Strange turn of a rotating playing card when I throw it

[JakubKivi]

I have observed that when i throw a card and give it a angular velocity, it "aim" to vertical and depending on direction start to rotate. For example if it rotates to the left in horizontal, vertically left side of cart goes up and right goes down. Conversely for the right rotation. I am not sure if my english is good enought to explain so i made a simple picture. I rejected a magnus force becouse it could only turn card without changing angle (i guess). What is the force making card to do this?

 

[FactChecker]

A single playing card is turned too much by winds and other things to make a reliable experiment. Try the entire deck of cards in its box. The inertial moments of a body will cause cross-rotations unless there is symmetry. The box of cards has a lot of symmetry. Even then, it should be stable in two primary axes (with the largest and smallest inertial moments) and instable in the intermediate axis. This is called the "tennis racket theorem".

If you are talking about the aerodynamics of a single playing card, here is a guess:
A playing card is often not flat, but is bent like a wing. If you toss a card forward in a rotating manner, one side is going forward faster than the other side. It may have more lift than the slower side and may make that side rotate up.

 

[DaveE]

A playing card is often not flat, but is bent like a wing. If you toss a card forward in a rotating manner, one side is going forward faster than the other side. It may have more lift than the slower side and may make that side rotate up.

Or down. Turn the card over so the bend goes from convex to concave and the effect should reverse if this is the cause.
OTOH, even a flat wing can generate lift since the fall due to gravity creates a positive angle of attack. This will also be greater at higher velocity. So if the effect doesn't reverse when you turn the card over FactChecker may still be right. I'm guessing that the flat card may stop in the vertical plane, since the AOA goes to zero? Maybe I'll try some experiments to see, or not. If you guys try it please report back.

 

[JakubKivi]

I have tried with all cards from the deck, so that's why I am asking. All of the card do the same thing independent of angle of atack or the aspect ratio or size/weight of card. Also it doesn't reverse when I turn the card over. I have also been thinking that it's because of the pressure difference and the lift, but I guess that pressure over and under a card doesn't change due to angular speed.

 

[vanhees71]

If you could do the experiment in a vacuum then you'd have a top spinning around its center of mass. The center of mass is free falling and the rotation of the cards around the center of mass is described by Euler's equations of the free top. In the most general case where all three principle values of the tensor of inertia are different, these equations lead to quite complicated non-linear equations whose solutions are expressible only with help of elliptic functions.

Nevertheless there's of course an exact special solution, which is the rotation around one of the principle axes. Then you can look at small deviations from this special solution to investigate the stability of the solution. It turns out that the rotation around the axis of the smallest or the around axis of the largest principle moment of inertia are stable while the one around the axis with the middle principle moment of inertia is unstable.

 

[A.T.]

For example if it rotates to the left in horizontal, vertically left side of cart goes up and right goes down. Conversely for the right rotation.

Sounds like a combination of aerodynamic torque and gyroscopic effect. The spin axis rotates around an axis that is perpendicular to the spin axis and the aerodynamic torque.

 

[FactChecker]

How are you spinning it? It would be very hard to do it by hand without some persistent unintentional motion. If you have ever tried to suppress a bad motion when firing a handgun, then you know how hard that is to detect and control.

 

[A.T.]

For example if it rotates to the left in horizontal, vertically left side of cart goes up and right goes down. Conversely for the right rotation.

Sounds like a combination of aerodynamic torque and gyroscopic effect. The spin axis rotates around an axis that is perpendicular to the spin axis and the aerodynamic torque.

Here a similar banking phenomenon described for Frisbee (section 2.2):
https://scripts.mit.edu/~womens-ult/frisbee_physics.pdf

 

[rcgldr]

Sounds like a combination of aerodynamic torque and gyroscopic effect. The spin axis rotates around an axis that is perpendicular to the spin axis and the aerodynamic torque.

Here a similar banking phenomenon described for Frisbee (section 2.2): https://scripts.mit.edu/~womens-ult/frisbee_physics.pdf

The precession related roll is what an Aerobie flying ring eliminates with it's open ring shape and outer edge "spoiler". It moves the center of aerodynamic force to nearly eliminate aerodynamic torque, and small adjustments are done by bending the ring so it's flexed slightly upwards or downwards.

 

[A.T.]

The precession related roll is what an Aerobie flying ring eliminates ...

But if @JakubKivi wants to actually reproduce the effect more reliably than with playing cards, I would try CDs.

 

[FactChecker]

I can only think of three good explanations for a repeatable asymmetric behavior:
1) some asymmetric shape of the card
2) some part of the throwing motion that is causing it
3) the difference between the aerodynamics of the forward-moving side verses the backward moving side.

 

[rcgldr]

For a playing card, or flat disc, ..., the center of aerodynamic force is in front of the center of mass, similar to a conventional wing. This results in an aerodynamic upwards pitching torque, that due to gyroscopic effects, results in a rolling reaction.

 

[A.T.]

3) the difference between the aerodynamics of the forward-moving side verses the backward moving side.

This could play some role, but it's mostly what I and @rcgldr described above. See also here (section 2.2):
https://scripts.mit.edu/~womens-ult/frisbee_physics.pdf

 

[FactChecker]

I would have to study the frisbee physics link to see if and why it indicates that direction of roll. I would have thought that a net lift requires a downward velocity in the trailing downwash. That implies a net nose-down torque on the wing. Most airplanes need a downward aerodynamic force from the tail to counteract that. With the spin of the diagram shown in post #1, that would cause a "left-wing-down" roll -- not the roll shown in the diagram.

 

[A.T.]

That implies a net nose-down torque on the wing. Most airplanes need a downward aerodynamic force from the tail to counteract that.

Are you talking about torque around the airplanes center of mass here? That can be different from the torque around the center of the wing.

 

[rcgldr]

I would have to study the frisbee physics link to see if and why it indicates that direction of roll. I would have thought that a net lift requires a downward velocity in the trailing downwash. That implies a net nose-down torque on the wing. Most airplanes need a downward aerodynamic force from the tail to counteract that. With the spin of the diagram shown in post #1, that would cause a "left-wing-down" roll -- not the roll shown in the diagram.

Most of the trailing downwash is related to the downwards acceleration of air above and about 1/3rd or so behind the leading edge of an airfoil. This would correspond to an upwards pitching torque due to lift, and would apply to a playing card or flat disc.

However, a cambered airfoil produces a downwards pitching torque, and in the case of a Frisbee, the camber related downwards pitching torque is greater than the upwards pitching torque related to the lift vector being in front of the center of mass. This is not mentioned in that Frisbee physics pdf file, and it predicts the wrong roll direction (unless the Frisbee is thrown upside down).

For for a Frisbee cambered down (the normal way), you throw with the outside edge downwards and it rolls to horizontal and beyond. For a flat disk or upwards cambered disk (upside down Frisbee, paper plate with edges up, ...), you throw with the outside edge upwards and it rolls to horizontal and beyond.

The Aerobie is designed so that when "tuned" (flexed a bit up or down to adjust camber), you throw with the outside edge horizontal, and it remains horizontal throughout it's flight.