Subject: Aircraft Structure and Design هياآل و تصميم طائرة: الموضوع Weekly Hours : Theoretical :3 Units : 7 3: نظري : الساعات األسبوعية 7: الوحدات

Tutorial : 1 1: مناقشة Experimental : 1 1: عملي

Week Contents األسبوع المحتويات 1 Introduction 1 مةمقـد 2 Structure components \

Airworthiness /مكونات الهيكل سالمة الطيران

2

3 Wing structure type \ Fuselage design, configuration

/نوع هيكل الجناح الهيئة، تصميم الجذع

3

4 Definitions \ Fuselage design, configuration

/تعاريف ةالهيئ، تصميم الجذع

4

5 Aircraft structure alloys \ Wing design, configuration

/سبائك هيكل الطائرة الهيئة، تصميم الجناح

5

6 General engineering theory of bending

نظرية االنحناء الهندسية العامة

6

7 Wing design, configuration 7 الهيئة، تصميم الجناح 8 Approximations for thin-walled

sections\ Empennage design, configuration

/تقريب المقاطع ذات الجدار النحيف

الهيئة، تصميم الذنب

8

9 Structural idealization \ Empennage design, configuration

/المقطع ) تبسيط(أمثلة الهيئة، تصميم الذنب

9

10 General case of loading \ Undercarriage design, configuration

/الحالة العامة للتحميل الهيئة، تصميم العربة السفلى

10

11 Shear of open tube (constant wall thickness, no booms) \ Undercarriage design, configuration

سمك جدار ثابت (إجهاد القص للمقاطع المفتوحة /)بدون عقد الهيئة، ربة السفلى تصميم الع

11

12 Shear center for thin-walled open tubes without booms \ Undercarriage design, configuration

مرآز القص للمقاطع المفتوحة ذات الجدار /النحيف بدون عقد

الهيئة، تصميم العربة السفلى

12

13 Shear of open tube (constant wall thickness with booms) \ Preliminary weight analysis

سمك جدار ثابت (إجهاد القص للمقاطع المفتوحة /)مع العقد

التحليل االبتدائي للوزن

13

14 Shear center for thin-walled open tubes with booms \ Preliminary weight analysis

مرآز القص للمقاطع المفتوحة ذات الجدار /مع العقد النحيف

التحليل االبتدائي للوزن

14

15 Bredth-Batho formula for pure torsion \ Choice of engines

/ باثيو لاللتواء الصافي –صيغة بردث

اختيار المحرك

15

16 Shear in closed tubes 16 اجهاد القص للمقاطع المغلقة 17 Center of gravity 17 مرآز الثقل 18 Shear center for closed tubes \

Payload-range diagram /مرآز القص للمقاطع المغلقة النحيف مع العقد

الحمل– مخطط المدى 18

19 Span-Wise taper effect 19 تأثير االستدقاق على طول الجناح 20 Flight and gust envelope العصفة–مظروف الطيران

20

21 Angle of twist \ Wing and tail loads (for flight-gust envelope)

/زاوية االلتواء –مظروف الطيران ( أحمال الجناح و الذنب

)العصفة

21

22 Multi-cells multi-flanges wing sections

مقاطع الجناح متعددة الخاليا و متعددة الشفيرات 22

23 Air and inertia load distribution 23 توزيع أحمال الهواء و القصور الذاتي 24 Multi-cells multi-flanges wing

sections \ Drag estimation

/ مقاطع الجناح متعددة الخاليا و متعددة الشفيرات

تخمين الكبح

24

25 Shear center multi-cells multi-flanges wing sections \ Drag estimation

مرآز القص لمقطع الجناح متعددة الخاليا و /متعددة الشفيرات

تخمين الكبح

25

26 Bulkheads, wing ribs & Fuselage frames \ Drag estimation

أضالع الجناح و إطارات ، ) جدار(المقاطع /الجذع

تخمين الكبح

26

27 Fuselage frames (Direct stress distribution) \ Structural design and stress analysis

/توزيع االجهادات العمودية إلطارات الجذع

التصميم الهيكلي و تحليل االجهادات

27

28 Rib analysis 28 تحليل األضالع 29 Structural design and stress

analysis 29 التصميم الهيكلي و تحليل االجهادات

30 Fatigue, Fatigue failure and fail-safe design \ Structural design and stress analysis

/الفشل ألكللي و تصميم أمان الفشل ، الكلل

التصميم الهيكلي و تحليل االجهادات

30

):General Introduction(عاممدخل :تصميم و تطوير الطائرة .1-1

واع العوامل الرئيسية التالية المحفزة لتطوير إدراجيمكن ة أن ة الطائرات المختلف الموجودة في أوالجدي .الخدمة

:نمو حجم النقل الجوي - أ .انخفاض أجرة الرآوب .1 ).الخ...ة، الراحالسرعة(تحسين نوعية الطائرة .2 .اإلعمال و نمو دخل األفرادزيادة نشاط .3 .نمو سعة استيعاب الطائرة .4 .زيادة عدد الطيرات على خط الطيران الواحد، و زيادة عدد الخطوط .5 .االستخدام المتعاظم للتسهيالت األرضية و داخل الطائرة .6

. شرآة استثماريةأليوهو المعيار المعقول ) return on investment(عائد االستثمار . ب .صول على طائرات مدنية او عسكرية مختلفة األغراضللح: الزبون . ج .سياسية، اقتصادية، تكنولوجية، بيئية، الخ: اعتبارات مختلفة . د

: من األطوار األساسيةويمكن تحديد مراحل تصميم و تطوير الطائرة بما يلي

).Conceptual design phase(طور التصميم المفاهيمي .1 ).= = Preliminary( طور التصميم االبتدائي .2 ).= = Detailed ( تفصيليطور التصميم ال .3

:ويمكن إضافة مراحل أخرى تكميلية وهي ).manufacturing Prototype(تصنيع النموذج التجريبي .1 ).Testing(الفحص .2 ). Final production(التصنيع النهائي .3

ذه إنو يالحظ وار ه عماألط ة م ضهاتداخل ة . بع تنا الحالي ان دراس صميم، ف ل الت ساع مراح را الت نظادة بوقت مبكر .االبتدائيتختص بجزء من طور التصميم ة ع دأ الدعاي دأ . تب اج ويب وذج اإلنت از نم د اجتي بع

رام عملية. المطلوبة الفحوصات جميع االختبار ع إب ود البي ل عق تم قب اء و ت د أثن اج و بع سليم حسب . اإلنت الت .اإلنتاجية القدرة

.يوضح مراحل التصميم األساسية و بعض من تفصيالتها) 1-1 (المخطط :قسم التصميم االبتدائي .1-2

ائرات ن الط د م وع جدي صميم ن وير أو ت ى تط رار عل تم الق دما ي شكيل ،عن و ت ع ه راء المتب ان اإلج فدائي تلف االختصاصات، و التي تتضمن مهندمن مخ ) Project group(مجموعة المشروع سي التصميم االبت

