Artificial Gravity Sim?

[mc_axe]

Hello guys i was curius to visualise a somehow realistic behavior of falling objects inside Artificial gravity enviroments - rotating habitats - space centrifuges etc,
I knew in general that the largest the radius is the more natural artificial gravity behaves in comparison to real gravity, but i wanted to see something visualy:



In this example the "ground" is on r 250m, rotational rate is like 1,7rpm~ (resulting to ~1g) and the ball should hit the ground with ~1,9m abouts ofset, the girl is 1,69m.
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I pinned a syflex cloth ball-> to a null ->child of the centrifuge, and then i realesed it momentarily. But in order to get accurate results according to theory (hit the ground where it should be) i had to increase the mass by alot.
In other words (from a non rotating POV) the ball after release had to follow a completely straight path paralel to circumference in the moment of release, to prove that Newton is the man once again.

How will you do a simmilar animation so it is accurate without extreme tweeking, i was hoping that i can vizualize many balls falling from the "ceiling" to the "floor".
Or i wanted to throw a ball up and see the behavior, is realy interesting cause upwards movement will have the oposite effect.

[Daniel Brassard]

Have you adjusted the gravity force to your chosen unit in the simulation?

For gravity to be applied correctly in Softimage Sims, Softimage units has to be taken into consideration. Looking at the character size compared to the grid size, it look like you are 1 unit equal 1 metre.

http://softimage.wiki.softimage.com/xsi ... m#Ree52073

If the girl is 1,69m and Softimage unit is 10 cm, you could do your simulation by adjusting the girl size to 16.9 units tall (i.e 10 unit equal to 1 metre to avoid recalculating everything else). The default gravity force in Softimage is 98.1 dm/s (considering Softimage is 10 cm or 1 dm i.e one tenth of a metre).

Always keep the scale of Softimage units and your scene objects in mind when designing a rigid body simulation. As with other simulation calculations, scale is crucial when dealing with rigid bodies. Before you start to do a rigid body simulation, you need to define what unit of measurement a Softimage unit will mean in your world: 1 meter, 10 cm, 1 cm, 1 foot, etc. And you need to model your objects in reference to this and to make sure that their mass or density are also adjusted proportionally to reflects your chosen world units. Size does matter in simulations.

[mc_axe]

Thanks Daniel for the tip, it will save some zeros, i mean that ball weights like a planet now !

Btw what seems like a grid in the above gif is part of a circular structure that rotates alltogether
The force of gravity is zero and there is no other forces in the sim, the "fall" fom a different POV is actually an object flying in a str8 line(when released), like the example bellow:


a1 is the position of girl at them momment of release and a2 @ the momment of ball impact.

Is there any chance that Syflex has some default air ressistance for more natural cloth animations? Probably right?
That might explain why even when pinned at a null the object somehow "strugles" + the humongous mass input to overcome it.

[Mathaeus]

Is there any chance that Syflex has some default air ressistance for more natural cloth animations? Probably right?
That might explain why even when pinned at a null the object somehow "strugles" + the humongous mass input to overcome it.

By default, I don't think there's built in air resistance. There is optional 'air' force based on polygon normals or something like that, it's stronger along normals (like sail, creating a stronger resistance when it is orthogonal to wind). Built in drag is related to cloth sim itself, don't believe there's some global (related to entire ball, here) drag force.
If you want to be sure, perhaps is better to start with ICE by building the particle simulation step by step.
By my understanding (could be completely wrong) non linear movement could be result of point of view. While movement probably is linear, looking from starting point from inner circle - but, outer circle (which is a target) is longer, so there is no parallel relation between corresponding points of these two. ' Force space' is curved, too, artificial gravity is (significantly) not a single direction. In any case, centripetal force is different thing than gravity. Theoretically, guy who is jogging through iconic 'centrifuge' in Odyssey 2001 movie, should be weighting more or less, depending of jogging direction.
From practical side, if your centrifuge is really big, perhaps you could into problems with precision.

[mc_axe]

non linear movement could be result of point of view

That is right, in non rotating (inertial) reference frame the ball travels a str8 path with constant speed.

Theoretically, guy who is jogging through iconic 'centrifuge' in Odyssey 2001 movie, should be weighting more or less, depending of jogging direction.

Good point Its really hard to simulate all that with fictitious forces vectors and such in rotating frame, that is why i wanted to do the sim in non rotating cause all these effects will happen automatically.
Also when ball is 10m beyond ground it "weights less" cause is on a smaller radius (centripetal is less).

