Archived How Do You Calculate Linear Drag Coefficient for Spherical Objects in Flight?

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Calculating the linear drag coefficient (b) for spherical objects in flight, such as a ping-pong ball, is challenging due to the lack of readily available tables specifically for linear drag coefficients, which differ from the standard drag coefficient (C_d). The formula b=6πμR is suggested for determining linear drag, where μ is the dynamic viscosity and R is the radius of the sphere. However, at speeds around 5 m/s, the flow is typically not in the linear drag regime, as indicated by the general drag curve. For those needing specific values, two tables of linear drag coefficients have been published recently. Understanding these distinctions is crucial for accurate modeling of flight dynamics.
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I'm trying to model the flight of a small spherical object (such as a ping-pong ball) through air at smallish velocities (\approx 5{_{m/s}}) with linear drag so that F_{d}=-bv. The problem is, I can't find a table of linear drag coefficients (b) anywhere; it's always just the normal drag coefficient C_{d} which is for when the drag force is proportional to v^2. I don't think you can just use C_{d}=b since they have different units.

However, I came across this, which I think is saying that b=6\pi \mu R, which would be good since I could look up \mu from say, here. Does that seem like a good idea?
 
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Well, 5m/s is not a speed at which a linear drag occurs.
To be sure of it, see that general curve :
https://commons.wikimedia.org/wiki/File:CX_SPHERE.png

But if you really wanted (I'm afraid it's too late) to calculate the flight of a sphere with a linear drag, I published recently these two tables of linear drag coefficients :
https://commons.wikimedia.org/wiki/...e_quelques_particules_en_Régime_de_Stokes.png
https://commons.wikimedia.org/wiki/File:Tableau_cx_lineaires_deuxieme.png

Friendly, Bernard of Go Mars
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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