:ويختصون في الفروع التالية. و الخبراء .وهم يختصون بتصميم الشكل الخارجي: خبراء االيرودينامية .1و .2 لمهندس زون وضع : الهياآ رح و ينج ي المقت اء الهيكل صميم البن اتهم ت ضعون بدراس ذين ي ادال األبع

.)Dimensioning & Optimization(واالختيارات المثلى للهيكل .و متابعة آخر إبداعات علم المواد. لتحديد أفضل طرق اإلنتاج الواجب إتباعها : و المواداإلنتاجخبراء .3وزن .4 ز : مهندسو ال د مرآ ع األوزان لتحدي ى توزي سيطرة عل ع أوزان المنتجات و ال ل م بهم التعام وواج

).Moment of inertia(الثقل و انجاز حسابات عزم القصور الذاتي .لتصميم منظومة السيطرة على الطيران وتحليل النوعية: الستقراريةألسيطرة و مهندسو ا .5 ).جسم الطائرة( لتصميم معدات و منظومات البدن : مهندسو المنظومات .6 .الختيار نوع و عدد المحرآات المطلوب: خبراء المحرآات .7

1

ة .8 صاد و المالي راء االقت ة : خب ة التخميني بهم حساب الكلف ون واج ذين يك ةاألوال ائرة، ولي شغيلية للط و الت .وآذلك التدقيق عن قرب للنواحي المالية لمجمل المشروع

ال م بأعم شكل دائ ا ب ذي يكون مرتبط دائي و ال سام فالمشروع، بخال عمل فريق التصميم االبت اقي أق ب :إضافة للواجبات األساسية حسب اختصاصاتهم المشروع، يتكون من النشاطات التالية

.مع قسم التسويق لنوع الطائرة الجديد بالتعاوناألولية و وضع اللمسات للمواصفات السوقتحليل .1 .اقتراح الحلول المختلفة ألي مشكلة تصميم معطاة .2ان تقييم مختلف اقتراحات التصميم باستخدام طرق التصميم االبتدائي لكي يتم اتخاذ .3 القرار على أساس بي

.مختلف اآلراءيل األب .4 د تفاص ع و تحدي ا، وض م مواجهته ي ت شاآل الت اث للم ة ح ثال االيرودينامي اقي م ل و ب و الهيك

.الخ...مثال تطوير طرق تخمين الكبح، الوزن. مساحات العملستقبل في .5 ذلك الوسطاء للم اليين و آ ائن الح المحرك و أجزاء تخص أمور مناقشات مع الزب الطائرة آ

.الخ..العجالت .ةتعزيز قسم المبيعات بالمعطيات الفني .6 .إجراء دراسات تطوير المنتج بهدف زيادة استخدام الطائرة .7

ل ألغراض إجراء انسيابي لتصميم عام مطور و مؤلف )2-1(في المخطط برمجة الحاسوب و هو يمث

.األساسية األولية للطائرة) Configuration(عرض تصميم لشكل الهيئة

REQUIREMENTS

WILL IT WORK? WHAT DOES IT LOOK LIKE? WHAT REQUIREMENTS DRIVE THE DESIGN? WHAT TRADE-OFF SHOULD BE CONSIDERED? WHAT SHOULD IT WEIGHT AND COST?

CONCEPTUAL DESIGN

FREEZE THE CONFIGURATION DEVELOP LOFTING DEVELOP TEST AND ANALYTICAL BASE DESIGN MAJOR ITEMS DEVELOP ACTUAL COST ESTIMATE

PRELIMINARY DESIGN

DESIGN THE ACTUAL PIECES TO BE BUILD DESIGN THE TOOLING AND THE FABRICATION PROCESS TEST MAJOR ITEMS, STRUCTURE, UNDERCARRIAGE…ETC FINALIZE WEIGHT AND PERFORMANCE ESTIMATE

DETAIL DESIGN

Figure (1-1): Main design procedure stages FABRICATION

2

INITIAL ESTIMATE OF EMPTY & TAKE OFF WEIGHT

INPUT MISSION AND PERFORMANCE CRITERIA

. PAYLOAD . RANGE . CRUISE ALTITUDE . CRUISE SPEED . TAKE OFF FIELD LENGTH

. LANDING FIELD LENGTH OR APPROACH SPEED

. CLIMB REQUIREMENTS CONFIGURATION GEOMETRY AND DATA TECHNOLOGY DATA . AERODYNAMICS . PROPULSION . STABILITY AND CONTROL . AIRFRAME AND SYSTEM . WEIGHT DATA

- WING SIZING - NO. OF ENGINES - ENGINE CONF. & SIZING

LAYOUT DESIGN - GENERAL ARRANGEMENT - GEOMETRY PARAMETERS

EXCEPT EMPENNAGE

WEIGHT AND BALANCE - GROUP WEIGHT - WING LOCATION - LOADING C.G. LIMITS - HORIZONTAL TAIL SIZE - AERODYNAMIC C.G.

LIMITS - VERTICAL TAIL SIZE

MISSION PERFORMANCE - CRUISE SPEED - PAYLOAD-RANGE

DIAGRAM

CHANGE WEIGHT

AIRPLANEBALANCE

CHANGE WEIGHT, WING & ENGINE SIZE

FIELD PERFORMANCE - UNDERCARRIAGE

DESIGN - TAKE OFF FIELD LENGTH - LANDING FIELD LENGTH

PERFORMANCE CRITERIA MET

EVALUATION AND OUTPUT - THREE-VIEW DRAWING - WEIGHT-BALANCE DIAGRAM - DRAG-POLARS, LIFT CURVES - OFF DESIGN PERFORMANCE - WEIGHT STATEMENT - OPERATING COST

YES

YES NO

NO

Figure (1-2): Generalized design procedure

3

:)Airworthiness(سالمة الطيران تم متطلبات ة األخرى التي ي ده سالمة الطيران هي أنظمة وقواعد التصميم واالشتغال و األنظم ا تحديل ران سلطات من قب ى مصنعي الطي ة و تفرض عل ذه مستخدمي الطائرات والمحلي ة له ضمن الحدود اإلقليمي . لعموم الناساألمانن لضمان مستوى معين مالسلطات

ائرة، • زاء الط صميم أج ى ت ر عل د األث د بعي ة و القواع ذه األنظم دن،له اب، آالب صورة الرآ مق .الخ...المنظومات

• .على المصمم اختيار قوانين سالمة الطيران المالئمة لغرض تصميم الطائرة وفقا لهذه القوانين .آخرقواعد سالمة الطيران تختلف من بلد إلى •

ين من ا مستوى مع ان و تفرض قواعد السالمة آما قلن ى أن، فيجب األم درة عل و اإلقالع تظهر الطائرة الق

اورة مع التسلق ذلك المن ررة و آ ال و الطيران للمسفة المق ار األحم ادة طي سبقا، بقي سرعة المحددة م ررة لل المقران ثناءأللطيار متعبة أو تصبح الطائرة غير قابلة للقيادة أنمرخص، دون اجع في إن . الطي شل الف ة الف احتمالي

