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'»RESENTATION OF FLIGHT CONTROL DESIGN 
AND HANDLING QUALITY COMMONALITY 
BY SEPARATE SURFACE STABILITY AUGMENTATION 
FOR THE FAMILY OF COMMUTER AIRPLANES 

Prapared Fop: NASA Grant NGT-800T: 3'J>t;?^ 
Preparad By: Douglas Hanslay 

Univaralty of Kansas 
AE 790 Dasign Team 
May 13, 1987 

Taam Laadar: Thomas Crelghton 

Taam Mambars: Raphaa 1 Haddad 

Louis Handrlch 
Douglas Hanslay 
Louisa Morgan 
Mark Russal 1 
Garald Swift 

Faculty Advisor: Dr. Jan Roskam 

Ackars Distinguished Professor of 

Aerospace Engineering 



(1I4S4-CB-182567) PBESEHTITlOlf OP FLXGilT ««« loai, 

COKTBOL DESIGS ASD HAHDLIMG QOALITY H88-19471 

AIEPLAHES (Kansas a.i..,".rp^°-""Jlc\ 01C GS/OS V^O 



PRESENTATION OF FLIGHT CONTROL DESIGN 
AND HANDLING QUALITY COMMONALITY 
BY SEPARATE SURFACE STABILITY AUGMENTATION 
FOR THE FAMILY OF COMMUTER AIRPLANES 



Prepared Fori 
Prepared By: 



Team Leader: 
Team Members: 



NASA Grant NGT-8001 

Douglas Hensley 

University of Kansas 
AE 790 Design Team 
May 13, 1987 

Thomas Creighton 

Raphael Haddad 
Louis Hendrich 
Douglas Hensley 
Louise Morgan 
Mark Russel I 
Gerald Swift 



Faculty Advisor 



Dr. San Roskam 

Ackers Distinguished Professor of 

Aerospace Engineering 



TABLE OF CONTENTS 



List of Symbols ii 

1. Introduction 1 

1. 1 Background History 1 

1.2 Incorporating Flight Control Design 

and Handling Quality Commonality 2 

1.3 Design Objectives 3 

2. Design Results of Augmenting for Common Handling 

Qua lities S 

2.1 Longitudinal Open and Closed Loop Dynamics 5 

2.2 Lateral-Directional Open and Closed Loop 
Dynamics 15 

2. 3 Rol 1 Mode Dynamics 19 

3. Requirements of System Implementation 21 

3.1 Separate Surface Control Surface Requirements. . 21 

3.2 Technology Requirements 24 

3.3 System Implementation 28 

4. Conclusions and Recommendations 31 

4.1 .Conclusions 31 

4.2 Recommendations 32 

5. References 33 

Appendix A: Calculations for Longitudinal Dynamics.. 35 
Appendix B: Calculations for Latera 1 -Direct iona 1 

Dynami cs 39 

Appendix C: Calculations for Roll Mode 43 



LIST OF SYMBOLS 

SYMBOL DEFINITION UNITS 

b Wing Span ft 

C.G. Center of Gravity 

c Mean Geometric Chord ft 

CL Lift Coefficient 

Cm Pitching Moment Derivative /rad 

Des Desired, Design 

EHA El ectrohydrostat ic Actuator 

Ixx,Iyy,Izz Moment of Inertia Slug ft* 

K Gain 

L,M,N Dimensional Derivative of Moment Variation 

P Rol 1 Rate 1/sec 

P. dot Roll Acceleration 1/seci 

q Dynamic Pressure psf 

S Surface Area ft* 

SSSA Separate Surface Stability Augmentation 

T Time Constant sec 

t Time sec 

Ul Velocity fps 

Xac Aerodynamic Center location 

Xcg Center of Gravity Location 

y Moment Arm in 

Y Dimensional Derivative of Side Force Variation 

Z Dimensional Derivative of Zs Force Variation 



ii 



Greek Symbols 



S 

a 

} 

Subscripts 



Angle of Attack 

Deflection Angle 

Eta, Efficiency 

Elevator Effectiveness 

Gust Speed 

Frequency 

Zeta, Damping Ratio 



deg, rad 
deg, rad 



f ps 
rad/sec 



D 


Dutch-Rol 1 


E 


Elevator 


H 


Horizontal Tail 


q 


Pitch Rate 


r 


Yaw Rate 


R 


Rudder 


SP 


Short Period 


V 


Vertical Tail 



/sec 
/sec 



111 



1. INTRODUCTION 

This is the sixth in a series of seven reports required 
for partial fulfillment of the requirements of NASA Grant NGT- 
8001. The first report (Reference 1) presented the results of 
the Class I design for the Family of Commuter Airplanes. The 
second report (Reference 2) determined the preliminary 
structure designs and weight penalties due to commonality for 
the Family of Commuter Airplanes. The third report (Reference 
3) presented the structural component designs common to the 
Family of Commuter Airplanes. The fourth report (Reference 4) 
contained the methodology and results of a cost analysis for 
the Family of Commuter Airplanes. The fifth report (Reference 
5) presented a study of advanced prop fans for the Family of 
Commuter Airplanes. The seventh report (Reference 6) contains 
the Class II design update for the Family of Commuter 
Ai rpl anes . 

This report contains the methodology and results for a 
flight control design and Implementation for common handling 
qualities by Separate Surface Stability Augmentation (SSSA) 
for the Family of Commuter Airplanes. 

Chapter 2 will present the open and closed loop dynamics 
and the design results of augmenting for common handling 
qua 1 i ties . 

Chapter 3 will present the physical and technology 
requirements for implementing the SSSA system. 

Chapter 4 will discuss the conclusions of this report and 
recommendations for changes or Improvement. 



1.1 Background History 

The Separate Surface Stability Augmentation (SSSA) 
concept was first implemented on a general aviation airplane 
by Donald J. Collins and Willard R. Bolton, JR. as the 
requirements for their doctoral thesis (References 7, 8). 

1 



This SSSA system was originally designed to improve the 
undesirable latera 1 -direct ional handling in approach and 
cruise flight conditions and poor ride qualities in turbulence 
at all speeds. This improvement in handling and. ride 
qualities was to be gained without the mechanical feedback to 
the pilot that was inherent with traditional stability 
augmentation systems (Reference 8). The system was 
implemented by dividing the normal control surface into two 
surfaces. The larger surface was the new primary control 
surface and was connected to the pilot's controls in the 
conventional manner. The smaller surface, the SSSA surface, 
was driven by electric actuators whose signals were sent by a 
computer. The computer, in turn, derived its signals from the 
gyroscopes and from pilot commands through the pilot 
controls. In this way, the SSSA surfaces were not connected 
directly to the pilot's controls and a force feedback from the 
SSSA system was not transmitted to the pilot (Reference 7). 



1.2 Incorporating Flight Control Design 
and Handling Quality Commonality 

In order to achieve the desired commonality goals for 
this Family of Commuter Airplanes, it was necessary not only 
to implement a common stability augmentation system, but to 
obtain through this system common handling quality 
characteristics throughout the family. Thus, the commonality 
goals could be met on a system level - for cost and 
maintenance purposes - and on a personnel level through cross- 
certification of the flight crews among the entire Family of 
Commuter Airplanes. 

This level of commonality, incorporating a common 
physical system that must produce stability augmentation 
tailored to the individual airplane's inherent qualities and 
to induce the airplane's response characteristics to a level 

2 



that is perceived by the pilot to be similar to the rest of 
the family's characteristics is ideal for SSSA. A common 
separate surface size could be chosen and simple changes in 
the gain required for stability augmentation could tailor the 
response of the system to each airplane. By implementing a 
desired command level into the gain of the normal feedback 
loop, this system can then be used to drive each airplane to a 
common level of handling quality characteristics. Because 
this entire system operates separate from the primary control 
surfaces, the pilot perceives that the handling qualities of 
each airplane is similar throughout the Family of Commuter 
Airplanes. 

In order to achieve a common "feel" for the forces 
required for the primary control surfaces, the stick force 
gradients of each airplane were modified through a stick force 
gain box. Because this report is focused exclusively on the 
stability augmentation system and its use to gain common 
handling quality characteristics, it will not present the 
methodology and results of the modification of the maneuver 
and velocity stick force gradients. These results are 
presented in Reference 6. 



