Artificial Gravity in Multi-Plane Rotating Systems

Abstract

The creation of artificial gravity is a key challenge for deep space exploration and long-duration space missions. This paper examines the method of multi-plane rotation, which allows for an even distribution of centrifugal forces inside the chamber while minimizing the Coriolis effect. Theoretical calculations considering angular velocity, moments of inertia, and structural stability are presented.

1. Introduction

Artificial gravity is essential for preventing the negative effects of prolonged exposure to microgravity, such as muscle atrophy and reduced bone density.

Traditional models use single-plane rotation, which creates uneven force distribution.

The proposed concept of multi-plane rotation suggests simultaneous movement of the structure in eight planes, ensuring stable artificial gravity without significant oscillations.

2. Fundamental Principles of Multi-Plane Rotation

2.1 Centrifugal Acceleration

Centrifugal acceleration in a conventional rotating module is defined as:

[ a_c = \frac{v2 r ]

where:

• ( \omega ) angular velocity,
• ( r ) radius of rotation.

The higher the angular velocity and chamber radius, the stronger the artificial gravitational force.

2.2 Distribution of Centrifugal Forces in an Eight-Plane System

The resultant acceleration in a system with eight planes of rotation is:

[ a_{res} = \sqrt{a_12 + a_52} ]

For each plane:

[ a_i = \omega_i^2 R ]

Thus, the total acceleration:

[ a_{res} = \sqrt{\sum_{i=1}4 R^2} ]

To achieve ( a_{res} \approx 9.81 ) m/s' (equivalent to Earths gravity), the optimal angular velocity is:

[ \omega_i = \sqrt{\frac{9.81}{R}} ]

For ( R = 6 ) m:

[ \omega_i \approx 1.28 \text{ rad/s} ]

3. Gyroscopic Stabilization and Inertial Moments

3.1 Balancing Gyroscopic Moments

For structural stability, moments of inertia must be calculated for each axis:

[ I_i = \frac{2}{5} M R^2 ]

Total moment of inertia across eight planes:

[ I_{total} = 8 \times I_i = 8 \times \frac{2}{5} M R^2 ]

For ( M = 15 ) t and ( R = 6 ) m:

[ I_{total} = 576000 , \text{kg} \cdot \text{m}^2 ]

To prevent undesirable oscillations, synchronized rotation across all axes is required.

3.2 Influence of Coriolis Force

One issue with traditional centrifuges is the Coriolis force, which causes disorientation when moving within the rotating module. It is defined as:

[ F_C = 2 m v \omega ]

In the eight-plane rotation system, this effect is minimized due to:

• uniform artificial gravity distribution,
• absence of abrupt transitions between movement directions,
• stability ensured via gyroscopic mechanisms.

4. Numerical Simulation of Stability

To verify dynamic characteristics, the following tools are proposed:

• MATLAB Simulink rotation dynamics simulation.
• ANSYS Fluent analysis of forces and stability.
• SolidWorks Motion kinematic modeling.

4.1 Optimization of Angular Velocities

If angular velocities are not equal, dynamic asymmetry may arise, leading to system instability. To prevent this, synchronization must be maintained:

[ \omega_i = \sqrt{\frac{9.81}{R}} ]

alongside adjustments to inertial properties.

4.2 Stability and Resonance Effects

If rotational frequencies match the natural frequency of the structure, destructive resonance oscillations may occur. System stability can be analyzed through:

[ f_n = \frac{1}{2\pi} \sqrt{\frac{k}{I_{total}}} ]

where ( k ) represents material stiffness.

Methods for stabilization:

1. Damping mechanisms installation of vibration-absorbing components.
2. Center-of-mass correction redistribution of density.
3. Synchronization of rotations precise velocity control.

5. Conclusion

The proposed eight-plane rotation system has several advantages:

• Compact design: optimized chamber size without massive structures.
• Stable artificial gravity: uniform force distribution.
• Energy efficiency: potential use of solar power.
• Reduced Coriolis effect: minimized motion disorientation.

Further investigation should include detailed numerical simulations and real-world testing of structural parameters.