7 . طيران)10 إلى 1( يكون اقل منأن يجب آخر أي جزء أوالهيكل

وانين ران آق سالمة الطي ايير القياسية ل دان ) Codes(يتم نشر المع ران . في عدد من البل ات الطي ثال متطلب ما ي بريطاني دني ف لطة )BCAR: British Civilian Airworthiness Requirements(الم شره س تن

دني ات المتحدة ). CAA: Civil Aviation Authority(الطيران الم ة للوالي ران الفيدرالي ا تعليمات الطي أمة دني )FAR: Federal Aviation Rules(األمريكي ران الم شرها إدارة الطي FAA: Federal( فتن

Aviation Administration.( :هيو يختلف حسب نوع المجموعة األداء مستوى مطلوب للمناورة و أدنى أنعلى BCAR تنصمثال

. الطائرات التي تتمكن من الطيران حتى و إن تعطل محرك واحدمجموعة: Aمجموعة : Bمجموعة .غير محددة

شل محرك واحد و األداءمجموعة الطائرات ذات قابلية :Cمجموعة د لكن التي تتمكن من الطيران مع ف بع .إتمام مرحلتي اإلقالع و التسلق

ة ي : Dمجموع اسو ه ي ال باألس د و الت رك الواح ائرات ذات المح وط تتم للط ك تح ألداءل ا إذا ل ل م تعط .المحرك

)Crash Airworthiness(سالمة الطيران عند التحطم

:اهم النقاط العامة لهذا النوع من سالمة الطيران .سالمة بعد الحادث) Cabin(على قيد الحياة إذا بقيت مقصورة الطائرة يجب أن يبقى الراآبون

ذلك إن رأس فيجب التحوط ل تحطم هو نتيجة إصابة ال ة . معظم ضحايا حوادث ال ى المصممين اخذ آاف فعلتحطم الخطوات د ال ل . المناسبة لحماية الراآبين في حالة النجاة بع ستخدم معامل التحمي ثال مجموعة الهياآل ت م

: القيم التاليةBCARوقد حددت . آعامل أمان عند تصميم البدن) Ultimate Load Factor(ألقصى ا

Acrobatic a/c Normal & Utility a/c Direction of load4.5 g 3.0 g Upward 9.0 g 9.0 g Forward 1.5 g 1.5 g Sideward

4

Fuselage Design

The main fuselage characteristics are: 1. It constitutes the shell containing the payload which should be carried to a certain

distance at a specified speed. The shell offers protection against climatic factors (cold, low pressure, a very high wind velocity and against external noise.

2. It is the most suitable part for housing the cockpit, usually in the nose. 3. The fuselage maybe regarded as the central structural member to whom the other

main parts are joined (wings, tail unit and in some cases the engines). 4. Most of aircraft systems are generally housed in the fuselage, it also some times

houses engines, fuel tanks and retractable undercarriage.

Fuselage design requirements: 1. The drag of fuselage should be low, since it represents ( OCD% ) 40to202. The structure must be sufficiently strong, rigid and light, possess a fixed useful

life and be easy to inspect and maintain. 3. Operating costs are influenced by the effect of the fuselage design on fuel

consumption and by manufacturing costs. 4. The fuselage does not merely serve to carry the empennage, but also affects the

tail configuration.

The shape of fuselage is derived from efficient arrangement of passengers or freight, see (figure.1).

The cylindrical arrangement is used for the following reason: 1. Structural design and manufacturing are considerably simplified. 2. It is possible to obtain an efficient internal layout with little loss of space. 3. The flexibility of the seating arrangement is improved. 4. Further development by increasing the length of the fuselage (stretching) is

facilitated.

Figure (1a): Fuselage with relatively large payload volume and efficient internal arrangement (Dassault Mercure)

1

2

Figure(1b): typical fuselage cross-section of transport aircraft

Figure(1c): typical fuselage cross-section of transport aircraft

Cabin design (configuration):

a- Cross-section: Configuration and dimension.

Circular cross-section is the simplest shape, see (figure 1), and the width ( ) can be evaluated from (figure 2) or calculated from the following formula:

fb

A)2N(*N*a)50100(*0.2bf +++++= l

Where

3

100 mm: Typical fuselage wall thickness. 50 mm : Distance between end arm set and wall. N : Number of set in a row. N+2 : Number of arm set. A : Minimum aisle width between arm sets (see figure 3). B : = = = without = =(see figure 3).

: From figure (4). l&a

Figure (3): Minimum aisle width for passenger transport

Figure (2): Fuselage width vs. "total set width"

Figure (4): Definition of set dimensions Table (1): Definitions of sets main dimensions

Note that no more than (three) sets abreast in arrow at each side of an aisle i.e. for seven to twelve sets row, two aisles are needed.

4

b- Cabin length.

The length of fuselage cabin cabin ( ) can be evaluate from figure (5) or is approximately:

cl

cl = number of seats in a column* maxp

Figurer (5): cabin length based on statistical correlation

c- Passenger seat.

Preliminary design is based on a certain standard type of seat, but airlines can lay down their own specification for cabin furnishing. Sets type are: Deluxe type : Set pitch is ( 38 - 40 in) 965 - 1016 mm Normal type : = = = ( 34 - 36 in) 865 - 914 mm Economy type: = = = ( 30 - 32 in) 762 - 812 mm

5

d- Flight desk.

The general configuration can be chosen by comparison with other a/c. Location and dimension of pilot seat and the flight controls can manipulated as shown in figure (6) where visibility from the cockpit during horizontal flight and during approach is assured .

Figure (6a): pilot seat for fighter a/c

Figure (6b): pilot seat for transport a/c 6

Fuselage main dimensions: The dimensions can be computed by approximated, simple two methods:

1. Quick method:- For fuselage with cylindrical mid section

)21(D4

volume,Vf

f2ff λ

−π

= l

)11()21(DareaWette,S 2f

32

fffw,f λ

+λ

−π= l

where 5.4Dratiofinessfuselage ffff ≥λ⇒==λ l

Cf A4eterdimfuselage,Dπ

=

where fuselage cross-section area ,AC

For fully stream lined shapes without cylindrical mid section:

)135.05.0(D4

volume,Vf

nf

2ff

l

ll +

π=

)3.0015.1()135.05.0(DareaWette,S 5.1f

32

f

nffw,f λ

++π=l

ll

where ,nl tionsecnosefuselagetheoflength

2. General method:- The general method depends on a diagram and illustrative figures. The following formulas are used:

max,fmax,fAC h.b.Kareafrontal,A =

)hb(K0.2lengthntialcircumfere,C max,fmax,fCf +=

)KK(Avolume,V tt,Vnn,VCCf lll ++=

)KK(CareaWetted,W tt,Wnn,WCfw,f lll ++=

The length of fuselage nose ( ) and fuselage tail ( ) are evaluated by comparison with other aircraft that is in service. The comparator aircraft should be of the same type, the same number of passenger.

nl tl

7

Figure (7a): factors for calculating the area, circumference, volume and wetted area

8

Figure (7b): definition of streamline body geometry

a/ccomparatorcn

cn * ⎟⎠⎞⎜

⎝⎛=

llll ;

a/ccomparatorct

ct * ⎟⎠⎞⎜

⎝⎛=

ll

ll

Fuselage weight The fuselage makes a large contribution to the structure weight, but it is

much more difficult to be predicted by general methods than the wing. The reason is the large number of local weight penalties in the form of floor, attachment, support structure at, bulk heads, doors, windows and other special structural feature. Fuselage weight is affected primarily by gross shell area ( ), which intern depend upon the overall dimensions of the fuselage as well as the design diving speed.

areawettedfuselageG SS ≡

For AL-alloy fuselage, the following simple weight estimation method can be used as a first approximation:

2.1G

f

tDwff S*

h*b*V*KW

f

l=

wfK : Constant, =0.23 if the weight is in (kg). DV : dive speed in (m/s).

