Drag force on a cone

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If the symmetry axis of the cone lies along the direction of travel, and if you are using the drag equation \begin{align} F_\mathrm{drag} = \frac{1}{2}C_d\rho Av^2 \end{align} to compute the drag force, then you should take $A$ to be the area of the base, namely the full area that would be obstructing your vision if you were looking at the object coming toward you.

This assertion is confirmed by Wikipedia when it defines the drag coefficient which uses the nice term "projected frontal area;"

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross sectional area of the vehicle, depending on where the cross section is taken. For example, for a sphere $A=\pi r^2$.

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Updated on June 14, 2020

Comments

  • user28324
    user28324 over 3 years

    I was asked to calculate the drag force on a cone with velocity 10 m/s, everything was okay until I needed to calculate the cross sectional area, the radius of the base was 0.5 m, radius of the top 0.0005 m, given that the cone falls top first, which one should I use?

    Should I get some kind of an average?

    • Kevin Kostlan
      Kevin Kostlan almost 10 years
      Remember: using things like cross-sectional area is an approximation.
  • David White
    David White over 5 years
    Don't forget to use the drag coefficient that corresponds to the shape of a cone.