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I highly recommend reading

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
The internal pressure of air is a big part of forces, and if it will be 1/3 of normal (used in some spacecraft's), and 1/3g (mars like) - it will be bigger, 3 times at least.

The main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is the difference in speeds between internal and external structure(there are some tricks trough).

With stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With the strongest material as we know at the moment(>100GPa), it may be 50 times bigger - so 180km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for the size of a craft with centrifugal style gravity.

A rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there is a linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder itself more robust helps)

The cylinder is more limited with the material strength we have and the amount of that material, and our wishes to move so much material.

P.S.

Here is some NASA stuff, about choosing sizes, masses of possible habitats, crew. It's from Space Settlements: A Design Study broader and more practical overview of that topic.

I highly recommend reading

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
The internal pressure of air is a big part of forces, and if it will be 1/3 of normal (used in some spacecraft's), and 1/3g (mars like) - it will be bigger, 3 times at least.

The main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is the difference in speeds between internal and external structure(there are some tricks though).

With stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With the strongest material as we know at the moment(>100GPa), it may be 100 times bigger - so 320km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for the size of a craft with centrifugal style gravity.

A rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there is a linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder itself more robust helps)

The cylinder is more limited with the material strength we have and the amount of that material, and our wishes to move so much material.

P.S.

Here is some NASA stuff, about choosing sizes, masses of possible habitats, crew. It's from Space Settlements: A Design Study broader and more practical overview of that topic.

I highly recommend to read

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
Internal pressure of air is big part of forces, and if it will be 1/3 of normal (used in some spacecrafts), and 1/3g (mars like) - it will be bigger, 3 times at least.

Main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is difference in speeds between internal and external structure(there are some trick trough).

With more stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With strongest material as we know at the moment(>100GPa), it may be 50 times bigger - so 180km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for size of a craft with centrifugal style gravity.

Rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder it's self more robust helps)

Cylinder is more limited with material strength we have and amount of that material, and our wishes to move so much.

P.S.

Here is some NASA stuff, about choosing sizes, masses of possible habitats, crew. It's from Space Settlements: A Design Study broader and more practical practical overview of that topic.

I highly recommend reading

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
The internal pressure of air is a big part of forces, and if it will be 1/3 of normal (used in some spacecraft's), and 1/3g (mars like) - it will be bigger, 3 times at least.

The main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is the difference in speeds between internal and external structure(there are some tricks trough).

With stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With the strongest material as we know at the moment(>100GPa), it may be 50 times bigger - so 180km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for the size of a craft with centrifugal style gravity.

A rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there is a linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder itself more robust helps)

The cylinder is more limited with the material strength we have and the amount of that material, and our wishes to move so much material.

P.S.

Here is some NASA stuff, about choosing sizes, masses of possible habitats, crew. It's from Space Settlements: A Design Study broader and more practical overview of that topic.

I highly recommend to read

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
Internal pressure of air is big part of forces, and if it will be 1/3 of normal (used in some spacecrafts), and 1/3g (mars like) - it will be bigger, 3 times at least.

Main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is difference in speeds between internal and external structure(there are some trick trough).

With more stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With strongest material as we know at the moment(>100GPa), it may be 50 times bigger - so 180km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for size of a craft with centrifugal style gravity.

Rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder it's self more robust helps)

Cylinder is more limited with material strength we have and amount of that material, and our wishes to move so much.

I highly recommend to read

O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.

Up to 16km radius is doable with usual materials. Conservative with old steel (1920) 3.2km

$\tiny \text{Source, O'Neill, G. K: The Colonization of Space, Physics Today, vol. 27, no. 9, Sept. 1974, pp. 32-40.}$

One foreseeable development is the use of near-frictionless (for example, magnetic) bearings between a rotating cylinder and its supporting structure, which need not be spun. For eight tons per square meter of surface density and a tensile strength of 300,000 psi, R would be 16 km, the total area would 50,000 km2, and the population would be between five million (low density) and 700 million (the ecological limit, the maximum population that can be supported).

This is with common materials, with 1g, and normal pressure.
Internal pressure of air is big part of forces, and if it will be 1/3 of normal (used in some spacecrafts), and 1/3g (mars like) - it will be bigger, 3 times at least.

Main problem here is this surrounding external supporting structure(how much material we may have) and interaction of internal structure with that external one, bigger is radius bigger is difference in speeds between internal and external structure(there are some trick trough).

With more stronger materials, not know at that time 1975, structure may be bigger, linear proportion here 5 times stronger material, 5 times bigger radius. With strongest material as we know at the moment(>100GPa), it may be 50 times bigger - so 180km radius (or bigger with 1/3g and 1/3 pressure)

But that's still not the limit, but probably good enough for size of a craft with centrifugal style gravity.

Rough estimation of limit is actually external structure and it's ability to hold 1bar pressure. And roughly there linear proportion between thickness of walls and radius of cylinder, more complex internal structure of cylinder also may help (remove pressure of air stress to walls - tethers inside with central axis - so making cylinder it's self more robust helps)

Cylinder is more limited with material strength we have and amount of that material, and our wishes to move so much.

P.S.

Here is some NASA stuff, about choosing sizes, masses of possible habitats, crew. It's from Space Settlements: A Design Study broader and more practical practical overview of that topic.