MSD : SAE Aero Aircraft Design & Build Preliminary Horizontal and Vertical Stabilizer Design, Longitudinal and Directional Static Stability Horizontal Stabilizer Parameters: 1. Ratio of horizontal tail-wing aerodynamic centers distance with respect to fuselage length 푙푎푐 /푙푓 2. Overall fuselage length 푙푓 3. Horizontal tail-wing aerodynamic centers distance 푙푎푐 4. Horizontal tail volume coefficient 푉퐻 5. Center of gravity location 푥푐푔 6. Horizontal tail arm 푙푡 7. Horizontal tail planform area 푆푡 8. Horizontal tail airfoil 9. Horizontal tail aspect ratio 퐴푅푡 10. Horizontal tail taper ratio 휆푡 11. Additional geometric parameters (Sweep Angle, Twist Angle, Dihedral) 12. Incidence Angle 푖푡 13. Neutral Point 푥푁푃 14. Static Margin 15. Overall Horizontal Stabilizer Geometry 16. Overall Aircraft Static Longitudinal Stability 17. Elevator (TBD in Control Surfaces Design) Vertical Stabilizer Parameters: 18. Vertical tail volume coefficient 푉푣 19. Vertical tail arm 푙푣 20. Vertical tail planform area 푆푉 21. Vertical tail aspect ratio 퐴푅푣 22. Vertical tail span 푏푣 23. Vertical tail sweep angle Λ푣 24. Vertical tail minimum lift curve slope 퐶 퐿훼 푣 25. Vertical tail airfoil 26. Overall Vertical Stabilizer Geometry 27. Overall Aircraft Static Direction Stability 28. Rudder (TBD in Control Surfaces Design) 1. l/Lf Ratio: 0.6 The table below shows statistical ratios between the distance between the wing aerodynamic center and the horizontal tail aerodynamic center 푙푎푐 with respect to the overall fuselage length (Lf). 2. Fuselage Length (Lf): 60.00 in Choosing this value is an iterative process to meet longitudinal and vertical static stability, internal storage, and center of gravity requirements, but preliminarily choose 푙푓 = 60.00 푖푛 3. Horizontal tail-wing aerodynamic centers distance 풍풂풄 : 36.00 in 푙푎푐 = 0.6 푙푓 푙푎푐 = 36.00 푖푛 4. Horizontal Tail Volume Coefficient (VH): 1.0 The table below shows the horizontal and vertical tail coefficients for various types of aircraft. 푙푡 푆푡 푉 = 퐻 푆푐 푉퐻 = 1 5. Center of Gravity Location (xcg):ퟎ. ퟑퟎ푐 Justification: a) Choose center of gravity aft of aerodynamic center to aid (give more room) with placing components to meet specified center of gravity location. b) If horizontal tail stabilizes aircraft pitching up, it generates a positive lift force, adding to the wing lift. c) 0.30푐 is the aft most recommended limit for center of gravity placement. 