is there Air Resistance in AR?

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Postby Ikerous » Fri Aug 10, 2007 4:49 pm

If density = m/v then the 1/m would cancel out with the mass from the density. Which would make acceleration independent of mass.

Also dv/dt = a v^2 + b is the simplest form for a differential equation
It quickly turns into t = int(dv/(av^2 + b)) which is no longer an o.d.e
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Postby JohnnyRoastbeef » Fri Aug 10, 2007 5:47 pm

Ikerous wrote:If density = m/v then the 1/m would cancel out with the mass from the density

Also dv/dt = a v^2 + b is the simplest form for a differential equation


That density is the density of the air. It's a different mass so they don't cancel.

You may be right about the second part. It's still a non-linear equation, it just may be separable is all.
Last edited by JohnnyRoastbeef on Fri Aug 10, 2007 6:27 pm, edited 1 time in total.
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Postby Ikerous » Fri Aug 10, 2007 5:53 pm

JohnnyRoastbeef wrote:That density is the density of the air.

Ooh! Then yeah you're totally right.

It's still a non-linear equation, it just may be separable is all.

Yeah that's basically what I meant. Seperable equations are probably the first thing taught in an o.d.e class. The resulting integral probably requires trig sub, but <3 trig subs. Looks like you'd just manipulate the constants then use tan^2 + 1 = sec^2 (with v = tan) making dv = sec tan

Edit: oh wait XD! The integral of 1/(x^2 + a^2) is 1/a arctan(x/a)
Which would make the whole thing pretty easy once you manipulate the constants
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Postby Ikerous » Fri Aug 10, 2007 6:37 pm

And this forum needs way more math/physics threads! :P
(Bumping to make the edit noticeable)
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Postby gamma57 » Fri Aug 10, 2007 6:43 pm

integral of 1/(v^2 + 1) dv = arctan(v)

so ya v(t) = tan( sqrt(b) * t * a ) * sqrt(b)
sqrt = square root.

Edit: LOL you beat me to it!


I love physics. Especially the non-linear kind that leads to chaos.
Last edited by gamma57 on Fri Aug 10, 2007 6:54 pm, edited 1 time in total.
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Postby Ikerous » Fri Aug 10, 2007 6:53 pm

gamma57 wrote:integral of 1/(v^2 + 1) dv = arctan(v)



so ya v(t) = tan( sqrt(b) * t * a ) * sqrt(b)
sqrt = square root.

Edit: LOL you beat me to it!


I love physics. Especially the non-linear kind that leads to chaos.

Ha yeah it just took me a while to realize it was arctan. Doing this stuff in a textbox is awful. Although it seems that a shoud be in the square root with b.
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Postby JohnnyRoastbeef » Fri Aug 10, 2007 7:17 pm

Ikerous wrote:
JohnnyRoastbeef wrote:That density is the density of the air.

Ooh! Then yeah you're totally right.

It's still a non-linear equation, it just may be separable is all.

Yeah that's basically what I meant. Seperable equations are probably the first thing taught in an o.d.e class. The resulting integral probably requires trig sub, but <3 trig subs. Looks like you'd just manipulate the constants then use tan^2 + 1 = sec^2 (with v = tan) making dv = sec tan

Hopefully everything would cross out nicely but who knows


It doesn't come to a trig substitution. If we had an object flying upward with drag, then you'd get the trig functions in there because there's a sign change in the equation. For falling objects, according to my TI-89 the integral (because of the minus sign on the g) is a nasty natural log. It's pretty messy, but when you carry it out to the second integral for the position you get the expected result (yay for figures).


Something that looks like a parabola at the top before you've built up enough velocity for the drag to matter, with the slope asymptotically approaching a line (terminal velocity) as time increases. So getting back to the original point here, since I've bothered to solve the equation, here's a plot of two falling objects with different masses. The mass of the green is half that of the mass of the blue. They start to diverge once the drag kicks in (as time increases). At the beginning (where velocity is still low) they're the same.
Image
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Postby manored » Fri Aug 10, 2007 11:07 pm

I think that there must be something at least simulating air resistence or penduluns would keep going back and forth forever... (Unleash im wrong in believing that gravith only wouldnt stop a pendulum)

Another question: Is there Friction in AR, I mean, will objects stop sliding down a hill if the angle is VERY SMALL?
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Postby gamma57 » Fri Aug 10, 2007 11:23 pm

I think there is a small amount of material-material friction, but its also simulated in a way. So it looks like there is a very low metal-metal friction, but metal-rubber is much higher.

This also seems to be only kinetic friction as opposed to static friction. Modeling just Kinetic would be easy but both would be a pain to code I imagine. Look at the low slope rubber and metal. They are not stuck to the slope, but moving really slow.(zoom in)


It also apears that the gravitational acceleration of each material is diffrent. This would be the simulated "Air Resistance" plus the fact that there seems to be a terminal velocity for objects. The endpoints of cloth and rope fall faster than the rope/cloth alone also.
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Postby manored » Sat Aug 11, 2007 5:53 pm

gamma57 wrote:This also seems to be only kinetic friction as opposed to static friction. Modeling just Kinetic would be easy but both would be a pain to code I imagine. Look at the low slope rubber and metal. They are not stuck to the slope, but moving really slow.(zoom in)
You are right! :) So, objects in fact never stop going down if the plataform is not 100% horizontal, but they can go very slow depending of the situation... interesting :)
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Re: is there Air Resistance in AR?

Postby The EVIL » Fri Jun 20, 2008 6:18 pm

well te cloth does fall slowly and i have seen some metal sheets fall quite quickly :|
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^LOL!^
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Re:

Postby Ralith » Tue Oct 21, 2008 6:39 am

NeXFerret wrote:WEIGHT DOES NOT AFFECT RATE OF FALL!

Drop an aluminium and lead cannonball in the same instant. They should hit the ground at exactly the same time if they are exactly the same shape.


Why does noone ever think of TERMINAL VELOCITY! High Weight = High Terminal Velocity = Accel at same rate but for longer = land quicker in long fall.
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