a result, conservation of momentum suggests the action should move only very slightly.

The valve stem, on the other hand, has a very low mass. However, there is regulated high pressure air pushing the valve stem. The conversation of energy is in play to determine how the valve opens.

Note that if the hammer does not have enough velocity, it is possible that the conversation of momentum causes the entire action to move in a way that there is not enough impact to open the valve.

Assuming there is enough energy, and that the action is massive enough, the kinetic energy of the hammer is then applied as force times distance to push the valve back by a displacement. This is a highly non-linear formula because once the valve opens, pressurized air exhausts via the exhaust port, which reduces the force acting on the valve. This, in return, increases the displacement of the valve stem.

2.3 Upon the valve stem reaching is maximum displacement

At this point, all the kinetic energy of the hammer is transferred. The valve stem is displacement to the maximum. Part of the kinetic energy of the hammer is now stored as the valve return spring compresses. The force due to the valve return spring, combined with the residual pressure in the plenum, starts to push the valve stem back to shut off the valve.

However, at this point, this combined force is not only acting on the valve stem, but also the hammer. This combined mass determines how quickly the valve can close.