SPINNING THE AIRCRAFT
- Spinning is a complicated subject to analyze in detail. It is also a subject about which it is difficult to make generalizations which are true for all aircraft. One type of aircraft may behave in a certain manner in a spin whereas another type will behave completely differently under the same conditions. This article is based on a deliberately spinning the aircraft to the right although inverted and oscillatory spins are discussed in later paragraphs.
- The accepted sign conventions applicable are given in the Table and Fig below.
Sign Conventions used
|Positive Direction||Forwards||To right||Downwards|
|Moment of Inertia||A||B||C|
|Positive Direction||Rolling moment to||Pitching moment||Yawing moment to|
- Phases of the Spin, The spin manoeuvre can be divided into three phases:
- The incipient spin.
- The fully developed spin.
- The recovery.
- The Incipient Spin. A necessary ingredient of a spin is the aerodynamic phenomenon known as autorotation. This leads to an unsteady manoeuvre which is a combination of:
- The ballistic path of the aircraft, which is itself dependent on the entry attitude.
- Increasing angular velocity generated by the autorotative rolling moment and drag-induced yawing moment.
- The Steady Spin. The incipient stage may continue for some 2-6 turns after which the aircraft will settle into a steady stable spin. There will be some sideslip and the aircraft will be rotating about all three axes. For simplicity, but without suggesting that it is possible for all aircraft to achieve this stable condition, the steady spin is qualified by a steady rate of rotation and a steady rate of descent.
- The Recovery. The pilot initiates the recovery by actions aimed at first opposing the autorotation and then reducing the angle of attack (α) so as to unstall the wings. The aircraft may then be recovered from the ensuing steep dive.
THE STEADY ERECT SPIN
- While rotating, the aircraft will describe some sort of ballistic trajectory dependent on the entry manoeuvre. To the pilot this will appear as an unsteady, oscillatory phase until the aircraft settles down into a stable spin with steady rate of descent and rotation about the spin axis. This will occur if the aerodynamic and inertia forces and moments can achieve a state of equilibrium. The attitude of the aircraft at this stage will depend on the aerodynamic shape of the aircraft, the position of the controls and the distribution of mass throughout the aircraft.
Motion of the Aircraft
- The motion of the centre of gravity in a spin has two components:
- A vertical linear velocity (rate of descent = V).
- An angular velocity (Ω radians per sec) about a vertical axis, called the spin axis. The distance between the CG and the spin axis is the radius of the spin (R) and is normally small (about half wing span).
The combination of these motions result in a vertical spiral or helix. The helix angle is small, usually less than 10°. Fig below shows the motion of the aircraft in spin.
- As the aircraft always presents the same face to the spin axis, it follows that it must be rotating about a vertical axis passing through the centre of gravity at the same rate as the CG about the spin axis. This angular velocity may be resolved into components of roll, pitch and yaw with respect to the aircraft body axes. In the spin illustrated in Fig above (b) the aircraft is rolling right, pitching up and yawing right. For convenience the direction of the spin is defined by the direction of yaw.
- In order to understand the relationship between these angular velocities and aircraft attitude it is useful to consider three limiting cases:
- Longitudinal Axis Vertical. When the longitudinal axis is vertical the angular motion will be all roll.
- Lateral Axis Vertical. For the aircraft to present the same face (pilot’s head) to the spin axis, the aircraft must rotate about the lateral axis. The angular motion is all pitch.
- Normal Axis Vertical. For the aircraft to present the same face (inner wing tip) to the axis of rotation, the aircraft must rotate about the normal axis at the same rate as the aircraft rotates about the axis of rotation. Thus the angular motion is all yaw.
- Although these are hypothetical examples which may not be possible in practice, they illustrate the relationship between aircraft attitude and angular velocities. Between the extremes quoted in the previous paragraph, the motion will be a combination of roll, pitch and yaw, and depends upon:
- The rate of rotation of the aircraft about the spin axis.
- The attitude of the aircraft, which is usually defined in terms of the pitch angle and the wing tilt angle. Wing tilt angle, often confused with bank angle, involves displacement about the normal and the longitudinal axes.