1.3 Design Obiecttves 

It was mandatory for the augmentation system to meet 
certain minimum criteria for this design project. In the 
Longitudinal, Latera 1 -Directiona 1 and Roll modes, each 
airplane was required to meet the Class I handling qualities 
for all flight conditions at both the forward and aft C.G. 
locations. In addition, this SSSA system must have sufficient 
control power to maintain these Class I handling qualities "in 
gust conditions for all flight phases. This requirement is to 
reduce pilot work load and to ensure that the system will be 
reliable and safe in up to 1 percent probability gusts and in 
thunderstorm gust conditions. 

3 



The stick forces for the primary flight control surfaces 
must have common maneuver and velocity gradients in all flight 
conditions at the forward and aft C.G. locations. These 
conditions are presented in Reference 6. 

The physical constraints require that all SSSA surfaces 
must be of common size and geometry. The actuators for all 
control surfaces must be common; this may require that the 
surfaces requiring greater control forces for deflection will 
have a greater number of actuators. This may incur certain 
weight penalties in favor of commonality requirements. 



2. DESIGN RESULTS OF AUGMENTING 
FOR COMMON HANDLING QUALITIES 

The purpose of this section is to present the un- 
augmented characteristics and the augmented design results of 
the handling qualities for the Family of Commuter Airplanes. 
These results will be presented for the Longitudinal, Lateral- 
Directional and the Roll modes. 



2.1 Longitudinal Open and Closed Loop Dynamics 

From Figures 2.1 and 2.2, it can be seen that the 

critical minimum and maximum U,'n and Z for Level I handling 

sp /sp 

qualities in the longitudinal mode occurs at: 

TABLE 2. 1 Critical Short-Period Frequencies and 
Damping Ratios 



7^ = 0.3 for all conditions, 



'sp 
Cruise Speed: 

Min. ^'n : 7.3 rad/sec 50 Pax - Fore C.G. 

spmax 

Max. uJn : 1.75 rad/sec 75 Pax - Aft C.G. 
spmax ' 

Min. Control Speed: 

Min. U'n : 3.6 rad/sec 50 Pax - Fore C.G. 
spmax 

Max. Wn : 1.2 rad/sec 75 Pax - Aft C.G. 
spmax 

And from Table 2.2, it can be seen that all of the 
airplanes in the family meet the Level I handling qualities in 
the longitudinal mode in all flight conditions except for the 
50 Pax - Aft C.G. at both the cruise and min. control speed. 

Therefore, the primary requirement of the augmentation 
system was to drive the handling qualities of each airplane to 
a level of commonality. 

5 



ORIGlNi^iL PAGE IS 
OE POOR QUALIT35 



too 



I 



1 r 



Note: The boundaries for values of n/a 



outside the range shown are defined by 
straight-line extensions 



10 






1.0 

Crotse Spee<^ 

O 25 Pckl! - Fortf CG. 

• -Aft C.6. 
°36 1>o,v-PoreC.6. 
■ - A^t C.&. 
A 50 P»x-Fef«C6. 
A -Aft 66. 
O 7S P*y- For* C.6. 

• -AftC.G. 
V|ooP<«- FortfC.6. o.l 
▼ -AftC.G. 




^/(X '^ ^VkAD 



FIGURE 2. 1 Cruise Speed Longitudinal Short Period 
Frequency Requirements 



G 



100 



' I I I I I I I I I -T— r- 

Note: The boundaries for values of n/a greater 
than 100 are defined by straight-line extensions. 
The Level 3 boundary for n/oi less than 1.0 is «lso 
defined by a straight-line extension 



Mm. Control 5pgg^ 



O 25ftx-FofeC.&. 

• -Aft C.6. 

m -Arte. 6. 

A 50 Pbiy- Pore C.6. 

▲ -A/t C.^. 

O 75 ?*-Y-ForeC.Q>. 

• -/l-ftC.G. 

V /C>oP«X- FoffC.s. Q , 
▼ -MiC.G. 




(raiDseO 



Note: ?or Class I,II-C, and IV airplanes, 
oijigp shall alv;ays be greater than 0.6 

radians per second for Level 3 



\.0 



JO 



"/qc~ «Vrad 



\00 



FIGURE 2.2 Mln. Control Speed Longitudinal Short Period 
Frequency Requirements 



ORIGIN.AiL' PAGE IS 
OE POOR QUALITX 



-7 



TABLE 2.2 Longitudinal and Lateral -Directional 
Handling Qua 1 ities 



LEVEL OF FLYING QUftLlTIES 



Airplane 


Flight 


Cond i t i ort 




?sp \ }d 






C.G. 


LocAt ion 


»P 


D 












Leve 1 S^t i sf i ed 






fwd 


& 


cruise 






1 


&5 


• ft 


e 


cruise 






1 




fwd 


9 


Vmc 






2 




• ft 


9 


Vmc 






1 




fwd 


9 


cruise 






] 


.3£ 


• ft 


9 


cruise 






1 




fwd 


9 


Vmc 






1 




• ft 


9 


Vmc 






1 




fwd 


9 


cruise 






1 


50 


• ft 


9 


cruise 


a 




1 




fwd 


9 


Vmc 






1 




• ft 


9 


Vmc 


a 




1 




fwd 


9 


cruise 






S 


75 


•ft 


9 


cruise 






1 




fwd 


9 


Vmc 






a 




• ft 


9 


Vmc 






1 




fwd 


9 


cruise 






a 


lOO 


• ft 


9 


cruise 






t 




fwd 


9 


Vmc 






a 




• ft 


9 


Vmc 






1 



8 



Using the analysis presented in Appendix A for the 

longitudinal dynamics, a trade study was performed to observe 

the effects changing the design short period frequency had on 

required elevator area. The graphical results of this study 

are presented for the critical forward C.G. locations for all 

airplanes in the family in Figure 2.3. It can be seen that as 

the OJ n is raised to high levels, the required elevator area 
sp 

to cause the airplane to react with the desired quickness 

increased sharply for the most critical airplane. As the **^n 

sp 

was lowered to very slow response characteristics, the 

elevator area required once again began to increase as this 

control power was required to make the airplane react more 

sluggishly than its inherent short period frequency. While it 

is obvious that the minimum required elevator area occurs in 

the region of It/n = 1.5 rad/sec, this could not be chosen as 

sp 

a design point. This is because the critical maximum ^n 

" ^ spmin 

for all of the airplanes is at 1.75 rad/sec for the 75 Pax 

airplane Aft C.G. at cruise speed. In order to have qualities 

that exceeded the minimum Class 1 handling requirements by a 

reasonable margin, a design point of Un = 1.85 rad/sec and 

sp 

"X = 0.5 was chosen. The location of this design point in 
rsp 

relation to the open loop characteristics is shown on the root 
loci in Figures 2.4 and 2.5. 

From the spreadsheet analysis presented in Appendix A, 
this design point resulted in minimum gain and SSSA elevator 
surface area size requirements for the longitudinal SSSA 

system (Table 2.3). 



oid'jiHi-^ Page is 

OE EOOR QUAL,lT3a 



-a(H 



Mo- 
r- 



tal 



i. .-tt -^ 



xr 



k 






D iSPdX - Fore C6 For All Airflfcives 

D3fcPaY 

ASOftxX 



-aicsijti U^s L«5 rai/ittr 



:;kj 



- — H»- 




HftJ 



CriniSft 5p«t4 
-£le(«t»rj»rea ! 



^hbrtPcnod ^retuency/^s^'vi^a((/5ec 



l)MI Arflanes CrjticaJ for LFori Cia. .. 
And MiK Control I^eei j iOw* 2/ f/^ 



::-■_■;_:—■ ) 


- .-r:-;!:! 




.-1^1 






■| ;:r. 