GS : Gross shell area in ( 2m ). tl : The distance between quarter (1/4) root chord of the wing and

quarter (1/4) root chord of the tail, i.e. between aerodynamic centers for the wing and the tail, in (m).

ff h,b : Fuselage maximum width and height, in (m). To the total basic weight that calculated by above formula:- 8% : should be added for pressurized cabin. 4% : = = = for rear fuselage mounted engines. 7% : = = = if the main u.c. is attached to the fuselage. 10% : = = = for freighter aircraft. The nominal fuselage weight is about ( MTOW%)128(Wf −≅ ),

(MTOW) is maximum takeoff weight. tl .c.aTail.c.aWing

9

1

3.Wing Design 3.1. Basic requirement:

1. The aircraft must satisfy the performance figures laid down in the design specification with

best economic yield and operation flexibility. 2. Flight characteristics must be satisfactory both at high and low flying speeds. 3. It must be possible to design the structure within the external lines and the general

arrangement which satisfies demands regarding, strength, rigidity, weight, service life, accessibility …etc.

4. Sufficient space must be provided for fuel and to permit the attachment and retraction of main u.c.

Wing design is a highly iterative process, practically in the preliminary stage; the following

comments maybe help to speed it up:

1. it is convenient to make a distinction between:- a) Wing size (area). b) Basic shape (plan form, section and twist). c) High – lift devices.

2. In case of low speed aircraft, it is probably best to determine the aspect ratio first; the wing loading and type of high lift devices are dealt with next.

3. In case of high speed jet aircraft the span loading and wing loading many are dealt with first. 4. The wing sweep and mean thickness/chord ratio of high subsonic a/c are based primarily on

the Mach number in high speed flight. 5. On high subsonic, long rang a/c the high lift configuration is likely to be decided after a

satisfactory wing shape, for high speed flight, has been obtained. 6. A final check on low speed performance, fuel tank volume and buffet margins may lead to

corrections of wing area which have only minor affect on high speed performance. 3.2. Wing location: Low wing: Advantage: 1. Good visibility in a turn during take off and landing. 2. Acts as an emergency dissipater in case of crash, with good possibility of survival. 3. Passenger seats can be arranged on the middle portion of the wing. 4. In small a/c, concentrated load and occupants could be reacted directly by the low wing. 5. Short u.c. 6. Simple flap and ailerons control mechanism. 7. Continuous wing structure. 8. Conventional tail is quit sufficient.

2

Low wing: disadvantage: 1. High interference drag. 2. Special equipment must be used during loading and unloading. 3. Because of ground effect, large ground clearance is wanted which means long leg u.c. 4. For a wing mounted engine, a high a/c (long u.c.) is needed.

High wing: Advantage: 1. Very suitable for military transportation (IL-76, IL-86, C-5A). 2. High ground clearance, i.e. minimum ground effect. 3. Suitable for wing attached engine. 4. Continuous wing structure. 5. High aerodynamic efficiency.

High wing: Disadvantage:

1. Low visibility in a turn during take off & landing. 2. T–tail is needed. 3. The energy dissipated finally by the wing, and it may be as a heavy weight, crush on the

passenger. 4. The passenger's seats need to be arranged on a torque box and not directly on the floor. 5. In small a/c occupants weight should transmitted to the fuselage and up to the wing, i.e.

weight penalty. 6. Long u.c. attached to the wing, or a complicated short u.c. with small track if attached to the

fuselage.

Mid wing: This type is chosen, generally, when minimum drag in high speed a/c is needed case for

fighters and high speed transporter. The advantages and disadvantages are moderated and between what for high wing and low wing.

3.3. Wing characteristics (see figure 1):

λ ; Taper ratior

t

CC

chordrootchordtip

==

GS ; Gross or Design wig area ∫=2/b

0

dyC2

The area enclosed by the wing outlines including wing flap in the retracted position, and aileron, but excluding fillets or fairings.

netS ; Net wing area, the gross wing area minus the projection of the central wing part.

3

wetS ; Exposed or wetted wing area which is the net external wing surface area that exposed to the airflow. If the wing contains nacelles, the wetted area should be reduced by total area of wing in side the nacelle structure.

⎥⎦

⎤⎢⎣

⎡λ+τλ+

⎟⎠⎞

⎜⎝⎛+=

11

ct25.01S2S

rnetwet

( ) ( )[ ]rt ctct=τ SMC,C ; Geometric or standard mean chord.

bS

spanareawingC ==

AR ; Aspect ratioSb

Cb 2

==

rC ; Root chordARS

12Ct

λ+=

λ=

Quarter chord line; is the line passes through points at 0.25C for all sections.

25.0Γ ; Angle of dihedral, the angle between the projection of the quarter chord line on the (YOZ) plane and y-axis. The negative angle is called anhedral.

25.0Λ ; sweep angle, the angle between the projection of the quarter chord line on the (XOZ) plane and the Y-axis. ( .E.LΑ ) is for leading edge and ( E.TΑ ) is for trailing edge.

For straight taper wing, the relation between sweep angles at section (1) and section (2) is:

( )2112 ee11

AR4TangTang −

λ+λ−

+Λ=Λ

Where (e) is a fraction of the chord. For example at leading edge ( 0.0e1 = ) and at trailing edge ( 0.1e2 = ).

For wing or tail plane with straight trailing edge, i.e. ( 0.1e,0.0 2.E.T ==Λ )

Figure (1a): wing characteristics definitions

4

( )0.125.011

AR4Tang0.0 25.0 −

λ+λ−

+Λ=

λ+λ−

=Λ11

AR3Tang 25.0

ε ; wing twist, angle of incidence of wing section relative to that of root section, measured in

plane parallel to (XOZ) plane. Positive twist, (wash-in), nose rotated upwards. Negative twist, (wash-out), = = downwards.

gε ; Geometric twist is the twist of the chord line of a section relative to the chord line of root section.

aε ; Aerodynamic twist is the twist of the zero-lift line of a section relative to the zero-lift line of

root section.

