Horizontal Component of Lift

When an aircraft turns, where exactly is the HCL force being exerted from?

The wing...through it's center of pressure. The ailerons rotate the wing about it's CG...and point the Lift vector somewhere in the direction of the turn. Now the wing's Lift force provides a vertical and horizontal force. The wing's horizontal component of the Lift vector provides the "centripetal" force required to "pull" the airplane off of it's straight path and into a turn.
 
When an aircraft turns, where exactly is the HCL force being exerted from?

It's being exerted exactly from all over the wing. ;)

There is no one source of lift; lift is the total of the pressure differences existing all over the top and bottom surfaces. It's similar to saying "where is the weight of the aircraft?" Well, it's everywhere.

However, for many purposes, we can use the CG as being representative of weight. In the same way, we can pretend that lift acts at one point. That point is usually the aerodynamic center of the wing, and is located pretty close to the 1/4 chord point. This is not the same as the center of pressure. You can pretend that lift is located at the center of pressure, too, but the center of pressure moves about with the angle of attack, so it's a pretty inconvenient location.
 
That's a good point. Aerodynamic center is the point that lift effectively acts through. Center of Pressure, would be the force that provides a pitching moment for stability purposes....and counterbalances the effects of Center of Gravity.
 
That's a good point. Aerodynamic center is the point that lift effectively acts through. Center of Pressure, would be the force that provides a pitching moment for stability purposes....and counterbalances the effects of Center of Gravity.

The aerodynamic center is used almost exclusively for stability purposes, too. You rarely (never?) see any references to the CP in discussions of stability issues, for the reason I mentioned. It moves around with AOA and makes calculations difficult. For an aircraft to be stable, the CG must lie ahead of the AC, not the CP. Consider if the CG were just slightly ahead of the center of pressure; pilot pulls back on the yoke, increasing the AOA, and the CP runs forward of the center of gravity and the pitch up continues all by itself.

The AC is effectively the CP moved mathematically to a different location. To make this work, you have to add in a constant, negative (nose down) pitching moment associated with the airfoil. If you look at any airfoil data, you will see a (mostly) horizontal line at the bottom indicating a constant pitching moment that doesn't vary with AOA. This is the beauty of the AC.

However, past the stall, the negative pitching moment gets much larger. This is a reflection of the CP moving far backwards at the stall.
 
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