D.Henslcy 



5-0^-87 



r— 1 

FIGURE 2.3 Required Elevator Area Variation 
due to Short Period Frequency 



/O 



ORIGINAL PAGE IS 
OF fOOR QUALITX 




D. Hen$ley 



H-TS-Br 



FIGURE 2.4 Cruise Speed Longitudinal 
Short Period Root Locus 



// 



ORIGINAL PAGE IS 
£aB;;»QQ]^ QUALITY 




D,H«r\sleY 



CHECK 



H-Z8^7 



I .- I I 

FIGURE 2.5 Min. Control Speed Longitudinal 

Short Period Root Locus 



/^- 



TABLE 2.3 Longitudinal SSSA Requirements 
for Critical Conditions 

Design ^'n = 1.85 rad/sec 
sp 

Design 7, = 0.5 
7sp 

Critical Conditions: Min. Control Speed, o- = 21 fps 

w 

25 Pax 36 Pax 50 Pax 75 Pax 100 Pax 

Fore Aft Fore Aft Fore Aft Fore Aft Fore Aft 

Ko! -.314 -.261 -.179 -.071 .642 .312 -.263 -.386 -.225 -.407 

Kq -.146 -.180 .189 .094 .923 .136 -.105 -.370 .039 -.317 
Percent S required: 

12.7 1.8 16,8 8.9 28.4 13.9 4.2 -8.6 9.0 -2.8 



The critical requirements occurred for the 50 Pax - Fore 
C.G. which required 28.4 percent of the elevator to be 
designated for SSSA. This was rounded to 30 percent which 
resulted in each airplane being able to safely compensate for 
the following gust conditions at the Min. Control Speed. 

TABLE 2.4 Longitudinal SSSA Gust Performance 

SSSA S^ = 30 Percent or 12.6 ft2 - 25, 36, 50 Pax 

43 ft 2 - 75, loO Pax 

25 Pax 36 Pax 50 Pax 75 Pax 100 Pax 

Fore Aft Fore Aft Fore Aft Fwe Aft Fore Aft 

Gust Speed (fps), 

f^ 49.5 345.3 37.4 70.7 22.2 45.3 149.2 -73.4 69.8 -221.9 

Typical gain schedules for the critical airplane - 50 Pax 
- Fore C.G. are presented for K« in Figure 2.6 and Kq in 
Figure 2.7. 



13 



IS T 



50 Pax- Fert C.6. 
Mm. Conirol SpefiJ 




SAS-bmH- 



5 /o 

FIGURE 2.6 Typical K ti Gain Schedule for 
Longitudinal Dynamics 

.ZOr 



.13 '■ 






« 



? 



CI 



JOS" 




SAS-liijirf 



S lO 15 

E/evqfor D«flex+<op,^F ^de^. 

I CURE 2.7 Typical Kq Gain Schedule for 

Longitudinal Dynamics 



/</ 



2.2 Lateral -Directional Open and Closed Loop Dynamics 

The lateral directional open loop dynamics for the Family 
of Commuter Airplanes are presented for forward and aft C.G. 
at cruise and min. control speed in Figures 2.8 and 2.9. From 
these figures, and from Table 2.2, it is obvious that all of 
the airplanes - in their basic state - meet the Level 1 
Latera 1 -Directional handling requirements except for the 75 
and 100 Pax - Fore C.G. at both cruise and min. control speed. 

Due to the indirect manner in which the augmentation 
system affects the lateral directional Dutch roll frequency 
and Dutch roll damping, and because of the extensive 
interaction that occurs in this mode, it was decided to drive 
each airplane to a common Dutch roll damping and to let the 
Dutch roll frequency "fall-out" of the calculations. Using 
the spreadsheet methodology presented in Appendix B, basic 
calculations revealed that the minimum acceptable "^ that 
resulted in Class I handling qualities for all airplanes in 
all flight conditions was "X = 0.27. A conservative, but more 
realistic figure of "% = 0.29 was chosen as the design goal. 

The resulting handling qualities are shown in Figures 2.8 
and 2.9. The spreadsheet analysis also resulted in the 
minimum gain and SSSA rudder control surface area requirements 
for the Latera 1 -Directlona 1 SSSA system presented in 
Table 2.5. 



15 



>[Ai; FACE n 

OF POOR QUAUXSa 



s^.: 



"""::. :l 



De3«gn?ps-2S 








D .25 ftjx -Fore C.6. 

• -Aff C6. 

D 36 Pax -Fore U. 
■ -Aft-CGu 

ASOPaX -ForeCt. 

Ji -Af+Ct. 

75fl»< -ForeCfr. 

♦ -AH-C.6. 
■^|OOP«KK-ftreC.Gu 

▼ ■ ' rAffCfi. ■ 
-^Jesign BmaH Mariliea by Ftags. 



Ci ftd/sec. 



— I— 

•a* 






CALC 



P Mens>e> 



•1-21-87 



FIGURE 2.8 Cruise Speed Latera 1 -Directiona 1 
Root Locus 






UNIVERSITY OF KANSAS 



V^ 



m 



L _- 



;;:;.:. ;:i,::in- 



ORTGINAU PAGE IS 
OF POOR QUAUXM 






Dts»3n?D'-^^ 



Sii::i;-?-!'^^ 






'^^t~^ 



D :: -*f+£.6. 

D 3fcfta -ForeCfe 
D -AftCA. 

^50PM-^r«C.6. 

il ; -WC.G. 

:0-7i'RM-foreC-5. 

O .. -AHJLb. 






.;bei»a'»^**i^**^*^- 



f D-indfeec. 



:B^ ;_ 



^ 




iiReatiAxis 




D.Henslcy 



ZZI 



FIGURE 2.9 Min. Control Speed 



Lateral -Directional Root Locu 
UNIVERSITY OF KANSAS 



/7 



TABLE 2.5 Lateral Directional SSSA Requirements 
for Critical Conditions 



Design % = 
'^D 



.29 



Critical Conditions: Min. Control Speed, ^ =21 fps 

25 Pax 36 Pax 50 Pax 75 Pax 100 Pax 

Fore Aft Fore Aft Fore Aft Fore Aft Fore Aft 

Kr .156 .179 .026 .052 -.074 .167 .218 .445 .021 .319 

Percent S„ required: 

15.4 24.0 28.2 15.7 20.4 

The critical requirements occurred for the 50 Pax which 
required 28.2 percent of the rudder to be designated for 
SSSA. This was rounded to 30 percent which resulted in each 
airplane being able to safely compensate for the following 
gust conditions at the min. control speed. 

TABLE 2.6 Latera 1 -Di rectiona 1 SSSA Gust Performance 

SSSA S = 30 percent or 18 ft2 - 25, 36, 50 Pax 

35.7 ft2 - 75, 100 Pax 

25 Pax 36 Pax 50 Pax 75 Pax 100 Pax 
Gust Speed ( fps) , 
a 40.8 26.2 22.3 40.2 30.8 

A typical gain schedule for the 50 Pax - Fore C.G. is 
presented in Figure 2.10. 



18 




SAi-Limf 



/O lo ZO 

Ruic/cr DA-f lection, ^n ** ^f3 



FIGURE 2.10 Typical Kr Gain Schedule for 
Lateral-Dlrectlonal Dynamics 



2.3 Roll Mode Dvnainieg 



The critical open loop dynamics in the Roll mode consists 
primarily of the roll time constant, T , and the time 
requirement to reach a minimum roll angle. These minimum 
Level I requirements are presented In Table 2.7. 



Table 2.7 Roll Mode Minimum Requirements 



Flight Condition 

Cruise 

Min. Control 



ILs (sec) 
1.4 
1.4 



t (sec) 

1.9 
1.8 



Phi (dee) 

45 
30 



19 



From the spreadsheet analysis of Appendix C, these valuer 
were calculated for each airplane at cruise and min. control 
speeds at fore and aft C.G. locations. The results of these 
calculations are presented in Table 2.8 

Table 2.8 Roll Mode Dynamics 

25 Pax 36 Pax 50 Pax 75 Pax 100 Pax 

Fore An Fore Aft Fore Aft Fore An Fore Aft 
Cruise: 

T ,(sec) .145 .221 .152 .267 .305 .157 .533 .299 .648 .349 

Phi,(de() 112.2 107.3 111.7 104.4 102.0 111.4 55.8 64.6 51.9 62.7 

P,(sec'S 1.12 1.12 1,12 1.11 1.11 1.12 0.68 0.70 0.67 0.70 

P.dot,(sec'S 2E-5 9E-4 3E-5 3E-3 7E-3 4E-5 3E-2 4E-3 5E-2 8E-3 

Hin. Control: 

T ,(sec) .223 .341 .234 .411 . .470 .243 .838 .470 1.018 .549 

K 

Phi,(de{) 60.7 56.2 60.3 53.6 51.6 59.9 34.9 44.1 31.4 41.8 
P,($ec'S .67 .67 .67 .66 .65 .67 .50 .56 .47 .55 
P.dot,(sec"^) 9E-4 lE-2 lE-3 2E-2 3E-2 lE-3 8E-2 2E-2 9E-2 4E-2 

It is apparent that within each group of airplanes with 
the same planform - single body and twin body - that these 

critical characteristics are inherently very similar. For the 
following reasons: 

1) The similarity of the open-loop dynamics within each 
group of common planform. 