6. Horizontal Tail Arm 풍풕 : 35.2537 in 푙푡 = 푙푎푐 − 푥푐푔 − 푥푎푐 푙푡 = 35.2537 푖푛 2 7. Horizontal Tail Planform Area (St): 3.6352 푓푡 푙푡 푆푡 푉 = = 1 퐻 푆푐 2 푆푡 = 3.6352 푓푡 8. Airfoil Selection: NACA-0021 Justification: a) Choose symmetric airfoil as the horizontal tail should behave in a similar manner when at a positive or negative angle-of-attack b) Horizontal tail should never stall, specifically it should at least stall later than the wing for recovery c) Maximize 퐶 퐿푚푎푥 푡 d) Maximize 퐶 퐿훼 푡 e) Minimize overall drag f) Minimize overall size NACA-0009: NACA-0010: NACA-0015: NACA-0018 NACA-0021: NACA-0024: NACA-0018, NACA-0021, NACA-0024 Airfoil Comparison: 9. Aspect Ratio 푨푹풕 : 4 Justification: a) It is recommended that the aspect ratio of the tail be such that the span is longer than the propeller diameter to ensure that a portion of the tail is out of the wake or downwash of the wing, increasing tail efficiency 휂 . b) Horizontal tail aspect ratio should be lower than that of the wing to increase stall angle and allow for recovery if needed c) It is recommended that: 2 퐴푅 = 퐴푅 푡 3 푤 퐴푅푡 = 4 10. Horizontal Tail Taper Ratio 흀풕 : 0.7 a) For transport aircraft, the horizontal tail taper ratio is usually between 0.4 and 0.7 b) To ensure a higher stall angle than the wing through a lower Oswald efficiency factor and a lift distribution that is less elliptical, choose 휆푡 = 0.7 11. Additional geometric parameters (Sweep Angle, Twist Angle, Dihedral): N/A a) For the benefits of applying the any of the above parameters to the horizontal geometry, refer to the preliminary wing design parameter selection document b) In the preliminary design phase, it is recommended to make these parameters have the same values as those of the wing. 12. Horizontal Tail Incidence Angle 풊풕 : 4.2300 deg - Determine horizontal tail incidence angle to trim (longitudinal) aircraft at cruise 퐶푚 = 퐶푚 + 퐶푚 + 퐶푚 = 0 푐푔 푐푔 푤 푐푔 푡 푐푔 푓 퐶 + 퐶 훼 + 퐶 + 퐶 훼 + 퐶 + 퐶 훼 = 0 푚0푤 푚훼 푤 푤 푐푟푢푖푠푒 푚 0푡 푚훼 푡 푤 푐푟푢푖푠푒 푚0푓 푚훼 푓 푤 푐푟푢푖푠푒 푥 푥 푥 푥 푑휀 퐶 + 퐶 푐푔 − 푎푐 + 퐶 푐푔 − 푎푐 훼 + 휂푉 퐶 휀 + 푖 − 푖 − 휂푉 퐶 1 − 훼 + 푚 푎푐 푤 퐿0푤 푐 푐 퐿훼 푤 푐 푐 푤 푐푟푢푖푠푒 퐻 퐿훼 푡 0 푤 푡 퐻 퐿훼 푡 푑훼 푤 푐푟푢푖푠푒 푘2−푘1 푥=푙푓 2 1 푥=푙푓 2 휕휀푢 푤 훼 + 푖 Δ푥 + 푤 Δ푥 훼 = 0 36.5푆푐 푥=0 푓 0푤 푓 36.5푆푐 푥=0 푓 휕훼 푤푐푟푢푖푠푒 푖푡 = 4.2300 푑푒푔 13. Neutral Point 풙푵푷 :0.7067푐 퐶 퐶 푥푛푝 푥푎푐 푚훼 푓 퐿훼 푑휀 = − + 휂푉 푡 1 − 푐 푐 퐶 퐻 퐶 푑훼 퐿훼 푤 퐿훼 푤 푥푁푃 = 0.7067푐 14. Static Margin: 0.3548 푆푡푎푡푖푐 푀푎푟푔푖푛 = 푥푁푃 − 푥푐푔 