Air friction formula?

Discussion in 'Physics & Math' started by Alien Mastermind, Oct 23, 2004.

  1. Alien Mastermind Registered Senior Member

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    I've been searching for this formula for quite a while now, with no results...

    So simply put:

    Anyone can give me the formula for the force of air friction? My guess is that lots of variables are involved here, and I would expect the formula to be beyond my comprehension, but I'm willing to give it a try.

    Thanks for any input.
     
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  3. Yuriy Registered Senior Member

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    Dear A.M.,
    You have asked very tough question.
    I could mention Stokes formula
    F = akSv
    where a is some numerical coefficient (usually close to 1), k is medium’s (air) viscosity, S is normal cross section of body and v is its velocity in respect to medium. But this formula works only for well-streamlined bodies (like ball) and at v small enough in comparison with so called the Raynolds first critical velociyu. For example, this formula very well works for balls dropping in oil.
    I could mention Karman formula which works at creation of so called “Karman chain” of vortices behind streamlined body.
    I could mention my own formula which works at creation of so called “vortical boiling” (when surface of the streamlined body creates vortices and/or rotons; is used for golf balls, in blades of jet engines, uranium cassettes in reactors, and so on). Etc, etc….
    The problem is that no one of these formulas will be useful in your case of an arbitrary body and arbitrary regime of streamlining. There is no such formula in Physics – too complex phenomena are happened at such streamlining. It is why physicists build Air-tubes – to recreate the real conditions of streamlining and simply measure the friction force

    So, my advice is: If you really want know value of this force for your device, go in library and find reports on streamlining experiments with bodies like yours and in range of velocities like you are expecting to have.
    And good luck with this…..
     
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  5. Persol I am the great and mighty Zo. Registered Senior Member

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    The only real way to do it is numerical simulation on a computer, everything else is a rough estimate.
     
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  7. Yuriy Registered Senior Member

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    Simulation of what?
     
  8. Persol I am the great and mighty Zo. Registered Senior Member

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    Air flow.... FEA for fluids basically.
     
  9. Yuriy Registered Senior Member

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    How you will simulate turbulent effects, if nobody knows how to describe them, at all? What equations, models and conditions of initiating of different possible turbulence you will be programming at Computer simulation?
     
  10. Persol I am the great and mighty Zo. Registered Senior Member

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    Turbulent effects are the result of small surface/mass changes. The simulations take this into account.
     
  11. Yuriy Registered Senior Member

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    Please, show us the simpleast procedure of simulation of simpliest type of turbulence you know
     
  12. Persol I am the great and mighty Zo. Registered Senior Member

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    You're looking for simple? You're going to be disappointed...

    The simplest way is to use the navier-stokes equations and just treat the result as an average. That's cheating though, and you don't really 'see' the turbulance.

    To get slightly more complicated you can introduce the reynolds stress (tied in with roughness of object) into the navier-stokes equations.

    To get anywhere near reality you move onto computers. You break the object and air into an adaptive mesh for FEA. You introduce friction where two meshes meet and there is a different velocity/material. Depending on the resolution of your mesh you can go all the way from currents (small matrix) to detailed turbulance (large matrix).

    Since this is remarkably slow, people are currently researching a method of a 'threaded' numerical simulation. Basically saying that you have cells which are under the same basic condition... calculate once and applying to all increase the speed. I haven't seen much on this lately though.


    The first two are modeling the results of turbulance. The last two are actually modeling the turbulance... but to varying degrees of accuracy. The field is still a very hot research topic.
     
  13. Yuriy Registered Senior Member

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    1,080
    As you understand, you have described well known principles of simulation of ... the turbulence in so called the Reynolds stress model, which has nothing to do with turbulence caused by phenomena of vortex creation, for example (or with instabilities of flows, like Garter’s, or Hamlet’s, or any torn off Prandtl layers, and so on , and so on). But all types of known and even unknown yet mechanisms of turbulence will take place in case of any real body of general shape streamlined by air. So, there is no practical use in advice: go, do simulation on PC. BTW: the numerical simulation of turbulence for today is the most complex and complicated problem known in whole Cybernetics. It was why your advice so amazed me…
     
  14. Persol I am the great and mighty Zo. Registered Senior Member

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    Agreed.
    Obviously.
    I disagree with you here. For the majority of problems (especially if you are only concerned with drag) the computer simulations work fine. It's not exact, and I don't expect it to be... but it does give you a close estimate of the stress, force and drag on an object.

    Your only other real option is to make a scale model and test it (which introduces other problems depending on your surface - magnus effect, etc).

    I'm assuming that he doesn't wants something more than the stokes forumla, but that accuracy is not his number one concern. The PC simulation is ideal for this.

    We really need to know why he wants to know.
     
  15. Yuriy Registered Senior Member

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    I agree.
     
  16. Alien Mastermind Registered Senior Member

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    Well guys, all of this has been very interesting to read. But quite frankly, it is beyond me, as I have feared at first. What I need is a way to compare the air friction of a parachute + person vs. the air friction of a person. So I guess my only way now is to simply search for these values, since creating my own computer simulation is out of the question... Thanks though, lots of useful input there guys.
     
  17. Persol I am the great and mighty Zo. Registered Senior Member

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    Oh, well that's not to complicated. I'll try and get back to you soon, but dinner just came.

    Sorry for the extra stuff...
     
  18. Yuriy Registered Senior Member

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    Dear A.M.,
    Now, when you formulated your problem, everything came to order:
    1. First of all, "parachute" problem has nothing to do with air friction force - so, you should find data on air-resistance force for parachutes (it strongly depends on shape of parachute). Such data you can find only in special books or sites: by my best knowledge there is no physical theories of that force (mostly because experimental data can be easily obtained and are much more accurate then any possible theoretical results)
    2. If you need that data for serious purposes (I am scared with necessity of comparison “parachute + body” and "body ... without parachute") you should pay attention at what load these parachute data was obtained. Because changing the shape of load you can get dramatically different data for the same parachute.
    So, good luck...
     
    Last edited: Oct 24, 2004
  19. Persol I am the great and mighty Zo. Registered Senior Member

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    F = ½ *(rho)*Cd*A*v^2
    rho = 1.22 kg/m3
    Cd = drag coefficient
    A = area of the chute
    v = velocity

    You'll have to look up Cd depending on the shape/make of the parachute.

    The force on a person alone will be equal to their weight during most of the trip. A person will accelerate to terminal velocity and then the force down (wieght) will be equal to force up (the air resistance).
    Hehe.
     
  20. Alien Mastermind Registered Senior Member

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    Actually that was very interesting and informative. Thank you

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    Not to worry, I am not about to commit siucide just yet.

    Now regarding the pretty formula of Persol here. What exactly is rho? And the units for that is kg/m^3, I assume? The rest seems pretty clear. Thanks very, very much.
     
  21. Yuriy Registered Senior Member

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    rho is density of air.
     
  22. Alien Mastermind Registered Senior Member

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    Thanks! I will try this in the context of my problem. I'll let you guys know tomorrow how this works sout.
     
  23. geistkiesel Valued Senior Member

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    You might try searching on 'wing design in aeronautical engineering', 'viscouis flow dynamics' etc,
     

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