# Homework Help: Space Station and motion sickness

1. Oct 1, 2007

### eanderson

In designing rotating space stations to provide for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than two revolutions per minute. On the other hand, the magnitude of the centripetal acceleration at the astronauts' feet should equal the magnitude of the acceleration due to gravity on earth. Thus, to eliminate the difficulties with motion sickness, designers must choose the distance between the astronauts' feet and the axis about which the space station rotates to be greater than a certain minimum value. What is this minimum value?

2. Oct 1, 2007

### mgb_phys

Hint:
The 'centrifugal force' on a rotating body like this if F = m w^2 r where w ( really omega) is in rad/s

3. Oct 1, 2007

### eanderson

ok so what is m? and rad/s? rotations per second?

Set the magnitude of centripetal acceleration equal to the magnitude of the acceleration due to gravity on earth and solve for the radius of the circle.

thats a clue i was given after i missed the question the first time

4. Oct 1, 2007

### mgb_phys

The force due to gavity is F = m g
The force created by the rotation is F = m w^2 r
You need to find the w such that these are equal.

5. Oct 1, 2007

### eanderson

im still lost...w = omega = ??, the clue tells me to solve for radius

what i took from the clue is this

a=v^2/r
a=9.8 because thats acceleration due to gravity on earth
9.8=v^2/r....how do you find v

6. Oct 1, 2007

### mgb_phys

Simply set the two equations equalt to each other. F = mg = m w^2 r
The mass cancels - you have learn't that acceleration of a falling body doesn't depend on mass?
So, g = w^2 r or r = g/w^2
w is the rotation rate in radians/second, there are 2*pi radians in a circle and you have been told that the maximum rotation rate is 2 rotations/min.
So convert 2 rotations / minute into radians/second and put into the above equation.

ps. Omega is the greek letter used as a symbol for rotation rate and is what probably appears in your textbook - it looks like a curly 'w'

7. Oct 1, 2007

### TVP45

What is the source for your information?

8. Oct 2, 2007

### TVP45

Hi,
I asked about the source of your question because it has some of the characteristics of an urban legend. It appears many places with only the rotation speeds changed. It appears to be based on research from the 1960s that is now considered flawed.

Based on that research, the minimum radius would be somewhere in the 200-300 meter range. That number got some traction in the Arthur C. Clarke story 2001, A Space Odyssey.

Recent work, however, suggests a radius of somewhere between 25 and 100 meters will work as well. There is a lot of research currently being done at Johnson Space Center, Brandeis Univ, etc. etc. You might Google those, particularly looking at short-radius centrifuge.

9. Oct 2, 2007

### mgb_phys

Sorry TVP45 - wasn't sure if you were talking to me or the OP?
I thought the limit was pretty unrealistic, the difference in 'weight' between the head and the feet I wouldn't have thought was very discernable - the other problem would be the coriolis force which would make people think they are twisting to the side.

But since the OP didn't know what radians were I thought this might be a point too far - it is obviously some homework set by a teacher from either memory or an old textbook.

10. Oct 2, 2007

### HallsofIvy

The question is WHO are you asking for the source? mgb_phys is just stating well known physics formulas. Are you asking eanderson about the source for " Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than two revolutions per minute"? I suspect that was from his homework assignment!

11. Oct 2, 2007

### TVP45

My apologies. I goof up the indentation on this forum sometimes. I was addressing the OP.
mgb, the Coriolis force is the originally identified problem, but those studys did not include intent. Astronauts routinely adapt to larger inputs.