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
๐๐๐ /๐๐
2. Overall fuselage length ๐๐
3. Horizontal tail-wing aerodynamic centers distance ๐๐๐ 4. Horizontal tail volume coefficient ๐๐ป
5. Center of gravity location ๐ฅ๐๐
6. Horizontal tail arm ๐๐ก 7. Horizontal tail planform area ๐๐ก 8. Horizontal tail airfoil 9. Horizontal tail aspect ratio ๐ด๐ ๐ก 10. Horizontal tail taper ratio ๐๐ก 11. Additional geometric parameters (Sweep Angle, Twist Angle, Dihedral) 12. Incidence Angle ๐๐ก 13. Neutral Point ๐ฅ๐๐ 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 ๐๐ฃ 19. Vertical tail arm ๐๐ฃ 20. Vertical tail planform area ๐๐ 21. Vertical tail aspect ratio ๐ด๐ ๐ฃ 22. Vertical tail span ๐๐ฃ 23. Vertical tail sweep angle ฮ๐ฃ
24. Vertical tail minimum lift curve slope ๐ถ๐ฟ๐ผ ๐ฃ
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 ๐๐๐ 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 ๐๐ = 60.00 ๐๐
3. Horizontal tail-wing aerodynamic centers distance ๐๐๐ : 36.00 in ๐๐๐๐๐
= 0.6
๐๐๐ = 36.00 ๐๐ 4. Horizontal Tail Volume Coefficient (VH): 1.0 The table below shows the horizontal and vertical tail coefficients for various types of aircraft.
๐๐ป =๐๐ก๐๐ก๐๐
๐๐ป = 1
5. Center of Gravity Location (xcg):๐.๐๐๐ 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) 0.30๐ is the aft most recommended limit for center of gravity placement. 6. Horizontal Tail Arm ๐๐ : 35.2537 in
๐๐ก = ๐๐๐ โ ๐ฅ๐๐ โ ๐ฅ๐๐
๐๐ก = 35.2537 ๐๐ 7. Horizontal Tail Planform Area (St): 3.6352 ๐๐ก2
๐๐ป =๐๐ก๐๐ก๐๐
= 1
๐๐ก = 3.6352 ๐๐ก2 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 ๐ถ๐ฟ๐๐๐ฅ ๐ก
d) Maximize ๐ถ๐ฟ๐ผ ๐ก
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 ๐จ๐น๐ : 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 ๐ .
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:
๐ด๐ ๐ก =2
3๐ด๐ ๐ค
๐ด๐ ๐ก = 4
10. Horizontal Tail Taper Ratio ๐๐ : 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 ๐๐ก = 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 ๐๐ : 4.2300 deg
- Determine horizontal tail incidence angle to trim (longitudinal) aircraft at cruise ๐ถ๐๐๐
= ๐ถ๐๐๐ ๐ค+ ๐ถ๐๐๐ ๐ก
+ ๐ถ๐๐๐ ๐= 0
๐ถ๐0๐ค
+ ๐ถ๐๐ผ๐ค๐ผ๐ค๐๐๐ข๐๐ ๐
+ ๐ถ๐0๐ก+ ๐ถ๐๐ผ ๐ก
๐ผ๐ค๐๐๐ข๐๐ ๐+ ๐ถ๐0๐
+ ๐ถ๐๐ผ๐๐ผ๐ค๐๐๐ข๐๐ ๐
= 0
๐ถ๐๐๐ ๐ค+ ๐ถ๐ฟ0๐ค
๐ฅ๐๐
๐ โ
๐ฅ๐๐
๐ + ๐ถ๐ฟ๐ผ๐ค
๐ฅ๐๐
๐ โ
๐ฅ๐๐
๐ ๐ผ๐ค๐๐๐ข๐๐ ๐ + ๐๐๐ป๐ถ๐ฟ๐ผ ๐ก