0lr0lga ) == α−α+ε=ε For any section, for example at tip section:

t0lr0ltgta )))) == α−α+ε=ε

0l=α ; Angle of attack for zero-lift line i ; Wing angle of incidence, (angle of wing section), the angle between the root chord and the

airplane reference axis (axis passes from tail to nose). C ; MAC, mean aerodynamic chord, the chord of an equivalent untwisted, unwept and non-tapered

wing, for which the total lift and pitching moment are essentially equal to the lift and pitching moment on the

actual wing.

5

3.4. Determination of (MAC): *Analytical method:

∫=2/b

0

2dyCS2C

; ∫=2/b

0

CydyS2y

For straight taper wing:

λ+λ+λ+

=1

1C32C

2

r

)1(321*

2by

λ+λ+

=

*Graphical method: (see figure 2). At root side draw ( tC ) at each side, and at tip draw ( rC ) at each side. The

interception point of diagonals indicates the position of ( C ) and ( y ). *For (rectangular & trapezoidal) wing: 1. Determine (MAC) of the rectangular and taper portions separately, ( 21 C&C ). 2. determine the areas ( 21 A&A ) as follow (see figure 2 ):

For rectangular 111 CaA =

For trapezoidal 222 CaA =

21

2211

AAACACC

++

=

21

2211

AAAyAyy

++

=

21

2211

AAAyAyy

++

=

rC

tC

a/c nose

1x

1y

2x

2y

1a 2a

Figure (3): multi-area method

Figure (2): graphical method

6

*Elliptical wing (see figure 3): 1. Divided the wing into

(n) umber of strips of equal width. ( yΔ ).

2. Measure the mean chord of each strip ( iC ) and the distance ( iy ) from this mean chord to the airplane center line.

3. Prepare a table as shown below (Table 1).

4. ∑∑=

)C()C(

C2

;∑∑=

)C()yC(

y ;∑∑=

)C()xC(

x

1 2 3 4 5 6 7 Strip

number Strip chord

22× Distance to

42× Distance to

62×

1 1C 21C 1y 11Cy 1x 11Cx

2 2C 22C 2y 22Cy 2x 22Cx

3 3C 23C 3y 33Cy 3x 33Cx

. . . . . . .

. . . . . . .

. . . . . . . ∑ )C( ∑ )C( 2 ∑ )yC( ∑ )xC(

And finally figure (5) can be used to evaluate mean aerodynamic chord ( C ).

a/c nose

2/biy

iC

YΔ ix

Figure (4): strips method for irregular wing area

Table (1): strips method

7

3.5. How to evaluate wing size: Wing loading ( s

w ) and aspect ration ( AR ) is chosen by comparison with similar a/c. The

wing loading for short range subsonic transporter lies in the range of (300 to 500 2mkg ). The weight of the a/c is gusted as first start from comparator a/c. then:-

( )swWSW =

( WS ) is in 2m and then all other dimensions are evaluated. Taper ratio is assumed and thickness ratio is taken from NACA.

Figure (5): diagram for the mean aerodynamic chord of straight tapered wings with or without prismoidal inboard section.

8

3.6. Airfoil section:

Requirements 1. The basic airfoil must have a low profile drag coefficient for the range of lift coefficients used

in cruising flight. 2. For the inboard sections with flaps extended, the drag must be low in high lift condition,

practically during take off and climb. 3. The tip section should have high maximum lift coefficient and gradual stalling characteristics. 4. The inboard wing sections should have high maximum lift with flaps extended. 5. The critical Mach number should be sufficiently high. 6. The pitching moment coefficient should be low. 7. The aerodynamic characteristics should not be extremely sensitive to manufacturing variations

in the wing shape, contamination and dirt…etc. 8. The wing sections should have the largest possible thickness ratio in the interest of low

structure weight; a sufficient internal space must be provided for fuel tanks, main u.c., mechanical controls…etc.

Zero lift line: is a line passing through T.E. at angle ( 0L=α ) with the direction of airflow.

0L=α : It is an angle, if the airflow makes it with the chord line the lift becomes zero. .c.a : Aerodynamic center is appoint a bout which the pitching moment ( .c.aM ) is independent of

angle of attack (α ), for design purpose, ( C25.0.c.a = ). For subsonic airfoils:

* Airfoil circumference ⎟⎠⎞

⎜⎝⎛ +=

ct25.01C*2 .

* Airfoil cross section area C*t*68.0≈ .

Figure (5): geometric definitions of wing

9

3.7. High lift devices: They are mechanical devices, which used mainly to increase lift coefficient during take off and landing stages. They are mainly flaps, which are positioned at T.E., and slats, which are positioned at L.E. see table (2).

Table (2a) some flaps and slats configuration.

10

Table (2b) some airfoil characteristics.

11

From figure (6), the beneficial of using high lift devices is obvious, ( lCΔ ) is increment of lift coefficient due to T.E. flaps only, while dashed line is due to L.E. flaps or slats. The upper curve shows the effect of T.E. and L.E. high lift devices. 3.8. Airfoil section coding: Many airfoil sections were designed in many countries with their own coding. NACA (National Advisory Committee for Aeronautics) in USA grouped these sections in rational families and series. NASA (National Aerodynamic and a Space Administration) is responsible now. 1. 4- digit series, (for slower a/c):

Ex. NACA 34-4415 • (4) ⇒ The maximum camber ( cy ) value is at ( C04.0 ). • (4) ⇒ The position of maximum camber is at ( C4.0 ). • (15) ⇒ Section maximum thickness is ( C15.0 ). • (3) ⇒ Magnitude of leading edge radius, (6 is normal, 0 is sharp). • (4) ⇒ The position of maximum thickness is ( C4.0 ).

2. 5- digit series, (for slower a/c):

Ex. NACA 23015 • (2) ⇒ Design lift coefficient is of magnitude ( 3.02

3*102 = ).

• (30) ⇒ The position of maximum camber is at ( C15.0C*21*100

30 = ).

Figure (6): the effect of leading edge slat, flap and trailing edge flap upon lift and angle of basic wing section.

12

• (12) ⇒Section maximum thickness is ( C12.0 ). The design lift coefficient is the theoretical ( lC ) for the airfoil when (α ) is such that the slope of mean camber line at the L.E. is parallel to the free air stream velocity.

3. 6- digit series, (for slower a/c, laminar-flow wing sections):

Ex. NACA 412-63 (this is 5-digit airfoil in 6-digit series). • (6) ⇒ 6-digit series. • (3) ⇒ Position of minimum (negative) pressure, which is favorable gradient, is at

( C3.0 ). • (4) ⇒Favorable lift coefficient (designed) is ( 4.0 ). • (12) ⇒ Section thickness ratio is ( C12.0 ).

Ex. NACA 218-3 65,

• (6) ⇒ 6-digit series. • (5) ⇒ Position of minimum (negative) pressure, which is favorable gradient, is at

( C5.0 ). • (3) ⇒Favorable lift coefficient range is ( 3.0± ) above and below the design lift

coefficient where favorable pressure gradients exist on both surfaces. • (2) ⇒ Design lift coefficient is ( 2.0 ). • (18) ⇒ Section thickness ratio is( 18.0 ).

