# Roll Plane

As explained previously, roll stability derives primarily from the following three aircraft features:

low-wing Г, it is typically between 1 and 3 deg, depending on the wing sweep. For a straight-wing aircraft, the maximum dihedral rarely exceeds 5 deg. For a high-wing sweep, it may require an anhedral, as discussed herein.

2. Wing Position Relative to the Fuselage (see Figure 12.7). Section 12.3.3 explains the contribution to the rolling moment caused by different wing positions rela­tive to the fuselage. Semi-empirical methods are used to determine the extent of the rolling-moment contribution.

3. Wing Sweep at Quarter-Chord, Л/ (see Figure 12.8). The lift produced by a swept wing is a function of the component of velocity, Vn, normal to the c/ line; that is, in steady rectilinear flight:

Vn = V cos Л

When an aircraft sideslips with angle в, the component of velocity normal to the c/ line becomes (small в):

Vn = V cos^1/4 – в) = V(cos Л1/4 + в sin Д1/4в)

For the leeward wing:

VnJw = Vcos^1/4 + в) = V(cos Л1/4 – в sin Л1/4в)

The windward wing has V’n > Vn and vice versa; therefore, it provides ДLift as the restoring moment in conjunction with the lift decrease on the leeward wing. As Л1/4 increases, the restoring moment becomes powerful enough that it must be compensated for by the use of the wing anhedral.