2) The magnitude by which the family inherently exceeded 
the Level 1 minimum requirements. 

3) That the perception of the pilots in the twin-bodies 
would be unpredictably affected in the roll-mode due 
to their location away from the axis of rotation. 

it was decided that a roll-damper SAS would not be used in 
this Family of Commuter Airplanes. 



20 



3. REQUIREMENTS OF SYSTEM IMPLEMENTATION 

The purpose of this Section is to present the physical 
and technology requirements for implementing a Separate 
Surface Stability Augmentation System. A typical arrangement 
and block diagrams for the control systems will then be 
presented. 



3.1 Separate Surface Control Surface Requirements 

The surface areas required for the SSSA control surfaces 
in the Longitudinal, Latera 1 -Direct ional and the Roll modes 
can be summarized from Sections 2.1, 2.2, and 2.3 of the 
report as: 

TABLE 3.1 Summary of Control Surface Requirements 

Longitudinal Lateral-Directional Roll 

Elevator Area Rudder Area Aileron Area 

SSSA Percent of 

Prinary Surface 30 30 N/A 

25,36,50 Pax (ftj) 12.6 18 ' N/A 

75, 100 Pax (ft2) 43 35.7 N/A 

(Twin Bodies) 

As explained earlier in this report, the design goal of 
commonality being the primary design driver rather than 
individual optimization for each airplane is the reason a 
common control surface size was chosen for each airplane. The 
selected surfaces that will be controlled by the SSSA system 
for each airplane are represented in Figures 3.1, 3.2, and 
3.3. A note for Figure 3.2, the surface areas indicated on 
the aileron or the spoiler are suggested locations that could 

21 





FIGURE 3. i Required Surf 

Longitudinal Dynamics 



PI 



•Sii 



SI 




:i.z 



ORIGINAE PAGE IS 
OE POOR QUALITY 



'J' 




FIGURE 3.2 



O 

O 







Required Surface Area for 
Lateral -Directional Dynamics 



FIGURE 3.3 Suggested Surface Areas for 
Roll-Mode Dynamics 



23 



be retro-fitted as SSSA control surfaces if pilot perceptionfe 
indicate that such a system would be required to achieve 
greater common handling characteristics in the Roll mode. 



3.2 Technology Requirements 

In order to meet the goal of maximizing commonality 
throughout the Family of Commuter Airplanes, it was crucial 
for the entire stability and handling qualities augmentation 
system to be similar. This ruled-out the use of mechanical or 
hydraulic linkages for this system as such linkages would 
require a system specifically tailored for the physical 
constraints of each airplane. According to Reference 9, a 
control system driven by electric signals avoids the 
complexity and individual design required by a fully 
mechanical or hydraulic system. It also avoids the non- 
recurring cost required by mechanical /hydraul ic systems for a 
Vehicle System Simulator (or "Iron Bird"). The result of 
using a system driven by electric signals is a decrease in the 
design and development costs as well as the installation and 
testing costs for the system. 

The ideal actuator to be used for this system, and that 
is available through current technology, would be 
e 1 ectrohydrostatic actuators <EHA's). As described in 
References 10 and 11, these actuators are driven by a 
localized hydraulic system pressurized by a high-power- ( rare 
earth) magnet electric motor. They can be activated by 
electric or light signals and are ideal for usage with the 
primary flight control system elements such as the elevators, 
ailerons and rudder. Figure 3.4 shows an example of an 
E 1 ectrohydrostatic actuator. 

Figures 3.5 and 3.6, courtesy of Reference 12, 
demonstrate additional characteristics of EHA's. Figure 3.5 
shows typical hinge moments, rates, horsepower, estimated 
weights and electrical bus power requirements for a control 

24 



Hydraulic 
Piston 



ORIGINAL PAGE IS 
m EOOR QUALITY 



Accumulator 



Rare Eartli 

Magnet 

Electric Electrical 

Motor Connector 



Hydraulic 
Pump and 
Manifold 



Hydraulic 
Cylinder 



Trunlon 
Support 




Position 
Sensor 



FIGURE 3. A Example E 1 ectrohydrostatic Actuator 



z^r 



•lAbLt. 1 
BUS SUMMARIES 



\CTUATOR & # 



.. AILERON 1 

-. AILERON 2 

I. AILERON 1 

I. AILERON 2 

.. SPOILER 1 

-. SPOILER 2 

.. SPOILER 3 

.. SPOILER 4 

i. SPOILER 9 

i. SPOILER 10 

I. SPOILER 11 

R.. SPOILER 12 

STABILIZER 1 

STABILIZER 2 

L ELEVATOR 1 

L. ELEVATOR 2 

L. ELEVATOR 3 

R. ELEVATOR 1 

R.. ELEVATOR 2 

R. ELEVATOR 3 

RUDDER 1 

RUDDER 2 

RUDDER 3 



CONNECTED ACTUATOR 
HORSEPOWER OUTPUT 



BUS LOCATION 



rotal Connected Bus H.P. 
Bus Power In kW. 
Est. Cont. Load kW 



.88 

3.70 
5.35 

5.35 
3.70 



2.48 



2.48 



1.99 



25.93 

26.77 

2.68 



HP - (RATE) (HM) x 60 
360 X 5252 

Pbus - HP X .746 - 1.033 x HP (kW) 
.85 X .85 



.88 
.88 

4.79 



4.79 
15.63 

2.48 

2.48 

1.99 



33.92 

35.02 

3.50 



.88 



6.28 
6.28 



15.63 



2.48 



2.48 



1.99 



36.02 

37.19 

3.72 



Max. 
Rate 



VS 



30 
30 
30 
30 

60 
60 
60 
60 

60 
60 
60 
60 

5 
5 

30 
30 
30 

30 
30 
30 

35 
35 
35 



Max Acrofiroi 

Act. H.M. tOg^MT 

FT - LBS. i,\% 



925 
925 
925 
925 

1945 
2516 
2812 
3300 

3300 
2812 
2516 
1945 

98500 
98500 

2600 
2600 
2600 

2600 
2600 
2600 

1790 
1790 
1790 



iS-'io 



20'i^ 



20'2 ^ 



AO-fcO 



Zo-iS" 



20 



-aC 



2o- * S 



FIGURE 3.5. Performance Character! st i 



cs 



of Typical EHA ' s 



0705S/0 



ro e. T w c^^ 

2- STAB Tfiinrx is e.k>»a, 
C C>OTft.0ttIS t_ UJT 






OF FOO?. QUALITY 



ACTUATOR ASSEMBLY WEIGHT VS. SWEPT VOLUME 

DOT IS SECONDARY ACTUATOR 

• CROSS IS FLIGHT CONTROL 

O ALUMINUM ACTUATOR 

A ALUMINUM TANDEM ACTUATOR 

STEEL ACTUATOR 

D STEEL TANDEM ACTUATOR 




§ 



o 



• < ttrttt* 

10 100 

S WEPT VOLUME! I N3) 

FIGURE 3.6 EHA Weight to Swept-Volume Comparison FIGURE 115 



system for a similar airplane. Figure 3.6 shows a comparison 

of the weight of an EHA as a function of swept volume with 

conventional hydraulic actuators. While this figure indicated 

3 
11.5 lbs for a 95 in swept volume - appears to be high 

compared to conventional hydraulic actuators, each EHA is a 

self-contained unit and their use will save weight on the 

overall system by eliminating the need for a central hydraulic 

system and long runs of redundant high-pressure tubing 

required by conventional hydraulic systems. 