Ex. NACA 215-64A

• (6) ⇒ 6-digit series. • (4) ⇒ Position of minimum (negative) pressure, which is favorable gradient, is at

( C4.0 ). • (A) ⇒ Section is straight on both surfaces from about ( C8.0 ) to the T.E. • (2) ⇒ Design lift coefficient is ( 2.0 ). • (15) ⇒ Section thickness ratio is( 15.0 ).

Ex. NACA 215-642

• (6) ⇒ 6-digit series. • (4) ⇒ Position of minimum (negative) pressure, which is favorable gradient, is at

( C4.0 ). • ( ) ⇒ Section has cusped T.E. (without A). • ( 2. ) ⇒ low drag range is ( 3.0± ) above and below lift coefficient ( 2.0 ). • (2) ⇒ Design lift coefficient is ( 2.0 ). • (15) ⇒ Section thickness ratio is ( 15.0 ).

13

Ex. NACA 215-64A • (6) ⇒ 6-digit series. • (4) ⇒ Position of minimum (negative) pressure, which is favorable gradient, is at

( C4.0 ). • (A) ⇒ Section is straight on both surfaces from about ( C8.0 ) to the T.E. • (2) ⇒ Design lift coefficient is ( 2.0 ). • (15) ⇒ Section thickness ratio is ( 15.0 ).

4. 7- digit series:

Ex. NACA 315-747A . • (6) ⇒ 7-digit series. • (4) ⇒ Extent of region of favorable pressure gradient over upper surface from ( C4.0 ) of

L.E. at the design lift coefficient. • (7) ⇒ Extent of region of favorable pressure gradient over upper surface from ( C7.0 ) of

L.E. at the design lift coefficient. • (A) ⇒ Section is straight on both surfaces from about ( C8.0 ) to the T.E. • (3) ⇒ Design lift coefficient is ( 3.0 ). • (15) ⇒ Section thickness ratio is ( 15.0 ).

3.9. Wing aerodynamic characteristics:

How to start: The weight of the a/c and wing loading are usually given. The aspect ratio and taper ratio

must be assumed or given. Wing area, wing-span, standard mean chord, mean aerodynamic chord…etc, must be evaluated. 3-D wing drawing should be done where all dimensions were indicated clearly.

This procedure is valid for horizontal and vertical tail planes.

Evaluation lift curve for unflapped wing:

1. Chose suitable airfoil, NACA ( 615632 − ). 2. Determine slope of lift curve for wing section,( oa ), for two dimension in compressible

flow, for standard roughness and ( 6106Re ×= ), as follow: Take a straight portion of the lift curve, see figure (7).

05.1C =Δ l o10=αΔ

14

.radper0165.63.57105.0

.degper105.01005.1Cao

=×=

==αΔ

Δ= l

3. Determine ( 1a ), lift curve for unfflaped wing for sub-sonic aircraft at low Mach no.:

( )K1cosa

1a1

eo1τ++

Λ=

K : Factor from sheet 01.01.01W , upper curve. τ : = = = 01.01.01W , upper curve.

)1.(AR.45tantan 25.0

25.0e λ+Λ

−Λ=Λ

4. Determine ( M,1a ), lift curve for unfflaped wing for sub-sonic aircraft at high Mach, but

below the critical Mach no.:

( )K1cosa1

a1

eM,oM,1τ++

Λ=

( )e22

o

e

oM,o

cosM1

aaaΛ−

=β

=

25.0Λ : Sweep back of quarter chord line. M : Mach number.

oa : slope of lift curve of airfoil section in 2-D, incompressible flow, at low Mach no.

M,oa : slope of lift curve of airfoil section in 2-D, incompressible flow, at high Mach, but below the critical Mach no. which is ( ecosM Λ ).

K : Aspect ratio correction factor. τ : Taper ratio correction factor.

eβ : Prandtl-Glauert factor, ( )e22 cosM1 Λ− .

eΛ : Effective sweep back in degree.

Ex. A straight rectangular wing, deg105.0a0.2, M 7.3),ratio(aspect o per=<= . Find wing lift curve slope. .radper0165.63.57*105.0ao == 0.025.0 =Λ : For straight wing ( 0=Λ ). 1.0= λ : for rectangular wing. .37AR = . From sheet 04.0K01.01.01W =⇒ .

15

Since ( radper0165.6aa2.0M oM,o ==⇒< ).

⇒==Λ

21233.11*0165.6

3.7cosa

AR

eM,ofrom sheet 19.001.01.01W =τ⇒

( ) deg/082.0arad/677.4a21381.04.0*19.00.11*0165.6

1a1

111

=→=⇒=++=

5. lift curve slope can be evaluated also as flow:

radper

ARaE

afao

o1

π+

= .

f : Correction factor for wing taper 995.0≈ .

E : June's edge velocity factorspanwing

tersemiperimeplanform

For straight tapered wing,)1(AR

2Eλ+

λ=

For the previous ex.:

137.1)0.11(*3.7

0.1*21E =+

+=

rad/278.4

3.7*0165.6137.1

0165.6995.0a1 =

π+

=

The value from this method is not far away from the previous value, 4.677 / rad. For subsonic high Mach no.

2

22

1

AR2

cosk1

AR2

21a

⎟⎟⎠

⎞⎜⎜⎝

⎛π

+Λ

+π

πβ

=

β

β

Λ=Λβ

21tan

tan ; π

β=

2ak o ; 2M1−=β

16

17

3.1. How to draw wing lift cure:

Usually wing section lift curve is available from NACA sheets, while lift cure for a wing, as 3-D object, is not available and should be evaluated during design stage. This lift curve is evaluated by aerodynamic wing testing in a wind tunnel. For preliminary test stage there are many simple ways to draw such curve without wind tunnel testing. The following procedure can be used:

1. since lift curve slope ( 1a ) is known and ( αΔ ) is the same, then:

i. 82.0082.0101 =×=×Δ=Δ aCL α . ii. Zero lift angle ( 0=Lα ) does not change with aspect ratio, and from figure (7b) its value

( deg0.50 −==Lα ). iii. Draw a straight line, from point (O) at ( O5−=α ), with slope ( 105.0=Oa ). Extend this

line until it will intercept line ( MaxL CC ,l= ). For our example NACA 615632 , 4.1max, =lC . The point interception is ( A′ ).

iv. Measure the distance between ( A ) and ( A′ ), peak point on origin lift curve along line ( MaxL CC ,l= ). The distance is ( OAA 4=′ ).

2. Maximum wing lift curve ( MaxLC , ) variation due to surface roughness and Reynolds number ( Re ) influence is calculated.

i. Choose surface roughness (standard surface roughness) and Reynolds number value at take off ( 6102Re ×= ).

ii. From origin NACA 615632 sheet, the following data is available.

iii. Draw the relation ship between ( MaxLC , ) and ( Re ), the relation is assumed linear. For

smooth roughness there are three points. For standard roughness there is one point. So the second line is drawn from point (d) parallel to the firs line.

iv. At ( 6102Re ×= ) for standard roughness, the actual maximum lift coefficient is then ( 25.1, =MaxLC ).

