# How To Calculate Drag Coefficient?

1. ### FredericChopin

101
We know that the drag force on an object is defined as:

FD = ρ*v2*CD*A/2

, where ρ is the density of the fluid the object is travelling in, v is the velocity of the object, CD is the drag coefficient of the object and A is the surface area of the object.

Rearranging the formula to find drag coefficient, we have:

CD = (2*FD)/(ρ*v2*A)

But suppose we needed to find the drag coefficient of an object in order to find the drag force on the object; in other words, let's say we didn't have any data on both drag coefficient and drag force. How would one find drag coefficient without using the above formula?

I heard that another way to find it was:

CD ≈ 0.01*θ

, where θ is the angle of attack of the object in radians.

What I don't like about this formula is the "≈" sign, and so I avoid using it completely.

Is there another formula to find the drag coefficient of an object?

Thank you.

Last edited: Jan 29, 2013
2. ### cjl

Figure out a nice, easy way to do that, and you'll have basically solved aerodynamics.

Good luck.

3. ### AlephZero

7,248
There are hundreds of different formulas. The hard question is deciding which one applies to your situation.

In practice, that usually involves doing experiments, not theory.

### Staff: Mentor

The drag coefficient on an object is regarded as a function of the Reynolds number, based on the relative velocity between the object and the free stream. There are graphs and tables of drag coefficient as a function of Reynolds number for many typical shapes like a sphere or an air foil (the latter also involves dimensionless geometric ratios such as angle of attack). You can find information of this type in handbooks or online. The graphs and tables were developed from experimental data on objects of these shapes taken, for example, in wind tunnels. The graphs apply to all objects having geometrically similar shapes. So you can apply the graphs to your object, as long as it one of the shapes that has been studied.

It is also possible to predict the drag coefficient as a function of Reynolds number theoretically if the flow is laminar. This can be done by solving the differential fluid mechanics equations. Reasonably good theoretical estimates for high Reynolds numbers can also be made using computational fluid dynamics packages that include turbulent flow approximations.

5. ### FredericChopin

101
Would you be able to show me the formula to calculate Reynold's number and then the formula showing the relationship between the drag coefficient and the Reynold's number of an object?

### Staff: Mentor

Google Drag of a Sphere, and choose the NASA site.

419
8. ### FredericChopin

101
@Chestermiller:

The drag formula is the formula I'm trying to avoid using to find drag coefficient; what I'm looking for is another formula that can find drag coefficient which doesn't use drag in its calculation.

You said that there's a relationship between Reynold's number and drag coefficient, which, when put in a formula, can find drag coefficient; that I'm interesting in and am looking for, but unfortunately, the NASA website only says that drag coefficient is mostly constant amongst a number of Reynold's values and doesn't mention a formula.

@bigfooted:

I looked at the "Viscous Flows" section but there was nothing about drag coefficient I could find. I will, however, keep the weblink handy.

@All:

After some researching, I found a Physics Forum post about the relationship between drag coefficient and Reynold's number:

What Astronuc is saying in his equations looks exacty like what I'm looking for - a different approaching to calculating drag coefficient. I'm having trouble understanding what he is saying in his calculations, however. Would anybody be able to help me with this?

Thank you to all who have posted so far.

9. ### FredericChopin

101
Maybe I should be a little more clear with my question.

What I'm looking for is a formula that calculates drag coefficient without using drag force in its calculation. This is why I avoid using the drag formula to calculate drag coefficient.

Chestermiller introduced the relationship between drag coefficient and Reynold's number, and I was happy to look into that since Reynold's number doesn't require drag force in its calculation.

I'm sorry if I confused anyone.

### Staff: Mentor

The NASA website, and many other web sites (and books) as well, presents a graph of drag coefficient vs Re for a sphere. If you need this relation in the form of an equation, then you have to fit an equation to the graph. At low Reynolds numbers, the drag coefficient is equal to 24/Re, which is the Stokes solution for creeping flow. You can start off with this. How you fit an equation to a graph is a matter of your personal choice. I suggest piecewise linear in the logs.

### Staff: Mentor

What you are asking is basically impossible without an aerospace engineering degree and/or CFD software. Figuring out the drag coefficient of an object is difficult because it depends on geometry and surface roughness.

12. ### bigfooted

419
Take a more thorough look at the course note I referred to.
The section on Navier-Stokes equations gives you the general fluid dynamics equations.
However, they are too complicated to solve analytically, and even numerically they are challenging.
The section on exact solutions talks about how to simplify the equations, using appropriate assumptions, to something that can be solved analytically.
The section on stream functions explains a well known method to analyze incompressible fluid flow.
The section on drag on spherical particles explains how to get the exact solution for the drag coefficient of a sphere in creeping flow, as a function of the Reynolds number.

As you see, even for a sphere in the limit of very low Reynolds numbers, it takes some effort to get the drag coefficient. The analysis get more complicated when you move to slightly more complicated flows like Stokes flow. And that's not even turbulent. And it's still a sphere we're talking about.

For general drag coefficients of objects in high Reynolds (high velocity) flows, there are no analytical expressions. Only measurements, detailed simulations and curve fits to these results. And these results are valid only for very specific shapes.