I don't think there's built in air resistance

Hmm it might be some incredibly small amount to prevent bugs not sure, well something resulted to a decel during that constant velocity flight.
When i increased the mass i got more accurate result, but then... when i increased by alot it also accelarated somehow!.

Im guessing if its not the air ressistance, then it can be maybe some energy stored in the springs or something, while nailed to a null the object is under some kind of stress, each frame the null moves a litl bit more than a meter.
Also nail null has something like a fade profile, maybe i need to adjust it so it nails everything equally.

If you want to be sure, perhaps is better to start with ICE by building the particle simulation step by step.

I wish i was that good :]

[Daniel Brassard]

If their is no air resistance, no gravity and no other forces applied to each object, they are traveling at the same angular velocity of 1.7 rpm or 10.2 degree per second. The ball should therefore hit the girl.

In order not to be hit by the object, the girl need to move faster (different angular velocity upon release of the object), she need to move away from the object in order not to be hit (constant or sudden acceleration) or their is some air resistance due to the artificial environment (oxygen) which would cause the object to decelerate during travel from point a to point b.

I assume the girl is 250 metre from the centre (foot rest). What is the distance of the object from the centre upon release?

As for a force in an artificial environment, the floor in rotation will exert a centrifugal force toward the centre which for the girl will feel like the floor is constantly pushing against her foot (therefore artificial gravity).

Math is fun.....

[Daniel Brassard]

Assuming the object is released 50 metre from the centre (200 meter from the girl), the distance travelled by the object will be

hyp x hyp = adj x adj + opp x opp
R2 x R2 = R1 X R1 + Opp x Opp
Opp x Opp = R2 x R2 - R1 x R1
Opp = 244.95 metres

R2 is the distance from the centre to the girl foot rest
R1 is the distance from the centre to the object ( add the circumference of the object for big objects to determine the point of impact, I assume a particle)
Opp is the opposite distance (blue line in your diagram), this is a right triangle calculation using the Pythagorean formula

the angle Tetha travelled will be arcsin (opp/hyp)

Tetha = arcsin (244.95/250) = approx. 78.5 degrees

at a rate of 10.2 degree per second, the object will reach the girl in approx. 7.69 seconds ( at 24 frame per second, you would need approximately 185 frames minimum to complete your simulation for this scenario).

She will have travelled in the artificial habitat approximately 342.25 metres from the release point at a constant speed (angular velocity) of 1.7 rpm (10.2 degree per second).

arc length S = 2 x pi x R2 x Tetha / 360
S = 2 x pi x 250 x 78.5 / 360
S = 342.25 metres

[Daniel Brassard]

P.S.

This scenario does not take into account coriolis forces (the object is pushed at a specific velocity toward the girl on release which will describe a curve from the girl point of view, like your first image)
https://en.wikipedia.org/wiki/Coriolis_force

or mass that exert its own gravity on other surrounding objects in the scene.
https://en.wikipedia.org/wiki/Gravity
https://en.wikipedia.org/wiki/Gravitational_constant

[Daniel Brassard]

In your first image, it look like you are trying to simulate the coriolis effect.

Let say you are throwing an object directly to the girl when at the location a1 in your diagram. The object is at 50 metre from the centre and the girl at 250 metre from the centre (foot rest).
The velocity of the object upon release is 20 metre per second.

The distance to travel will be 250 m - 50 m = 200 metres
The velocity is 20 m/s so the object will reach the floor in (200 m / 20 m/s) = 10 second

The girl is travelling in an arc at an angular velocity rate of 1.7 rpm or 10.2 degree per second. in 10 second, the girl will have travelled 102 degrees.

To find the distance travelled, the girl will be at 2 x pi x radius x degree / 360 = 2 x pi x 250 m x 102 degree / 360 degree = 445.06 metres

So the object will fall in a curved trajectory 445.06 metre away from the girl. If you want it to fall 1.9 m from the girl, you will need to change the angle of the throw or the initial velocity.

[mc_axe]

Hey Daniel thanx for taking the time to answer, i hope you find it interesting like I do, im big fan of Artificial Gravity btw.

Like you said im trying to visualize both coriolis and centrifugal force. I found a crazy paper expalining all that "weird behavior" (curved fall etc), in a rotating frame with vector quantities fictitious forces, but is too scary to look at

However Im preety possitive, that we can visualize simmilar behavior by solving the problem or simmulating in non rotating frame.
Bellow ill let some more accurate figures + an 'ofset' calc in non rotating frame that uses some geometry aswell and explaing why ball stays behind.

