###### Abstract  
This paper shows the development of a numerical analysis model, which enables the calculation of the cargo transport capacity of a vehicle that circulates through a vacuum tube at high speed, whose effectiveness in transport is analyzed. The simulated transportation system is based on vehicles moving in vacuum tubes at high speed, a concept commonly known as Hyperloop, but assuming the vehicles for cargo containers. For the specific vehicle proposed, which does not include a compressor and levitates on magnets, the system formed by the vehicle and the vacuum tube has been conceptually developed, establishing the corresponding mathematical relationships that define its behavior. To properly model the performance of this transport system, it has been necessary to establish the relationships between the design variables and the associated constraints, such as the Kantrowitz limit, aerodynamics, transport, energy consumption, etc. Once the model was built and validated, it was used to analyze the effects of the variation of the number of containers, the operating speed and the tube length, considering the total and specific consumption of energy. After finding the most efficient configuration regarding energy consumption and transport effectiveness, the complete system was calculated. The results obtained constitute a first approximation for the predesign of this transport system and the built model allows different alternatives to be compared according to the design variables. mathematical modeling; high-speed transport; freight transport; sustainable transport +
Footnote †: journal: _arxiv. within a single capsule/pod As for the infrastructure, a linear geometry has been studied, with a straight tube with zero slopes, and which can be 500, 750 or 1000 km long between origin and destination. Due to work limitations, other issues such as technical and economic feasibility [3], control loops, stability, infrastructure, vehicle structure, heat transfer, EDS geometry and electrical systems are out of scope and may be eligible for additional work. This research paper can be compared to other cutting-edge work on high-speed transportation systems but differs in some significant respects. These differences are listed below. Reference [4] models a high-speed transportation system and optimizes it, but the system is for passengers instead of cargo and the number of capsules per vehicle is not varied when the energy consumption is minimized. Reference [5] models the system, but it does not use formulae to optimize the system, as the article is only a technology review. Reference [6] models the system and optimizes it, although the system optimization only focuses on levitation and propulsion (electromechanics) and leaves out the other subsystems. References [7; 8; 9] also model the system, but their model is used to study dynamics, so the system is not optimized, and capacity is not discussed. Reference [10] discusses transport capacity after building a model, which is based upon logistics relations rather than the physical relations coming from the physical phenomena that occur in the system. Reference [11] focuses on the aerodynamics and thermodynamics of the Hyperloop, but these models also leave out the other subsystems. References [12; 13] limit their analyses to aerodynamics, with a different approach (experimental and numerical, respectively), although the other subsystems are also out of scope. The main contribution of this work is the determination of the most suitable masses and volumes for freight transport using containers in a vehicle that travels at high speed in a vacuum tube levitating on magnets, with the objective of achieving the highest effectiveness possible and allowed. It is important to remark that effectiveness is the sum of efficiency (lower energy consumption per ton and kilometer transported) and efficacy (higher cargo throughput in the transportation system). In order to attain this objective, the procedure of analysis has been altered in regard to the previous research.