2. THE NATURE OF THE SPIN
2.1 SPIN PHASES
The spin manoeuvre has traditionally been divided into four stages (Figure 1). Spin entry, incipient spin, steady spin, and spin recovery. Spin entry from unstalled flight may be delioberate - usually as a training rather than an operational manoeuvre - or inadvertent - occurring usually during low speed manouvres.
A deliberate spin is initiated by slowing the aircraft towards the stall speed and then applying full rudder deflection to promote stalling and a large loss of lift due to increased flow incidence on the rearward travelling wing, while maintaining attached flow due to reduced flow incidence on the forward travelling wing. The resulting differential lift produces a rolling moment in the direction of the rearward travelling wing, and initiates the spin manoeuvre with a large rate of roll.
Aircraft with high "spin resistance" generally require vigorous and precise control movements to initiate the spin. In contrast, inadvertent "spin entry" can result with aircraft which are susceptible to spinning either during steep turns at low speeds, or during the low speed portions of aerobatic manoeuvres such as at the top of a loop or barrel roll.
The 'incipient spin' is the transition between 'spin entry' and the 'steady spin'. Recovery from an inadvertent spin is most effectively achieved in this phase, so it is important for pilots to be able to recognise the manoeuvre and to apply appropriate recovery action. The incipient phase is considered to end when the airspeed has become steady and a vertical trajectory has been reached. For practical purposes, the 'steady spin' is reasonably well established after two to three turns.
During the 'incipient spin' the aicraft flight path changes from horizontal to vertical, the angle-of-attack increases to well beyond the stall value, and the rotation in yaw increases to match or frequently exceed that in roll.
In the 'steady spin' or 'equilibrium spin' the aircraft describes a steep spiral motion about a vertical axis, in which spin rate, angle-of-attack, sideslip angle and vertical velocity are constant. In many cases the motion does not reach a steady state, but may exhibit an oscillation about the nominal equiliobrium point, with a frequency higher than the spin rate.
'Spin recovery' for most configurations is achieved primarily by use of full rudder deflection to arrest the large rate of yaw. Often the elevator and aileron, if applied correctly, can increase the speed of recovery. For certain aircraft their use is essential while in others, they are sufficiently capable of stopping the spin even with full pro-spin rudder deflection maintained.
2.2 THE STEADY SPIN
The 'steady spin' phase is of particular importance since it represents a stable equilibrium flight condition from which recovery may be impossible. Because the motion is steady, it is also more tractable to analysis than the other phases.
Some aircraft exhibit more than one 'steady spin' condition or mode, in which case the sequence of control movements applied during the entry and incipient phases will determine which of the the modes is reached. However, the characteristics of the mode depend only on the aircraft aerodynamic and inertia characteristics and on the control settings. There is also a dependency on air density and hence altitude, but this will not be discussed here.
From stability considerations, the 'steady spin' may be referred to as a point of stable equilibrium similar to a trimmed condition in level flight. Figure 2 shows this condition and also another stable equilibrium, the 'deep stall'.
All these cases are in equilibrium since in each there is a balance of forces and moments about all axes; the steady spin is the most complex in that the balance occurs in the presence of large angular rotations about the roll and yaw axes.
The key to spin recovery is to design the aircraft with sufficient control power to unlock this stable condition.
The dynamics of the 'steady spin' were understood and described in detail many years ago. A comprehensive description is given by Gates and Bryant in Reference 1 in 1926. As with other branches of flight dynamics, the difficult problems associated with an analysis of the spin arise not from the system dynamics, but from the complexity of the aerodynamic forces. The more important aerodynamic forces acting in the steady spin are briefly described below.
2.3 THE BALANCE OF FORCES AND MOMENTS
Figure 3 from Reference 1 shows that the balance of forces in a 'steady spin' is such that drag is equal to the weight and the lift is equal to the centrifugal force. In the steady spin, the spin radius is only of the order of a few feet, the resultant force is almost normal to the wing and acts approximately at the wing semi-chord, and the normal acceleration is low.
In practice, the actual balance is slightly more complex in that aerodynamic sideforces exist such that the lateral axis is not necessarily horizontal but may be tilted. The amount of tilt is directly related to the spin helix angle and to the angle of sideslip adopted in the spin. The sideslip is determined primarily by the rolling moment characteristics as explained later.
To illustrate the balance of moments in a 'steady spin' the primary aerodynamic contributions are discussed. Rotary-balance data measured on an aircraft with standard layout will be used to illustrate the discussion. The moments are referred to aircraft body axes. Because of the large variation in onset flows over a spinning aircraft, the choice of axis system has little significance. The less important aerodynamic contributions are neglected in thsi discussion but are described in detail in Reference 1.
Equilibrium of pitching moments is reached when the nose-down aerodynamic moment is equal to the large nose-up inertia moments, as shown in Figure 4. The aerodynamic contributions are from the wing normal force which, for a stalled wing, acts at the wing sem-chord and from the tailplane normal force. The inertia is proportional to the square of spin-rate and reaches a maximum at 45 degrees angle-of-atatck. Movement of the elevator adds an increment to the aerodynamic curve but normally this is not of sufficient magnitude to unlock the balance of pitching moments.
Of prime imnportance for roll equilibrium is the balance of the aerodynamic contributions due to roll rate and to sideslip. The inertia moment may be positive or negative depending on the wing tilt angle - having a zero value for zero tilt. Figure 5 shows the typical variation of aerodynamic rolling moments with spin rate and sideslip for a given angle-of-attack. Note that, for a significant change in spin-rate, the rolling moments can be balanced by a modest change in sideslip angle. As with the pitching moment balance, movement of the aileron adds an increment to the rolling moment curve but the magnitude is normally insufficient to unlock the balance of rolling moments.
The two largest aerodynamic yawing moment contributions for the example configuration are due to spin-rate and rudder deflection, as shown by Figure 6; by comparison the contribution due to sideslip is small, and, as with the rolling moment equation, the inertia contribution is zero for zero wing tilt. Since the rudder can alter the yawing moment curve appreciably, the key to unlocking the balance of moments is a spin is therefore, to generate a large yawing moment with the rudder.
In order to emphasize the major contributions, the wing tilt and hence rolling and yawing inertia contributions are closely related and are determined essentially by the pitching moment; that the sideslip is determined by the balance of rolling moments, and that although all three control surfaces may be effective in changing the balance of moments - and hence spin conditions - the rudder is the most effective means of unlocking this balance. For aircraft of substantially different inertia loading and layout this emphasis may change.
2.4 INCIPIENT SPIN AND SPIN RECOVERY
These two phases are characterised by the transition between two extremely different flight conditions. Upon entry the aircraft has low angular velocity, moderate linear velocity, constant potential energy, and is flying at low angles-of-attack. The transition through to the 'steady spin' involves an initial increase in roll rate followed by an increase in yaw rate giving a large resultant angular rotation; a decrease in linear velocity and a constant reduction in potential energy, with the angle-of-atatck increasing to large values.
The aerodynamic changes are equally dramatic and involve changes from attached to unattached flow over large areas of the aircraft surfaces with consequent unsteady flow behaviour. During 'spin recovery' these changes are reversed with additional transients occurring due to the dissipation of angular momentum.
Although some progress has been made towards understanding the aerodynamic behaviour occurring during the spin, reliable methods for spin prediction do not yet exist. Even the methods for the prediction of steady spin behaviopur only yield gross trends and so extensive scale model testing is required toreduce project risks and provide a basis for the flight development phase.
