Success Criterion Isolation

The force experienced at the top of the solenoid relative to the plate distance of ρ is created by the interaction of the pulsed and the induced electromagnetic fields. This force is acting on both the solenoid top and the surficial ERC in the under-side of the object above. The force must exceed the inertia of the object above to create maglev thrust and initiate propulsion. Any object’s inertia is a product of the mass and change in acceleration or local gravity. In orbit, a degree of gravity is present, anchoring satellites and the moon to their respective orbits. To determine the contextual object above’s inertia, the standard G = 9.8 m/s2 is used to generate the upper bound value for force required to move that object from it’s resting orbit.
With the inertial force for a chosen mass and gravity set as the left hand side of (17) and all other factors except the currents \(I_{s}\)and \(I_{e/p}\) being determined by coil winding geometry, the equation can be simplified to optimise the power supply system. The reduction of all coil design and resulting elliptical factors into a single multiplier ϖ of the plates induced current \(I_{P}\) allows designs to be quickly inspected for validity in the same manner as (10) above. Any inertial force requirement can be set then a required current found for comparison to the induced current, if the induced current is larger than that required, maglev propulsion is a success. Alternatively, if the induced current far exceeds the required current, (18) could be rearranged to find the largest accelerable mass for any design. The derivation path is applicable to any two coil context however the interaction formulae do change based on winding geometry categories.
\(F_{\text{sz}}\left(\rho\right)=\ \varpi\ I_{P}\ \)=\(\text{ϖ\ }\frac{\text{L\ }\frac{dI_{S}(t)}{\text{dt}}\ }{M}=ma=\ F_{\text{ma}}\)
Magnetic force interaction simplification (18)
The satellite propelled cargo containers will be accelerated at tiered rates according to their contents. Construction materials and non-sensitive bulk cargo could potentially be launched at up to 50 G pulsed acceleration however sensitive equipment will be limited to 20 G acceleration change in line with NASA’s 2018 Mars Rover orbital entry speed.
While the scenarios above discuss a steel plate’s decomposition for electromagnetic analysis, from the presented dimensions the calculated mass exceeds that of a 20-ft shipping container with a cargo mass capacity of 25,400 kg. This leads to the conclusion that a variety of container designs can be substituted within that representative plate mass \(m_{p}\) and then optimised to achieve success. To assess the viability of the overall system, both the cargo mass \(m_{c}\) and container mass \(m_{p}\) must be totalled \(m_{t}\) then later optimised with respect to the solenoid strength and power storage capacity.
To accelerate the proposed cargo and plate at 50 G for a 1 second pulse requires a force \(F_{t50}\) of 1749 kN to overcome inertia while\(F_{c20}\) = 392 kN is the local minima at 22% of \(F_{t50}\). Considered in reverse, \(F_{t50}\) is 446% of \(F_{c20}\) resulting from the 178.5% increase from \(m_{c}\) to \(m_{t}\) and increase of acceleration by 250% from 20G to 50G. With the force requirement being met by a sum of propulsion pulse vectors, the required force output per individual satellite is lower however the composition of this function must be investigated specifically due to the multitude of mutual inductances. Swarm force distribution function aside, achieving the minima of 392 kN force in \(F_{c20}\) for scenario 1\(a_{e}\) requires a pulse induced current \(I_{1e}\) of 23.5x106 A and\(I_{1x}\) of 1.2x106 A when considering the minimum ERC scenario 1\(a_{x}\). While the peak current and minimum ERC size scenario is optimal, no presented scenario achieved the required current induction for successful maglev propulsion. Division of the induction requirement between four tethered satellites under the plate does not achieve the requisite current with the presented design either. Despite this, the investigation of the problem context and construction delivered valuable design conclusions.