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Natural Science Forum / Physics / General Physics / July 2008Modelling air resistance
I think I've read that one may assume that projectiles experience air resistance proportional to the cube of their speed and I know I've read that one may assume that projectiles experience air resistance proportional to their speed (for example in Simmons _Differential Equations with Applications and Historical Notes_). How may one model air resistance simply?  SignatureHe is not here; but far away The noise of life begins again And ghastly thro' the drizzling rain On the bald street breaks the blank day. >I think I've read that one may assume that projectiles experience air >resistance proportional to the cube of their speed and I know I've read >that one may assume that projectiles experience air resistance >proportional to their speed (for example in Simmons _Differential >Equations with Applications and Historical Notes_). How may one model >air resistance simply? Laminar, turbulent, sub-sonic, trans-sonic or super-sonic? Distant from other surfaces or nearby? The simple answer is that one can't model it simply. The resistance experienced is mainly proportional to the pressure drag. Except for very "slippery" objects or very long ones where skin friction becomes significant. Refer to the work of Bernoulli, Reynolds, Prandtl, Kutta, von Kaman, Busemann, Sänger and Mach of course. Light reading: "Mechanics of Fluids"; B.A. Massey Signature/"\ Bernd Felsche - Innovative Reckoning, Perth, Western Australia \ / ASCII ribbon campaign | Science is the belief in X against HTML mail | the ignorance of the experts. / \ and postings | -- Richard Feynman > >I think I've read that one may assume that projectiles experience air > >resistance proportional to the cube of their speed and I know I've read [quoted text clipped - 5 lines] > Laminar, turbulent, sub-sonic, trans-sonic or super-sonic? > Distant from other surfaces or nearby? Low speed, no turbulence. > The simple answer is that one can't model it simply. Surely one _can_, it just may not be a good model. > The resistance experienced is mainly proportional to the pressure drag. > Except for very "slippery" objects or very long ones where skin [quoted text clipped - 4 lines] > > Light reading: "Mechanics of Fluids"; B.A. Massey SignatureHe is not here; but far away The noise of life begins again And ghastly thro' the drizzling rain On the bald street breaks the blank day. >> >I think I've read that one may assume that projectiles experience air >> >resistance proportional to the cube of their speed and I know I've read >> >that one may assume that projectiles experience air resistance >> >proportional to their speed (for example in Simmons _Differential >> >Equations with Applications and Historical Notes_). How may one model >> >air resistance simply? >> Laminar, turbulent, sub-sonic, trans-sonic or super-sonic? >> Distant from other surfaces or nearby? >Low speed, no turbulence. Proximity to a surface is significant. Boundary layer fluid dynamics are non-trivial. How do you know that there'll be no turbulence? Have you calculated the Reynolds number? >> The simple answer is that one can't model it simply. >Surely one _can_, it just may not be a good model. IME, you can only understand what's good enough if you know what's too good. A scale analysis helps. You can "ignore" the terms that are insignificant in the particular case that you're looking at. >> The resistance experienced is mainly proportional to the pressure drag. >> Except for very "slippery" objects or very long ones where skin [quoted text clipped - 4 lines] >> >> Light reading: "Mechanics of Fluids"; B.A. Massey Signature/"\ Bernd Felsche - Innovative Reckoning, Perth, Western Australia \ / ASCII ribbon campaign | Science is the belief in X against HTML mail | the ignorance of the experts. / \ and postings | -- Richard Feynman >I think I've read that one may assume that projectiles experience air > resistance proportional to the cube of their speed and I know I've read > that one may assume that projectiles experience air resistance > proportional to their speed (for example in Simmons _Differential > Equations with Applications and Historical Notes_). How may one model > air resistance simply? If you want a simple model then assume drag is approximately proportional to the square of speed.. http://en.wikipedia.org/wiki/Drag_(physics) The power required is propostional to the cube of velocity. > >I think I've read that one may assume that projectiles experience air > > resistance proportional to the cube of their speed and I know I've read [quoted text clipped - 9 lines] > > The power required is propostional to the cube of velocity. Thank you, I'll read that. SignatureHe is not here; but far away The noise of life begins again And ghastly thro' the drizzling rain On the bald street breaks the blank day. |
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