- The aircraft’s attitude in spin also has an important effect on the sideslip present (Fig above (c) ). If the wings are level, there will be outward sideslip, that is, the relative airflow will be from the direction of the outside wing (to port in the diagram). If the attitude of the aircraft is changed such that the outer wing is raised relative to the horizontal, the sideslip is reduced. This attitude change can only be due to a rotation of the aircraft about the normal axis. The angle through which the aircraft is rotated, in the plane containing the lateral and longitudinal axes, is known as the wing tilt angle and is positive with the outer wing up. If the wing tilt can be increased sufficiently to reduce the sideslip significantly, the pro-spin aerodynamic rolling moment will be reduced.
Balance of Forces in Spin
- Only two forces are acting on the centre of gravity while it is moving along its helical path (Fig above).
- Weight (W).
- The aerodynamic force (N) coming mainly from the wings.
The resultant of these two forces is the centripetal force necessary to produce the angular motion.
- Since the weight and centripetal force act in a vertical plane containing the spin axis and the CG, the aerodynamic force must also act in this plane, i.e. it passes through the spin axis. It can be shown that, when the wing is stalled, the resultant aerodynamic force acts approximately perpendicular to the wing. For this reason it is sometimes called the wing normal force.
- If the wings are level (lateral axis horizontal), from the balance of forces in Fig above:
|CL ½ρV2S||=||W Ω2 R
|R||=||g CL ½ ρ V2 S
|V||=||Rate of descent|
If the wings are not level, it has been seen that the departure from the level condition can be regarded as a rotation of the aircraft about the longitudinal and normal axes. Usually this angle, the wing tilt angle, is small and does not affect the following reasoning.
Effect of Attitude on Spin Radius
- If for some reason the angle of attack is increased by a nose-up change in the aircraft’s attitude, the vertical rate of descent (V) will decrease because of the higher CD (equation 1). The increased angle of attack on the other hand, will decrease CL, which, together with the lower rate of descent, results in a decrease in spin radius, (equation 2). It can also be shown that an increase in pitch increases the rate of spin, which will decrease R still further.
- The two extremes of aircraft attitude possible in the spin are shown in Fig below. The actual attitude adopted by an aircraft will depend on the balance of moments.
- The effects of pitch attitude are summarized below. An increase in pitch (e.g. flat spin) will:
- Decrease the rate of descent.
- Decrease the spin radius.
- Increase the spin rate.
It can also be shown that an increase in pitch will decrease the helix angle.
- In a steady spin, equilibrium is achieved by a balance of aerodynamic and inertia moments. The inertia moments result from a change in angular momentum due to the inertia cross coupling between the three axes.
- The angular momentum about an axis depends on the distribution of mass and the rate of rotation. It is important to get a clear understanding of the significance the spinning characteristics of different aircraft and the effect of controls in recovering from the spin.
Moment of Inertia (I)
- A concept necessary to predict the behaviour of a rotating system is that of moment of inertia. This quantity not only expresses the amount of mass but also its distribution about the axis of rotation. It is used in the same way that mass is used in linear motion. For example, the product of mass and linear velocity measures the momentum or resistance to acceleration of a body moving in a straight line. Similarly, the product of moment of inertia (mass distribution) and angular velocity measures the angular momentum of a rotating body (Fig below).
The concept of moment of inertia may be applied to an aircraft by measuring the distribution of mass about each of the body axes in the following ways:
- Longitudinal Axis. The distribution of mass about the longitudinal axis determines the moment of inertia in the rolling plane, which is denoted by A. An aircraft with fuel stored in the wings and in external tanks will have a large value of A, particularly if the tanks are close to the wing tips. The tendency in modern high speed aircraft towards thinner wings has necessitated the stowage of fuel elsewhere and this, combined with lower aspect ratios, has resulted in a reduction in the value of A for those modern high performance fighter and training aircraft.
- Lateral Axis. The distribution of mass about the lateral axis determines the moment of inertia in the pitching plane which is denoted by B. The increasing complexity of modern aircraft has resulted in an increase in the density of the fuselage with the mass being distributed along the whole length of the fuselage and a consequent increase in the value of B.
