What fun could you have with a fountain design in artificial gravity?

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SUMMARY

The discussion explores engineering a fountain inside a rotating hollow asteroid colony to visually demonstrate Coriolis and Euler pseudoforces under artificial gravity conditions. The colony parameters include a 10 km diameter asteroid rotating at 0.24 rpm to simulate 1/3g gravity. Calculations show that water jets at typical speeds (up to 15-20 mph) produce minimal Coriolis deflection, with streams landing only a few meters off-center, insufficient for dramatic visual effects. Analytical modeling using rotational kinematics and projectile motion equations confirms that closed-loop water trajectories require precise launch angles and velocities but result in subtle arcs rather than spectacular patterns. The discussion suggests that incorporating mechanical precession or gyroscopic elements might be necessary to create more visually striking fountain behaviors in such environments.

PREREQUISITES

  • Rotational dynamics and pseudoforces in non-inertial frames (Coriolis and Euler forces)
  • Projectile motion equations in rotating reference frames
  • Artificial gravity generation via centrifugal force in rotating space habitats
  • Numerical methods for solving nonlinear equations (e.g., using Excel Solver)

NEXT STEPS

  • Study advanced Coriolis force effects on fluid dynamics within rotating habitats
  • Explore gyroscopic precession mechanisms to enhance fountain motion
  • Use simulation tools to model fluid trajectories under varying rotation rates and nozzle parameters
  • Investigate design of rotating fountains with tilted or curved nozzles to amplify pseudoforce visualizations

USEFUL FOR

Space habitat designers, physicists studying artificial gravity environments, fluid dynamicists interested in rotating systems, and science fiction writers seeking realistic depictions of life and symbolism in rotating asteroid colonies.

  • #31
Ibix said:
It suspect a stream might break up due to interaction with increasingly fast-moving air.
I meant an approximate helix winding around the rotation axis. The airspeed would be decreasing as the water is slowed by drag.
 
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  • #32
A.T. said:
I meant an approximate helix winding around the rotation axis. The airspeed would be decreasing as the water is slowed by drag.
I had thought about that. Different places in the colony would produce different results. Interesting locations might include:
  • equator (my designs)
  • pole (your designs)
  • axis (a very long fall, and very wet)
  • somewhere between equator and pole (where you'd get planet-like Coriolis curvature)
 
  • #33
1250m radius cylinder
0.5g surface gravity
0 altitude (i.e., on the rim of the cylinder)
10m/s fountain velocity
94.8° angle (my 100° was a bit off - probably a messed up degrees-to-radians conversion).
1778963196157.webp
 
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  • #34
I've checked the above in Maxima, and I calculate the loop is about 10m high and 60-ish cm wide. That matches the aspect ratio of the loop drawn above. The 40m loop with a ~6m width comes from feeding in 20m/s launch velocity and angle of 99.7°:
1778964573418.webp

So I probably changed the launch velocity and forgot what I'd done this morning. Sorry.
 
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  • #35
And, of course, if you tilt a bit more anti-spinwards (102° in this case, still at 20m/s):
1778964962001.webp
 
  • #36
Ibix said:
And, of course, if you tilt a bit more anti-spinwards (102° in this case, still at 20m/s):
View attachment 371712
That's very cool. I like the effect.

I'm concerned about the "muzzle velocity".
20m/s is 45mph.
My "research" suggests that 20mph is terminal velocity for water streams/droplets. It would rapidly slow down from 45 to 20mph and, in doing so, break into droplets and probably not complete the arc in the same way.

(That being said, this is for a story, and is therefore is merely described by observation. I could probably get away with some writer's license. Furthermore, if any reader were to go to the trouble of proving me wrong; I would be extremely flattered. The Great Larry Niven had fans who would put his math through the wringer. High praise indeed.)
 
  • #37
Now that I'm playing around with this cool toy, I'm finding other story points to explore:

What would baseball look like?

Pitcher throwing a spinward pitch at 60mph would have to aim up at about 6 degrees to put the ball across the plate in the strike zone.
Ump throwing it back antispinward (at 60mph) would have aim up about 2 degrees to put it in the pitcher's glove.

(or vice versa, depending on which way they orient the baseball diamond)
1778970419950.webp

And, of course, every throw across the field would be somewhere between 2 and 6 degrees.


I guess the game would be full of "errors". (That's what they call it when someone misses a catch, right?)


(By comparison, a pitcher/ump in 1g on Earth normally throws a 60mph ball at about 2 degrees above horizontal.)
 
