Static and Dynamic Analysis of an Unconventional Plane:

Flying Wings

Sergio EstebanDepartment of Mechanical and Aerospace Engineering and

Engineering MechanicsUniversity of Missouri-Rolla

AIAA Region V Student ConferenceApril 27 & 28, 2000, Wichita, Kansas

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Outline

Introduction Motivation Analysis Results Conclusions Future Work Video Questions

Introduction

– What is a flying wing? Tailless airplane where all the surfaces are effectively used for lift.

– Why are they a hot prospect? Maximizing all lifting surfaces. Increase range and decrease the thrust requirements. Increase cargo weight.

– Present interest: Reconnaissance. Civil transport.

Motivation

– Senior design Request to build and fly an unconventional reconnaissance plane.

– Need for prediction of longitudinal and lateral characteristics for unconventional planes.

Challenges

– General literature approximates most stability derivatives with the tail contribution.

– Need for decoupling the derivative coefficients into wing and vertical surfaces contributions.

– Creation of automated code to analyze stability for unconventional planes.

Analysis Approach

Analysis Approach

– Decoupling stability derivatives. Extensive literature research (Smetana & Roskam). Wing, fuselage and vertical surfaces contributions.

– Determine stability requirements.

– Analysis of stability: MATLAB automated code (+15000 lines of code). Pure flying wings – no winglets. Flying wings with winglets.

– Determine winglets influence on lateral stability.

– Optimize winglets size and location to achieve stability.

Ala-Voladora MATLAB Code

Receive input from user. Initialize program. Iterative process. Solve equations of motion. Extract data. Output results.

Static Longitudinal Stability Criteria

– Conditions for static longitudinal stability: CM0

must be positive. CM

must be negative.

– To satisfy the above criteria: Sweep. Symmetric airfoils. Geometric twist. Reflex airfoils.

Longitudinal Stability Results

– CM0 = 0.039

– CM= -0.00719 per degree.

– Short period poles = -5.58 31.72i Damping ratio: S = 0.17 Natural frequency: nS

= 32.21

– Phugoid poles = -0.05 0.43i Damping ratio: P = 0.12 Natural frequency: nP

= 0.44

Phugoid Response after an Impulse Perturbation

0 10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

2Phugoid mode impulse-time response

Time (sec)

Am

plitu

de

Short Period Response after an Impulse Perturbation

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025Short-period mode impulse-time response

Time (sec)

Am

plitu

de

Suggested Static Lateral Stability Criteria

– Suggested conditions for static lateral stability: Cl

be negative with magnitude half of Cn.

– Military and civilian flying quality requirements. Four classes. Three flight phase categories.

– Class I, flight phase category A: Minimum Dutch Roll damping ratio of 0.19 Minimum Dutch Roll natural frequency 1.0 rad/sec

Lateral Results without Winglets

Lateral Stability Results without Winglets

– Cl= -0.012

– Cn= -1.26e-4 per degree.

– Dutch Roll poles = 0.07 1.02i Damping ratio: D = 0.068 Natural frequency: nD

= 1.02 rad/sec

Influence of Winglet Geometry on Damping and Natural Frequency Given target Dutch Roll damping ratio and natural

frequency, the following parameters can be used to determine winglet dimensions:– Winglet taper ratio.– Distance from the Xcg to the vertical tail aerodynamic

center.– Winglet leading edge sweep.– Distance from the vertical tail aerodynamic center to

the wing center line.

Dutch Roll Damping Ratio vs. Normalized Surface Area of Winglets

5 10 15 20 25 300.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Dutch Roll Damping ratio vs. % Sw for sweep 40 deg

%Sw

Dam

ping

rat

io

taper 0.2taper 0.4taper 0.6taper 0.8

Dutch Roll Natural Frequency vs. Normalized Surface Area of Winglets

5 10 15 20 25 302

4

6

8

10

12

14

16

18Dutch Roll Natural Frequency vs. % Sw for sweep 40 deg

% Sw

Nat

ural

freq

uenc

y

taper 0.2taper 0.4taper 0.6taper 0.8

Lateral Results with Winglets

Lateral Stability Results for Flying Wing with Winglets

– Cl= -0.026

– Cn= 0.049 per degree.

– Dutch Roll poles = -1.37 7.09i Damping ratio: D = 0.19 Natural frequency: nD

= 7.22 rad/sec

Dutch Roll Response With and Without Winglets

0 5 10 15-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Dutch Roll Impulse Time Response

Time (sec)

Am

plitu

deNo W inglets W inglets for Dutch damping ratio=0.19W inglets for Dutch damping ratio=0.25

Dutch Roll Response for Several Winglets

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.1

-0.05

0

0.05

0.1

0.15Dutch Roll Impulse Time Response

Time (sec)

Am

plitu

deW inglets for Dutch damping ratio=0.15W inglets for Dutch damping ratio=0.19W inglets for Dutch damping ratio=0.25

Conclusions

Conclusions

– Dynamic and static longitudinal stability achieved without winglets, however to achieve lateral stability winglets were required.

– Longitudinal stability can be achieved by: Proper location of center of gravity. Proper wing geometry

– Lateral stability can be achieved by: Proper winglet sizing (lv, v, Sv & zv).

– Dutch Roll lateral stability can be achieved without augmentation of flight controls.

Final Conclusion

The present stability analysis was implemented on an actual flying wing:

Flew successfully on April 1999.

Highly maneuverable.

Numerous acrobatic maneuvers:– Barrel rolls.– Hammer heads.– Loops.

Future Work

– Refinement of the code, and use of Visual C++ to develop a Windows based environment.

– Use it as a tool for stability analysis of unconventional designs.

Video

Questions?

Important Derivative Definitions

Longitudinal Stability– CLå

- change in lift coefficient with angle of attack.– CMå

- change in pitching coefficient with angle of attack.– CLq

- change in lift with varying pitching velocity– CMq

- change in pitching moment with varying pitching velocity.

Lateral Stability– Cl

- change in rolling moment due to a sideslip angle variation.– Cn

- change in yawing moment due to a sideslip angle variation.