- Normal Axis. The distribution of mass about the normal axis determines the moment of inertia in the yawing plane, which is denoted by C. This quantity will be approximately equal to the sum of the moments of inertia in the rolling and pitching planes. C, therefore, will always be larger than A or B.
- These moments of inertia measure the mass distribution about the body axes and are decided by the design of the aircraft. It will be seen that the values of A, B and C for a particular aircraft may be changed by altering the disposition of equipment, freight and fuel.
Inertia Moments in a Spin
- The inertia moments generated in a spin are described below by assessing the effect of the concentrated masses involved. Another explanation using a gyroscopic analogy, is given at the end .
- Roll. It is difficult to represent the rolling moments using concentrated masses, as is done for the other axes. For an aircraft in the spinning attitude under consideration (inner wing down pitching nose up), the inertia moment is anti-spin, i.e. tending to roll the aircraft out of the spin. The equation for the inertia rolling moment is:
|L = – (C-B) q r||(3)|
- Pitch. The imaginary concentrated masses of the fuselage, as shown in Fig below, tend to flatten the spin. The equation for the inertia pitching moment is:
|M = (C-A) r p||(4)|
- Yaw. The inertia couple is complicated by the fact that it comprises two opposing couples caused by the wings and the fuselage (Fig below). Depending on the dominant component, the couple can be of either sign and varying magnitude. The inertia yawing moment can be expressed as:
|N = – (B-A) p q||(5)|
- This is negative and thus anti-spin when B > A and is positive and pro-spin when A > B.
- The B/A ratio has a profound effect on the spinning characteristics of an aircraft.
- It is now necessary to examine the contributions made by the aerodynamic factors in the balance of moments in roll, pitch and yaw. These are discussed separately below.
- Aerodynamic Rolling Moments. The aerodynamic contributions to the balance of moments about the longitudinal axis to produce a steady rate of roll are as follows:
- Rolling Moment due to Sideslip. The design features of the aircraft, which contribute towards positive lateral stability, produce an aerodynamic rolling moment as a result of sideslip. It can be shown that, even at angles of attack above the stall, this still remains true and the dihedral effect induces a rolling moment in the opposite sense to the sideslip. In the spin the relative airflow is from the direction of the outer wing (outward sideslip) and the result is a rolling moment in the direction in which the aircraft is spinning. This contribution is therefore pro-spin.
- Autorotative Rolling Moment. In the chapter on flight controls, it is shown that the normal damping in roll effect is reversed at angles of attack above the stall. This contribution is therefore pro-spin.
- Rolling Moment due to Yaw. The yawing velocity in the spin induces a rolling moment for two reasons:
- Difference in Speed of the Wings. Lift of the outside wing is increased and that of the inner wing decreased, inducing a pro-spin rolling moment.
- Difference in Angle of Attack of the Wings. In a spin the direction of the free stream is practically vertical whereas the direction of the wing motion due to yaw is parallel to the longitudinal axis. The yawing velocity not only changes the speed but also the angle of attack of the wings. Fig 9-7 illustrates the vector addition of the yawing velocity to the vertical velocity of the outer wing. The effect is to reduce the angle of attack of the outer wing and increase that of the inner wing. Because the wings are stalled (slope of CL curve is negative), the CL of the
outer wing is increased and the CL of the inner wing decreased thus producing another pro-spin rolling moment.
- Aileron Response. Experience has shown that the ailerons produce a rolling moment in the conventional sense even though the wing is stalled.
- Aerodynamic Pitching Moments. The aerodynamic contributions to the balance of moments about the lateral axis to produce a steady rate of pitch are as follows:
- Positive Longitudinal Static Stability. In a spin the aircraft is at a high angle of attack and therefore disturbed in a nose-up sense from the trimmed condition. The positive longitudinal stability responds to this disturbance to produce a nose-down aerodynamic moment. This effect may be considerably reduced if the tailplane lies in the wing wake.
