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Lateral-Directional Stability 6.7 Dynamic Lateral-Directional Stability 6.10 Stability and Control Analysis Example: F-16A and F-16C

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Lateral-Directional Stability 6.7 Dynamic Lateral-Directional Stability 6.10 Stability and Control Analysis Example: F-16A and F-16C AE317 Aircraft Flight Mechanics & Performance UNIT D: Stability and Control Brandt, et.al., Introduction to Aeronautics: ROAD MAP . A Design Perspective Chapter 6: Stability and Control 6.6 Lateral-Directional Stability 6.7 Dynamic Lateral-Directional Stability 6.10 Stability and Control Analysis Example: F-16A and F-16C D-1: Longitudinal Stability & Control D-2: Lateral-Directional Stability Unit D-2: List of Subjects Static Directional Stability Static Lateral Stability Dynamic Lateral-Directional Stability F-16 Stability & Control Analysis Page 2 of 10 Unit D-2 Static Directional Stability Lateral (Rolling) and Directional (Yawing) Stability Analysis • Longitudinal (three DOF) stability analysis: x and z translation and longitudinal rotation (pitching about y axis) has been done in Unit D-1. • Another 3DOF stability analysis: lateral rotation (rolling about the x axis) and directional rotation (yawing about z axis), as well as y translation, needs to be done for complete aircraft stability and control analysis. Sideslip Angle • Instead of angle of attack for longitudinal stability analysis, the sideslip angle plays important role for lateral & directional stability analysis. • When an aircraft with good stability yaws, it generates rolling and yawing moments that tend to return back to equilibrium. These are called, positive lateral (rolling) and directional (yawing) stability, respectively. Static Directional (Yawing) Stability • Positive static directional stability requires that an aircraft, when is positive, generate a right-hand or positive moment around the z axis to reduce back to zero. This is usually achieved by a vertical stabilizer. Defining the yawing moment coefficient: C= N q Sb and slope: CC= , N ( ) NN the criterion for positive directional stability is: C 0 . N Page 3 of 10 Unit D-2 Static Lateral Stability (1) Static Lateral (Rolling) Stability • The requirement for positive static lateral stability is that an aircraft roll away from a sideslip. In other words, if an aircraft with positive static lateral stability is sideslipping to the right, so that is positive, then it will generate a moment that will cause it to roll to the left. • Because the positive direction for rolling about the x axis is to the right, an aircraft with positive static lateral stability will produce a negative rolling moment when its sideslip angle is positive. • Defining the rolling moment coefficient C= L q Sb and slope: CC= , the criterion for L ( ) LL positive static lateral stability is: C 0 . L Effects of Wing Sweep and Aspect Ratio • When the aircraft is yawed so that it has a positive sideslip angle (fig. 6.18), its right wing is less swept (more lift) relative to its velocity vector than its left wing: the aircraft will roll left. • Another way to look at it, is that the right wing has a higher aspect ratio than the left wing (higher lift-curve slope, fig. 6.22): the aircraft will roll left. • Note that the effect of wing sweep on C increases as angle of attack and lift on the wings increase. L • Also, the effect goes away when the wing is making zero lift. This is important for an aircraft that must make vertical climbs, where lift is zero (roll caused by sideslip is undesirable, because if the aircraft yaws the resulting roll will cause the airplane to make a "corkscrew" type flight path). Page 4 of 10 Unit D-2 Static Lateral Stability (2) Wing Placement on the Fuselage • Fig. 6.23 shows crossflow (sideways component of airflow) around three sideslipping fuselages with a wing attached at a different vertical position. (a) High wing: gets an upward crossflow component on its upwind wing and downward component on its downwind wing (roll "away" from the sideslip: contribute to positive lateral stability) (b) Mid wing: gets no effect (no net rolling moment and neutral lateral stability) (c) Low wing: opposite of high wing (roll "toward" the sideslip: contribute to negative stability) Wing Dihedral Effects • In fig. 6.24, the wing dihedral angle is the angle in a rear view of the aircraft between its y axis and a line drawn from the middle of the wing root to the middle of the wing tip. (a) Positive dihedral: positive sideslip angle results in a negative (roll "away") rolling moment (contribute to positive lateral stability) (b) Negative dihedral: opposite (roll "toward") rolling: contribute to negative lateral stability) Tall Vertical Tail Contributions • In fig. 6.25, it shows that a tall vertical tail contributes to positive lateral stability. Because its aerodynamic center is above the aircraft's center of gravity, it generates a negative rolling moment when the aircraft has a positive sideslip angle. This is a positive contribution