In my first example:
r= 250(m) the ground | girls feet
r= 240(m) the bottom of the ball
(aka ball and ground distance =10m)
Funny fact: Girl is sligtly away from ground zero aka the point where mass should fall if vertical fall (so its safe xd).
ω translated to rpm is :1,8991 @ r=250m we have 1g , 0.96g@ r=240m

Uc(centrifuge): Linear velocity at r=250m is about 49.51 m/s
Ub(ball): Linear velocity at r=240 is ~47.533 m/s

Ofset calc:

In non rotating frame the ball will fly a str8 path 70m till it hits the "ground" ( Pythagorian with hypo 250 and one of the legs 240) and it will do that in a specific amount of time (t1)
The triangle angle close to axis is 16.26 degress, that is an arc of length X1 = 70,9478(m) on the circle at r=250(m)
In the same time the rim will actully travel an arc of lenght X2=72,9166~ (m) with Uc

Ofset in terms of arc length = X1-X2=-1,968866(m)

[Daniel Brassard]

Hi Mc_Axe

Ofset calc:

In non rotating frame the ball will fly a str8 path 70m till it hits the "ground" ( Pythagorian with hypo 250 and one of the legs 240) and it will do that in a specific amount of time (t1)
The triangle angle close to axis is 16.26 degress, that is an arc of length X1 = 70,9478(m) on the circle at r=250(m)
In the same time the rim will actully travel an arc of lenght X2=72,9166~ (m) with Uc

Ofset in terms of arc length = X1-X2=-1,968866(m)

You have calculated the constant angular velocity of the girl at 49.41 m/s and the ball before release at 47.533 m/s. On release, if the ball continue on the tangential path at the speed of 47.533 m/s, it had to travel 70 m to reach the floor which would take 1.47 seconds. The girl would therefore travel 1.47 second x 49.41 m/s = 72.91 metres. This all make sense.

What I don't get is your arc length of travel for the ball. It look like your are projecting the 70 metre onto the circle to calculate your X1 (yes 70 meter projected on the arc of the bigger circle of radius 250 is 70.95 m) but why?

What is more important is to realise that the ball is not moving at a constant speed. You have stated that the gravity will change for the ball from 0.96 g to 1 g. Gravity and the change in gravity will influence the ball velocity during the fall. So the ball may start at 47.533 m/s but will hit the floor at a higher speed, therefore sooner. You need to take this into account in your simulation.

[mc_axe]

What is more important is to realise that the ball is not moving at a constant speed. You have stated that the gravity will change for the ball from 0.96 g to 1 g. Gravity and the change in gravity will influence the ball velocity during the fall. So the ball may start at 47.533 m/s but will hit the floor at a higher speed, therefore sooner. You need to take this into account in your simulation.

Hey Daniel!
My sim is probably showing a section of a spacecraft, with no air pressure inside, that is a simplification.

Calculation and simulation are both in non rotating frame, so after release assume no other force acting on the ball (previusly we had centripetal but now is gone).
The ball during flight is super calm traveling a straight path, like in the middle of nowhere in vaccum in deep space etc.

Thats why we can use a str8 line to find point of impact (small arc) and then compare with the actual motion of the centrifuge (big arc).
So typically we have no accelaration on the ball during flight (from a non rotating POV).
But regardless and that is the interesting part, with a camera on the ground we get the perception of a curved accelarated fall like shown in the gif.

If we had air inside that centrifuge i would expect, smaller ofset.

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About the gradient:

• In non rotating frme the ball will receive 1g centrpetal at 250m, only after 'setling' with the motion of the ground.
  So after the flight and some bounces, and some friction, till the ball aqcuires the required ω justifiing 1g in r=250m.
• In Rotating frame (more complex for me to grasp), we have a totally different concept with centrifugal and coriolis acting like body forces at all times during the fall

Im preety possitive that both methods can explain the behavior of the ball in relation with an observer on the 'artificial' ground.

[Daniel Brassard]

OK, got it. Your problem is this.

http://www.spacefuture.com/archive/inha ... vity.shtml

[mc_axe]

Woah! That is nice thank u Daniel, very well illustrated^^, makes it also more easy to understand.

Ill definatelly spent some time reading on the article, maybe a few times (100 xd) till i get the hang of it, it looks awesome, cant wait till i get in the parts figures that i barelly recognize .