So, I'm attempting to build an egg launching sled. This will be roughly 2.0 to 2.5 feet long, and be powered by surgical tubing. Ultimately, I would like to increase the range to around 100 feet. When the first phase is built and working (i.e. egg will launch), I will add automation mechanics: lead screw and carriage to re-set the launching sled, and a servo controlled release mechanism to fire. I think I have a pretty good design, but I'm very new to this, and need some basic context on the force required, if anyone knows and would be kind enough to offer some advice.
These are my questions:
1. How much force would I need to generate to launch an egg around 100' via the tubing? And is a 2' rig long enough?
2. If I succeed in building it, how do I size the motor and lead screw? I've spent a lot of time researching r/c hobby motors and typical d/c and servo motors/controllers, but I'm just not sure. Can anyone provide just a little context- for example, do I need a small, d/c gear motor or maybe a modified servo for the lead screw, or are we talking something similar to the d/c motors that drive scooters?
Any help would be much appreciated. I included a very basic image below of what I'm looking to build. But this is just for reference, not really to scale and no mechanical details included.