The system will also require typical controllers driven 
by electric signals. As stated previously in Section 1.2 of 
this report, simple adjustments in the gain requirements for 
these controllers can be used to tailor the handing qualities 
of each airplane to achieve the desired goal of common Level I 
handling characteristics. 

The requirements for the stick force gain box, previously 
mentioned in Section 1.3 of this report, to achieve common 
stick force gradients for the primary control surfaces are 
detailed in Reference 6. 



3.3 System Implementation 

As noted in Reference 12 and the characteristics 
presented in Figure 3.5, the performance of EHA' s is similar 
to standard hydraulic actuators. For this reason, the concern 
noted in Section 1.3 of this report concerning the possible 
need for an undue number of actuators driving the surfaces 
requiring greater control forces is apparently unfounded. 
Figure 3.7 demonstrates a typical physical arrangement of 
actuators, controllers and control surface areas f.or a 
horizontal tai 1 . 

Figures 3.8, 3.9 and 3.10 represent the block diagrams 
for the controllers. They are for an angle of attack 
controller, pitch damper and yaw damper respectively. 

28 







Conirol(e.rS 



FIGURE 3.7 Typical EHA and Controller Location 
For SSSA System 



2.9 



D Upvi^I^y s-ii-Q7 



0^co..-^^^y-> 




¥ 


F/«Va1-or 
Ac+u<rtor 


♦ 


% 










~ ■" 


i 




















oc-3en5or 























^At\^\e o? AHc\d<,c< 



Where k, Followi TAe Gam 5cHedi;l«f d(2p<c+«J ivt Fi^yor 2. 6 



FIGURE 3.6 SSSA Angle of Attack Compensator 



/COmm 



^«H 



K, 



liSSA 



E I e>/Oi for 
Ac+i;<»+-or 




Sensor 



^ PiK,V^ ftetfc , ^ 



Whef€ k^^^^^ PolloiaS fK£ G<»>n ScXcdJ^ <i«fiCMd (k, F.jyre 2.7 



FIGURE 3.9 SSSA Pitch Damper 



Connn " 



^^ 



'sSSA 



EI&vc^¥or 
AcfuQtor 






Yaw R^he 
5ensor 



^ VfllV «qf£j r 



WKc<-« K. Fol/oiu5 He Gam 5c>id«lole d«pic+«J in P/jur^. 2./0 
^SSSA 



FIGURE 3. 10 SSSA Yaw Damper 



20 



4. CONCLUSIONS AND RECOMMENDATIONS 

The purpose of this report was to present the results of 

a design study for implementing a flight controller and 

achieving handling quality commonality by Separate Surface 

Stability Augmentation for a Family of Commuter Airplanes. 
Stabil ity 

4. i Conclusions 

Stability augmentation by independently controlled 
surfaces is a feasible manner to achieve Level I handling 
qualities and to tailor the performance of each airplane to 
achieve common handling qualities throughout the Family of 
Commuter Airplanes. It was also demonstrated that this system 
was robust, for the most critical airplane and flight 
condition it can safely handle gusts up to thunderstorm 
intensity. 

This form of stability and performance augmentation is a 
unique method to achieve commonality on a system and personnel 
level throughout the Family. Variations of the gain schedule 
allows for the use of common control surface sizes and common 
handling qualities allows for cross-certification of flight 

crews throughout the Family of Airplane. Acquisition and 
design costs are decreased due to the design flexibility 

allowed by a system driven by electric signals. These costs 
are further decreased due to the use of E 1 ectrohydrostatlc 
actuators, which eliminate the need for a central hydraulics 
system and the complex tubing a central hydraulics system 
would require. Maintenance costs are also decreased as each 
surface is driven by a common actuator that is a self- 
contained unit. 



31 



4.2 Recommendations 

While this designer believes that the results and 
conclusions reached through this study generally indicated the 
feasibility and advantages that use of a Separate Surface 
Stability Augmentation system could gain in terms of system, 
personnel and . handling quality commonality, some 
recommendations for future consideration are in order. 

1) A detailed analysis of the control forces required to 
drive the larger control surfaces would be required 
to ascertain whether these surfaces would need a 
disproportionate number of EHA's. 

2) Tests would be needed to ensure that the primary 
control surfaces have enough control power to 
maintain acceptable handling qualities in the event 
of a hard-over system failure in any of the modes 
augmented. 

3) A more detailed analysis could be done to augment for 
a common Dutch-roll frequency in addition to the 
common Dutch-roll damping achieved in this study. 

4) A more advanced study using all six degrees of 

freedom rather than the approximations used in this 

study would provide definitive conclusions concerning 

the feasibility and advantages of using this form of 
stability augmentation and handling characteristics 

tai 1 or ing. 

5) Pilot reactions to the roll mode will be needed to 
determine if a roll damper will be required to drive 
these characteristics to a closer level of 
commonality. In particular, the pilot's perception 
of the differences in Lateral acceleration in the 
roll mode between the single body airplanes and the 
twin-body airplanes will be required. 



32 



5. REFERENCES 

1) University of Kansas, AE 790 Design Team; Class I Designs 
of a Family of Commuter Airplanes ; University of Kansas, 
1986. 

2) University of Kansas, AE 790 Design Team; A Class I I 
Weight Assessment for the Implementation of Commonality 
and Preliminary Structural Designs for the Family of 
Commuter Airplanes ; University of Kansas, 1987. 

3) Haddad, R. and Russell, M. , University of Kansas, AE 790 
Design Team; Presentation of Structural Component Designs 
for the Family of Commuter Airplanes ; University of 
Kansas, 1987. 

4) Morgan, L.K., University of Kansas, AE 790 Design Team; A 
Cost Analysis for the Implementation of Commonality in 
the Family of Commuter Airplanes ; University of Kansas, 
April 1987. 

5) Swift, J., University of Kansas, AE 790 Design Team; An 
Advanced Propfan Study for the Family of -Commuter 
Ai rpl anes ; University of Kansas, May 1987. 

6) Creighton, T. and Hendrich, L. , University of Kansas, 
AE 790 Design Team; Class II Design Update for the Family 
of Commuter Airplanes ; University of Kansas, May 1987. 

7) Collins, D.J.; Status Reports Separate Surface Stability 
Augmentation Design and Development ; Flight Research 
Laboratory, University of Kansas, November 1973. 

8) Bolton, W.R. Jr. and Collins, D.J.; A Separate Surface 
Stability Augmentation System for a General Aviation 
Ai rpl ane ; University of Kansas, April 1974. 

9) Cronin, M.J., Heimbold, R.L. and Howison, W.W.; 
Application of Advanced Electric/Electronic Technology to 
Contentional Aircraft ; NASA Contractor Report, NAS9- 
15863; Lockheed Company, CA, July 1980. 

10) The Boeing 7J7 Program ; Informational Brochure, Received 
1986. 

33 



11) Roskam, Jan; Airplane Design. Part IV: Layout Design of 
Landing Gear and Systems ? Roskam Aviation and Engineering 
Corporation, Ottawa, Kansas, 1966. 

12) Woods, E.J. 5 Personal Communication by Letter; October 
1986. 

13) Roskam, Jan; Part I; Airplane Flight Dynamics and 

Automatic Fl ight Contro 1 s ; Roskam Aviation and 

Engineering Corporation, Ottawa, Kansas, 1979. 

14) Roskam, Jan; Part II: Airplane Flight Dynamics and 

Automatic Fl i ght Contro 1 s ; Roskam Aviation and 

Engineering Corporation, Ottawa, Kansas, 1979. 

15) Roskam, Jan; Methods for Estimating Stability and Control 
Derivatives of Conventional Subsonic Airplanes ; Roskam 
Aviation and Engineering Corporation, Ottawa, Kansas, 
1983. 



34 



APPENDIX A: SEPARATE SURFACE CALCULATIONS 
FOR LONGITUDINAL DYNAMICS 

The purpose of this Appendix is to present a summary of 
the method and results used to determine the elevator area and 
gain requirements for a SSSA system to achieve the commonality 
design goals. 

