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G. Smith
G. Smith
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I am trying to plot a graph in ExcellExcel describing a free fall of an iron sphere dropped from an altitude of 12 km, while taking into account the different levels of air density affecting the drag.

The function looks like this: $$v\left(t\right)=\frac{m\cdot g}{b}\cdot \left(1-e^{\frac{-b\cdot t}{m}}\right)$$ where $b$ is the the constant of air resistance (that considers the area and shape of the object along with the density of the medium). The problem is that throughout the fall, the constant isn't constant, as air density increases with lower altitude.

Therefore the function requires plugging in both $t$ and $b$ – which are mutually dependent. That is to say, I simply don't know what $b$ corresponds to a given time (other than the initial $t_0$ at 12 km).

Even to calculate the terminal velocity $v_T=\frac{m\cdot g}{b}$ seems to be a problem, as I can't simply plug in any one $b$.

Let's say I am okay with simply taking a few discrete table air density values. What am I missing here in order to be able to "compose" the final graph?

I am trying to plot a graph in Excell describing a free fall of an iron sphere dropped from an altitude of 12 km, while taking into account the different levels of air density affecting the drag.

The function looks like this: $$v\left(t\right)=\frac{m\cdot g}{b}\cdot \left(1-e^{\frac{-b\cdot t}{m}}\right)$$ where $b$ is the the constant of air resistance (that considers the area and shape of the object along with the density of the medium). The problem is that throughout the fall, the constant isn't constant, as air density increases with lower altitude.

Therefore the function requires plugging in both $t$ and $b$ – which are mutually dependent. That is to say, I simply don't know what $b$ corresponds to a given time (other than the initial $t_0$ at 12 km).

Even to calculate the terminal velocity $v_T=\frac{m\cdot g}{b}$ seems to be a problem, as I can't simply plug in any one $b$.

Let's say I am okay with simply taking a few discrete table air density values. What am I missing here in order to be able to "compose" the final graph?

I am trying to plot a graph in Excel describing a free fall of an iron sphere dropped from an altitude of 12 km, while taking into account the different levels of air density affecting the drag.

The function looks like this: $$v\left(t\right)=\frac{m\cdot g}{b}\cdot \left(1-e^{\frac{-b\cdot t}{m}}\right)$$ where $b$ is the the constant of air resistance (that considers the area and shape of the object along with the density of the medium). The problem is that throughout the fall, the constant isn't constant, as air density increases with lower altitude.

Therefore the function requires plugging in both $t$ and $b$ – which are mutually dependent. That is to say, I simply don't know what $b$ corresponds to a given time (other than the initial $t_0$ at 12 km).

Even to calculate the terminal velocity $v_T=\frac{m\cdot g}{b}$ seems to be a problem, as I can't simply plug in any one $b$.

Let's say I am okay with simply taking a few discrete table air density values. What am I missing here in order to be able to "compose" the final graph?

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jflint
jflint
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Free Fall with Drag and Varying Air Density

I am trying to plot a graph in Excell describing a free fall of an iron sphere dropped from an altitude of 12 km, while taking into account the different levels of air density affecting the drag.

The function looks like this: $$v\left(t\right)=\frac{m\cdot g}{b}\cdot \left(1-e^{\frac{-b\cdot t}{m}}\right)$$ where $b$ is the the constant of air resistance (that considers the area and shape of the object along with the density of the medium). The problem is that throughout the fall, the constant isn't constant, as air density increases with lower altitude.

Therefore the function requires plugging in both $t$ and $b$ – which are mutually dependent. That is to say, I simply don't know what $b$ corresponds to a given time (other than the initial $t_0$ at 12 km).

Even to calculate the terminal velocity $v_T=\frac{m\cdot g}{b}$ seems to be a problem, as I can't simply plug in any one $b$.

Let's say I am okay with simply taking a few discrete table air density values. What am I missing here in order to be able to "compose" the final graph?