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  • #38
Ibix said:
In Bakerloo did Ali Khan
A stately hippodrome decree
Where Alf the bread deliv'ry man
Collided with a draper's van
While doing sixty three.
I take it that's an "Ibix original" :smile:
 
  • #39
DaveC426913 said:
Now that I'm playing around with this cool toy, I'm finding other story points to explore:

What would baseball look like?
Pandora's box: ex USA a plethora of exotic games: cricket, rugby, soccer etc !
 
  • #40
neilparker62 said:
I take it that's an "Ibix original" :smile:
Can't claim credit - I think I learned it from my mother, but where she got it I don't know.
 
  • #41
DaveC426913 said:
I'm concerned about the "muzzle velocity".
20m/s is 45mph.
My "research" suggests that 20mph is terminal velocity for water streams/droplets. It would rapidly slow down from 45 to 20mph and, in doing so, break into droplets and probably not complete the arc in the same way.
You can get similar effects at any speed, although the loops are narrower. Use my 10m/s settings and increase the angle a degree or so. Once you go beyond the loops you get funny triangular trajectories for a bit, too.
 
  • #42
DaveC426913 said:
TL;DR: If you were gong to construct a fountain inside a hollow-rotating asteroid colony, what could you do to highlight the weird effects?
Can you be a bit more specific about the fountain environment?

I suppose that the asteroid can be modeled as a spherical shell in which the gravitational field is zero. You put a fountain inside as shown in post #30.

Let ##\vec L## be a vector of magnitude 110 m pointing from the base of the fountain to its nozzle. I have two questions:
1. Does ##\vec L## point towards the center of the sphere?
2. What is the angle between ##\vec L## and the angular velocity ##\vec{\omega}## of the asteroid?
 
  • #43
kuruman said:
Can you be a bit more specific about the fountain environment?

I suppose that the asteroid can be modeled as a spherical shell in which the gravitational field is zero. You put a fountain inside as shown in post #30.
1779382476843.webp

Gravity due to mass is zero.
Artificial gravity due to rotation is 0.5g.
(see specs, top-left in diagram)

kuruman said:
Let ##\vec L## be a vector of magnitude 110 m pointing from the base of the fountain to its nozzle.
It's a rigid tower, 110m tall. The water shoots out from the top: 15mph at an angle of 55 degrees. (grey vectors)
(see specs, top-right in diagram)

I think this renders your questions moot, no?

kuruman said:
I have two questions:
1. Does ##\vec L## point towards the center of the sphere?
2. What is the angle between ##\vec L## and the angular velocity ##\vec{\omega}## of the asteroid?


You can play with the numbers as you see fit in this calculator. It produced the blue curves seen in the diagram (everything else was added by me).

It will show you relative vectors and absolute vectors.
 
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  • #44
The calculator assumes that you have a rotating floor such that the angular velocity of rotation is perpendicular to the floor. It provides a path given an initial velocity and position for a mass moving without friction across the floor. It is not the hollow asteroid that you mentioned in post #1.

So when I look in the post #43 figure, the water emerging from the nozzle is moving in the plane of the rotating platform, correct? I am asking because I want to do some trajectory calculations and be sure that I understand the problem correctly.

Is it the case then that we have a rotating platform on which we shoot a puck from some initial position with some initial velocity. If the puck zaps dots on the platform as it moves across it to edge of the platform, what would the path look like when we connect the dots? Is this a fair assessment of the problem?

I should point out that several years ago I did a similar calculation of how a spaceship with thrusters on all sides can move through a rotating tunnel without touching the walls and exit at the opposite side. It should not be too hard to adapt the previous solution to this problem.
 
  • #45
kuruman said:
The calculator assumes that you have a rotating floor such that the angular velocity of rotation is perpendicular to the floor. It provides a path given an initial velocity and position for a mass moving without friction across the floor. It is not the hollow asteroid that you mentioned in post #1.
"The effect is not unlike the acceleration due to real gravity."

OK, it's not a 100% match.

kuruman said:
So when I look in the post #43 figure, the water emerging from the nozzle is moving in the plane of the rotating platform, correct?
The water is emitted in at 55 degrees from horizontal at 15mph.

This is all specified in the diagram.


kuruman said:
Is it the case then that we have a rotating platform on which we shoot a puck from some initial position with some initial velocity. If the puck zaps dots on the platform as it moves across it to edge of the platform, what would the path look like when we connect the dots? Is this a fair assessment of the problem?
I am not prepared to say so, no. Not off-hand. But I'm interested to see your simulations.

One thing that the sim doesn't factor in is air resistance, which is not insignificant.
 
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