Лемешко Андрей Викторович. Artificial Gravity in Multi-Plane Rotating Systems

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 within a hollow spherical habitat, which allows for a uniform distribution of centrifugal forces while minimizing the Coriolis effect. Theoretical calculations for a system with a radius of 6m show the feasibility of generating stable artificial gravity of ~1g at a low angular velocity of approximately 0.9 rad/s (~8.6 RPM). The analysis includes revised moments of inertia for a spherical shell, gyroscopic stability considerations, energy requirements, and resonance analysis, providing a foundational technical assessment of this innovative concept.

Keywords: artificial gravity, multi-plane rotation, centrifugal force, gyroscopic stability, moment of inertia, Coriolis effect, structural resonance, angular velocity, space habitat, dynamic equilibrium

Table of Contents

-1- Introduction

-2- Fundamental Principles of Multi-Plane Rotation

2.1 Centrifugal Acceleration

2.2 Distribution of Centrifugal Forces in an Eight-Plane System

-3- Gyroscopic Stabilization and Inertial Moments

3.1 Balancing Gyroscopic Moments

3.2 Energy Requirements for Spin-Up 3.3 Influence of Coriolis Force

-4- Numerical Simulation and Stability Analysis

4.1 Preliminary Dynamic Assessment

4.2 Stability and Resonance Effects

-5- Conclusion and Next Steps

-6- References

-7- Appendix A. Key Parameters of the Multi-Plane Rotational System

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 (e.g., centrifuges or toroidal stations), which can create uneven force distribution and strong Coriolis forces, leading to discomfort and nausea (see Fig. 1).

0x01 graphic

*[Figure 1: Traditional single-plane rotating space station (torus design). Illustration of uneven gravity gradients and the Coriolis effect on a moving astronaut.]*

The proposed concept of multi-plane rotation suggests the simultaneous movement of a hollow spherical structure in eight distinct planes. This approach is designed to ensure a more stable and uniform artificial gravity field while actively minimizing the disorienting effects associated with conventional designs.

2. Fundamental Principles of Multi-Plane Rotation

2.1 Centrifugal Acceleration

Centrifugal acceleration in a conventional rotating module is defined as:
(2.1)a_c = ' " r
where:

-- --- angular velocity (rad/s)

-- r --- radius of rotation (m)

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 proposed system consists of a hollow sphere rotating around four orthogonal axes, the combined motion of which defines eight planes of rotation. All axes intersect at the center of the sphere.

The resultant acceleration for a point located on the inner surface of the sphere (at radius R) is derived from the vector sum of its position vectors in each rotational plane. For a symmetric system with equal angular velocities in all planes, the magnitude of the resultant acceleration is:
(2.2)a_res = -(" a')

For each plane, the contribution is:
(2.3)a = ' " R

Thus, for four orthogonal pairs, the total acceleration is:
(2.4)*a_res = -(4 " (' " R)') = 2 " ' " R*

To achieve Earth-equivalent gravity (*a_res - 9.81 m/s'*), the required angular velocity per plane is:
(2.5)* = -(9.81 / (2 " R))*

For a habitat radius of *R = 6 m*:
(2.6)* - -(9.81 / 12) - 0.904 rad/s* (approximately 8.6 RPM)

0x01 graphic

[Figure 2: Schematic of the hollow spherical habitat. Arrows indicate the four primary axes of rotation. A point on the inner surface is shown, with vectors illustrating the centrifugal accelerations from two of the rotational planes.]

3. Gyroscopic Stabilization and Inertial Moments

0x01 graphic

Figure 3: Principle of Multi-Plane Degrees of Freedom Application

3.1 Balancing Gyroscopic Moments

The structural geometry is defined as a thin-walled spherical shell. The moment of inertia for a thin-walled sphere of mass M and radius R about any diameter is:
(3.1)*I_shell = (2 3) " M " R'*

This is larger than that of a solid sphere because its mass is concentrated at the periphery. For the multi-plane system, the total rotational inertia that must be managed is the sum of the moments for each axis:
(3.2)*I_total = 8 " I_shell = 8 " (2 3) " M " R'*

For a module with a mass of *M = 15,000 kg* and radius *R = 6 m*:
(3.3)*I_total = 8 * (2/3) * 15000 * 36 = 2,880,000 kg"m'*

This value, five times larger than the initial solid-sphere estimate, represents the significant combined rotational inertia that must be stabilized to prevent unwanted precession. Synchronized rotation across all axes is essential to maintain equilibrium.

3.2 Energy Requirements for Spin-Up

The kinetic energy required to spin up the habitat to its operational angular velocity is:
(3.4)*E_kinetic = (1 2) " I_total " ' = (1 2) " 2.88e6 " (0.904)' - 1.18 MJ*

This substantial energy requirement must be factored into the mission design, likely necessitating a gradual spin-up using efficient electric thrusters or flywheel energy storage systems.

