1. DYNAMICS & CONTROL QDR 1 TEAM 4
Jared Hutter, Andrew Faust, Matt Bagg, Tony Bradford,
Arun Padmanabhan, Gerald Lo, Kelvin Seah
October 30, 2003

2. OVERVIEW Concept Review Class 1 Tail Sizing
Class 1 Control Surface Sizing
Believability Check
Verification of Sizing with Rudder Deflection in One-Engine Inoperative (OEI) Flight Conditions
Follow-Up Actions
ITERATIONS

3. CONCEPT REVIEW Vertical Tails Horizontal Tail Main Wing Engine Engine
Avionics Pod
Landing Gear

4. CLASS 1 HORIZONTAL TAIL SIZING
Tail Volume Coefficient Approach (Raymer, p.124)
Equation used to find Horizontal Tail (HT) Area:
Tail Volume Coefficient Estimate
Raymer, Homebuilt, = 0.50
AAE 451 Average, ≈ 0.43
Selected larger value because
Table 6.4 suggests that twin engines
typically require larger tails.
where
HT Volume Coefficient
Wing Chord, 3.1 ft
Wing Area, 47.8 ft2
Moment Arm, 7.3 ft

5. CLASS 1 HORIZONTAL TAIL SIZING
Based on = 0.50, the Horizontal Tail area was calculated to be:
Aspect Ratio Selection
We want where is now 5.0.
Selected = 3.0
Historically, many horizontal tails have
aspect ratios of ≈ 3.
The tail protrudes ≈ 1¼ ft on each side;
looks just about right.
= ft2

6. CLASS 1 VERTICAL TAIL SIZING
Same Tail Volume Coefficient Approach.
Equation used to find Vertical Tail (VT) Area:
Tail Volume Coefficient Estimate
Raymer, Homebuilt, = 0.04
AAE 451 Average, ≈
Selected = 0.04
where
VT Volume Coefficient
Wing Span, 15.5 ft
Wing Area, 47.8 ft2
Moment Arm, 7.3 ft

7. CLASS 1 VERTICAL TAIL SIZING
Based on = 0.04, the Vertical Tail area was calculated to be
Aspect Ratio
Not important, because we want
Taper Ratio
Suggested Range:
Prefer a high taper ratio for a small half-span.
Selected = 0.6
= 4.04 ft2
Half Span

8. CLASS 1 TAIL SIZING INITIAL RESULTS
HORIZONTAL TAIL
VERTICAL TAIL
1.10 ft
1.25 ft
3.0 ft
1.84 ft
5.51 ft
= ft2
½ = 2.02 ft2
1.376 ft
1.84 ft
Recall:
= 0.50
= 0.04

9. CLASS 1 CONTROL SURFACE SIZING
Chord-wise Span-wise
Ailerons 0.15 cW ~ 0.25 cW 0.5 bW ~ 0.9 bW
Elevator 0.25 cHT ~ 0.5 cHT ~ 0.9 bHT
Rudder 0.25 cVT ~ 0.5 cVT ~ 0.9 bVT
Raymer:
Initial Estimate:
Chord-wise Span-wise
Ailerons cW ft
Elevator cHT ft
Rudder cVT bVT

10. BELIEVABILITY CHECK Symbol Computed Typical 1. 0.195 0.3 to 0.9
Description of Symbols Used:
Variation of aircraft lift coefficient with elevator deflection angle.
Variation of aircraft pitching moment coefficient with elevator deflection angle.
Variation of aircraft pitching moment coefficient with dimensionless rate of change of angle of attack. (Important for Short Period damping.)
Variation of aircraft pitching moment coefficient with pitch rate (damping in pitch).
Variation of aircraft yawing moment with sideslip (weathercock stability).
All numbers are in units of rad-1.
Symbol Computed Typical
to 0.9
to -2
to -15
to -30
to 0.20
Low elevator effectiveness?
Low weathercock stability?
Low damping in Short Period mode?
We MAY need bigger tails!

11. RUDDER DEFLECTION IN OEI CONDITIONS
Roskam (AAE 421 Textbook)
Required rudder deflection:
DRnO: = 28 ft/s
Deflection Limit: = 25°
FAR 23, 25 requires that
In this case, = 37.6 ft/s
for  = 0°
deflection limit
1.2
stall speed

12. RUDDER DEFLECTION IN OEI CONDITIONS
ref. “Airplane Flight Dynamics and Automatic Flight Controls” (Roskam) Section 4.2.6
[rad]
where
@ 2,000 ft
 [slug/ft3]
V [ft/sec]
P [hp]
yT [ft]
for fixed pitch

13. ITERATIONS Varied Tail Volume Coefficients.
Performed Believability Check with Stability and Control Derivatives.
Analysis of OEI Rudder Deflection.

14. CLASS 1 TAIL SIZING RESULTS
HORIZONTAL TAIL
VERTICAL TAIL
= ft2
1.261 ft
2.102 ft
½ = 3.03 ft2
1.802 ft
1.864 ft
3.0 ft
1.864 ft
6.727 ft
2.102 ft
New Volume Coefficients:
= 0.70
= 0.06
Chord-wise Span-wise
Elevator ft ft
Rudder cVT ft

15. RUDDER DEFLECTION IN OEI CONDITIONS
Roskam (AAE 421 Textbook)
Required rudder deflection:
DRnO: = 28 ft/s
Deflection Limit: = 25°
FAR 23, 25 requires that
In this case, = ft/s
for  = 0°
deflection limit
stall speed
1.2

16. FOLLOW-UP ACTIONS Class 2 Sizing for Tails and Control Surfaces
Further analysis on
Desired static margin
Aircraft performance parameters
Other static stability issues

17. QUESTIONS?