falling playing cards

Any physicists in the house? This film at SciCast shows a neat trick with dropping playing cards, where if you drop them end-on they flutter, but if you drop them side-on they parachute down and hence can be aimed rather accurately. Now, my explanation for this has long gone thus:

The playing card’s terminal velocity when dropped flat is lower than the laminar/turbulent transition speed. So the airflow around stays laminar, and the cards fall smoothly. When dropped end-on they rapidly start to flutter — like the opposite of a flag, with the air staying still and the flag moving through it. You’d still expect the flag to flutter, and that flutter is what sets the cards tumbling.

However, my colleague who’s writing up my notes isn’t convinced. Which is fair enough, because, hey, it’s 15 years since I didn’t do any fluid dynamics. She replies:

What I’ve been looking at is that low Reynolds number gives you laminar flow and high R number gives you turbulence, but the R number is also related to the scale length of the object moving through the fluid. I’d like to say that only the speed of the object matters but I’m not sure how the horizontal card can suffer from air resistance which causes it to fall slowly and for this air resistance to not have an effect on the turbulence it feels. Suddenly I regret not paying more attention in second year.

My thinking on that:

The swept volume for the horizontal card is still larger. The flow might be laminar, but there’s more air involved which implies more work done to displace it.

Anyone else like to weigh in?

2 thoughts on “falling playing cards”

  1. My explanation would be something like this:
    Consider a card falling with its face at 45 degrees:
    There will be vortex shedding off the bottom corner. This will cause greater “air resistance” at the bottom corner at the top corner, and thus a greater force exerted on the card by the air at the bottom corner than at the top corner. From a point of view moving with the card’s centre of gravity, the card will start to turn and “level out”.
    If we apply this to our two situations, we see that for a card that is nearly face down, any slight deviations in inclination will lead to the card returning to normal. The face down situation is therefore stable.
    However, for a card which is edge-on, any slight deviations will be enhanced. The edge-on situation is therefore unstable. The fluttering of the card is caused by a combination of the rotational inertia of the card, and shedding of vortices off the corners.

  2. I think the stability of the airflow around the card is at least partly a red herring – laminar or turbulent wouldn’t affect a steel plate falling, for example.
    I think the issue is the orientation of the card putting the card itself in a stable or chaotic (in the sense of “sensitive dependence on initial conditions”) domain.
    Dropped edge on, a small deviation (either the card is dropped at a small angle, bent, or turbulence moves it) turns into a larger and larger deviation as the card falls, because the energy of the card falling is being diverted into rotating the card more and more “sideways” as it were, which then pushes the card further and further from the straight path it would fall on if it was a sphere.
    On the other hand, dropped flat on, small deviations tend to correct, keeping the card in a stable domain.
    I think that as long as the *card* is in a stable rather than a chaotic domain, the turbulence or linearity of the airflow around it is not going to make that much difference.
    Of course, if the airflow around the card is in a chaotic domain (i.e. a gale) then there’s enough energy in that system to drag the card into chaos right along with it.
    No jokes about the Gupta Effect, please.

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