# Stability and Control Theory

4.1 INTRODUCTION

The detailed study of helicopter stability and control is a complex matter that is beyond the scope of this book. Therefore, a simpler approach will be taken making use of several common assumptions: the rotor speed remains constant; in disturbed flight the rotor behaves as if the motion were a sequence of steady conditions; and the lateral/directional and longitudinal motions are decoupled. The rotor is, therefore, regarded as responding instantaneously to speed and angular rate changes. Stability and control theory aims primarily at finding the factors involved in designing an aircraft with satisfactory flying qualities and in order to make an accurate assessment of an aircraft’s handling qualities it is important that these factors are understood. The main rotor provides the largest contribution to the total stability and the way in which it flaps is most important. Consideration of rotor flapping in the hover and forward flight, before an investigation of helicopter stability, will be instructive.

Practical helicopter and autogyro flight was not possible until rotor hinges were fitted to relieve the large bending stresses and rolling moments that arise in forward flight. The most important of these hinges is the flapping hinge that allows the blade to flap, that is to move out of the plane of rotation. However a blade that is free to flap experiences large Coriolis moments [4.1] in the plane of rotation and therefore a further hinge called the drag or lag hinge is required to relieve these moments. Finally, another hinge, the feathering hinge, is provided to allow adjustment of the blade pitch, or feathering, angle. A rotor incorporating these hinges is referred to as fully articulated. The sequence of hinges is not always the same. The flapping hinge is usually the most inboard hinge but some helicopters have intersecting flapping and drag hinges and some have the drag hinge outboard of the feathering hinge. Also, as described below, hinge axes are not always mutually perpendicular.

It is advantageous to provide aerodynamic damping to the flapping motion of a rotor blade. A blade that is free to flap will move such that the combination of the lift, blade weight and centrifugal force are in equilibrium. However a further spring effect can arise if reduced lift occurs with increased flap. Such a positive pitch-flap coupling can be engineered by arranging for the blade pitch to be reduced with increased flap angle by means of a skew of the flap hinge line so that it is no longer perpendicular to the radial axis of the blade. The angle of skew is referred to by the symbol S3, hence the name the delta three hinge. The blades of a two-bladed rotor are usually mounted as a single unit on a teetering hinge. There are no drag hinges as underslinging the rotor greatly reduces the lagging moments generated by the Coriolis effect. When the underslung rotor flaps the radial velocities of points above the hinge line are negative whereas those below are positive. The corresponding Coriolis forces are of opposite sign and if the hinge height is chosen carefully the moment at the blade root can be reduced to a second-order effect. Preconing also helps in this respect.

Several problems are associated with articulated rotor heads. The bearings of the hinges and dampers operate under very high centrifugal loads, requiring frequent servicing and maintenance. When the number of blades is large the hub can become extremely complex and bulky, especially if automatic blade folding is incorporated; thereby contributing a large proportion to the total drag of the helicopter. Improve­ments in blade design and construction have led to the development of the hingeless rotor. The flapping and lagging hinges have been dispensed with, the motion in these two senses being allowed by flexible elements within the hub and blade root.