# Lateral Stability: Roll Plane (Roll Moment, L)

Roll stability is more difficult to analyze compared to longitudinal and lateral sta­bilities. A banked aircraft attitude through a pure roll keeps the aircraft motion in

 Figure 12.5. Lateral stability

the plane of symmetry and does not provide any restoring moment. However, roll is always coupled with a yawed motion, as explained previously. As a roll is initiated, the sideslip velocity, v, is triggered by the weight component toward the down-wing side, as shown in Figure 12.5. Then (see the previous section), the sideslip angle is в = tan-1(v/u). The positive angle of roll, Ф, is when the right wing drops as shown in the figure (the aircraft is seen from the rear showing the V-tail but no windscreen). A positive roll angle Ф generates a positive sideslip angle, в. The angle of attack increases the sideslip.

Recovery from a roll is possible as a result of the accompanying yaw (i. e., cou­pled motion) with the restoring moment contributed by increasing the lift acting on the wing that has dropped. Roll static-stability criteria require that an increase in the roll angle, Ф, creates a restoring moment coefficient, Cl (not to be confused with the sectional aerofoil-lift coefficient). The restoring moment has a negative sign.

Having a coupled motion with the sideslip, Figure 12.6 shows that Cl is plotted against the sideslip angle в, not against the roll angle Ф because it is в that generates the roll stability. The sign convention for restoring the rolling moment with respect

 Figure 12.6. Lateral stability: fuselage contributions

to в must have Qp negative; that is, with an increase of roll angle Ф, the sideslip angle в increases to provide the restoring moment. An increase in в generates a restoring roll moment due to the dihedral. At zero Ф, there is no в; hence, the zero rolling moment (Cl = 0).

The wing dihedral angle, Г, is one way to increase roll stability, as shown in Figure 12.5. The dropped wing has an airflow component from below the wing gen­erating lift, while at the other side, the airflow component is from the upper side of the wing that reduces the angle of attack (i. e., the lift reduction creates a restoring moment).

The position of the wing relative to the aircraft fuselage has a role in lateral stability, as shown in Figure 12.6. At yaw, the relative airflow about the low wing has a component that reduces the angle of attack; that is, the reduction of lift and the other side act in opposite ways: a destabilizing effect that must be compensated for by the dihedral, as explained previously. Conversely, a high-wing aircraft has an inherent roll stability that acts opposite to a low-wing design. If it has too much stability, then the anhedral (-ve dihedral) is required to compensate it. Many high – wing aircraft have an anhedral (e. g., the Harrier and the BAe RJ series).

An interesting situation occurs with a wing sweepback on a high-speed air­craft, as explained in Figure 12.8. At sideslip, the windward wing has an effectively reduced sweep; that is, the normal component of air velocity increases, creating a lift increment, whereas the leeward wing has an effectively increased sweep with a slower normal velocity component, thereby losing lift. This effect generates a rolling moment, which can be quite powerful for high-swept wings; even for low – wing aircraft, it may require some anhedral to reduce the excessive roll stability (i. e., stiffness) – especially for military aircraft, which require a quick response in a roll. Tu-104 in Figure 12.7 is a good example of a low-wing military aircraft with a high sweep coupled with an anhedral.

The side force by the fuselage and V-tail contributes to the rolling moment, as shown in Figure 12.8. If the V-tail area is large and the fuselage has a relatively smaller side projection, then the aircraft CG is likely to be below the resultant side force, thus increasing the stability. Conversely, if the CG is above the side force, then there is a destabilizing effect.

Figure 12.8. V-tail contribution to roll

12.3.1 Summary of Forces, Moments, and Their Sign Conventions

Given below is the summary of sign convention in the three planes.

 Longitudinal Static Stability Directional Stability Lateral Stability Angles Pitch angle a Sideslip angle в Roll angle, Ф Positive Angle Nose up Nose to left Right wing down Moment Coefficient Cm Cn Ci Positive Moment Nose up Nose left Right wing down

12.4 Theory

Forces and moments affect aircraft motion. In a steady level flight (in equilibrium), the summation of all forces is zero; the same applies to the summation of moments. When not in equilibrium, the resultant forces and moments cause the aircraft to maneuver. The following sections provide the related equations for each of the three aircraft planes. A sense of these equations helps in configuring aircraft in the con­ceptual design phase.