- Damping in Pitch Effect. When the aircraft is pitching nose-up the tailplane is moving down and its angle of attack is increased (the principle is same as the damping in roll effect). The pitching velocity therefore produces a pitching moment in a nose-down sense. The rate of pitch in a spin is usually very low and consequently the damping in pitch contribution is small.
- Elevator Response. The elevators act in the conventional sense. Down-elevator increases the nose-down aerodynamic moment whereas up-elevator produces a nose-up aerodynamic moment. It should be noted, however, that down-elevator usually increases the shielded area of the fin and rudder.
- Aerodynamic Yawing Moments. The overall aerodynamic yawing moment is made up of a large number of separate parts, some arising out of the yawing motion of the aircraft and some arising out of the side slipping motion. The main contributions to the balance of moments about the normal axis to produce a steady rate of yaw are as follows:
- Positive Directional Static Stability. When sideslip is present keel surfaces aft of the CG produce an aerodynamic yawing moment tending to turn the aircraft into line with the sideslip vector (i.e. directional static stability or ‘weathercock effect’). This is an anti-spin effect, the greatest contribution to which is from the vertical fin. Vertical surfaces forward of the CG will tend to yaw the aircraft further into the spin, i.e. they have a pro-spin effect. In a spin outward sideslip is present which, usually produces a net yawing moment towards the outer wing, i.e. in an anti-spin sense. Because of possible shielding effects from the tailplane and elevator and also because the fin may be stalled, the directional stability is considerably reduced and this anti-spin contribution is usually small.
- Damping in Yaw Effect. Applying the principle of the damping in roll effect to the yawing velocity, it has been seen that the keel surfaces produce an aerodynamic yawing moment to oppose the yaw. The greatest contribution to this damping moment is from the rear fuselage and fin. In this respect the cross-sectional shape of the fuselage is critical and has a profound effect on the damping moment. The following figures give some indication of the importance of cross-section:
|Cross-Section||Damping Effect (Anti-Spin)|
|Round top / flat bottom||1.8|
|Round bottom / flat top||4.2|
|Round bottom / flat top with strakes||5.8|
Effect of Fuselage on Damping in Roll
Damping effect = Damping from body of given cross-section ⁄ Damping from circular cylinder
Fuselage strakes are useful devices for improving the spinning characteristics of prototype aircraft. The anti-spin damping moment is very dependent on the design of the tailplane/fin combination. Shielding of the fin by the tailplane can considerably reduce the effectiveness of the fin. In extreme cases a low-set tailplane may even change the anti-spin effect into pro-spin.
- Rudder Response. The rudder acts in the conventional sense, i.e. the in-spin rudder produces pro-spin yawing moment and out-spin rudder produces anti-spin yawing moment. Because of the shielding effect of the elevator (para 29c), it is usual during recovery to pause after applying out-spin rudder so that the anti-spin yawing moment may take effect before down-elevator is applied.
Balance of Moments
- In para 16 it was seen that the balance of forces in the spin has a strong influence on the rate of descent. It does not, however, determine the rate of rotation, wing tilt or incidence at which the spin occurs. The balance of moments is much more critical in this respect. The actual attitude, rate of descent, sideslip, rate of rotation and radius of a spinning aircraft can only be determined by applying specific numerical values of the aircraft’s aerodynamic and inertia data to the general relationships discussed below.
- Rolling Moments. The balance of rolling moments in an erect spin is:
- Pro-spin. The aerodynamic rolling moments in an erect spin are:
- Autorotative rolling moment.
- Rolling moment due to sideslip.
- Rolling moment due to yaw.
- Anti-spin. The inertia rolling moment, – (C – B) r q, is anti-spin.
These factors show that autorotation is usually necessary to achieve a stable spin. A small autorotative rolling moment would necessitate larger sideslip to increase the effect of rolling moment due to sideslip. This, in turn, would reduce the amount of wing tilt and make the balance of moments in yaw more difficult to achieve, however the balance of moments in this axis is not as important as in the other two.
- Pitching Moments. In para 25 it was seen that the inertia pitching moment, (C – A) r p, of the aircraft is always nose-up in an erect spin. This is balanced by the nose-down aerodynamic pitching moment. The balance between these two moments is the main factor relating angle of attack to rate of rotation in any given case and equilibrium can usually be achieved over a wide range. It can be shown that an increase in pitch will cause an increase in the rate of rotation (spin rate). This, in turn, will decrease the spin radius (para 16).