3.3 Influence of Coriolis Force

The Coriolis force, which causes disorientation when moving within a rotating frame, is defined as:
(3.5)*F_C = 2 " m " v " *
where:

-- m --- mass of the moving object (kg)

-- v --- velocity of the object relative to the rotating frame (m/s)

-- --- angular velocity of the rotating system (rad/s)

0x01 graphic

[Figure 4: Schematic of absent Coriolis force]

The low angular velocity ( - 0.9 rad/s) of this design directly minimizes the Coriolis force, potentially reducing motion sickness compared to faster-spinning traditional designs.

4. Numerical Simulation and Stability Analysis

4.1 Preliminary Dynamic Assessment

A preliminary analysis of the system's dynamics was conducted based on the calculated moment of inertia. For instance, to maneuver the entire station with an angular acceleration of = 0.001 rad/s', the required control torque would be:
(4.1)*N_control = I_total " = 2,880,000 " 0.001 = 2,880 N"m*

This is equivalent to the force from two thrusters applying 1,440 Newtons of force at a 1-meter moment arm. This calculation highlights the need for a powerful and precise attitude control system to manage the substantial gyroscopic stiffness.

4.2 Stability and Resonance Effects

If rotational disturbances approach the natural frequency of the structure, destructive resonance can occur. The natural frequency for torsional oscillation is:
(4.2)*f_n = (1 2) " -(k / I_total)*
where:

-- f_n --- natural frequency of the structure (Hz)

-- k --- torsional stiffness of the structure (N"m/rad)

-- I_total --- total moment of inertia (kg"m')

Using a representative torsional stiffness value for a aerospace-grade aluminum alloy (e.g., 7075-T6), k - 5e6 N"m/rad:
(4.3)*f_n = (1/2) " -(5e6 / 2.88e6) - 0.21 Hz*

This low natural frequency indicates a risk of resonance with low-frequency oscillations, necessitating the inclusion of damping systems.

Methods for stabilization:

-- Damping mechanisms: Installation of vibration-absorbing components (e.g., elastomeric mounts, tuned mass dampers).

-- Active control systems: Using reaction wheels or control moment gyros to actively counteract unwanted precession and oscillations.

-- Synchronization of rotations: Precise electronic control of individual drive motors to maintain phase synchronization across all planes.

5. Conclusion and Next Steps

The proposed eight-plane rotation system within a hollow spherical shell offers several advantages:

-- Uniform Gravity: Potential for a more even distribution of artificial gravity.

-- Low Coriolis Effect: Due to the low operational angular velocity.

-- Structural Efficiency: A sphere is an efficient pressure vessel and structural form.

However, the analysis has identified key technical challenges:

-- High Moment of Inertia: Leading to significant energy requirements for spin-up/maneuvering and strong gyroscopic effects.

-- Low Resonance Frequency: Requiring careful dynamic design and likely active damping systems.

Further investigation must include detailed multi-body dynamics simulations in software like MATLAB Simulink or ANSYS to model transient states and control algorithms, followed by sub-scale prototype testing to validate the principles of synchronized multi-axis rotation.

References

[1] K. Tsiolkovsky, The Exploration of Cosmic Space by Means of Reaction Devices, 1903.

[2] T. W. Hall and M. Johnson, "Designing Rotating Spacecraft: Artificial Gravity," Journal of Aerospace Engineering, vol. 22, no. 4, pp. 456-472, 2006. doi: 10.1061/(ASCE)0893-1321(2006)22:4(456)

[3] R. W. Stone, An Overview of Artificial Gravity, NASA SP-314, 1973.

[4] G. Cl"ment and A. Bukley, Artificial Gravity, Space Technology Library. Springer, 2007. doi: 10.1007/978-0-387-72438-2

[5] W. H. Paloski, J. J. Bloomberg, M. F. Reschke, A. P. Mulavara, and G. Cl"ment, "Artificial Gravity: A Strategy for Mitigating Spaceflight-Associated Health Risks," NASA Technical Reports Server, 2019. [Online]. Available: https://ntrs.nasa.gov/citations/20190029345

[6] L. R. Young, C. M. Oman, D. M. Merfeld, K. H. Sienko, and M. Shelhamer, "Human Neurovestibular System and Artificial Gravity," Journal of Vestibular Research, vol. 19, no. 1-2, pp. 41-47, 2009. doi: 10.3233/VES-2009-0182

7.Appendix A. Key Parameters of the Multi-Plane Rotational System

Parameter	Symbol	Value	Units	Notes
Mass of habitat module	M	15,000	kg	Thin-walled spherical shell
Radius of rotation	R	6	m	Inner surface radius
Angular velocity per plane		1.28	rad/s	For Earth-equivalent gravity
Total moment of inertia	I_total	2,880,000	kg"m'	Based on shell geometry
Total kinetic energy	E_kinetic	2,355,840	J	For 8 planes: E = ""I_total"'
Natural frequency estimate	f_n	~0.094 - 0.164	Hz	For k = 10 - 3"10 N"m/rad

Note: Natural frequency range depends on material stiffness. For aluminum alloys (e.g., 7075-T6), torsional stiffness k typically lies between 10 and 3"10 N"m/rad. These values are used for preliminary resonance analysis.

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Аннотация: 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.

Лемешко Андрей Викторович Artificial Gravity in Multi-Plane Rotating Systems

Лемешко Андрей Викторович
Artificial Gravity in Multi-Plane Rotating Systems