6.2
THE 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 move
s 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 han
d 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
.