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I'm thinking about that guy that jumped from the highest point ever free-falled from and broke the sound barrier.

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- Thread starter pitchwest
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- #1

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I'm thinking about that guy that jumped from the highest point ever free-falled from and broke the sound barrier.

- #2

SteamKing

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First, figure out what function you are talking about. Velocity versus time? distance versus time?

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I was thinking that I'd have to first find an equation for the amount of air at different altitudes. Then calculate the level of air resistance and apply it to the amount of air equation. Then figure out how that applies to gravity at different altitudes.

I hope that helps clear up what I'm getting at.

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SteamKing

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You should review Newton's Law of Gravitational attraction: F = Gm1m2/r^2

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SteamKing

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jtbell

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If the drag coefficient is constant, it's possible to solve the differential equation of motion exactly for certain cases. With a variable drag coefficient, you'd have to solve the differential equation numerically.

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I'd also like to know if he slowed down to the standard terminal velocity eventually.

- #9

cjl

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To put it another way, the object's drag coefficient increases with air density.

This is not true. Drag coefficient is independent of air density. In fact, that's a large part of the reason why you want a drag coefficient in the first place - it's dimensionless, and largely independent of both air density and airspeed (across a fairly broad range of speeds, though if you start approaching the speed of sound or higher, this can change), and is effectively only dependent on the geometry of the object in the flow.

Drag force increases with air density (all else equal), but not drag coefficient.

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[tex]F(h) = \frac 1 2 \rho(h) v^2 C_dA - mg(h)[/tex]

Here,

The first part is drag to air resistance. The term ρ(

The final term is just gravitational force. A simple linear model of gravitational acceleration

- #11

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At extreme heights there's less gravity.

At 128100 feet, the force of gravity is about 1% percent less than at the sea level. This can be ignored for any practical purpose, because the other errors and uncertainties in the model will most likely be far greater than that.

- #12

256bits

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This is not true. Drag coefficient is independent of air density. In fact, that's a large part of the reason why you want a drag coefficient in the first place - it's dimensionless, and largely independent of both air density and airspeed (across a fairly broad range of speeds, though if you start approaching the speed of sound or higher, this can change), and is effectively only dependent on the geometry of the object in the flow.

Drag force increases with air density (all else equal), but not drag coefficient.

That is not true either.

Drag coefficient may be dimensionless but it does vary with speed, density, and viscosity of the medium. Drag coefficient can be plotted against another dimensionless number called the Reynold`s number which incorporates velocity, dynamic viscosity, density and a characteristic length. One can use kinematic viscoscity in favour of density and dynamic viscoscity.

In addition, temperature of the medium will also affect the viscosity, and for gases the kinematic viscosity will increase with temperature.

As the speed of the object increases through the medium particular flow seperation points are reached which will change the coefficient of drag. The range of CD will vary from attached laminar flow at slow speeds, where the coefficient can be quite high ( > 1.0 ), to that at detached turbulent flow where it can be much lower.

- #13

cjl

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That is not true either.

Drag coefficient may be dimensionless but it does vary with speed, density, and viscosity of the medium. Drag coefficient can be plotted against another dimensionless number called the Reynold`s number which incorporates velocity, dynamic viscosity, density and a characteristic length. One can use kinematic viscoscity in favour of density and dynamic viscoscity.

In addition, temperature of the medium will also affect the viscosity, and for gases the kinematic viscosity will increase with temperature.

As the speed of the object increases through the medium particular flow seperation points are reached which will change the coefficient of drag. The range of CD will vary from attached laminar flow at slow speeds, where the coefficient can be quite high ( > 1.0 ), to that at detached turbulent flow where it can be much lower.

This is true, but I didn't want to overcomplicate matters for the time being. For fairly high reynolds numbers and low mach numbers (which is the case for the majority of objects traveling in air between, say, 20 and 200 miles per hour), the drag coefficient is approximately constant (for a given shape). As you said though, it isn't a simple subject.

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