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

[A.T.]

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.

 

[DaveC426913]

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)

 

[Ibix]

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).

 

[Ibix]

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°:

So I probably changed the launch velocity and forgot what I'd done this morning. Sorry.

 

[Ibix]

And, of course, if you tilt a bit more anti-spinwards (102° in this case, still at 20m/s):

 

[DaveC426913]

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.)

 

[DaveC426913]

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)

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.)

 

[neilparker62]

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"

 

[neilparker62]

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 !

 

[Ibix]

I take it that's an "Ibix original"

Can't claim credit - I think I learned it from my mother, but where she got it I don't know.

 

[Ibix]

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.

 

[kuruman]

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?

 

[DaveC426913]

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.

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

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?

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.

 

[kuruman]

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.

 

[DaveC426913]

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.

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.

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.