Project: Hypergravity Habitat
Document type: preliminary engineering sizing and parameter study
Status: working document for pre-feasibility review
Scope: relationship between target effective gravity, lateral acceleration, radius, speed, angular rate, infrastructure size, and first-order cost drivers
This document provides first-order sizing relationships for candidate Hypergravity Habitat configurations. It is not a construction proposal and should not be read as a final engineering design.
Its purpose is to make the dominant physical relationships explicit before architecture selection. For a terrestrial circular platform, target effective gravity is treated as the vector result of Earth gravity and generated lateral acceleration.
For a body moving in a circle:
a_c = v² / r = ω²r
where:
a_c is centripetal acceleration in m/s²,v is tangential speed in m/s,r is radius in m,ω is angular velocity in rad/s.On Earth, a circular platform combines vertical gravity with horizontal centripetal acceleration:
g_eff = √(g² + a_c²)
Solving for the required lateral acceleration:
a_c = g × √(g_rel² − 1)
where g_rel is the desired resultant effective gravity in multiples of 1 g.
The bank angle or cabin-tilt angle needed to align the floor with the resultant load vector is:
θ = arctan(a_c / g)
| Target resultant effective gravity | Required lateral acceleration | Required lateral acceleration | Approximate resultant-vector angle |
|---|---|---|---|
| 1.05 g | 3.14 m/s² | 0.320 g | 17.8° |
| 1.10 g | 4.49 m/s² | 0.458 g | 24.6° |
| 1.20 g | 6.50 m/s² | 0.663 g | 33.6° |
| 1.25 g | 7.35 m/s² | 0.750 g | 36.9° |
| 1.50 g | 10.96 m/s² | 1.118 g | 48.2° |
These requirements influence operating speed, track design, comfort, land use, safety, and feasibility.
| Radius | Circumference | Diameter | Approximate enclosed area |
|---|---|---|---|
| 100 m | 0.63 km | 200 m | 3.1 ha |
| 200 m | 1.26 km | 400 m | 12.6 ha |
| 400 m | 2.51 km | 800 m | 50.3 ha |
| 500 m | 3.14 km | 1.0 km | 78.5 ha |
| 1,000 m | 6.28 km | 2.0 km | 314 ha |
| 2,000 m | 12.57 km | 4.0 km | 1,257 ha |
Larger radii reduce angular rate but increase land use, guideway length, civil infrastructure, and likely cost.
Using the resultant-gravity model above:
| Radius | Speed for 1.10 g resultant | Speed for 1.25 g resultant |
|---|---|---|
| 100 m | 76 km/h | 98 km/h |
| 200 m | 108 km/h | 138 km/h |
| 400 m | 153 km/h | 195 km/h |
| 500 m | 171 km/h | 218 km/h |
| 1,000 m | 241 km/h | 309 km/h |
| 2,000 m | 341 km/h | 437 km/h |
These values show why modest resultant gravity increases can still imply demanding operating speeds at large radius.
| Radius | Lap time at 1.10 g | Angular rate at 1.10 g | Lap time at 1.25 g | Angular rate at 1.25 g |
|---|---|---|---|---|
| 100 m | 30 s | 2.02 rpm | 23 s | 2.59 rpm |
| 200 m | 42 s | 1.43 rpm | 33 s | 1.83 rpm |
| 400 m | 59 s | 1.01 rpm | 46 s | 1.29 rpm |
| 500 m | 66 s | 0.91 rpm | 52 s | 1.16 rpm |
| 1,000 m | 94 s | 0.64 rpm | 73 s | 0.82 rpm |
| 2,000 m | 133 s | 0.45 rpm | 104 s | 0.58 rpm |
Angular rate is important for vestibular and Coriolis effects. A large radius can reduce angular-rate concerns but may require high speed and very large land area.
A circular railway or maglev system must be evaluated against multiple coupled variables:
No single radius is optimal without weighting these variables against scientific requirements.
The sizing relationships suggest that early demonstrators should not aim immediately for large human-habitat systems.
More credible early steps include:
A human-rated railway or maglev habitat would require a much more demanding safety and operations case.
At this stage, cost should be treated parametrically rather than as a single headline number. Main drivers include guideway length, civil works, vehicle or payload-module design, power, control and safety systems, support buildings, environmental control, emergency infrastructure, permitting, commissioning, energy, maintenance, staffing, payload operations, and data management.
The following placeholder uses a notional high-quality circular guideway or railway construction cost of 25 M€/km. This number is not a validated estimate and must be replaced with project-specific cost data.
| Radius | Circumference | Placeholder guideway cost |
|---|---|---|
| 100 m | 0.63 km | 15.7 M€ |
| 200 m | 1.26 km | 31.4 M€ |
| 400 m | 2.51 km | 62.8 M€ |
| 500 m | 3.14 km | 78.5 M€ |
| 1,000 m | 6.28 km | 157.1 M€ |
| 2,000 m | 12.57 km | 314.2 M€ |
This table includes only guideway length. It excludes land, vehicles, buildings, laboratories, power, control, safety systems, contingency, and operations.
Smaller radii reduce land use and guideway length, but increase angular rate, curvature, wear, and gravity gradients. Larger radii reduce angular rate and improve some human-factors constraints, but increase land use, required speed, capital cost, and emergency-response complexity.
This document should be followed by reproducible calculations for emergency stopping distance, propulsion power, aerodynamic drag, rolling resistance or maglev power demand, vibration assumptions, ride-quality limits, banking geometry, gravity gradients, payload-environment variability, land-use constraints, energy, and operational cost.
All future calculations should state equations, units, assumptions, and uncertainty.
The sizing model shows that even modest resultant hypergravity levels may require substantial lateral acceleration. This strengthens the case for staged demonstrators, careful modelling, and architecture-neutral trade studies before any large facility is proposed.
The most immediate engineering output should be a reproducible parameter model that allows reviewers to vary target gravity, radius, speed, angular rate, bank angle, land use, and cost assumptions.
Project: Hypergravity Habitat · Status: exploratory research documentation · License: see repository license and file-level notes