- #1
tjs53
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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?
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?