A. 1 Angle of Attack and Pitch Rate Gain Requirements 

From Section 6.2.3 of Reference 13, the 2-Dimens ional 
short period approximation was found to bes 

Un = Zk Mq / Ul - M« (A.l) 

sp ^ 

?sp " "^""^ * Z«/U1 + Mk) / 2Ungp (A. 2) 

Where M« is the dominant term for short period frequency and 
Mq is the dominant term for short period damping. 

From Table 6.3 of Reference 13, 

_ _ -2 

M« = q S c Cm « / lyy (sec ) (A. 3) 

Mq = "q S C2 Cmq / 2 lyy Ul (sec" ) (A. 4) 

The relationships for angle of attack and pitch rate gains 
were found in Reference 13 to be: 

K« = ACm« / Cm 6E (A. 5) 

Kq = (^Cmq / Cm6E) c/2Ul (A. 6) 

where Cm « was determined as: 

ACttiK. =CZo(Mq/Ul - (AUJn„„) 23 / (q S c/ I yy ) (A. 7) 

des ^ sp ^ 

where AltVi =Wn . - ^n . . 
sp spdes spbasic 

and 

ACmq_, =-[2IyyUl/q S c2D(2l>!n >&? „ + Z «/Ul + M «) (A. 8) 

des sp /sp 

where A~l =7 . "'? ^ j 
7sp rspdes /spbasic 

The inter-related nature of Un and '^ when either is 

sp I sp 

modified was ignored for simplicity of the model. 

These gains were calculated based upon the normal control 
surface sizes and must be multiplied to account for the ratio 
of Separate Surface sizes to the primary control surface 
sizes. 

35 



A. 2 SSSA Longitudinal Surface Sizing Requirements 

The minimum required surface areas were determined for 
one percent probability and thunderstorm gusts. Using the 
VonKarman scales in Section 9.8.1 of Reference 14, the root- 
mean-square gust intensity and the resulting change in angle 
of attack due to gust perturbation were determined to be: 

TABLE A. 1 ; Longitudinal Gust and Perturbations 

Clear Air Thunderstorm 

Cruise Min. Control Crui se Mln. Contro 1 



or , (fps) 


4.6 


6.6 


21 


21 


« . , ( rad) 
gust* 


.0066 


.0316 


.0302 


. 1012 



« At 500 ft. altitude 

It is obvious that the critical flight condition that 
will size the surface required for the SSSA system is for a 
thunderstorm gust at min. control speed. The required 
elevator area was determined according to the method of 
balancing moments in the longitudinal axis as presented in 
Section 6.6.5 of Reference 13. 



Cm«A« g^ = Cm 5E ii 6E (A. 9) 

where: ASEmax = i 20 deg. 

Cm (X = Cm«w^^.^ + Cm«j„_ 
oasic des 

From Reference 13, Section 4.1.4, the relationship of the 
elevator to the affected horizontal tail area was determined 
to be : 

CmSE = -CL(xH n^ Sh/S (Xach - Xcg) Z^ (A. 10) 

From this, it is obvious that the percentage of required 
elevator area that must be dedicated to SSSA is: 

Percent S^ = -( Cm SE ) (Sh/S ) / [ (Xach-Xcg ) (CL oH) (Hu.) (t ,) ] (A. 11) 
E req H t 

where: Cm SE = Cm «< A « ^/ASE) 
req gust *^ 

36 



For a chosen elevator size for the SSSA control surface', 
the maximum gust intensity that the system can overcome was 
found as: 

'^wMax"^^^^^^"'^''''^^""'req^ ( -CL «H)rij^(Sh/S) (XacH-Xcg )'t^ (A. 21) 
From these relationships, a spreadsheet analysis was 

defined to show simultaneously the effect of design choices on 

the requirements for all of the airplanes. This facilitated 

the trade study shown in Section 2.1 of this report, from 

which the design point was chosen. A sample spreadsheet is 

presented for the design point at the critical min. control 

speed in Table A. 2. 



37 



! TABLE 


A. 2 


Sample Spr 


eadsheet for 


Longitudlna 


1 Dynamics 


^^Ul 


HIN. CONTROL 
Bust=21 fps 


25-Fore 


25-Aft 


36-Fore 


36-Art 


50-Fore 


50-Aft 


75-fore 


75-Att 


lOO-Fore 


100-flft 






















Z-alpha 


-223.3370 


-236.3080 


-182.1430 


-193.3620 


-128.0730 


-212.6880 


-179.7080 


-286.4610 


-148. 290-^ 


-243.5^080 


n-q 


-.8800 


-.3750 


-.6130 


-.6430 


-.4810 


-.5330 


-1.1390 


-1.2420 


-1.0560 


-1.1600 


i>-i 


207.5000 


207.5000 


207.5(XiO 


207.5000 


201, 2(M 


207.5000 


207.5000 


207.5000 


207.5000 


207. :«0 


'4n.sp.des 


1.S500 


1.8500 


1.3500 


1,3500 


1.3500 


1.3500 


l.S5<*) 


1.3500 


l.S5(* 


1.35^) 


Mn.sp. basic 


1.7920 


lAlZO 


1,3960 


1.1720 


.3300 


.8740 


1.5890 


1.4400 


1.4540 


1.5390 


D.Hn.sp 


.0580 


.4370 


.4540 


.6730 


1.0200 


.9760 


.2610 


.4100 


.3560 


.3110 


q.bar 


51.1700 


51.17CO 


51.1700 


51.1700 


51.1700 


51.1700 


51.1700 


51.1700 


51.1700 


51. 170(1 


Sh 


120.0000 


120.0000 


120.0000 


120.0000 


120.0000 


120.0000 


410.0000 


410.CKX)0 


410.i5(XiO 


410.0000 


S 


592.'0000 


592.0000 


592,0000 


592,0000 


592,0000 


552.0000 


1182.0000 


1132.00C0 


llffi.OOOO 


1132.0000 


C-bar 


7.4500 


7.4500 


7 Am 


7.4500 


7.4500 


7.4500 


S.9700 


8.7700 


8.9700 


3.9700 


lyy 130433.0000 122535.'D0O0 ; 


235569.0000 : 


J09114.00C'C 465510.0000 408670.0000 505579.0000 44C9S8.0000 771875.0000 655374,0000 


Ca.dE. avail 


-1.7360 


-1,6730 


-1.9400 


-I.S820 


-2,3890 


-2.3570 


-3.4150 


-3.2600 


-3.9740 


-3.8410 


n. alpha. dot 


-.2030 


-.2020 


-.1400 


-.1490 


-.1080 


-.1200 


-.2310 


-.2410 


-.2030 


-.2240 


Cfl.a. basic 


-1.3080 


-.5430 


-1.4720 


-.7120 


-.3080 


-.3950 


-1.3940 


-.2920 


-2.1310 


-1.1380 



OP Pr.:-}^ PAGE /o 
DUALITY 



d.Ca.a.des 
K-a 

d.Ca.a.req 

Zeta.sp.des 
Zeta.sp.res 
D.Zeta.sp 



.5455 
-.3142 



.4374 
-.2607 



.3465 
-.1736 



.1.336 
-.0710 



-1.5337 
.6420 



-.7357 
.3121 



.3968 
.2626 



1.2571 

-.3^6 



.0934 
-.2248 



.5000 
.3599 
.1401 



-.1056 

.5000 
.3693 
.1307 



-1.1255 

.5000 
.2718 
.2282 



-.5734 

.5000 
.2^1 
.2119 



-2.3417 

.5000 
'.2010 

.2990 



-1.1307 

.5000 
.2797 
.2203 



.4972 

.5000 
.3810 
.1190 



.9651 -1.2376 



.5000 
.4773 
.0227 



.5000 
.3239 
.1711 



1.5641 
-.4072 



.3761 

.5000 
.4306 
.0694 



D.Caq.des 



14.1246 
-.1461 



16.8356 
-.1801 



-20.4325 

.1391 



-9.3346 
.0938 



-122.3050 
.9228 



-17.3339 
.1358 



16.5285 
-.1046 



55.3575 
-.3703 



-7.1714 
.0390 



56.2381 
-.3163 



3ust Speed 

D.a.s'jst-rad 
D.de.iea»-deg 
D.a3/dE.!iiax 



Kach.bar 
i(cg.bar 
Xach-XcgBar 
d. alpha. H 
Tau.E 



21.0000 

.1012 

20.0000 

.2899 



D.Di.dE.req -.2210 



4.1500 

.1450 

4,0«)50 

3.9610 

.5400 



21.00CO 

.1012 

20,OOC!0 

.2899 

-.0306 

4.1500 

.2800 

3.3700 

3.9610 

.5400 



21.0000 

.1012 

20.0000 

.2399 

-.3263 

4.6760 

.2010 

4.4750 

3.5610 

.54*50 



2i.0O(X) 
.1012 

20.CO00 
.2699 

-.1677 

4.6760 

.3350 
4.3410 
3.9610 

,5400 



21.0'DCO 
.1012 

20.0000 
.2399 

-.6769 

6.0400 

.5300 
5.5100 
3.9610 



21.0000 
.1012 

20.'DOO0 
.2399 

-.3278 

6.0400 

.6030 

5.4370 

3,9610 

,5400 



.1012 

20.0000 
.2399 

-.1441 

4.2330 

.6020 

3.6310 

4.9530 

.5400 



21.0*X^ 
.1012 

20.'0000 
.2S99 

.2798 

4.2S30 

.7690 

3. 5140 

4.9530 

.5400 



21.0000 

.1012 

20.0000 
.2999 

4.942C' 

