Drag Coefficient -- What is the constant K?

In summary, the drag coefficient, often represented as the constant K, quantifies the drag force experienced by an object moving through a fluid, such as air or water. It is a dimensionless number that depends on the shape of the object, flow conditions, and surface roughness. The drag coefficient is crucial for engineers and designers in optimizing the performance of vehicles and structures by minimizing resistance and improving efficiency.
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eliasss
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TL;DR Summary
What is the constant K in the drag coefficient?
As I understand, the drag coefficient looks as follows:

CD=CD0+CL/πAe

however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this:

CD=CD0+k1CL+k2CL^2

could someone help? Thanks!
 
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Welcome to PF.

Maybe one is the induced drag, that is due to air moving around the end of the wing.
Induced drag is proportional to lift, not to the square of the airspeed.
 
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eliasss said:
TL;DR Summary: What is the constant K in the drag coefficient?

As I understand, the drag coefficient looks as follows:

CD=CD0+CL/πAe
This assumes that CD is a linear function of CL, which is an ok assumption as long as you are linearizing in a small region of flight condition.
There are good reasons to analyze stability and control in small flight condition regions using linearized equations.
eliasss said:
however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this:

CD=CD0+k1CL+k2CL^2
This models CD as a function of CL and CL^2. It allows more accuracy for a larger region of flight condition where the relationship between CD and CL has begun to curve. The parameters, k1 and k2 need to be estimated. k1 is probably very close to ##1/(\pi A e)##. But a lot of analysis gets much more difficult when the equations are nonlinear.
CORRECTION: There is no reason to think that k1 is close to ##1/(\pi A e)##. I was thinking that it was a Taylor series expansion around the linearization point.
 
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FAQ: Drag Coefficient -- What is the constant K?

What is the drag coefficient (Cd)?

The drag coefficient (Cd) is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment, such as air or water. It is used in fluid dynamics to characterize the drag force experienced by an object moving through a fluid, taking into account factors like shape, surface roughness, and flow conditions.

What does the constant K represent in relation to drag coefficient?

The constant K is often used in equations related to drag, particularly in empirical formulas that relate the drag force to the velocity of an object and the fluid density. It can represent various factors depending on the specific context, such as the shape of the object, flow conditions, or other coefficients that influence drag.

How is the drag coefficient determined?

The drag coefficient is typically determined through experimental measurements in wind tunnels or water channels. It can also be calculated using computational fluid dynamics (CFD) simulations. The Cd value is derived from the ratio of the drag force to the dynamic pressure of the fluid and the reference area of the object.

What factors influence the value of the drag coefficient?

Several factors influence the drag coefficient, including the shape and size of the object, the surface texture, the Reynolds number (which relates to the flow regime), and the angle of attack. Different shapes, such as streamlined versus blunt bodies, will have significantly different Cd values.

Can the drag coefficient change with speed?

Yes, the drag coefficient can change with speed due to variations in the flow regime around the object. At low speeds, flow may be laminar, leading to a lower Cd, while at higher speeds, flow may transition to turbulent, resulting in a higher Cd. This behavior is often characterized by the Reynolds number.

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