- Yawing Moments. The balance of yawing moments in an erect spin is:
- Yawing moment due to applied rudder.
- A small contribution from the wing, due to yaw, is possible at large angles of attack.
- Yawing moment due to sideslip (vertical surfaces forward of CG).
- Inertia yawing moment, (A – B) pq, if A > B.
- Inertia yawing moment, (A-B) pq, if B>A.
- Yawing moment due to sideslip (vertical surfaces aft of the CG).
- Damping in yaw effect.
It can be seen that in-spin rudder is usually necessary to achieve balance of the yawing moments and hold the aircraft in a spin.
- Normal Axis. For conventional aircraft (A and B nearly equal), it is relatively easy to achieve balance about the normal axis and the spin tends to be limited to a single set of conditions (angle of attack, spin rate, attitude). For aircraft in which B is much larger than A, the inertia yawing moment can be large and thus difficult to balance. This is probably the cause of the oscillatory spin exhibited by these types of aircraft.
- Yaw and Roll Axis. The requirements of balance about the yaw and roll axes greatly limit the range of angle of attacks in which spinning can occur and determines the amount of sideslip and wing tilt involved. The final balance of the yawing moments is achieved by the aircraft taking up the appropriate angle of attack at which the inertia moments just balance the aerodynamic moments. This particular angle of attack also has to be associated with the appropriate rate of spin required to balance the pitching moments and the appropriate angle of sideslip required to balance the rolling moments.
Effect of Controls in Recovery from a Spin
- The relative effectiveness of the three controls in recovering from a spin will now be considered. Recovery is aimed at stopping the rotation by reducing the pro-spin rolling moment and/or increasing the anti-spin yawing moment. The yawing moment is more important but, because of the strong cross-coupling between motions about the three axes through the inertia moments, the rudder is not the only means by which yawing may be induced by the pilot. Once the rotation has stopped the angle of attack is reduced and the aircraft recovered.
- The control movements which as experience has shown, are generally most favourable to the recovery from the spin have been known and in use for a long time, i.e. apply full opposite rudder and then move the stick forward until the spin stops, maintaining the ailerons neutral. The rudder is normally the primary control but, because the inertia moments are generally large in modern aircraft, aileron deflection is also important. Where the response of the aircraft to rudder is reduced in spin, the aileron may even be the primary control although in the final analysis it is its effect on the yawing moment, which makes it work.
- The initial effect of applying a control deflection will be to change the aerodynamic moment about one or more axes. This will cause a change in aircraft attitude and a change in the rates of rotation about all the axes. These changes will, in turn, change the inertia moments.
Effect of Ailerons
- Even at the high angle of attack in spin the ailerons act in the normal sense. Application of aileron in the same direction as the aircraft is rolling will therefore increase the aerodynamic rolling moment. This will increase the roll rate (p) and affect the inertia yawing moment, (A – B) p q. The effect of an increase in p on the inertia yawing moment depends on the mass distribution or B/A ratio:
- B/A > 1. In an aircraft where B/A > 1, the inertia yawing moment is anti-spin (negative) and an increase in p will decrease it still further, i.e. make it more anti-spin. The increase in anti-spin inertia yawing moment will tend to raise the outer wing (increase wing tilt), which will decrease the outward sideslip. This will restore the balance of rolling moments by decreasing the pro-spin aerodynamic moment due to lateral stability. The increase in wing tilt will also cause the rate of pitch, q, to increase, which, in turn:
- Causes a small increase in the anti-spin inertia rolling moment, – (C – B) rq, (C > B) and thus helps to restore balance about the roll axis (para 32).
- Further increases the anti-spin inertia yawing moment.
- B/A < 1. A low B/A ratio will reverse the effects described above. The inertia yawing moment will be pro-spin (positive) and will increase with an increase in p.
