Centripetal Acceleration Calculator

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So I was working on this story that takes place on a rotating torus-shaped space station. It became important to know exactly how fast the station would have to rotate to provide a certain level of centripetal acceleration (the equivalent of gravity, for practical purposes) to someone standing inside the rim.

It's been a long time since college physics, but it seemed like it took me even longer to plow through those old equations and figure out how to derive just one set of results. What I really wanted was to play around with different values, a process that would have taken hours on paper. So instead I spent those hours constructing a CGI script that would let me play around the values with ease. It worked so well for me, I thought other folks might be able to get some use out of it.

Here's how it works. You provide two of the three values that dictate characteristics of your station (ac, r, and/or Δt); the script calculates the one you leave out. You can choose the units for input also; if they differ from G, meters, or seconds, respectively, the results are provided in both the default and specified units. You can also set the desired output units for the unknown value.

The results print in a table that provides acceleration values for different levels of the station, moving closer to the hub in subsequent rows.

The script is written in Perl, with most of the units conversions provided by Daniel Muey's Math::Units module. Perl is not the best for casual math calculations, so there are sometimes small rounding errors in the results. Also, the script isn't really designed to squeal at invalid input. One of these days I'll fix that up.

The initial values when you access the script are the ones I finally settled on for my station. (Yeah, it's big. But the station figures in two stories I've already published, and I intend to write more set on it, so it was probably past time to nail down the dimensions.)

Have fun, and let me know if you find the calculator useful.
 

Centripetal Acceleration Calculator

centripetal acceleration (ac)  
radius (r)  
period of rotation (Δt)  
show circumference (2πr)  
show tangential velocity (vt)  
ac r  Δt 
1.25 G10000.00012 m6.21371 mi179.51958 s
1.125 G9000.00011 m5.59234 mi179.51958 s
1.0 G8000.00009 m4.97096 mi179.51958 s
0.875 G7000.00008 m4.34959 mi179.51958 s
0.75 G6000.00007 m3.72822 mi179.51958 s
0.625 G5000.00006 m3.10685 mi179.51958 s
0.5 G4000.00004 m2.48548 mi179.51958 s
0.375 G3000.00003 m1.86411 mi179.51958 s
0.25 G2000.00002 m1.24274 mi179.51958 s
0.125 G1000.00001 m0.62137 mi179.51958 s
0.0 G0.0 m0.0 mi179.51958 s