Aeronautical Engineering/CM and CG location @ stability
I am designing an ultralight airplane that uses a e423 airfoil. All my books and guides cover mainly conventional airfoils without a whole lot of information on airfoils like this. In a traditional airfoil, the center of lift is at roughly 25% of the chord. For the e423 airfoil, Xfoil is showing it at a max of nearly -25% of the chord for the flight conditions. I know this is fairly accurate from all the information I do have, however I don't quite understand why. I know these airfoils tend to pitch down so that is obviously related. Anyway, a good rule of thumb seems to be that the elevator hinge point should be about 2.5x the wing chord from the CM or center of lift. The CG should always be ahead of the CM also. So that would mean that if I have a chord of 54 inches, the CM is located at about 13.5 inches ahead of the wing at the highest angle of attack? So the CG should be located at an absolute minimum of 14 inches ahead of the leading edge? Would the elevator hinge point still be at about 135 inches back from the CM? I have a hard time finding the answers to these questions. If it helps, the airplane has a chord of 54 inches, a total span of 35 feet with a 2 foot fuselage taking up the center so a surface area of 148.5 feet. Gross weight is 475 pounds. Elevator chord is 2.25 feet by 11.5 feet span. Would this be a relatively stable airplane if I followed the above locations? Is there any advice you can offer or a place I should look?
Brad - You need a basic book on aerodynamics. The E423 is a cambered airfoil and therefore develops a nose-down pitching moment. And the center of pressure (center of lift) varies with angle of attack. But, the airfoil quarter chord position is the aerodynamic center where the pitching moment coefficient does not vary with angle of attack. So, to simplify the aerodynamics, we usually assume lift is acting through the wing 25% chord (aerodynamic center AC, or line of aerodynamic centers on a swept wing). The airfoil moments are taken about the AC and we combine that with the other aircraft pitching moments taken about the center of gravity CG when finding aircraft stability and control. I believe you are getting confused by center of lift and pitching moments.
You haven't told me anything about the geometry of your airplane. If the tail is behind the wing, and the CG is behind the AC (the usual situation), an increase of nose-up pitching moment with increase in lift can be offset by the moment from the tail. The aircraft can be made stable. The moment generated by the tail depends on the moment arm to the CG and the tail lift (size, shape, angle of attack, elevator, etc.). So there is no magic number for the tail moment arm. If the moment arm is small, the tail must be larger than if the moment arm is large. But the airplane grows and drag goes up. This is part of the designer's trade off.
Likewise, the CG location and travel affects the tail size and moment arm. If the CG location is too far forward or aft, the tail may not generate enough moment to maintain stability. Usually, we want the CG aft of the AC because if it is forward, the tail has to generate a down load for stability and the wing has to work harder to keep the plane in the air.
The elevator hinge line relates to the required lift of the tail and the force required by the control system (stick force). Another requirement of the overall design process.
Hope this helps. Look up aircraft stability and control in the literature.