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B How to calculate Drag Coefficient?

  1. Jul 25, 2016 #1
    As I have looked through the internet and did my research I have found some information on how to calculate the drag coefficient, however none of what I have search for matches what I need. Currently I am doing a physics assignment for grade 12 and I am investigating the physics behind parachutes, for this task I want to mainly focus on how each different factor affects the decent speed of the parachute. So far what I have got are the equation for calculating the drag coefficient, however I am very confused with the equation which can calculate the drag coefficient. Here is how I am confused: according to the following websites:




    The drag coefficient can be calculated with equation(s) shown on the websites. The drag coefficient can be calculated with a velocity as one of the variables, as the velocity changes then the drag coefficient would change too (right?). From my current understanding the velocity is how fast the object/parachute is traveling in the medium (assuming terminal velocity). But the velocity which the parachute is traveling through the medium depends on other factors such as mass (am I right?).

    However these websites below tells me that no matter what size or mass these objects have, the drag coefficient would remain the same/relative to the corresponding forms/shapes of the object:




    Wouldn’t the mass or size of these objects change the velocity which they travel through the medium? Thus changing the drag coefficient according to the equation? I am very confused.
  2. jcsd
  3. Jul 25, 2016 #2
    The drag would be the same for an object not moving, in fact that's how it is calculated in a wind tunnel.
  4. Jul 25, 2016 #3
    What would I do with the velocity variable in the drag coefficient equation?
  5. Jul 25, 2016 #4
    Please post the equation and link. Drag coefficients do not contain velocity.

    you might mean drag force which is velocity dependent typically on v or v^2.
  6. Jul 25, 2016 #5

    FD = ½ r Cd A v2

    https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/Images/rktvrecv.gif <-- Image Link
  7. Jul 25, 2016 #6
    As I suspected, plug in units both sides. The drag force and drag coefficient are different things.

    What are you trying to calculate?
  8. Jul 25, 2016 #7
    I am certainly not good at physics.

    I am trying to calculate the decent velocity of a parachute if given:
    • Area of the Parachute
    • Mass on Parachute
    • Air Density
    Last edited: Jul 25, 2016
  9. Jul 25, 2016 #8
    In short, I want to use the equation below to workout the decent velocity:
    v = sqrt( (8 m g) / (pi r Cd D2) )

    • D is the chute diameter in meters
    • m is the rocket mass in kilograms
    • g is the acceleration of gravity = 9.8 m/s2
    • pi is 3.14159265359
    • r is the density of air
    • Cd is the drag coefficient of the chute
    • v is the speed we want at impact with the ground (3 m/s or less)
    but how do I work out the Drag Coefficient for a parachute?
  10. Jul 25, 2016 #9
    Personally i would tie one end to a force meter and the other end of the force meter to a fan. You will also need a wind speed meter.

    Measure the wind speed and force, calculate the drag coefficient.
  11. Jul 25, 2016 #10


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  12. Jul 25, 2016 #11
  13. Jul 25, 2016 #12


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    At the end of the day, you generally can't "calculate" the drag coefficient except for a few very specific shapes. You have to determine it experimentally in most cases, usually by measuring the force at a known velocity and back-solving the equation. In effect, a drag coefficient attempts to distill a lot of very complex physics into a very simple relation between force and dynamic pressure.

    Also, the velocity in question is the relative velocity between the object and the medium through which it travels.
  14. Jul 25, 2016 #13
    You are confusing the two sides of the equation. The drag force and drag coefficient depend on the velocity but, from the other side of the force balance equation, the force depends on the weight (mass) of the object. When you set the two sides of the equation equal to one another, you can solve for the velocity. But, as far as the drag force is concerned, you only need to know the velocity.
  15. Jul 28, 2016 #14

    David Lewis

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    It depends. On a small parachute, CD can vary significantly with respect to speed because Reynolds number goes up in direct proportion to speed (and in most cases, CD goes down as Re goes up). Whereas the CD of large parachutes tends to be fairly invariant with respect to Re.
  16. May 30, 2017 #15
    I'm wondering if there are any online or free tools that would allow calculation of drag force or drag coefficient, for any arbitrary shape that I define. I find some interesting free CFD tools available, such as Flowsquare (2D), simFlow (3D), and OpenFoam (3D), but these seem to be more for visualizing flows and vortices than actually calculating practical things like drag.
  17. May 30, 2017 #16


