Stability of rocket during flight; why does the lift force change direction when the center of pressure moves?

Question

I am currently learning about fins and the role they play in the stability of a rocket during flight. I came across a relatively minor problem.

Here is one of the resources I'm looking at: http://www.nakka-rocketry.net/fins.html

My question is, why does the lift force change direction when the center of pressure is located above the center of gravity? Apologies if it's a bad question but I haven't covered anything related to lift or drag in a very long time.

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In Fig. 1A, the rocket is shown during the powered flight This is an ideal state, with all the forces acting through the CG and no external (perturbing) forces present. The rocket is stable and accelerating with exclusively linear motion along the line of thrust.

In Fig. 1B, a perturbing force is introduced, in this example, the force due to a gust of wind. The resultant of this pressure force acts through the CP, causing the rocket to rotate about its CG, changing slightly the angle of attack (alpha).

This change in angle of attack immediately generates a lift force, acting as shown (normal to the body) through the CP. This force balances the force due to wind, and the rocket remains stable, with its flight path only slightly altered.

Fig. 2A illustrates a rocket with the CP, CG locations reversed, that is, the CP is ahead of the CG. This is an undesirable scenario. In this figure, the rocket is initially stable, being in the same ideal situation as in Fig. 1A, with no perturbing forces present. Along comes a disturbing force, again a gust of wind, as illustrated in Fig. 2B. The wind force acts with its resultant through the CP, again generating a slight rotation, and consequential change in angle of attack. Again, a lift force is generated due to the change in angle of attack, but this time the lift force acts in the same direction as the wind force. The consequence of this is an unchecked rotation of the rocket about its CG, as shown. The rocket becomes unstable, that is, its flight path is no longer linear motion, but rotational motion is introduced. The rocket tries to turn around and fly backward. The thrust force from the motor does not allow this, of course, and so the rocket tumbles out of control.

Answer 1

For the example given at that link, the direction of the lift force changes because the angle of attack is reversed between the two cases. Source

Note that the perturbing wind in both cases comes from the right. The stable rocket tends to rotate to the right (into the wind), the unstable rocket tends to rotate to the left (with the wind).

Answer 2

Note that in both cases the rocket is not moving along it’s axis, but rather it’s traveling straight up in the diagram. That’s what the diverging lines labeled with the angle of attack mean.

That in turn is causing aerodynamic lift, similar to the lift from a wing or angled hand in an air stream.

This “lift” is not the same as the engine thrust which is the dominant force “lifting” the rocket. Rather, it’s a sideways push on the rocket body.

Answer 3

Think of the center of gravity (CG) as a pivot point or a fulcrum on a balanced lever. If a force is applied away from the CG, it will cause the rocket to rotate around the CG. In particular, lift and other disturbance forces (e.g. wind) will always act at the center of pressure (CP) which can be and often is located away from the CG.

The main question addressed in the link is: how will the rocket naturally respond to a disturbance wind coming from the right hand side of the rocket with the CP ahead of (bow) or behind (aft) the CG.

In the stable case, the wind distubance force pushes the rocket leftward at the CP point aft of the CG. Remember that the CG is the picot point, so all rotations will be around the CG. This causes the rocket to rotate slightly clockwise, making it deviate slightly from it’s vertical velocity direction and thus giving it a small angle of attack. Fortunately, this angle of attack also produces a lift force which acts in the opposite direction (rightward). So with the CP aft of the CG, the rocket naturally tries to counteract disturbance wind with lift pointing in the opposite direction.

If the unstable case, we analyze the same disturbance force pointing in the same leftward direction. But now the CP is ahead (bow) of the CG. So when the wind pushes at that point, it rotates the rocket counterclockwise (pivot point is still the CG. This creates an angle of attack in the opposite direction, creating a lift force that also points in the leftward direction. With both wind disturbance and lift pointing in the same direction, there is nothing to stop the counterclockwise rotation and the rocket will spin out of control.