calculation of wing loads

7/23/2019 Calculation of Wing Loads

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National Aerospace University

named after N.Ye. Zhukovsky

Kharkiv Aviation Institute

Guide for home taskby course Strength of airplanes and helicopters

CALCULATION OF WING LOADS

Kharkiv, 2015


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Manual is dedicated to calculation of loading for highly-aspect ratio wing. Itconsists of the following sections: wing geometric parameters and mass dataestimation; loads calculation and diagrams plotting of shear forces, bending andreduced moments by wing span.


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INTRODUCTION

The given home task is continuation of your home task on department"Designing of planes and helicopters ". In this task you have defined take-off mass ofthe plane, its cruiser speed, mass of a wing, mass of fuel, mass of a power-plant,mass of the landing gear, mass of useful load. From this task you have allgeometrical sizes of the plane: the wing area, wing span, swept-back wing, chords ofa wing, position of engines, the landing gear, etc.

The given home task should be included into your course project and after yourcourse project should be included into your baccalaureate project.

For all students we give critical loading condition C - flight on cruise speed VCon cruise altitude HCwith maximal maneuveringload factor n

land airfoil.Students are obliged to follow these requirements according to international

standard:

1. All diagrams at the figures should contain starting and ending values of theillustrated variable (not literal expression of the variable).

2. All diagrams should be built to some scale (the scale should be the same forall diagrams illustrated at one figure). The shape of the curves shouldcorrespond to the functions.

3. All calculations should be made with high accuracy.4. The cover page is executed according to Appendix 5.5. Each table must be on one page.6. Each table and drawing must have heading.7. Standard rule for whole world from the beginning you should write down

formula, next step you should substituted numbers and at last write downresult with units.

8. You should not rewrite reference data, drawings from manual, andexplanations.

9. Home task must be printed.In explanatory book you should print home task content in next execution

sequence:1. Three main views of your plane.2. Table 1. Main data of the plane.

3. Determination of limit load factor.4. Air loads allocation on wing span.5. The wing structure mass load allocation.6. Calculation of the total distributed load on a wing.7. The shear forces, bending and reduced moments diagrams plotting.8. Load checking for wing root cross section.9. Calculation of shear forces position in the design cross section

10. Filling the result table.


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1. AIRPLAIN GENERAL DATA

By data your plane you should fill the next table.

Table 1 Main data of the plane

Airplane category Transport (for example)Take-off mass (kg)-MtDesign cruise airspeed (km/h) - VC

Design airspeed (km/h) - VDesign cruise altitude of flight (m) - H

Wing mass (kg) - mwTotal fuel mass (kg) - mfMass of engine (kg)- meMass of main leg of landing gear (kg)- mmlWing area (m2) - Sw Wing span (m) (for swept wing) - LwWing taper

Wing aspect ratio

Swept wing (degree by 25% chord) -0.25

Wing angle of incidence ( degree) - a 2 (for example)

Comment.a. Masses in integer kg.

b. Speeds in integer km/h


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1.1. WINGS GENERAL DATA

The airplane category (transport, normal, acrobatic, etc.), take-off mass t aregiven to the final developments assignment.

From previous course project by discipline Airframe the following data is madeout:

1) Wing geometrical data;2) Masses of wing-accommodated units (masses of engines, landing gears,

external and internal fuel tanks, etc.), and each of themes centers of gravity;3) Airfoils relative thickness.4) Cruise speed and cruise height.If the geometrical sizes not specified in exposition (lengths of root and tip chords,

centers of gravity aggregates for units etc.) are possible to remove directly from thedrawing.

It is impossible to select a delta-wing airplane as in the given manual the designprocedure of a highly-aspect wing is explained as the prototype.

1.2. WINGS GEOMETRICAL DATA

Geometrical data of a wing make out from exposition of the airplane. By thesedata it is necessary to execute figure of a half-wing in two projections (top and frontviews).

If a plane has swept-back wing and the sweep angle on the leading edge aremore than 15 it is necessary to enter an equivalent straight wing and all furthercalculations to carry out for this equivalent wing. A straight wing enter by turn of aswept-back half-wing so that the stiffness axis of a straight wing was perpendicular toaxes of a fuselage, thus the root br and tip bt chords sizes decrease, and the sizeLw/2 of a semi span is increased. The sizes Lw/2, br and bt, are required for thefurther calculations and they are taken directly from the figure. At turn of a swept-backwing it is possible to mean, that the stiffness axis is located approximately on distance0.4 bfrom the leading edge where bis the wing chord.

