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Wind Resistance
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Does anybody know any equations that incorperate wind resistance? Like an equation that could tell me the force of a bullet, but not the simple F=ma equation. And if its not too much trouble, could you tell me how to use the equation as well? Its for a physics project in school. Thanks.
Wise Man says: "Take a dog off its leash and it will wander."
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Re: Wind Resistance
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on 2006-01-12 21:21:21 (edited 2006-01-12 21:21:47)
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wind resistance is effectively a force due to friction. an object will have a function to calculate the µ (friction coefficient), which i should think would increase linear to velocity. see: http://en.wikipedia.org/wiki/Drag_(physics) hope this helps you get started! 
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Re: Wind Resistance
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OK, so the equation is D=1/2p*v^2*A*C So to find "p" (the density of the fluid, air in this case), I tried to use the Barometric Formula, P=Poe^(-Mgz/(RT)), but I hit some trouble. -What does the "e" stand for? -Is temperature, for this equation, in degrees Celsius? -What is all this mol^-1 business? I also don't understand how to find "A", the reference area, for the drag equation. And where can I find the drag coefficient for a bullet?
Wise Man says: "Take a dog off its leash and it will wander."
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Re: Wind Resistance
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on 2006-01-26 21:52:23 |
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*sigh* People these days... Really though, - e = Euler's Number - Generally speaking, Yes - Where is "all this mol^-1 business" you speak of? Don't worry about calculating the air density, try this. About reference area, I'm not sure. Drag coefficients differ from object to object. Usually you are either given µ for a physics problem, or you calculate it for yourself using the object and a few trials. |
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Re: Wind Resistance
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I got it all figured out now. Air density can be calculated with: p=P/RT p is air density in kg/m^3 P is pressure in pascals R is the gas constant T is temp. in Kelvins Reference area is the cross-sectional area of the projectile, perpendictular to its direction of motion.
Wise Man says: "Take a dog off its leash and it will wander."
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Re: Wind Resistance
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In fact you HAVE to use the F=ma equation (hey, it's the very basis of mechanics), you just have to add the expression of the force of the air on the ball. However, solving the equation you get afterwards is not that simple. If your object is not to fast, Fair = -k*v (don't forget the vectors), where k is a constant and v the speed. (the minus is because the force opposes itself to the movement) There are many formulas that enables you to calculate k. For instance the simplest : k=0.25*S where S is the "apparent" surface (in the case of a bullet, I guess you could use S=Ï€.R²) However, for faster objets (bullets), the resistance can be defined as Fair = -k*v² Now, as F = ma, you have : -k*v² + m*g = m*(dv/dt) (don't forget the vectors) So you get the differential equation : dv/dt = -(k/m)*v² + g It's first degre, but unfortunatly not a linear equation, which makes it harder to solve. Besides, you have to solve the equation in 2D. Here are the axis : ^ z | | | -------> x On the x axis : The equation becomes : dvx/dt = -(k/m)*vx² (1) On the z axis : dvz/dt = -(k/m)*vz² + g (2) Now, let imagine there becomes a point where the force of the air is exactly the same as gravity. You will then have a "limit speed" vl which is : vl²=m*g/k, or if you prefer vl = sqrt(m*g/k) Now, we will insert this in the equation (2) : dvz/dt = g * (1 - (vz/vlz)²) That is : dvz/(1 - (vz/vlz)²) = g dt We integrate the equation to get the time equation: int (dvz / (1-(vz/vlz)²) = g*t + C You get : vlz * argth(vz/vlz) = g*t+C Now, v(0) = Initial speed of the bullet, you insert it in the equation to get C and you get your final time equation. You then do exactly the same to your equation (1) (which should be much easier). With your new time equation, you can know the position of your bullet at any moment, and hence its trajectory. ******************************************************************** Now, if you absolutely wish a more difficult approach, you can say that your bullet is a corpse travelling in a fluid, hence the fluid exercices drag on the bullet. The drag equation is : D = (1/2) Cd * A * Ï * v² Where D is the drag force Cd a drag coefficient A your apparent surface (or body's cross-sectional surface, you can use the same formula as the one I gave you above) Ï is the air's density v the velocity of your bullet This equation comes from the much more compicated Bernouilli theorem : the difference of pression between the "front" and "back" of your bullet because of the air's flow diffence creates a force (exactly the same reason airplanes can fly). Now you should recon that the expression of this force is quite the same as the one I gave above Now, I recon I don't have of clue of the Value of Cd you should use (generally I used values around 0.25 up to 0.4). You should refer to a handbook of aerodynamics to get a proper value. You insert this expression in your F=ma equation and voilà ! I know it's hard to understand with all the ASCII. Feel free to ask questions. Sorry for the messy english. I'll mail you a scan of everything on a paper if you wish. It will be far easier to understand. |
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Re: Wind Resistance
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Thanks for all the help, I got 98% on my project.
Wise Man says: "Take a dog off its leash and it will wander."
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