Kinda ran out of steam on the math here, but figured it was worth publishing partly finished. The concept works, but the math is a little harder than I initially thought it would be, so I'm unsure exactly how much thrust this idea would create. My intuition is that it'd be on the order of magnitude of the amount of forward thrust as a car engine makes.
Radvic's Analysis of Mechanical Abomination as a Form of Airship Propulsion (Work in Progress)
There have been several proposals for propulsion for a zeppelin type project. From vague applications of explosive seals, to airbased seal propellors to fast falling areodynamic airships. Here, we propose a separate, previously undiscussed (on SV) method of propulsion, lovingly named the Mechanical Abomination (MA). The concept is to modify the Macerator V2.0 slightly to make a type of perpetual motion machine, creating an endless cycle of thrust. To my knowledge, this construction would require two modifications to the Macerator seal: 1, the Macerator no longer minces objects, and 2, the Macerator is triggered via a tripwire. For the purposes of this article, I will describe such seals (store something at rest via tripwire, then release it at 20 m/s via a second tripwire) as Thrusters. Given the minor nature of these modifications, I expect it would take something like one to three days to construct a Thruster seal.
General Concept
Macerators don't have a recoil to them. This means they are imparting force to a system. Thrusters take this concept, make it easier to harness by not mincing contents, and automate it via tripwires.
Method
Take one thruster seal and affix it over a box (box construction material currently unspecified, likely wood, could be granite). We will call this Thruster seal Thruster 1. Have Thruster 1 face another box with a thruster seal, with the two boxes connected via a ninja-wire, and looping over a length of material (likely wood, possibly granite). We will call the second thruster seal Thruster 2, the connecting ninja wire the Wire, and the material all these are on and around the Assembly. Add a third and fourth Thruster in front of the second Thruster. Store a block of mass M into Thruster 1, and have it unseal it into the box of Thruster 2. Mass M then falls into the box of Thruster 2, imparting a force to the system. Thruster 1, Thruster 2, Thruster 3, Thruster 4, Mass M, and the Wire, and the Assembly now begin moving forward due to conservation of linear momentum, and everything aside from the Assembly begins rotating around the Assembly due to conservation of angular momentum. Have a tripwire at the bottom of the box mass M falls into store mass M into Thruster 2. Next, wait until the Wire rotates Thruster 2 into the position Thruster 1 was in relative to the Assembly. Have it activate a tripwire which unseals mass M from Thruster 2, which shoots it forward, landing into the box of Thruster 3. Wait until Thruster 3 has rotated into position, and have it launch mass M into Thruster 4. Wait until thurster 4 is in position, and launch mass M into Thruster 1. Repeat.
The net effect of this is to create some forward momentum with each unsealing of mass M, and some angular momentum. The problem of created angular momentum can be solved by having an even number of Mechanical Abominations, with an equal number rotating clockwise and counterclockwise.
Analysis of impulse provided by an individual Mechanical Abomination
Each time that a thruster unseals mass M, we get an impulse of 20 m/s * M added to the system. To determine exactly how much thrust this adds to the system with each iteration, we consider each relevant interaction the system undergoes by considering three different times and the transitions between them. At time 1, mass M is sealed. At time 2, mass M is flying towards the Thruster box ahead of it. At time 3, mass M has collided with the thruster box ahead of it and is at an equilibrium with the system. This then cycles back to time 1.
To do the math, we will make the following assumptions:
Mass of the Wire is negligible.
The Wire sufficiently connects Thruster Boxes such that they do not vary in their placement relative to each other.
Angular momentum is solved via symmetry and thus ignored.
All of the material strengths are sufficient to not break with the forces undertaken.
Mass of Thruster boxes = 5 kg per box
Mass of Assembly = 10 kg
Mass of Mass M = 100 kg
Number of Thruster boxes = 4 per Mechanical Abomination
At Time 1, all is considered at rest.
At Time 2, Mass M is traveling forward at 20 m/s with a net momentum of m * v = 2000 kgm/s
At Time 3, Mass M has come to equilibrium with the rest of the system, meaning momentum at Time 2 = momentum at Time 3, or
p_2 = p_3
Where we solved for p_2 earlier as 2000 kgm/s
p_3 is equal to the linear momentum of each of the constituent parts. Or,
p_3 = p_thrusterboxes + p_mass_M + p_assembly
Due to the thruster boxes being connected to each other via the Wire and rotating around the Assembly, we know the net momentum of the thruster boxes is:
p_thrusterboxes = m_thrusterboxes * number_thrusterboxes * v_assembly
We also know the momentum of the assembly is given by
p_assembly = m_assembly * v_assembly
and momentum of mass M is
p_Mass_M = m_Mass_M * v_Mass_M
Which gives us one equation and two variables... which I can't be bothered to solve right now (proper solving would account for angular momentum and use that equation to calculate forward impulse, but that will be dependant on r_perp, which will depend on the scale we make these machines). Regardless, p_3 is going to be larger than p_1, and should have a net forward moving action on the system. The exact values of which are difficult to determine (feel free to expand on this work if you want).