At calculation of Lw/2 semi span size the plane's design is taken into account:a low-wing, a mid-wing or a high-wing monoplane. In these designs carrying ability of

the fuselage part of wing owing to influence of interference is various. For a low-wingmonoplane it is recommended do not take into account bearing ability of an fuselagepart of wing and to accept value equal to distance from the tip of a half-wing(straightened in case of a swept-back wing) up to an onboard rib as Lw/2parameter.For a mid-wing monoplane and a high-wing monoplane in quality semi span wereceive the distance from the tip of a wing up to an axis of the plane as Lw/2. Thewing area Swis determined by the formula:

Sw= 0.5 (br+ bt) Lw. (1.2.1)


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The received value of the area must coincide with the area of the airplane withswept-back wing for mid-wing and high-wing airplanes. For convenience of realizationof the further calculations figures of a wing (see fig. 1.2.1, 1.2.2 and 1.2.3) shouldcontain maximum quantity of the information. So, on the top view of a half-wingfollowing characteristic lines are put by dotted, a stroke dotted or by light lines: acenter-of-pressure line, the center of gravity (c.g.) line of cross sections of a wing andlines of spars.

The locations of aggregate's centers of gravity (landing gears, engines, fuel tanksetc.) are indicated by the sign, and value and direction of the appropriate massconcentrated forces - by vectors. The areas are occupied by fuel tanks, on bothprojections are shaded. Centers of tanks weight are also indicated by the

sign. Infigures the geometrical sizes and numerical values of the concentrated forces are putdown.

The explanatory book should contain geometrical and aerodynamic characteristics

of the chosen airfoil. In the final development it is supposed, that all wing crosssections have the same aerofoil.

The relative coordinate of a center-of-pressure line can be found by the scheme:the given design limit loading condition - lift coefficient (for cases B, Cand Dit iscalculated) - the appropriate angle of attack (see ap. 1) - relative coordinate ofcenter-of-pressure line cp.

The wing's gravity center in cross section is located approximately on distance of40 - 45 % of a chord from the leading edge.

Gravity centers coordinates of aggregates are made out from the description ofthe airplane - prototype or chosen independently, being guided by the knowledgeacquired in another subject matters of aggregate's design features. For example, thecenter of gravity for a turbojet is placed in area of the turbine compressor, but not inarea of a jet nozzle.

At gravity center positions estimation of landing gear primary struts if the onesare located in a wing, it is possible to use the following statistical data:ll= (0.2 0.25)Lw, bl= (0.5 0.7) b, where the Lwis a wing span, the bis a wingchord; the ll - is the landing gear base, the bl - is a distance from the leading edgewing to gravity center of the primary strut in the retracted position.


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Fig.1.2.1. Diagrams of distributed loads and shear forces

leadin ed e

center of ravit

fuel tankengine

rear spar

q

qtqa

qf Z

Q

Qt

Qd

Qc

0

Lw/2

0

rear spar

br b

front spar


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Fig.1.2.2. Diagrams of bending moment Mand reduced moment Mz.

M, kNm

Mtot

Md

Mc

Z

mz, kN Z

Mz, kNm Z

Mz,t

Mz, d

Mz, c


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Fig. 1.2.3. Plotting of equivalent straight wihg.

equivalent straight wing

swept wing

axis ofstiffnes

reduced axis

center of

pressure

center ofwing gravity

stiffness axis

Z

center of fuel

gravity

e

Z

d

h

X

rkck

center of gravityfor k-th aggregate


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2. DETERMINATION OF LIMIT LOAD FACTOR.

For strength calculation it is necessary to know design airspeeds and loadfactors. For determination of those values for transport airplanes initial conditions aretake-off mass Mt[kg], Lw- wing span, Sw wing area, cruising airspeed of an airplaneVCat the cruise altitude of flight Hc, the wing sweep on the chords fourth 0.25.

In design office (DO) calculations are carried out for all altitude range. In thishome task (HT) you have the cruising airspeed VC and cruising altitude HC fromtechnical data of plane.

For your plane you should take wing airfoil from lecturer. The more speed of theplane, the thinner wing airfoil is. At speeds 400-700 km/h airfoils are recommended

with relative thickness c = 12-15 %. For planes which flies with speeds 700-950 km/h

airfoils are recommended with relative thickness c = 8-12 %.According to ARU-25, FAR-25, JAR-25 maneuvering maximum limit load factor

does not depend from altitude and en-route mass and are determined by the formula:l

y max man

t

108862.1

4536n

M

; (2.1)

where Mtis the design maximum takeoff mass in kilograms; except thatnly max manmay not be less than 2.5 and need not be greater than 3.8.

