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I have a CPP setup for a cloth simulation. Currently it takes in forces for wind simulation and gravity and these forces act on individual "point masses". I'm trying to figure out how to model an inflatable tube man with it:

enter image description here

I'm not too great at physics, but I've done some research. I know it's probably gonna involve Bernoulli's equation, the inverse relationship between velocity of the air particles within the tube and pressure, and $F = P/A $

But I don't know how to bring it all together into a formula for force. I don't know if Area would be the diameter of the "tube" because doesn't the tube constrict and fold on itself? Is it easier to have pressure be randomly simulated, or actually compute it from velocity of particles?

Ultimately I want to come up with a formula for the force caused by air pressure, kinda like how I used the formula below for wind:

$$F_{\rm wind}(i,j)=C_{\rm wind}\left[n_{i,j}\cdot\left(v_{\rm wind}-v_{i,j}\right)\right]n_{i,j} $$

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    $\begingroup$ CPP as in C-plusplus? You're after simulating a chaotic motion, i.e. non-linear behavior, so you will need some good fluid dynamics code... Do you plan to code that from scratch?? $\endgroup$
    – rfl
    Commented Apr 30, 2022 at 20:33
  • $\begingroup$ Im not sure, probably? Do you have any resources on where to start? $\endgroup$
    – Melanie
    Commented Apr 30, 2022 at 20:45
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    $\begingroup$ Not my area of expertise; commercial products that do finite element simulations are very very expensive. Perhaps you can find some free code online, dunno. Coding this from scratch would be a PhD's worth of work I'd think. $\endgroup$
    – rfl
    Commented Apr 30, 2022 at 20:58

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Great question. I think you'll have a hard time modelling this from first principles, but the important physics is clear enough.

Imagine the tube begins in a perfectly upright position and imagine an orderly laminar flow inside. There is no lateral force on the tube in this geometry, so it begins to fall over due to gravity.

When the tube is bent, the air inside has to make a turn, which by conservation of momentum imparts an outward force to the tube. This force acts to keep the man upright.

If the wind speed is too high, then this force is strong enough to make the upright position stable. However, if we turn down the wind speed, there's a bifurcation and the man begins to fall over.

The guy doesn't fall over completely though... at some point a crease is formed and it goes from an open tube to an inflating balloon. This inflationary epoch continues until the crease gets all the way to the end and the tube re-opens. In the meantime the cloth on the other side of the crease is just evolving under the force of gravity.

The way I would model this is by a bunch of rigid rods, with the restoring torque in the tube regime acting as a function of the angle between the segments (imagine the torque as proportional to the crossed product of each segment, or something). But then I would put in some creasing angle which cuts off the flow above it and changes to the inflating motion.

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  • $\begingroup$ thank you so much for this answer! could you expand a little bit on the last paragraph -- I'm not a physics person by nature and got a bit lost $\endgroup$
    – Melanie
    Commented May 1, 2022 at 5:42
  • $\begingroup$ i get the part of the rigid rods -- but how do you start out the simulation? Like how do you decide how to "pivot" the rods? (lets assume a constant speed bc thats what we have rn) $\endgroup$
    – Melanie
    Commented May 1, 2022 at 6:29

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