- Due to secondary effects associated with directional stability, the reversal point actually occurs at a B/A ratio of 1.3 (Fig below). Thus:
- B/A > 1.3. Aileron with roll (in-spin) has an anti-spin effect.
- B/A < 1.3. Aileron with roll (in-spin) has a pro-spin effect.
- Some aircraft change their B/A ratio in flight as stores and fuel are consumed. The pilot has no accurate indication of the value of B/A ratio and, where this value may vary either side of 1.3, it is desirable to maintain ailerons neutral to avoid an unfavourable response, which may delay or even prohibit recovery.
- An additional effect of aileron applied with roll is to increase the anti-spin yawing moments due to aileron drag.
Effect of Elevators
- In para 29 it was seen that down-elevator produces a nose-down aerodynamic pitching moment. This will initially reduce the nose-up pitching velocity (q). Although this will tend to reduce alpha, the effect on the inertia yawing and rolling moments is as follows:
- Inertia Yawing Moment (A – B) p q. If B > A, the inertia yawing moment is anti-spin. A reduction in q will make the inertia yawing moment less anti-spin, i.e. a pro-spin change. When A > B, however, down-elevator will cause a change in inertia yawing moment in the anti-spin sense.
- Inertia Rolling Moment -(C – B) r q. The inertia rolling moment is always anti-spin because C > B. A reduction in q will therefore make it less anti-spin, which is again a change in the pro-spin sense.
The result of these pro-spin changes in the inertia yawing and rolling moments is to decrease the wing tilt thus increasing the sideslip angle and rate of roll. It can also be shown that the rate of rotation about the spin axis will increase.
- Although the change in the inertia yawing moment is unfavourable, the increased sideslip may produce an anti-spin aerodynamic yawing moment if the directional stability is positive. This contribution will be reduced if the down elevator seriously increases the shielding of the fin and rudder.
- The overall effect of down-elevator on the yawing moments therefore depends on:
- The pro-spin inertia moment when B > A.
- The anti-spin moment due to directional stability.
- The loss of rudder effectiveness due to shielding.
In general, the net result of moving the elevators down is beneficial when A > B and rather less so when B > A, assuming that the elevator movement does not significantly increase the shielding of the fin and rudder.
Effect of Rudder
- The rudder is nearly always effective in producing an anti-spin aerodynamic yawing moment though the effectiveness may be greatly reduced when the rudder lies in the wake of the wing or tailplane. The resulting increase in the wing tilt angle will increase the anti-spin inertia yawing moment (when B > A) through an increase in pitching velocity. The overall effect of applying anti-spin rudder is always beneficial and is enhanced when the B/A ratio is increased.
- The effect of the three controls on the yawing moment is illustrated in above three figures.
- Fig above shows an aircraft in an inverted spin but following the same flight path as in Fig of flat spin above. Relative to the pilot the motion is now compounded of a pitching velocity in the nose-down sense, a rolling velocity to the right and a yawing velocity to the left. Thus roll and yaw are in opposite directions, a fact that affects the recovery actions, particularly if the aircraft has a high B/A ratio.
- The inverted spin is fundamentally similar to the erect spin and the principles of moment balance discussed in previous paragraphs are equally valid for the inverted spin. The values of aerodynamic moments however are unlikely to be the same, since in the inverted attitude, the shielding effect of the wing and tail may change markedly.
- The main difference will be caused by the change in relative positions of the fin and rudder and the tailplane. An aircraft with a low-mounted tailplane will tend to have a flatter erect spin and recovery will be made more difficult due to shielding of the rudder. The same aircraft inverted will respond much better to rudder during recovery since it is unshielded and the effectiveness of the rudder is increased by the position of the tailplane. The converse is true for an aircraft with a high tailplane.
- The control deflections required for recovery are dictated by the direction of roll, pitch and yaw, and the aircraft’s B/A ratio. These are:
- Rudder to oppose yaw as indicated by the turn needle.
- Aileron in the same direction as the observed roll, if the B/A ratio is high.
- Elevator up is generally the case for conventional aircraft but, if the aircraft has a high B/A ratio and suffers from the shielding problems previously discussed, this control may be less favourable and may even become pro-spin.