3. WINGS MASS DATA

Unit's masses (if these data are absent in the description of the prototype) are

set with the help of statistical data for the transport airplanes adduced in tab. 3.1.Thusthe mass of one of primary struts makes usually 45 % from mass of the whole landinggear.

From home task by department "Designing of planes and helicopters" you havetotal fuel mass in wing. The half-wings each have three fuel tanks from safetyconditions as minimal. In this project you can suppose that fuel load is concentratedfor simplicity. From statistic we know that in the first tank is placed 45% from total fuelmass in half-wing, in the second tank 35%, in the third tank 20% (see fig. 3.1).

Approximately by axes xrelative coordinates of centers of mass for tanks are equal

f

x=0.4=40% from leading edge. Approximately by axes z relative coordinates of

centers of mass for the first tanks is equal =0.2, for the second tank - z=0.5, for the

third tank - =0.8.

From the point of view of strength fuel is expedient to place in a wing. Thereforein the final development it is necessary to place the greatest possible fuel content in awing and the rest of fuel to place in a tail unit.

If in a wing there are freights dropped in flight (external fuel tanks) or fuel fromwing fuel tanks is consumed non-uniformly in this case strength of the given crosssection of a wing is calculated from the loadings appropriate not to take-off mass Mt,

but to the flight Mfl one.


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Table 3.1.Assemblages and payloads relative mass in the percent share from transport airplane

take-off mass

Take-off mass, tons

t 10 50 100 150 200Assemblages relative mass %

wThe wing

12.2 10.2 9.5 9.1 8.8

lThe landing gear

4.5 4.0 3.8 3.7 3.6

The power plant

ppJet planes

12.3 11.0 10.5 10.2 10.0

pp Turboprops planes16.4 15.6 15.3 15.1 15.0

Total load

tl 43.3 45.8 53.7 61.4 67.6

Note: the total load Mtlis equal to the sum of the fuel and the payload.

Let in a wing there is a freight dropped in flight with weight of G* (the tank-section containing fuel with weight G*), which gravity centre is located in the -cross section with coordinate z (fig. 3.2). Bending moment in the designing crosssection 1-1 depends from the relative -section's position and

force coordinate

which is the resultant of an air load, operating on a segment covered withScutarea,located on the right of the 1-1 cross section. Considering approximately, that airloading is constant on all wing area, we can write down:

cut cut

y t t

w w

S SP M g G

S S (3.1)

wheret t

G M g- is take-off weight of plane, Sw wing area.

If the G* load is present, the 0 bending moment in the 1-1 cross section is

defined by the formula:

0 = *cutt 0 1

w

SG z G ( z z )S

. (3.2)

At the G*loads dropping the force is decreased by the value

* cut

y t

w

SP ( G 2G )

S . (3.3)

Thats why the * loads post dropping bending moment in 1-1 section is equal

to

* = *cut cut t 0 0

w w

S 2SG z G z

S S

.


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Fig. 3.1. Disposition of fuel tanks.

Fig. 3.2. Disposition of dropping cargo G*and forcePyrelatively designingcross section I-I.

The 0 and * , moments are equal to each other if the given identity is right*

1 0 cut wz z z z ( 2S / S ) .

If the load has the z z* coordinate, than at its dropping * > 0 , therefore,

the bending moment is increased in the 1-1 section.Thus, to the 1-1 designing cross section a case when freights dropped in flight

are not taken into account, and fuel from tanks sections is consumed which gravitycenters coordinates exceed the z* is more dangerous. At this stage the calculations

1-st fueltank

2-nd fueltank

3-rd fueltank

c.g. c.g.c.g.

xfFrontspar

X

Z

Rear spar


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are necessary to perform for the Gfl flight mass which can be received, subtractingfrom the Gt take-off weight the dropped freights and burnt out fuel. Mass of thedropped freights and burnt out fuel in the further calculations is not taken intoaccount.

The z0parameter is defined from the geometrical construction (fig.3.3) or by the

formula

z l b a

b a0

0

3

2 .

For all student designing cross section is assigned under z=0.2. In this case

designing flight mass Mflis equal:

fl t fM M 0.2M , (3.4)

where Mfis total fuel mass.

