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What is the curve that is travelled when air resistance is included?

I found that there are different air resistances, which curves would these types produce?

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- Thread starter guysensei1
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What is the curve that is travelled when air resistance is included?

I found that there are different air resistances, which curves would these types produce?

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mfb

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arildno

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For air resistance proportional to the velocity, you may derive analytical expressions for the curve, that typically(if I remember correctly) involves the hyperbolic functions and their inverses.

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cjl

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For air resistance proportional to the velocity, you may derive analytical expressions for the curve, that typically(if I remember correctly) involves the hyperbolic functions and their inverses.

Unfortunately, for the vast majority of cases, this is not a physically realistic solution, since air resistance is proportional to the square of the velocity (and there is no nice, analytical solution for that).

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arildno

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Your point being?Unfortunately, for the vast majority of cases, this is not a physically realistic solution, since air resistance is proportional to the square of the velocity (and there is no nice, analytical solution for that).

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cjl

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Your point being?

My point being that if you care about physical reality, rather than mathematical prettiness, the existence of a solution for drag proportional to velocity isn't terribly useful or relevant.

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arildno

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Any relevance to my first post?My point being that if you care about physical reality, rather than mathematical prettiness, the existence of a solution for drag proportional to velocity isn't terribly useful or relevant.

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mfb

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Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".

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What is the curve that is travelled when air resistance is included?

I found that there are different air resistances, which curves would these types produce?

This question is not well posed. When there is air resistance, there is also lift. Both depend on the shape and the mass distribution of the body, and its orientation and rotation. These effects can be very significant, in which you can certainly convince yourself by comparing the flight of a glider and a ball.

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cjl

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Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".

It's not so much that the flow is laminar, it's that the flow (for very low reynolds numbers) is dominated by viscous, rather than inertial forces. Laminar (but inertially-dominated) flow still has drag that scales as v

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Khashishi

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Short answer: there is no simple closed form except in very extraordinary circumstances.

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arildno

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Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".

Quite so.

And?

It doesn't follow from this that what I wrote in my post was wrong. I pointed out that there were cases with air resistance in which analytical expressions could be found, I did not say that that was generally true.

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