to lateral stability. • In addition, placing an aircraft's horizontal tail on top of its vertical tail (T-tail) will create an effect of an end-plate on the vertical tail. This will increase the effective aspect ratio of the vertical tail, and therefore increase its lift curve slope. This will also make the aircraft's rolling moment (due to sideslip) more negative (contribute to positive lateral stability). Page 5 of 10 Unit D-2 Dynamic Lateral-Directional Stability Three Modes of Dynamic Lateral & Directional Stability • Most aircraft exhibit three distinctive dynamic lateral-directional modes: spiral, Dutch roll, and roll modes. Each mode has unique characteristics, and each is influenced in different ways by the same aircraft features that contribute to static lateral and directional stability. Spiral Mode • The spiral mode typically involves a gradual increase in bank angle, causing the aircraft to make a descending turn. As bank angle increases, the aircraft's node drops father below the horizon, and its speed increases (death spiral). • The requirement for positive spiral mode stability is that an aircraft, when disturbed (rolling) from wings-level flight, should generate a moment that tends to return it to wings level. • If CC 23, the aircraft's static directional stability turns it into the direction it is slipping, NL reducing the yaw and preventing its lateral stability from rolling it out of the turn. In this situation, the aircraft often has a very dangerous (divergent) spiral mode. • To correct this situation: increase dihedral and/or sweep, or mount the wing higher on the fuselage to increase C . Alternatively: reduce the size (but not the height) of the vertical tail, or move it closer L to the aircraft's center of gravity to reduce C . N Page 6 of 10 Unit D-2 Dynamic Lateral-Directional Stability (Continued) Dutch Roll Mode • If CC13, an aircraft's lateral stability is out of balance with and overpowers its directional NL stability. When a disturbance causes aircraft to yaw, its powerful lateral stability causes it to roll away from the yaw before its directional stability can turn it into the sideslip. This triggers an oscillating rolling and yawing maneuver (side-to-side rolling motion). Because of its motion, the name came from a famous Dutch ice skater of the time. • The period of Dutch roll can be shorter than the pilot's reaction time (difficult to correct). • To correct this situation: decrease dihedral and/or sweep, or mount the wing lower on the fuselage to decrease . Alternatively: increase the size (and reduce the height) of the vertical tail, or move it farther away from the aircraft's center of gravity to increase . Roll Mode • The roll mode is the aircraft's response to aileron inputs. When the pilot deflects ailerons, the resulting rolling moment causes the aircraft to begin to roll. As the roll rate increases, the motion of the wings causes an additional relative wind component that increases the angle of attack on the down-going wing and decreases it on the up-going wing. This, in turn, creates a moment opposite the rolling moment created by the ailerons, which gradually builds until the aircraft reaches a steady roll rate. • The roll rate (sensitivity) can be adjusted by changing the size of control surfaces (control authority) and/or software changes of fly-by-wire flight control system. Adverse Yaw and Spins • Part of the roll mode is a yaw response that is caused by differential drag on the two wings. The wing with the aileron deflected trailing-edge-down creates more lift than the one with the aileron deflected up. This, in turn, creates more drag on the wing with the greater lift. If the wings are long (i.e., sailplane), this differential drag can create a powerful yawing moment away from the direction of the roll. This is called an adverse yaw. • At best, the adverse yaw can delay the turn; at worst (if at high angle of attack near stall), it can push the aircraft into a rotating stalled condition, called a spin. • To reduce adverse yaw: use differential ailerons that deflect trailing edge up much more than they deflect trailing edge down. This works because the trailing-edge-up deflection is so extreme that it causes flow separation and additional drag to balance the additional drag due to lift of the opposite trailing-edge-down aileron. C L C N Page 7 of 10 Unit D-2 F-16 Stability & Control Analysis (1) Stability & Control Analysis Example: F-16A & F-16C Fig. 6.27 illustrates F-16A (early model) and F-16C (later model): the difference is the stabilator. The increase in stabilator area was made for F-16 to increase pitch control authority. Table 6.3 lists descriptive data for each aircraft. Determine the effect of this change on the F-16's neutral point location and SM, for both subsonic and supersonic flight. F-16 Subsonic Flight Analysis The stability analysis begins by estimating the location of the aerodynamic center of the wing/strake/fuselage combination, which will be the same for both aircraft.
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