Path of falling person inside B5 rotating space station

[Robert100]

I started working on a few "Babylon 5" related physics problems involving angular motion. It is easy to come up with problems that use formulas involving angular velocity and acceleration, rate of rotation, apparent "g"s, number of rotations that the space station completes in a given amount of time, etc.

But I was interested in analyzing episode 22, season 2 of Babylon 5, "The Fall of Night", where Captain Sheridan is forced to jump from a cable car, which traveling through the otherwise empty core of the rotating space station. (He must escape a bomb set by an assassin.) The "gravity" there is essentially zero, and the speed with which he leaves the cable car is low. However, the speed at which he will impact the floor, a minute later, will be fatal. According to a statement in the episode, the floor is rotating at 60 miles/hour (about 27 meters/second.)

Spoliers aside, someone with their own method of propulsion flies up to meet Sheridan in mid-air, grabs hims, and gently changes his angular speed to match that of the space station floor, in about 30 seconds. Plenty of time to gently get up to 60 miles/hour. We can assume an inner radius (cable car to floor) of perhaps 230 meters (outer radius of the station is much larger, but irrelevant to this problen.)

I wanted to calculate the "distance" that Sheridan travels during this descent, knowing his initial angular speed (0 m/s), final angular speed (27 m/s), vertical distance traveled (assume perhaps 200 m ?) Why assume 200 meters? He seems to have traveled at some slow speed for 20 seconds, before being caught by his rescuer, so I am tenatively assuming that he traveled perhaps 30 m - and only then was force applied.

Here's my problem: I just realized that since he is being given a constant, sideways acceleration (to increase his angular velocity), he no longer will travel in a straight line: He will now spiral out towards the floor. So what "distance" is this?

In otherwords, what is the shape of the curved path that Sheridan follows? Are there any analyses of this path available? Any suggestions on how to calculate the distance travelled? I have seen many analyses of objects being dropped, and how they appear to spiral down (depending on your frame of reference), but all the analyses I have seen are about freely falling objects - but in this case the object has an acceleration.

Any suggestions would be much appreciated.

Thanks much,

Robert

 

[Xezlec]

So, the danger was just that he would hit the floor (with very little velocity), but the floor is moving sideways so fast that it's like jumping out of a car? I'm not sure that's plausible.

- If he had gently floated to the floor he would have time to extend his legs and catch up to 60 MPH, I would think.

- Is there any air? If so, the air would probably be spinning with the floor, which would increase his angular velocity and therefore, by what is commonly called "centrifugal force", he would effectively be accelerating downward relative to the floor.

- If this person *only* increased his tangential velocity, they would be doing him a disservice, since how hard he would hit the floor would increase a lot. Instead, they should push him in a direction simultaneously tangential to "catch up" with the floor and also inward to slow his effective descent.

If this all sounds confusing, it's just because it has to do with the relationship between angular and linear velocity.

 

[astrokreng]

I find this problem very interesting and challenging. The first thing I would do is to gather all the necessary information and data, such as the radius of the space station, the initial and final angular velocities, and the vertical distance traveled. Then, I would use the equations of angular motion to calculate the time it takes for Sheridan to reach the floor, assuming a constant acceleration due to the change in angular velocity.

Next, I would plot the trajectory of Sheridan's path using the equations of motion for a projectile in a circular motion. This will give us a visual representation of his path and help us determine the shape of the curved path he follows.

To calculate the distance traveled, we can use the arc length formula, which takes into account the radius and angle swept by the object. However, since Sheridan is also accelerating, we may need to use calculus to integrate the distance traveled over time.

Another approach could be to use computer simulations to model the path of Sheridan's fall and calculate the distance traveled. This would also allow us to adjust variables such as the initial and final angular velocities to see how they affect the path and distance traveled.

Overall, this is a complex problem that requires a thorough understanding of angular motion and projectile motion, as well as the ability to apply mathematical and computational tools. It would be interesting to see a detailed analysis of this scene in the show, or to conduct experiments in a rotating space station to observe the actual path and distance traveled in such a scenario.