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November 17th, 2014, 02:45 PM   #1
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calculations invloving drag

how are calculations that include the force of drag on projectile motion generally done/?


the force of drag depends on the velocity of the object, which makes sense, and according to Wikipedia it depends on the square of the velocity...

but now setting up a simple formula for velocity is not obvious since the force of drag, which affects the velocity, is itself dependent on the square of the velocity....
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November 17th, 2014, 05:27 PM   #2
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Math Focus: Wibbly wobbly timey-wimey stuff.
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Originally Posted by Kinroh View Post
how are calculations that include the force of drag on projectile motion generally done/?


the force of drag depends on the velocity of the object, which makes sense, and according to Wikipedia it depends on the square of the velocity...

but now setting up a simple formula for velocity is not obvious since the force of drag, which affects the velocity, is itself dependent on the square of the velocity....
Actually drag forces can be proportional to the velocity or proportional to the square of the velocity. It depends on which circumstance you are using. The motion equation then becomes, ala Newton's 2nd:
$\displaystyle \sum F = ma - (drag) = m \frac{dv}{dt} - kv^2 = 0$

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January 9th, 2015, 01:04 PM   #3
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ok, so for a projectile assuming its launched from ground.... and assuming the simpler case where it is not the square of the velocity I have:

ma=-mg-kv in the y component

so I get dv/dt= -g-(k/m)v...

I attempted to solve this first ;order linear d/e, using an algorithm to found online, so correct me if wrong:

y component of v= -(m/k)g +ce^((-km)(t))

and I could solve for c using an initial velocity of my choice.

for the x component, its simply: ma=-kv, dv/dt=-(k/m)v

so solving for the x component: v= ce^(-k/m)t

again solving for c with a initial velocity of my choice...




Now how do I solve the d/e with the exponential assumption?

I think the x component is easy: ma=-kv^2, dv/dt= -k/m(v^2)

v=m(1+c)/kt...

but for the y component...how do you solve an exponential fit order d/e?
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January 9th, 2015, 07:42 PM   #4
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Drag Equations

Here is a link. Im working on the same thing

Flight Equations with Drag
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