๐0 + ๐๐ค โ ๐๐ก โ ๐๐๐ป๐ถ๐ฟ๐ผ ๐ก 1 โ
๐๐
๐๐ผ ๐ผ๐ค๐๐๐ข๐๐ ๐ +
๐2โ๐1
36.5๐๐ ๐ค๐
2 ๐ผ0๐ค+ ๐๐ ฮ๐ฅ
๐ฅ=๐๐๐ฅ=0 +
1
36.5๐๐ ๐ค๐
2 ๐๐๐ข
๐๐ผฮ๐ฅ
๐ฅ=๐๐๐ฅ=0 ๐ผ๐ค๐๐๐ข๐๐ ๐
= 0
๐๐ก = 4.2300 ๐๐๐ 13. Neutral Point ๐๐ต๐ท :0.7067๐
๐ฅ๐๐
๐ =
๐ฅ๐๐๐
โ๐ถ๐๐ผ ๐
๐ถ๐ฟ๐ผ๐ค
+ ๐๐๐ป๐ถ๐ฟ๐ผ ๐ก
๐ถ๐ฟ๐ผ๐ค
1 โ๐๐
๐๐ผ
๐ฅ๐๐ = 0.7067๐ 14. Static Margin: 0.3548 ๐๐ก๐๐ก๐๐ ๐๐๐๐๐๐ = ๐ฅ๐๐ โ ๐ฅ๐๐
๐๐ก๐๐ก๐๐ ๐๐๐๐๐๐ = 0.3548
15. Horizontal Stabilizer Geometry
16. Overall Aircraft Longitudinal Stability Criteria for Longitudinal Static Stability
๐ถ๐๐ผ=
๐๐ถ๐๐๐ผ
< 0
๐ถ๐0
> 0
๐ถ๐0
= ๐ถ๐0๐ค+ ๐ถ๐0๐ก+๐ถ๐0๐
๐ถ๐0= ๐ถ๐๐๐ ๐ค
+ ๐ถ๐ฟ0๐ค ๐ฅ๐๐
๐ โ๐ฅ๐๐๐ + ๐๐๐ป๐ถ๐ฟ๐ผ ๐ก
๐0 + ๐๐ค โ ๐๐ก +๐2 โ ๐1
36.5๐๐ ๐ค๐
2 ๐ผ0๐ค+ ๐๐ ฮ๐ฅ
๐ฅ=๐๐
๐ฅ=0
๐ถ๐๐ผ
= ๐ถ๐๐ผ๐ค+ ๐ถ๐๐ผ ๐ก
+ ๐ถ๐๐ผ๐
๐ถ๐๐ผ= ๐ถ๐ฟ๐ผ๐ค
๐ฅ๐๐
๐ โ๐ฅ๐๐๐ โ ๐๐๐ป๐ถ๐ฟ๐ผ ๐ก
1 โ๐๐
๐๐ผ +
1
36.5๐๐ ๐ค๐
2๐๐๐ข๐๐ผ
ฮ๐ฅ
๐ฅ=๐๐
๐ฅ=0
๐ช๐๐ถ ๐/๐๐๐ -1.4679
๐ช๐๐ 0.1281
18. Vertical tail volume coefficient ๐ฝ๐ : 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.
๐๐ฃ =๐๐ฃ๐๐ฃ๐๐
๐๐ฃ = 0.06 19. Vertical tail arm ๐๐ : 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. ๐๐ฃ = 36.1102 ๐๐
20. Vertical tail planform area ๐บ๐ฝ : 1.1521 ๐๐ก2
๐๐ฃ =๐๐ฃ๐๐ฃ๐๐
= 0.08
๐๐ฃ = 1.1521 ๐๐ก2
21. Vertical tail aspect ratio ๐จ๐น๐ : 1.84 Choose vertical tail aspect ratio such that it matches that of the C-130 (Table 6.6). ๐จ๐น๐ = ๐.๐๐ 22. Vertical tail span ๐๐ : 17.4716 in
๐ด๐ ๐ฃ =๐๐ฃ
2
๐๐ฃ
๐๐ฃ = 17.4716 ๐๐ 23. Vertical tail sweep angle ๐ฒ๐ : 18.8 deg Choose vertical tail sweep angle such that it matches that of the C-130 (Table 6.6). ฮ๐ฃ = 18.8 ๐๐๐
24. Vertical tail minimum lift curve slope ๐ช๐ณ๐ถ๐ : 0.0011137 [1/deg]
- Determine minimum vertical tail lift curve slope so to meet the static directional stability
requirement ๐ถ๐๐ฝ> 0
๐ถ๐๐ฝ
= ๐ถ๐๐ฝ๐ค๐+ ๐ถ๐๐ฝ ๐ฃ
๐ถ๐๐ฝ= โ๐๐๐๐ ๐
๐๐๐ ๐๐
๐๐+ ๐๐ฃ๐ถ๐ฟ๐ผ๐ฃ
๐๐ฃ 1 โ๐๐
๐๐ฝ
๐ถ๐ฟ๐ผ๐ฃ๐๐๐
= 0.0011137 1/๐๐๐
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 ๐ถ๐ฟ๐ผ๐ฃ๐๐๐
c) Refer to symmetric airfoil plots when choosing the horizontal tail airfoil
NACA-0009 (As Stabilizer not Airfoil, from XFLR5)
๐ผ (deg) ๐ถ๐ฟ๐ฃ
0 0
5.00 0.314
๐ถ๐๐ผ =ฮ๐ถ๐ฟ๐ฃฮ๐ผ
๐ถ๐ฟ๐ผ๐ฃ= 0.1214 [1/deg]
26. Vertical Stabilizer Geometry
27. Overall Aircraft Directional Stability Criterion for Directional Static Stability
๐ถ๐๐ฝ=
๐๐ถ๐๐๐ฝ
> 0
๐ถ๐๐ฝ
= ๐ถ๐๐ฝ๐ค๐+ ๐ถ๐๐ฝ ๐ฃ
๐ถ๐๐ฝ= โ๐๐๐๐ ๐
๐๐๐ ๐๐
๐๐+ ๐๐ฃ๐ถ๐ฟ๐ผ๐ฃ
๐๐ฃ 1 โ๐๐
๐๐ฝ
๐ช๐๐ท ๐/๐๐๐ 0.2847