6.2THE LANGUAGE The science of stability and control is complex, and only an orderly, step-by-step approach to the problem will yield sufficient understanding and acceptable results. This process must begin by defining quite a number of axes, angles, forces, moments nvenient definitions for positive moments. Positive moment directions are defined consistent with the right hand rule used in vector mathematics, physics, and mechanics. This rule states that if the thumb of a person’s right hand is placed parallel to an axis of a coordinate system, then the fingers of that hand will point in the positive direction of the moment about that axis. Since the moment about the aerodynamic center of an airfoil or wing was defined in Chapter 3 as being positive in a nose-up direction, the right-hand rule requires that the lateral
(spanwise) axis of the aircraft coordinate system be positive in the direction from the right wing root to the right wing tip. A natural starting point for the coordinate system is the aircraft’s center of gravity, since it will rotate about this point as it moves through the air. The aircraft’s longitudinal axis (down its centerline) is chosen parallel to and usually coincident with its aircraft reference line (defined in Chapter 4), but positive toward the aircraft’s nose so that a moment tending to raise the left wing and lower the right wing is positive. This axis is chosen as the x axis to be consistent with performance analysis. Making x positive toward the front allows the aircraft’s thrust and velocity to be taken as positive quantities. Since a rotation about the longitudinal axis to the right or clockwise is positive, for consistency it is desired that a moment or rotation about the aircraft’s vertical axis such that the nose moves to the right be considered positive. This requires that the vertical axis be positive downward so that the right-hand rule is satisfied. The only choice which remains is whether the lateral or vertical axis should be the y axis. The y axis is generally taken as vertical in performance analysis, but an x,y,z coordinate system must satisfy another right-hand rule in order to be consistent with conventional vector mathematics. The right-hand rule for 3-dimensional orthogonal (each axis perpendicular to the others) coordinate systems requires that if the thumb of a person’s right hand is placed along the coordinate system’s x axis, the fingers point in the shortest direction from the system’s y axis to its z axis (try this on Figure 6.1). To satisfy this right-hand rule as well as all the previous choices for positive directions, the coordinate system’s y axis must be the aircraft’s lateral axis (positive out the right wing), and the z axis must be the vertical axis (positive down). A coordinate system such as this which has its origin at the aircraft center of gravity and is aligned with the aircraft reference line and lateral axis is referred to as a body axis system.