Are recoil operated crossbows/ballistae feasible?

Question

• This question is specifically about stationary or vehicle mounted crossbows, not man-portable ones
• The projectile size would measure about 1.8 - 2 meters in length, so the crossbow would have corresponding proportions
• The materials would be wood and metal/metal compounds, no plastics
• The goal is to have a siege engine capable of cocking itslef, like a recoil operated firearm would

The easiest concept I have in my head for this would be as follows:

1. There's a carriage riding on two rails that carries the projectile
2. The carriage has two holes on the sides
3. A wire is threaded through these holes
4. At the front of the crossbow two springs are placed around the wire
5. When the carriage gets released and propells the projectile it hits the springs and gets pushed back into it's resting position

(simple sketch of it)

1. Could the cocking springs provide enough energy to push against the limbs and get the carriage back into it's resting position?
2. Are there any pitfalls with a system like this?
3. Is there a more efficient way to build a recoil operated crossbow?

Answer 1

To make my comment into an actual answer, this design is not feasible because the energy balance doesn't add up. All the energy that you have available is stored in the limbs being pulled back. Now you need to do three things with it:

1. Accelerate the projectile
2. Reload the crossbow
3. Overcome friction in the system

The problem is, that the energy required for reloading is exactly the same as you started out with, but you still want to accelerate your projectile, so both together doesn't work. Not to mention friction losses of the sliding action and in the springs, so even without projectile it would probably not work.

The reason automatic firearms can do this, is that they tap the high pressure gas in the barrel, basically using some of the chemical energy in the gunpowder.