푆푡푎푡푖푐 푀푎푟푔푖푛 = 0.3548 15. Horizontal Stabilizer Geometry 16. Overall Aircraft Longitudinal Stability Criteria for Longitudinal Static Stability 푑퐶푚 퐶 = < 0 푚훼 푑훼 퐶푚0 > 0 퐶 = 퐶 + 퐶 퐶 푚0 푚0푤 푚0푡+ 푚0푓 푥=푙푓 푥푐푔 푥푎푐 푘2 − 푘1 2 퐶푚 = 퐶푚 + 퐶퐿 − + 휂푉퐻퐶퐿 휀0 + 푖푤 − 푖푡 + 푤푓 훼0 + 푖푓 Δ푥 0 푎푐 푤 0푤 푐 푐 훼 푡 36.5푆푐 푤 푥=0 퐶 = 퐶 + 퐶 + 퐶 푚훼 푚훼 푤 푚훼 푡 푚훼 푓 푥=푙푓 푥푐푔 푥푎푐 푑휀 1 2 휕휀푢 퐶푚 = 퐶퐿 − − 휂푉퐻퐶퐿 1 − + 푤푓 Δ푥 훼 훼 푤 푐 푐 훼 푡 푑훼 36.5푆푐 휕훼 푥=0 푪풎휶 ퟏ/풓풂풅 -1.4679 푪풎ퟎ 0.1281 18. Vertical tail volume coefficient 푽풗 : 0.06 The following table shows the vertical tail characteristics for various aircraft. Because our aircraft configuration and mission requirements are very similar to the C-130, many vertical tail parameters are chosen so that they match those of that aircraft. 푙푣푆푣 푉 = 푣 푆푏 푉푣 = 0.06 19. Vertical tail arm 풍풗 : 36.1102 in During the preliminary design phase, the vertical tail arm is selected to be equal to the horizontal tail arm, then adjusted after further iterations if needed. 푙푣 = 36.1102 푖푛 2 20. Vertical tail planform area 푺푽 : 1.1521 푓푡 푙푣푆푣 푉 = = 0.08 푣 푆푏 2 푆푣 = 1.1521 푓푡 21. Vertical tail aspect ratio 푨푹풗 : 1.84 Choose vertical tail aspect ratio such that it matches that of the C-130 (Table 6.6). 푨푹풗 = ퟏ. ퟖퟒ 22. Vertical tail span 풃풗 : 17.4716 in 2 푏푣 퐴푅푣 = 푆푣 푏푣 = 17.4716 푖푛 23. Vertical tail sweep angle 횲풗 : 18.8 deg Choose vertical tail sweep angle such that it matches that of the C-130 (Table 6.6). Λ푣 = 18.8 푑푒푔 24. Vertical tail minimum lift curve slope 푪 : 0.0011137 [1/deg] 푳휶풗 - Determine minimum vertical tail lift curve slope so to meet the static directional stability requirement 퐶푛훽 > 0 퐶푛 = 퐶푛 + 퐶푛 훽 훽 푤푓 훽 푣 푆푓푠 푙푓 푑휎 퐶 = −푘 푘 + 푉 퐶 휂 1 − 푛훽 푛 푅푙 푆푏 푣 퐿훼 푣 푣 푑훽 퐶퐿 = 0.0011137 1/푑푒푔 훼 푣푚푖푛 25. Vertical Tail Airfoil: NACA-0009 a) Choose symmetric airfoil as the vertical tail should behave in a similar manner when at a positive or negative angle-of-attack b) To minimize structure and weight, choose airfoil with smallest thickness that meets 퐶퐿 훼 푣푚푖푛 c) Refer to symmetric airfoil plots when choosing the horizontal tail airfoil NACA-0009 (As Stabilizer not Airfoil, from XFLR5) 훼 (deg) 퐶퐿푣 0 0 5.00 0.314 Δ퐶퐿 퐶 = 푣 푙 훼 Δ훼 퐶 = 0.1214 [1/deg] 퐿훼 푣 26. Vertical Stabilizer Geometry 27. Overall Aircraft Directional Stability Criterion for Directional Static Stability 푑퐶푛 퐶 = > 0 푛훽 푑훽 퐶푛 = 퐶푛 + 퐶푛 훽 훽 푤푓 훽 푣 푆푓푠 푙푓 푑휎 퐶 = −푘 푘 + 푉 퐶 휂 1 − 푛훽 푛 푅푙 푆푏 푣 퐿훼 푣 푣 푑훽 푪풏휷 ퟏ/풓풂풅 0.2847 .