.6590 

4.2330 

4.9530 

,5400 



21.00ft) 

.1012 

20.0000 
.2999 

.1^D90 

4.9420 

.3'j20 

4. 1400 

4.553'C 

.54'0O 



D.Sh.req 
I Sh.rgq 



'^fi.isn in. 



2.1S34 20.1312 
1,3237 16. 3177 



34,1013 16.6868 17.3003 -33.1335 
23.4132 13.7057 4.2156 -S.5326 



-■■' w- ..'v 



Psrcent - Bh 30.0000 30.^S0C 30.0CCO 30.0000 :O.0m 
3h - m 36.0000 36.0000 36.0000 36.^:'000 36.'}C00 



30,0000 
36.0000 



JJ , vWv 

123.0000 123. «*0 



30.0000 30.0000 



l:",Ou;i'i 



Sust - Wi.j 



49.4343 



2642 37,4536 70,7076 



:.<=: ■■JtJi 



22, 1679 



2:i,?0'4 



28 



APPENDIX B; SSSA CALCULATIONS FOR 

LATERAL-DIRECTIONAL DYNAMICS 

The purpose of this Appendix is to present a summary of 
the method and results used to determine the rudder area and 
gain requirements for a SSSA system to achieve the commonality 
design goals. 

B.l Yaw Rate Gain Requirements 

From Section 6.3.5 of Reference 13, the Dutch Roll 
approximation for Lateral -Directional dynamic stability was 
found to be: 

^r\^ = Vl/Ul (YpNr + NpUl - NpYr)' (B.l) 

■^P = -l/2Wnp (Nr + Y pui ) (B.2) 

Because of the inter-related nature of the Dutch roll damping 
and frequency and the rather common usage of yaw rate sensors, 
it was decided to choose a design damping ratio and to allow 
the Dutch roll frequency to result from the nature of the 
equations. 

With the yaw rate as the measured quantity, its 
relationship to Dutch roll damping and frequency through the 
dimensional derivative, Nr, was found in Table 6.8 of 
Reference 13 to he'- 

Nr = q S b2 cnr / 2 Izz Ul (B.3) 

The relationship for the yaw rate gain was found in Reference 
13 to be: 

Kr = (ACnr / CngR) (b / 2 Ul) (B.4) 

where: LCnt = -2 Izz Ul/q S b2(2UnpA^jj + Y^/U1) (B.5) 

where: A^^^ = Redesign " "^Dbasic 
This gain was calculated based upon the normal control surface 
sizes and must be multiplied to account for the ratio of the 
Separate Surface size to the primary control surface size. 



39 



The change in the dimensional derivative, Nr, required a 
recalculation of the resulting Dutch roll frequency by 
Equation (B.l). The relationships of _, n_ and j. n_ were 
then checked to insure all airplanes met Level 1 handling 
requirements at all flight conditions and C.G. locations for 
the chosen design point. 

B.2 SSSA Lateral-Directional Surface Sizing Requirements 

The minimum required surface area for the rudder was 
determined for one percent probability and thunderstorm 
gusts. Using the VonKarman scales of Section 9.8.1 of 
Reference 14, the root-mean-square gust intensity and the 
resulting change In sideslip due to gust perturbation was 
found to be: 

TABLE B. 1 Latera 1 -Directlona 1 Gusts and Perturbations 

Clear Air Thunderstorm 

Cruise Min. Control Cruise Min. Contro 1 



(T^, (fps) 


A. 6 


8.71 


21 


21 


^gust'^^-^^ 


.0066 


.0419 


.0302 


.1012 



* at 500 ft. altitude 

It is obvious that the critical flight condition that 
will size the surface required for the SSSA system is for a 
thunderstorm gust at min. control speed. The required rudder 
area was determined according to the method of balancing 
moments in the Latera 1 -directional axis. 

"""^ ^^gust = ^"SJ^^SRmax '^'^' 

or 

Cn SR = Cn p ( A e . / A 6R ) 
'^ ^gust max 

where: A SR = i 40 dee 

max ^ 



40 



From Reference 15, Sections 12.1 and 12.3, the relationship o'f 
the rudder to the affected vertical tail area was determined 
to be: 

CnsR = -(CySR, . /Sv, . )ASv (Lvcos w+Zvs in «/b ) (B.7) 
basic basic 

From this it is obvious that the percentage of the required 
rudder area that must be dedicated to SSSA is: 



% SR=(-l/Cy6R ) (b/Lvcos «+Zvsin«) (CnpAp */ASR„ ) (B.8) 
basic gust max 

For a chosen rudder size for the SSSA control surface, the 
maximum gust intensity that the system can overcome was found 
as: (B.9) 

^.m^v^^^^^^'^mov/^^P^ (-CySRK= = ,-^/Svw^„.^) (Sv) (Lvcos «+Zvsin«/b) 
vmax max basic oasic 

From these relationships, a spreadsheet analysis was 
defined to show simultaneously the effect of design choices on 
the requirements for all of the airplanes. A sample 
spreadsheet is presented for the design point at the critical 
min. control speed in Table B.2. 



41 



TABLE B.2 



ORIGMAE P7:GS 15 
OF POOR QUALITY 

Sample Spreadsheet for Lateral -Directional Dynamics 



NIN.C{MTRaL 
Lat-Direct 
U-l 
S 
Sv 
b 

Vbar 
Alpha (deg) 
Lvilv, Alpha 
Meight 
■ 
Izz 



25 -Fore 25 - Aft 36 - Fore 36 - Aft 50 - Fort 50 - Aft 75 - Fort 75 - Aft 100 -For* 100 -Aft 



207.5000 

592.0000 

170.0000 

84.3000 

51.1700 

9.0000 

23.9500 

24739.0000 

768.2919 

177066.0000 



207.5000 

592.0000 

170.0000 

84.3000 

51.1700 

9.0000 

23.9500 

23381.0000 

726.1180 

180634.0000 



207.5000 

592.0000 

170.0000 

64.3000 

51.1700 

9.0000 

28.3900 

30334.0000 

942.0497 

284424.0000 



207.5000 

592.0000 

170.0000 

84.3000 

51.1700 

9.0000 

2B.3900 

28574.0000 

887.3913 

310361.0000 



207.5000 

^.0000 

170.0000 

84.3000 

51.1700 

9.0000 

37.4700 

43141.0000 

1339.7826 

580046.0000 



207.5000 

592.0000 

170.0000 

84.3000 

51.1700 

9.0000 

37.4700 

25978.0000 

806.7702 

457113.0000 



207.5000 

1182.0000 

340.0000 

132.5000 

51.1700 

9.0000 

26.8600 

71419.0000 

2217.9814 

1779161.0000 



207.5000 

1182.0000 

340.0000 

132.5000 

51.1700 

9.0000 

26.8600 

44804.0000 

1391.4286 

1124871.0000 



207.5000 

1182.0000 

340.0000 

132.5000 

51.1700 

9.0000 

34.8200 

85044.0000 

2641.1180 

2328189.0000 



207.SD0O 

1182.0000 

340.0000 

132.5000 

51.1700 

9.0000 

34.8200 

50666.0000 

1573.4783 

1457506.0000 



N.B.basic 
N.r.basic 
¥.6.basic 
Y.r.basic 
Cn.B.basic 
Cn.r. basic 
Cy.dR. basic 
Cn.dR 