- A combination of high wing loading and high B/A ratio makes it difficult for a spinning aircraft to achieve equilibrium about the yaw axis. This is thought to be the most probable reason for the oscillatory spin. In this type of spin the rates of roll and pitch are changing during each oscillation. In a mild form it appears to the pilot as a continuously changing angle of wing tilt, from outer wing well above the horizon back to the horizontal once each turn and the aircraft seems to wallow in the spin.
- In a fully developed oscillatory spin the oscillations in the rates of roll and pitch can be quite violent. The rate of roll during each turn can vary from zero to about 200 degrees per second. At the maximum rate of roll the rising wing is unstalled which probably accounts for the violence of this type of spin. Large changes in attitude usually take place from fully nose-down at the peak rate of roll, to nose-up at the minimum rate of roll.
- The use of the controls to effect a change in attitude can change the characteristics of an oscillatory spin quite markedly. In particular:
- Anything, which increases the wing tilt, will increase the violence of the oscillations, e.g. in-spin aileron or anti-spin rudder.
- A decrease in the wing tilt angle will reduce the violence of the oscillations, e.g. out-spin aileron or down-elevator.
The recovery from this type of spin has been found to be relatively easy, although the shortest recovery times are obtained if recovery is initiated when the nose of the aircraft is falling relative to the horizon.
- Conclusions. The foregoing paragraphs make it quite clear that the characteristics of the spin and the effect of controls in recovery are specific to type. In general the aerodynamic factors are determined by the geometry of the aircraft and the inertial factors by the distribution of the mass. In the final analysis the only correct recovery procedure is laid down in the Aircrew Manual for the specific aircraft.
GYROSCOPIC CROSS-COUPLING BETWEEN AXES
- In the preceding paragraphs, the effects of the inertia moments have been explained by considering the masses of fuselage and wings acting either side of a centerline. The effect of these concentrated masses when rotating, can be visualized as acting rather in the manner of the bob-weights of a governor.
- Another, and more versatile, explanation of the cross-coupling effects can be made using a gyroscopic analogy regarding the aircraft as a rotor.
Inertia Moments in a Spin
- The inertia moments generated in a spin are essentially the same as the torque exerted by a precessing gyroscope. Figs below illustrate the inertia or gyroscopic moments about the body axes. These effects are described as follows:
- Inertia Rolling Moments (Fig below) . The angular momentum in the yawing plane is Cr, and by imposing a pitching velocity of q on it, an inertia rolling moment is generated equal to (-Crq), i.e. in the opposite sense to the direction of roll in an erect spin. The inertia rolling moment due to imposing of yawing velocity on the angular momentum in the pitching plane is in a pro-spin sense equal to (+Brq). The total inertia rolling moment is therefore equal to (B – C)rq, or since C > B: – (C – B) rq.
- Inertia Pitching Moments (Fig below). The angular momentum in the rolling plane is Ap and imposing a yawing velocity of r on the rolling plane rotor causes it to precess in pitch in a nose-down sense due to inertia pitching moment (-Apr). Similarly, the angular momentum in the yawing plane is Cr, and imposing a roll velocity of p on the yawing plane rotor generates an inertia pitching moment (+Crp) in the nose-up sense. The total inertia moment is therefore (C – A)rp. In an erect spin, roll and yaw are always in the same direction and C is always greater than A. The inertia pitching moment is therefore positive (Nose-up) in an erect spin.
- Inertia Yawing Moments (Fig 9-14). Replacing the aircraft by a rotor having the same moment of inertia in the rolling plane, its angular momentum is the product of the moment of inertia and angular velocity (Ap). Imposing a pitching velocity (q) on the rotor will generate a torque tending to precess the rotor about the normal axis in the same direction as the spin. It can be shown that this inertia yawing moment is equal in value to +Apq where the positive sign indicates a pro-sign torque. Similarly, the angular momentum in the pitching plane is equal to Bq and imposing a roll velocity of p on the pitching plane rotor will generate an inertia yawing moment in an anti-spin sense equal to -Bpq. The total inertia yawing moment is therefore equal to (A – B)pq, or if B > A: – (B – A)pq.