For smooth roughness

466.1103Re

58.1106Re

66.1109Re

,6

,6

,6

=→×=

=→×=

=→×=

Max

Max

Max

C

C

C

l

l

l

For standard roughness 40.1106Re ,

6 =→×= MaxCl

Smooth roughness

MaxLC ,

610Re×

Standard roughness

1.25

1.40

1.46

1.58

1.66

9

a

632

b

c

d

Figure (7a): Reynolds number-Lift curve relation

18

3. From point (O) with slope ( 082.01 =a ) draw a straight line till it intersect line ( 25.1, =MaxLC ) at ( B′ ). Then from point ( B′ ) move to the left a distance ( deg4 ) a long line ( 25.1, =MaxLC ) to point ( B ).

4. Copy the curved portion between ( AA ′& ) for the origin curved, on the new curve between ( BB ′& ).

-5 0 5 10 15 200

0.5

1

1.5

LC.coeffLift

6

2

106ReroughnessSandard

61563NACA

×=

82.0

1.05

4.1C Max,L = O4

4.1C Max,L = A

B B′

A′O4

Figure (7b): Wing & Airfoil characteristics.

O,attakofAngle α

19

3.11. Lift coefficient increment due to T.E. flaps:

1. Determine lift coefficient increment due to split flap. The following formula can be used, see figure (8):

321)6()( λλλ ×××=Δ

fARfCL

)(ARf : A parameter which is a function of aspect ratio. )6(f : A parameter which is a function of ( 6=AR ).

1λ : Correction factor depends on ( CC f ).

2λ : Correction factor depends on ( oδ ). 3λ : Correction factor depends on ( bb f ).

fC : Flap mean chord.

fb : Flap span. δ : flap deflection angle in degree.

The parameters ( δ&, ff bC ) are laid down (chosen) by the designer. Ex. A rectangular wing has a split flap, where 9=AR , 25.0=CC f , 12.0=ct , 6.0=bb f and

deg40=δ , find the increment in the lift coefficient. i. From figure (8a) with 9=AR , 1.1)6()( =fARf .

ii. From figure (8b) with 25.0=CC f , 65.01 =λ . iii. From figure (8c) with deg40=δ , 25.12 =λ . iv. From figure (8c) with 6.0=bb f , 65.03 =λ .

321)6()( λλλ ×××=Δ

fARfCL

581.065.025.165.01.1 =×××=

20

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

0 3 6 9 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Flap angle, δ in degree.

3λ

ct

12.0

15.0 18.0 21.0

30.0

ratioTaper,λ

51

41

21

11

2λ

CC

chordWingchordFlap f

1λ

ratioAspect,AR

( )( )6fAf

Figure (8): correction factors for split flap

8c

8b

8d

8a

bb

spanWingspanFlap f

21

Determine lift coefficient increment due to slotted flap. For full span slotted flap the following formula is used.

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

′′Δ

+′

′Δ=Δ 1,

6 CC

CC

aa

CCCC

L

NLLL

Where: C ′ : extended wing cord. a : Wing aspect ratio.

6a : Standard aspect ratio which is (6). LC ′Δ : lift coefficient increment based on extended wing chord C ′ and standard aspect

ratio (6). NLC , : lift coefficient of the actual wing where flaps are at neutral position. At each angle

of a take ( α ), there is a certain value for ( NLC , ).

2. Determine lift coefficient increment due to double slotted flap. Usually one is main flap and the other is auxiliary. The data is applicable to slotted or

split auxiliary flap with the deflection of the main not less than ( deg10 ). This data does not apply to flaps having in them selves a fixed slot or some similar arrangement. For obtaining the lift coefficient increment due to a double slotted flap, contributions of the main flap and the auxiliary flap are estimated separately, using the dotted curves in the upper set of curves of data sheet ( 08.01.01F ) for obtaining the lift coefficient increment due to the main flap and the curves of data sheet ( 09.01.01F ) for obtaining the contribution of the auxiliary flap.

⎟⎠⎞

⎜⎝⎛ −

′+

′Δ=Δ 1,

6, C

CCaa

CCCC NLTLL

ALLTL CCC ,, ′Δ+′Δ=Δ Where:

NLC , : lift coefficient of the actual wing at the chosen incidence with main flap and auxiliary at neutral position.

LC ′Δ : lift coefficient increment due to full span main flap with ( 0, =Afδ ), based on extended wing chord and aspect ratio ( 6=AR ), see data sheet ( 08.01.01F ).

ALC ,′Δ : lift coefficient increment due to full span auxiliary flap based on extended wing chord C ′ and standard aspect ratio (6).

TLC ,Δ : lift coefficient lift coefficient increment due to full span double slotted flap.

LCΔ : lift coefficient increment due to full span double flap with the wing at the chosen incidence, based on wing chord and aspect ratio of the wing.

22

Ex: Find lift coefficient increment due to a fixed hinge full span slotted flap having the following data:

10.1Cand065.1aa,ft2.10C,ft5.9C,45.,ft4.2c N,L6O

ff ===′==δ= Sol.

235.02.104.2

Ccf ==′

From sheet ( 08.01.01F ), upper curves (figure 9a) at Of

f 45&235.0Cc =δ=′ , then:

90.0CL =′Δ 074.15.9

2.10C

C ==′

( )( ) 15.1065.190.010.1

aa

CC 6

L

N,L ==⎟⎠⎞⎜

⎝⎛⎟⎠⎞

⎜⎝⎛

Δ

From sheet (08.01.01F), lower curves (figure 9b) at 15.1aa

CC 6

L

N,L =⎟⎠⎞⎜

⎝⎛⎟⎠⎞

⎜⎝⎛

Δ and074.1CC =′,

then: 16.1a

aC

C 6

L

L =⎟⎠⎞⎜

⎝⎛⎟⎠⎞⎜

⎝⎛

′ΔΔ

∴16.1aaCC

6LL ××′Δ=Δ

98.016.11065.1190.0CL =××=Δ

Note:

For the same data the optimum lC′Δ that can be obtained is ( 0.98) at ( deg55f ≈δ ), see sheet ( 08.01.01F ), upper curve, then:

20.1aa

CC 6

L

N,L =⎟⎠⎞⎜

⎝⎛⎟⎠⎞

⎜⎝⎛

Δ

And from lower curves

06.1C15.1aa

CC

L6

L

L =Δ→=⎟⎠⎞⎜

⎝⎛⎟⎠⎞⎜

⎝⎛

′ΔΔ

23

Figure (9a): lift coefficient increment due to full span slotted flaps.

Figure (9b): lift coefficient increment due to full span slotted flaps.

24

fδ

Figure (10): lift coefficient increment due to auxiliary flap for full span double slotted flaps. The main flap is slotted.

