Calculating gravity

[LOLZpersonok]

I'm currently jotting down ideas for a video game that I plan on making sometime in the future, and one of my ideas is that there will be a space station that the player can visit. This space station I'm making up is pretty much the same thing as the Stanford Torus, (click the link to see what I'm talking about - you might need to) only except my rendition is bigger. Here's the thing - though it wouldn't be necessary to know in the game, I think it'd be a fun bit of information.

 

Here are some facts about the Stanford Torus:

Supports roughly 10,000 people

Total diameter: 1.790 kilometres (1.11 miles)

Habitable tube diameter (the part where people would live in): 130 metres (430 feet) - only half of the tube can have buildings (Images on the Wikipedia article show the cross section)

Rotation: 1 revolution per minute - should simulate Earth gravity

Gravity: 1.0g (same as Earth)

Unsure of the population density - would like to figure this out and use it towards my station

 

Here are some facts about my station:

Supports roughly 150,000 people

Total diameter: Not sure yet (thinking maybe around 10 kilometres or 6.21371 miles)

Habitable tube diameter: Not sure yet

Rotation: Unsure - would like to figure this out

Gravity: 1.0g

Unsure of the population density - would like to know this

 

The thing is, I'm really bad at math. Like really bad. I don't know how to figure this all out. I want to calculate my station on the same scale as the Stanford Torus, only except with a population of 150,000. I want to know what the diameter of my station should be, what the habitable tube diameter should be and how fast it should rotate in order to simulate Earth's gravity. I'd also like to know the population density, just as a fun fact. Calculating the population density of this station would be more difficult than calculating the population density of a city on earth. So, I'm asking the help of people here. Someone should know how to do this, because I don't.

[Spartancloud]

Assuming that the total diameter is to the floor level in the habitat tube (which the rotation for 1 g of gravity seems to suggest), and the habitat tube diameter is the interior diameter, the floor area would be 7314049 m² and the population density is 0.013679 people/m², or 73.1 m²/person.

 

Using a total diameter of 10 km, and a population of 150,000 people, you would need a habitat diameter of around 349 m, to match the population density. And at that diameter you would need a rotation of 0.2991655 revolutions per minute to match the gravity.

 

At least that's what I calculated, there was some minor rounding but nothing to significant if this is just for a video game, hope that helps you out.

 

- Edit: If you want to know how to calculate that just let me know, and I can explain it. It's not terribly complicated to understand.

[LOLZpersonok]

7 hours ago, Spartancloud said:

Assuming that the total diameter is to the floor level in the habitat tube (which the rotation for 1 g of gravity seems to suggest), and the habitat tube diameter is the interior diameter, the floor area would be 7314049 m² and the population density is 0.013679 people/m², or 73.1 m²/person.

 

Using a total diameter of 10 km, and a population of 150,000 people, you would need a habitat diameter of around 349 m, to match the population density. And at that diameter you would need a rotation of 0.2991655 revolutions per minute to match the gravity.

 

At least that's what I calculated, there was some minor rounding but nothing to significant if this is just for a video game, hope that helps you out.

 

- Edit: If you want to know how to calculate that just let me know, and I can explain it. It's not terribly complicated to understand.

Thanks for that. I wouldn't have been able to figure it out myself, and Internet research did not help with it. It'll just be used as fun facts when I actually start making it.