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Aero Engineering 315

Aero Engineering 315. Lesson 37 Longitudinal Static Stability. Lesson 37 Objectives. Draw a stability curve (C m vs a) for tail and wing Draw a curve for positive, negative and neutral stability Understand tail and wing contributions to stability

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Aero Engineering 315

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  1. Aero Engineering 315 Lesson 37Longitudinal Static Stability

  2. Lesson 37 Objectives • Draw a stability curve (Cm vs a) for tail and wing • Draw a curve for positive, negative and neutral stability • Understand tail and wing contributions to stability • List factors that contribute to longitudinal static stability • State criteria for positive long-stat stability • Identify trim AoA and velocity • Predict changes in stability with changes in tail area, moment arm, incidence angle, camber, CG, etc. • Define neutral point and static margin • Know criteria for positive long-stat stability WRT CG and static margin

  3. Lw xw M M cg cg +Macwing Zero Lift Line C = (CLa,w xw/c )a + CMac,wing Moment Contribution from the Wing Recall: Mac,wing < 0 (for + camber) and Lw = CL q S = CLa,wa q S V a C (from wing) Positive slope(+) Summing the moments and dividing by qSc: a Negative (-) Intercept for symmetrical wing Form of: y = mx + b

  4. xt M cg Lt it at Zero Lift Line (CLat St xt ) S c (CLat St xt ) S c CMcg = - a + it Moment Contribution from the Tail at = a - it Lt = CLat a q St Symmetric airfoil St = tail area V C (from tail) Summing the moments and dividing by qSc: Positive (+) intercept (depending on it) a Negative slope (-) Form of: y = mx +b

  5. Wing Only Contribution Required Tail Contribution Contributions to Stability - Summary Result – Wing and Tail

  6. xt Lw xw M cg +Macwing Lt V a it at Zero Lift Line C = (CLaw - CLat )a + CMacw+ CLat it xt c xw c xt c St S St S C C M M a 0 Total Airplane Moment V Wing Tail Wing Tail

  7. Lw Lt M M M a 0 cg xt xw C = (CLaw - CLat )a + CMacw+ CLat it xt c xw c xt c St S St S C C Effects of configuration changes c.g. • Move CG Aft Less Stable • Larger tail (St) More Stable • Increased camber Decrease CMo • Larger distance to tail More Stable • Tail incidence Shifts CMo

  8. M cg a a C. G. Effect on Stability Center of Gravity moving aft C Bottom Line for stable, trimmed aircraft: • Stable ifCMa < 0 • Trimmed if sum of moments about CG = 0 • Trimmed at usable lift if CM0 >0

  9. Longitudinal Stability—Wing Effects • Locating wing a.c. farther forward of c.g. is more destabilizing • To improve stability (lower CMa): • ↓ (xcg – xac) Shorter moment arm (wing back or c.g. forward) • ↓ SW Smaller wing area (hard) • ↓ CLaW Less efficient wing (do we really want to?)

  10. M cg Longitudinal Stability—Tail Effects (CLa,t St xt ) S c (CLa,t St xt ) S c • Tail aft of cg is stabilizing • Canards are destabilizing • To improve stability (more negative CMa): C = - a + it • xt Longer moment arm • StLarger tail • CLa,tARt or eot (tail Oswald factor) or move tail out of downwash

  11. it > 0 it < 0 Longitudinal Stability—Tail Effects it = 0 Tail incidence angle, it, is the angle between Chord Line of the tail and Aircraft Zero-Lift-Line Tail leading edge down is positive

  12. Longitudinal Static Stability - Total Aircraft • Most parameters are fixed once the aircraft is built • C.G. can be moved • Cargo location • Fuel location • Weapons, stores, etc. • itchanges the trim angle of attack, ae • Variable geometry wings—change cg, CLaW and moment arm (xcg-xac)

  13. Conventional Tail - Stabilizing F-22 F-16

  14. Canards - Destabilizing Su-35 Long-Eze

  15. More Canards - Eurofighter

  16. X n X cg Neutral Point The Neutral Point (Xn) represents the c.g. location such that CMa = 0. It is the center of pressure for the entire aircraft. W Xcg is the distance from the leading edge of the wing to the CG Xn is the distance from the leading edge of the wing to the Neutral Point

  17. M L a a - C C = Static Margin: Stability Criteria Non-dimensional difference between Neutral Point (n.p.) and Center of Gravity (c.g.) where: • If S.M. > 0 (c.g. ahead of the neutral point) - aircraft is stable • If S.M. = 0 (c.g. at the neutral point) - aircraft is neutrally stable - aircraft is unstable • If S.M. < 0 (c.g. behind the neutral point)

  18. Typical Static Margin Values • Transports & Consumer AC: 0.05 to 0.20 Cessna 172 Learjet 35 Boeing 747 P-51 Mustang F-106 F-16A (early) F-16C X-29 0.19 0.13 0.27 0.05 0.09 -0.02 0.01 -0.33 More Stable More Maneuverable • Fighters: 0 to 0.05 • Fighters - FBW Much More Maneuverable Stabilized by AFCS

  19. NEUTRAL PITCH STABILITY IS EXHIBITED BY THE AIRCRAFT AT SMALL POSITIVE ANGLES OF ATTACK THE AIRCRAFT BECOMES INCREASINGLY UNSTABLE IN PITCH ABOVE 7° AOA EXCEEDING 14° AOA CAUSES A VIOLENT AND UNCONTROLLABLE PITCH-UP F-117Longitudinal Stability

  20. 7° AOA VORTEX • VORTEX FORMS AT WING ROOT

  21. ABOVE 14° AOA VORTEX • VORTEX SHIFTS OUTBOARD AND WING BEGINS TO STALL AT WING TIPS • STALL PROGRESSES TOWARDS WING ROOT • AC cp SHIFTS FORWARD RESULTING IN SIGNIFICANT NEGATIVE STATIC MARGIN • STATICALLY UNSTABLE -- OUT OF CONTROL

  22. Longitudinal Static Stability Summary • Axes, Moments, Velocities – Definitions • Static vs. Dynamic Stability • Absolute Angle of Attack • Moments and Forces • Static Longitudinal Stability • Wing Effects • Tail Effects • Static Margin

  23. Next Lesson (38)… • Prior to class • Review sections 6.1 - 6.4 and long-stat stability handout • Complete all homework problems • Read lateral/directional stability handout • In class • Discuss lateral/directional (roll/yaw) static stability Glider Design Project

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