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    The only one of those that I have heard of is OpenFoam, and it is a lot more powerful than just visualization. It is a C++ library used to generate your own custom solvers and could absolutely calculate approximate drag assuming you know how to program a solver to do it.
  18. May 30, 2017 #17
    Experience has shown that the drag force on an object in a fluid stream is proportional to the dynamic pressure, 1/2*rho*V^2, and the drag coefficient is the empirically determined constant of proportionality. Experiment has shown that this proportionality constant is usually well defined for a specific geometry, although it does depend upon the Reynold's Number of the flow in complicated ways for each geometry. Use of this quantity does, however, greatly simplify drag calculations, as all you need as inputs are the specific geometry, e.g., sphere, cylinder, etc., and Reynold's number. Numerical values can be found in most aerodynamic textbooks. In other words, the drag coefficient is not calculated. It is tabulated for specific geometries and Reynold's numbers.
  19. May 30, 2017 #18
    After further reading, simFlow turns out to be a GUI wrapper for OpenFoam. Man, that really bogs down my laptop, this stuff is computation-intense. I downloaded it because I found a demo showing how to get the drag coefficient for a 3-dimensional shape.
    My Reynolds number is in the 50K-100K range. This appears to be taken care of automatically in the software, given the velocity input and size of the object. I'm not interested in drag coefficients for standard objects like spheres and cylinders, I need to know the drag coefficient for a custom geometry. For my purposes, a 2D software package would work, but the only 2D one I've found is just for visualization of flows.
  20. May 31, 2017 #19
    Okay, I understand what you want to do. It's not easy to make such calculations on arbitrary 3-D shapes, but some are harder than others. There are complications that arise with transitions from laminar flow to turbulent flow, and these transitions at the surface of the body can cause huge changes in the global flow patterns. For instance, for spheres and cylinders, there form Von Karman vortex streets, or the shedding of vortices into the wake in alternative fashion from one side of the body to the other. It seems to me that any software package that can calculate the drag in such instances would have to be quite sophisticated. In addition, it may require much user input to guide the software during the calculation. I myself am not very familiar with any of the most recent software packages, but I'd guess that they are quite sophisticated. I thus suggest that you need to focus on a specific geometry for a specific range of Reynold's number. Do you have a particular shape in mind? What is it? In order to calculate a Reynold's number, you must have some idea of the overall size of the object.
  21. May 31, 2017 #20
    Yes, I know exactly the size of the object and the velocity range it would experience, which would determine the Reynolds number. The object is a water rocket, made from a soda bottle. Given that I have a nicely shaped nose cone, I want to get the drag coefficients for the model using different taper shapes at the tail end. The length is about 0.5 meters, the maximum velocity is about 70 m/s, giving a Reynolds number of about 2×106. (I wrote 50K-100K in a previous post, but that was just for the fins; my error.)

    The drag coefficient of a bullet (a hemisphere on a cylinder) is 0.295 according to this NASA page: https://spaceflightsystems.grc.nasa.gov/education/rocket/shaped.html

    That same page also says (at the bottom) that the drag coefficient of a model rocket is 0.75. Now, why would it be higher than a bullet shape? It seems to me that, for the same cross-sectional area and body length, a bullet with a pointy ogive-shaped nose would have a lower drag than a round-nose bullet. If they're including the drag of the fins too, then that might explain the value of 0.75, in which case 0.75 would be too high for the drag coefficient of just the rocket body.

    The page also says the drag can be reduced by adding a tapered fairing on the tail end.

    So I wanted to see for myself, using some CFD software, what the drag coefficient actually comes out to be, not for idealized shapes, but for my specific shape, with different variations in nose and tail geometries. Because a rocket body is radially symmetric, I thought perhaps a 2D software package would be sufficient, but the only one I found that can generate drag coefficients is simFlow+OpenFoam (see the demo I linked in my previous post above). I suspect my computer may not be up to the task -- not to mention a really steep learning curve.
    Last edited: May 31, 2017
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