Investigating Drag with Paper Cones

[CWatters]

There are some drag coefficients here..

https://en.wikipedia.org/wiki/Drag_coefficient
The Cd of a cone point first is given in the top right hand table as 0.5.
The Cd of a flat plate is given in the lower table as = 1.28

Note these are only a rough guide. The angle of the cone isn't specified.

 

[Jimmy87]

Yes I would expect a cone with a wider angle to fall more slowly than a cone with a narrow angle because Cd is higher.

Would a reasonable scientific explanation of this be to discuss how the rate in change of momentum of air particles changes between the flat circle and cone. Looking at the flat circle, air particles will undergo a change in momentum of 2mv when they strike the surface. The force would be the rate of change of momentum which would be dictated by the velocity of the object. If we look at the cone then the air particles strike the surface of the cone which is now at some angle compared to the normal of the cone. Therefore the momentum will go down by the sine of the angle between the air particle striking the surface and the normal. Is this ok to explain why a cone falls faster through the air?

 

[CWatters]

Perhaps but its not that simple. The shape behind the point of maximum cross sectional area also matters, perhaps not in this case (the back of a disk and the back of a cone are similar) but certainly for wing sections.

 

[NTL2009]

You might also consider adding a short string ( ~ 10 CM?) with a little weight on one end, and the other pulled through the tip of the cone, and attached on the inside. This would help keep the cone pointed down, and the weight would be more consistent cone-to-cone, as small variations in cone weight would not affect total weight very much (%-wise).

 

[f todd baker]

There seems to be a lot more floundering around than necessary in this discussion. You want to know how drag depends on the angle of your cone. It sounds like all your cones are constructed of the same amount of paper so their masses are equal. The area A is the orthographic projection which, simply put, is the area presented to the onrushing wind and that is the area of the base. The area of the base is A=πR² where R=rsinθ and r is the radius of the paper circle (6" for you) and θ is the angle of the cone. Therefore A=π(rsinθ )². You should therefore expect the measured drag to be proportional to the square of the sine of θ, F_D∝sin²θ.