Precession of a football in flight

[tjs53]

I'm interested in the change of orientation of a football as it travels through the air

Really quickly, I'm going to define a reference frame as such:
x-axis: from one touchdown to the other, and in this case, also the line from quarterback to receiver.
y: along the turf from sideline to sideline, parallel to any "yard line"
z: vertically upward

As a football travels along its trajectory, the direction in which the football seems to "point" changes. If you imagine a line drawn from the back tip to the front tip of the ball (the ball's axis of symmetry), this line begins inclined to level ground as it leaves the quarterback's hand. When the ball reaches its highest point, this line is level with the ground. And while descending, the line points below level.

Let's just briefly imagine the ball at it's highest point so that the axis of the ball is aligned with the x-axis. Clearly there are aerodynamic forces involved, since in space the ball's axis would remain constant throughout its flight. However, since the ball is spiraling about the x-axis, I think a more precise explanation is required. Drag and lift cause torques about the y-axis, so the change in angular momentum will also be about the y-axis. This means that precession has caused the ball axis to be aligned with a new vector in the x-y plane. The areodynamic forces have cause the ball's orientation to rotate such that the ball is now pointing "sideways".

In summary, in order for the front of a spiraling football to rotate downward, a torque about the z-axis (vertically upward) must be provided to change the angular momentum vector of the ball. Where do the torques about the z-axis come from?

 

[Andrew Mason]

In summary, in order for the front of a spiraling football to rotate downward, a torque about the z-axis (vertically upward) must be provided to change the angular momentum vector of the ball. Where do the torques about the z-axis come from?

I think you have analysed it correctly. There has to be a torque on the ball about the z-axis to cause the nose to dip down. The only forces that would seem to operate would be air or gravity. Gravity is in the wrong direction so it must be air flow. Perhaps the rifling of the ball creates a pressure difference from side to side as the ball passes through the air.

AM

 

[tjs53]

Yes, there are probably non-trivial pressure imbalances on the sides, but since the ball is rifled these imbalances rotate so that when averaged over a rotation, the imbalances would cancel.

 

[rcgldr]

or it could simply be that the precession effect is less dominant than aerodynamic effect trying to align the ball with the path.

 

[Andrew Mason]

or it could simply be that the precession effect is less dominant than aerodynamic effect trying to align the ball with the path.

I was watching some of the long quarterback throws yesterday. When the nose dropped as the ball came down, the ball was angled slightly to the right of centre (looking forward in the direction of the ball motion). That slight angle should give it a clockwise torque (looking down from above) about the vertical axis due to more air striking on the left side than on the right. This would cause the nose to keep dropping as it goes through the air if the ball is rotating clockwise from the QB's hand, which is the case with a right arm thrower (all the QBs in yesterday's games threw with their right arm). If the ball was rotating counter-clockwise (left hand thrower) the ball would have to point slightly to the left in order to have the nose rotate down.

AM

 

[randys006]

First, it has nothing to do with rotation or precession and everything to do with aerodynamic drag and the shape of the football. The primary effect of the spin is to provide the ball with a large amount of rotational energy to stabilize it against small wind effects.

Next, a minor correction: the torque is about the y-axis, not z. Drag acts equally on every point on the football's surface in a direction exactly opposite its velocity. For simplicity, consider a football moving straight ahead (in the x-direction) with its nose tilted slightly upward. In this orientation, the center of mass of the football is slightly below its tip. Points near the tip are above the COM and drag on these points creates a torque acting to raise the tip. Points farther back are below the COM and act to drop the tip. Because the football has much more surface area below the COM, the net torque causes the nose to drop. This happens even if the quarterback throws the ball at a "flat" angle (the axis of the football exactly aligned with its velocity), because gravity quickly acts to pull the velocity vector downward. Note that if the tip ever dropped below the axis of motion, the same effect would cause the rapidly dropping nose to slow down and possibly even begin to rise!

Note that the "nose drop effect" is highly dependent (probably nonlinear) on the speed of the football, so you may expect the effect to be much more pronounced for a pro quarterback (who throws quite fast) than for, say, a young high-school quarterback. It would be interesting to look at some tape and see if there is a noticeable difference!

Randy

 

[K^2]

Magnus effect is the source of the stabilizing force that aligns football with flight trajectory.

 

[D H]

First, it has nothing to do with rotation or precession and everything to do with aerodynamic drag and the shape of the football.

It has everything to do with rotation, precession, drag, and the shape of the football.

Next, a minor correction: the torque is about the y-axis, not z.

That, too, is incorrect.

Gyroscopic effects are very counter-intuitive. Apply a small torque to a rotating object such that the torque is normal to the axis of rotation and the object will precess in a direction that is perpendicular to the torque and the axis of rotation. The precession of the football in flight that tjs53 is asking about in the opening post is about the y-axis, and thus the torque must be about the z-axis.

 

[randys006]

Magnus effect is the source of the stabilizing force that aligns football with flight trajectory.

Cool, I either haven't heard that term before or I forgot it years ago ;). Either way, being a golfer, I did consider the effect before I posted and I don't believe it applies to OP's football because A) the spin axis is (nearly) parallel to the motion and the small vertical component of spin creates a force to the left/right anyway, not a torque, and B) the acceleration, given by the rate of spin times forward velocity divided by the mass of the football) is MUCH lower than other sports where the Magnus effect clearly applies, e.g. golf, table tennis, baseball. This is easy proven because you just don't see well-thrown footballs curving very much. I'm pretty sure the nose-drop effect is just drag sneaking through the thin boundary layer of air--feel free to comment if you disagree though, or if I'm just plain wrong ;).

Randy