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

In summary, the conversation discusses the difficulties of finding a table of linear drag coefficients for a spherical object in flight with linear drag. The speaker suggests using a formula that equates the drag coefficient C_{d} to b, but the other speaker points out that they have different units. However, they mention coming across a formula that may be a good solution, and provide a link to two tables of linear drag coefficients for spheres. The conversation concludes with a friendly reminder to check the general curve for confirmation.
  • #1
Screwdriver
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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 ([itex]\approx 5{_{m/s}}[/itex]) with linear drag so that [itex]F_{d}=-bv[/itex]. The problem is, I can't find a table of linear drag coefficients ([itex]b[/itex]) anywhere; it's always just the normal drag coefficient [itex]C_{d}[/itex] which is for when the drag force is proportional to [itex]v^2[/itex]. I don't think you can just use [itex]C_{d}=b[/itex] since they have different units.

However, I came across this, which I think is saying that [itex]b=6\pi \mu R[/itex], which would be good since I could look up [itex]\mu[/itex] from say, here. Does that seem like a good idea?
 
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  • #2
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
 

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

What is the Linear Drag Coefficient?

The Linear Drag Coefficient is a measure of the resistance an object experiences as it moves through a fluid, such as air or water. It is represented by the symbol Cd and is dependent on the size, shape, and speed of the moving object.

How is the Linear Drag Coefficient calculated?

The Linear Drag Coefficient is calculated by dividing the drag force by the product of the fluid density, the cross-sectional area of the object, and the square of its velocity. It can also be determined experimentally by measuring the drag force at different velocities and plotting a graph to find the slope, which is equal to the Cd value.

What factors affect the Linear Drag Coefficient?

The Linear Drag Coefficient is affected by several factors, including the shape and size of the object, the speed at which it is moving through the fluid, and the properties of the fluid itself, such as density and viscosity. Other factors, such as surface roughness and turbulence, can also impact the Cd value.

How does the Linear Drag Coefficient impact an object's motion?

The Linear Drag Coefficient plays a significant role in determining an object's motion through a fluid. As the Cd value increases, the drag force also increases, causing the object to slow down. This can lead to changes in velocity, acceleration, and ultimately the object's trajectory.

How is the Linear Drag Coefficient used in real-world applications?

The Linear Drag Coefficient is used in various fields, including aerodynamics, fluid dynamics, and sports. It is used to design more efficient and streamlined objects, such as airplanes and cars, and to improve performance in sports like cycling and swimming. It is also utilized in weather forecasting and environmental studies to understand the movement of air and water through different mediums.

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