1.4120 

-.4480 

-48.5350 

4.3040 

.0980 

-.1530 

-.3240 

.0920 



1.3840 

-.4390 

-51.3540 

4.5540 

.0980 
-.1530 
-.3240 

.0920 



1.6230 

-.3910 

-39.5830 

4.1600 

.1810 
-.2150 
-.3240 

.1090 



1.4870 

-.3590 

-42.0210 

4.4160 

.1810 
-.2150 
-.3240 

.1090 



1.2310 

-.3340 

-27.8320 

3.8600 

.2800 
-.3740 
-.3240 

.1440 



1.5620 

-.4240 

-46.2200 

6.4100 

.2800 
-.3740 
-.3240 

.1440 



.3210 

-.1120 

-29.7260 

3.3430 

.0710 
-.0780 
-.3240 

.0660 



.5070 

-.1770 

-47.3850 

5.3290 

.0710 
-.0780 
-.3240 

.0660 



.4060 

-.1430 

-24.53» 

3.6080 

.1200 
-.1310 
-.3240 

.0650 



.6490 

-.2280 

-41.1780 

6.0670 

.1200 
-.1310 
-.3240 

.0850 



Zeta.0.basic .2790 

tt).D.basic 1.2200 

Zeta.D«lln.O .3404 

Basic Class One Qualities 

Zeta.D - lin yes 

Nh.O - tin yes 

ZetafHn.D-iin yes 



Zeta.0.des 
d.Zeta.D 
d.Cn.r 
N.r.result 



.2900 

.0110 

.0707 

-.2412 



.2840 
1.2090 

yes 
yes 
yes 

.2900 

.0060 

.0611 

-.2064 



.2260 

1.2900 

.2915 

yes 
yes 

yes 

.2900 

.0640 

.0141 

-.3665 



.2270 

1.2360 

.2806 

yes 
yes 

yes 

.2900 

.0630 

.0280 

-.3126 



.2090 

1.1190 

.2339 

yes 

yes 
yes 

.2900 

.0810 

-.0527 

-.3816 



.2550 

1.2680 

.3233 

yes 
yes 

yes 

.2900 

.0350 

.1181 

-.2904 



.2220 
.5760 
.1279 

yes 

yes 
no 

.2900 

.0680 

.0451 

-.0473 



.2770 
.7310 
.2025 

yes 

yes 

yes 

.2900 
.0130 
.0920 
.0319 



.2030 
.6450 
.1309 

yes 

yes 
no 

.2900 

.0870 

.0055 

-.1380 



.2600 
.8220 
.2137 

yes 

yes 
yes 

.2900 

.0300 

.0849 

-.0808 



Kr 



.1561 



.1791 



.0262 



.0522 



-.0744 



.1666 



.2184 



.4452 



.0205 



.3191 



Zeta.D.des 


.2900 


.2900 


.2900 


.2900 


.2900 


.2900 


.2900 


.2900 


.2900 


.2900 


i*i.0.cc 


1.1996 


1.1852 


1.2886 


1.2323 


1.1222 


1.2564 


.5680 


.6976 


.6444 


.8038 


Zeta.!>iHn.D 


.3479 


.3437 


.3737 


.3574 


.3254 


.3643 


.1647 


.2023 


.1869 


.2331 


SAS - Class One Qualities 




















Zeta.D - ain 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


Hn.D - ain 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


Zeta<Nn.D-iin 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


Gust Response 






















Bust Speed 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


21.0000 


d.B-gust-rad 


.1012 


.1012 


.1012 


.1012 


.1012 


.1012 


.1012 


.1012 


.1012 


.1012 


D.dR.aax-deg 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


40.0000 


D.Sv.req 


26.2371 


26,2371 


40.8798 


40.8798 


47.9148 


47.9148 


53.2803 


53.2803 


69.4651 


69.4651 


Percent - Sv 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


30.0000 


Sv.aax 


51.0000 


51.0000 


51.0000 


51.0000 


51.0000 


51.0000 


102.0000 


102.0000 


102.0000 


102.0000 



Gust - lax 



40.8200 40.8200 26.1988 26.1988 22.3522 22.3522 



40.2025 



40.2025 



30.8356 



30.3356 



y^ 



APPENDIX a CALCULATIONS FOR ROLL MODE DYNAMICS 

The purpose of this Appendix is to present a summary of 
the method and results used to determine the aileron area and 
gain requirements for a SSSA system to achieve the commonality 
design goals. 

From Section 6.6.3 of Reference 13, the Rolling 
approximation was found to be: 

Tj^ = -1 / Lp (C. 1) 

And, 

Lpt 
Phi(t) = -LSA SA/Lp t + L SA 6A/Lp2 (e - 1) (C.2) 

The roll rate and the roll acceleration were also 
calculated for all airplanes, and the lateral acceleration for 
the twin-bodies was determined. 

P(t) = -LSA SA/Lp (1 - e^"^^) (0.3) 

P.dot(t) = LJA 6A e ^ (C.4) 

and the lateral acceleration was: 

Lat.acc = (y ) CP. dot ( t ) ] (C.5) 

where y = fuselage distance from Centerline 

y = 289 in. 
Due to the nearness of the grouping of time constants and 

roll rates within each group of similar planform, and the 

magnitude that these values exceeded the minimum Level I 

requirements, and augmentation system was not designed for the 

Ro 1 1 mode. 

These calculations were made in a spreadsheet analysis. 

A sample spreadsheet demonstrating Level I requirements is 

demonstrated in Table C.l. 



43 



TABLE C. 1 Sample Spreadsheet for Roll Mode Dynamics 

ROLL nODE 

CRUISE » 25-fore 25-A« 36-Fore Zb-Mt 50-fore SOHift 75-Fore 75-A« 100-Fore 100-A^t 




-i.9196 -4.5205 -6.5766 -3.7529 -3.2809 -6.3444 -1.8765 -3.3*09 -1.5435 -2.9611 

88.4574 57.788 84.0728 47.976 41.9419 81.1047 15.1456 26.9658 12.4659 23.1075 

5SSSS5555S 

1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 

112.2070 107.3068 111.7255 104.4271 102.0010 111.3701 55.7787 64.6199 51.9564 62.6734 

Level One yes yes yes yes yes yes yes yes yes yes 

P <rad/sec) 1.1155 1.1153 1.1155 1.1146 1.1133 1.1155 .6844 .7031 .6672 .7017 

P.dot .00002 .00094 .00003 .00335 .00718 .00004 .03738 .00412 .05793 .00878 

Lat Accel (ft/sec''2) .9003 .0992 1.3952 .2116 



APPROACH » 25-Fore 25-A« 36-Fore 36-Aft 50-Fore 50-Wt 75-fore 75-Aft 100-fore 100-Af t 



Lp 


-4.4867 


-2.9311 


-4.2643 


-2.4334 


-2.1274 


-4.1138 


-1.1936 


-2.125 


-.9816 


-1.8196 


L.da 


17.2738 


11.2847 


16.4176 


9.3687 


8.1903 


15.838 


2.6191 


4.6632 


2.1557 


3.996 


da (des) 


10 


10 


10 


10 


10 


10 


15 


15 


15 


15 


Tiee 


1.8 


1.8 


1.8 


1.8 


1.8 


1.8 


1.8 


1.8 


1.8 


1.8 


Phi (des) 


60.7218 


56.2320 


60.2759 


53.6773 


51.5947 


59.9465 


34.8871 


44.0978 


31.4499 


41.8732 


Level One 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


yes 


P <rad/sec) 


.6717 


.6685 


.6716 


.6635 


.6573 


.6715 


.5074 


.5619 


.4767 


.5532 


P.dot 


.00094 


.01007 


.00133 


.02048 


.03105 


.00168 


.07999 


.02663 


.09642 


.03955 



Lat Accel (ft/sec''2) 1.9263 .6414 2.3222 .9525 



OS £00R QUALITY 



9f