25

3

Table (3a) w

ing design data

26

Table (3b) w

ing design data

27

Figure (11)

28

12 11

11

12

7

11

14

29

13

30

3.12. Wing weight

Some of the non-optimum weight penalties in wing arise from joints, non-tapered skins, U.C. attachment, fairing etc. The following simplified expression can be used for general a/c with AL-alloy cantilever wings. It is valid for the case of wing mounted retractable U.C., but not for wing mounted engine:

3.0

wgross

rs55.0alt

s

ref75.0sw

gross

w

SWtbn

bb1bK

WW

⎟⎟⎠

⎞⎜⎜⎝

⎛×⎥

⎦

⎤⎢⎣

⎡+×=

The weight given by this equation includes the weight of high lift devices and ailerons. If spoilers and speed brakes are used, added ( grossW2.0.0 ). Reduce ( grossW05.0 ) for two wing mounted engines. Reduce ( grossW10.0 ) for four wing mounted engines. Reduce ( grossW05.0 ) if U.C. is not wing mounted. It can be seen from this equation that the wing structure weight decreases with increasing wing loading ( SWgross ), and this is the reason why all transport aircraft has been designed with large wing loading, i.e. relatively small wing area for given all up weight.

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grossW : Gross weight, maximum take off weight.

wK : Factor for proportionality, for transport a/c = kg5670Wif1067.6 gross

3 ≥× −

= kg5670Wif1090.4 gross3 ≤× −

sb : Structural wing span = )(cosb 5.0Λ refb : Reference span = m905.1

rt : Maximum thickness of root chord.

Tail Design Tail surface functions are:

1. To ensure equilibrium of moments I steady state flight by exercising a force at a

given distance from the center of gravity. 2. To ensure stable equilibrium, so after disturbance the equilibrium must be restored

with an adequate damping. 3. To generate forces for maneuvering the aircraft.

Type of surface controlling system:

1. Manual, direct mechanical transmission. The stick forces increase with

size, EAS and load factor. 2. Power assisted controls, by means of pneumatic or hydraulic ram which

exerts the multiple of the force applied by the pilot (boost ratio). 3. Power operated controls, in these systems the control surfaces are moved

by electrical, hydraulic or pneumatic means without direct physical effort by the pilot.

Horizontal tail plane:

The design of tail pane is always an iterative process. After initial choice of a certain shape parameters such as aspect ratio, thickness ratio, taper ratio…etc. The next stage is to choice the type of aerodynamic balance, whether the stabilizer will be fixed or adjustable and the type of control system, which is more difficult and more data needed. After these decisions have been taken a bout the previous assumptions, the tail plane shape or even the wing location will have to be revised. When designing tail plane, one should consider horizontal “tail plane volume” instead of “tail area” and so tail distance is evaluated.

• Bigger tail volume gives greater airplane stability. • Large c.g. movement needs large tail plane, vice verse. • Transport a/c needs large tail plane and seat arrangement.

Horizontal tail plane volume is defined as:

C.S.SV

wing

HHH

l= …. (1)

HS : Horizontal tail plane area. wingS : Wing area.

1

Hl : Distance from aircraft c.g. to horizontal tail a.c. C : Standard mean chord.

In the above formula, tail volume is related to wing area and to the SMC which has great importance on the airplane longitudinal stability and control. In table (1) a variety of horizontal tail volumes for many airplanes in service. ( HV ) is assumed and since ( ) is known from layout, then ( ) is evaluated and as aspect ratio is assumed then all other dimensions are computed. Horizontal tail usually uses symmetrical airfoils.

Hl

HS

Vertical tail plane:

The design of vertical; tail plane is more complicated than that of the horizontal tail plane. The following requirements are necessary:

1. The vertical plane must not stall as a result of an oscillation after deflection of the rudder or sudden engine failure.

2. Multi-engines a/c must remain controllable to ensure steady flight if an engine failed.

3. It should be possible to land transport a/c in cross wind up to ( hmk55 ). 4. The a/c must possess good directional and lateral static stability. 5. In small a/c, recovery from spin must be possible and rudder must be effective even

art large angle of attack.

Vertical tail plane volume is defined as:

b.S.SV

wing

VVV

l= … (2)

VS : Vertical tail plane area. wingS : Wing area.

Vl : Distance from aircraft c.g. to V. tail a.c. b : Wing span.

Here vertical tail is related to wing span which has a great significance on directional stability and control. ( VV ) is assumed, see table (2), by comparison with similar airplanes that in service. Vertical tail always uses symmetrical airfoils.

Tail surface configuration:

1. Group A: single fin with horizontal tail (or stabilizer) mounted either on the fuselage or on the fin structure. It is simple and stiff. For high wing location a T- tail is desirable to prevent tail fluttering due to a wake behind the wing.

2

2. Group B: twin fins may

used to minimize rolling moment due to large distance from fin a.c. to a/c longitudinal axis, for single large fin. It is also a good choice when a twin tail booms are used.

3

3. Group C: Vee (or butterfly) tail

which is adopted for sailplanes and some times on powered a/c to keep the tail surfaces clear of jet efflux. It has the following advantage:-

• Less drag interference. • Fewer tendencies toward rudder lock. • Fewer surfaces to manufacture.

Figure (1): Some tail plane configurations

Figure (2): Butterfly tail plane configuration

• High location of surfaces which reduce possibilities of tail buffeting due to wakes.

And it has the following disadvantage:

• More complicating operating system.

• Possible of interaction of elevator and rudder action.

• Not popular.

VHVee SSS += Tail group weight: This weight constitutes a small part of a/c weight which is a bout ( of

MTOW. But as it has a remote location from c.g, it has appreciable effect on the position of the a/c c.g.

%3to2 )

Accurate weight prediction is difficult due to the wide variety of tail plane configurations adopted and the limited knowledge of strength stiffness and other

conditions that controls the design, for example some highly maneuverable aircrafts ( ...37SU,35SU..,31MIG,29MIG,25MIG...,18F,15F,14F −−−−−−−− ) need twin fins, which increase tail group weight.

For relatively low speed, light a/c, the maneuvering loads are most important and the specific tail weight is affected by the load factor as follow:

[ ] 75.02

tailwtwttail S.nKW = wtK : Constant =0.64

( ) are in ( ) respectively. tailtail W&S kg&m2

If the tail plane area is not known, the total tail plane weight may be assumed

between ( ) of the empty weight. %0.4to5.3 For transport category a/c and executive jets, the design dive speed appears to have

a dominate effect as in the figure ( ).

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DV : Design dive (maximum)

speed in ( sm ) which is expressed in terms of ( EAS).

Λ : Swept back angle for tail plane.

VH k,k : Correction factors.

( ) for fixed stabilizers, (convention type).

0.1kH =

( ) for variable incidence stabilizers, (movable tail).

1.1kH =

( ) For fuselage mounted stabilizers. 0.1kV =

Figure (3): Normalized specific horizontal and vertical tail plane weights

( ⎥⎦

⎤⎢⎣

⎡+=

VV

HHV b.S

h.S15.00.1k ) For fin mounted stabilizers.

Hh : Height of horizontal tail plane above fin root.

fV bb ≡ : fin height, see figure (4).

Figure (4): Tail plane dimensions

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