Fig. 3.3. The scheme of calculation for coordinate z0.

4. WINGS LOADS CALCULATION

The wing is influenced by the air forces allocated on a surface and mass forcescaused by a wing structure and by the wing-arranged fuel, the concentrated forcesfrom the wing - arranged units' masses. Mass forces are parallel to air forces, but are

directed to the opposite side. The fuel tank is expedient to divide on tank-sections andmass of everyone tank-section to concentrate in its gravity center. Then the fuel-distributed load is possible to replace by a set from the concentrated forces.

In FAR, JAR, ARU load factors ny are prescribedin body frame of reference forplanexp, yp, zp(fig. 4.1). We must calculate wing loads in body frame of reference forwingxw, yw, zw(fig. 4.1). From aerodynamic we have speed frame of referencexa, ya,za (fig. 4.1). Therefore we must recalculate loads from body frame of reference forplanexp, yp, zptobody frame of reference for wing xw, yw, zw(fig. 4.1) with using ofspeed frame of referencexa, ya, za


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In speed (aerodynamic) coordinate system the resultant air force R has twocomponents: the Y - lift directed perpendicularly to vector of flight speed and the

Xa=Q - drag force directed opposite to flight (fig. 4.1).From designing you should know that wing has wing angle of incidence a. This

angle is angle between body axis for planexp

andbody axis for wingxw

(fig. 4.1).The lift coefficient is calculated in body frame of reference for plane xp, yp, zp

from equation of equilibrium because we have load factor from AR in body frame ofreference for plane:

2

l l H

fl fl y w

Vn M g n G C S

2

.

In the SI we have from this formula:l

fl

y 2

H w

2n M g C

V S

,

where H is air density on HC in SI, V=VC cruise airspeed in m/s, Mfl designing flight mass of plane in kg mass.

By the value of Cyyou can estimate the angle of attack with accuracy within1o,

drag coefficient Cx and the relative coordinate of pressure center Ccp fromaerodynamic characteristic of airfoil (Appendix 1).

The angle between the resultant air force R and Y lift force (fig. 4.1) isequal:

y

x1

y

xa

C

Ctg

C

Carctg

Y

Xarctg

(4.1)

From aerodynamic and designing you must know wing angle of incidence - a(fig. 4.1). You can take this angle from your home task by your airplane or fromstatistic take mean value a=2.

By those values we can calculate resultant air force R (seefig. 4.1):

For strength analysis of wing we must calculate loads in wing frame ofreference by resultant air force R. Lift force in wing frame of reference Yw is equal to:

, (4.2)

where 2 =-- is angle between resultant air force R and lift forceYwin wingframe of reference (seefig. 4.1).

Drag force in wing frame of referenceXwis equal to:

(4.3)


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Fig.4.1 Distribution of the aerodynamic load by axes.

On the basis of stated it is enough to plot diagrams of the shear force andbending moment by a wing from effect of the efforts in wing coordinate system. Theshear force and bending moment in the given cross section from the loads in wingframe of reference, we can receive by (4.2, 4.3).

The wing strength is determined in ultimate, instead of limit loading condition.Then also diagrams of shear forces and bending moments it is convenient to plotfrom ultimate, instead from limit loadings. At calculation of ultimate loads in thebeginning we find the ultimate load factor by the formula:

, (4.4)where the nl is the limit load factor for the given design limit loading condition;

the f- is the safety factor.According toAR-25, FAR-25, JAR-25unless otherwise specified, the factor of

safety of f=1.5must be applied to the prescribed limit load are considered external

load on the structure.By the value it is possible to find the ultimate loads. So, lift and a componentalong an axis yp from resultant mass load of a wing structure are found by theformulas:

. . , (4.5)

where the Gw, Mw are weight and mass of wing.In wing frame of reference, we must use (4.2, 4.3) and we have:

.

, [N],

, (4.6)


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where the Yw, Pww are resultant air force and resultant inertial force in wing frame ofreference.

Load components acting along the ywaxis from effect of a concentrated massof the aggregate is calculated by the formula:

.

(4.7)

where the Gg, Mag - are the units weight [N] and units mass [kg].

4.1. AIR LOADS ALLOCATION BY THE WING SPAN.

The Y air load in wing frame of reference is allocated according to the relativecirculation low, i.e.

.

,

wL5.0

zz , (4.1.1)

where )z( - is relative circulation, Mfl - is the designing flight mass of the plane(3.4), nu ultimate load factor, Lw wingspan, - is distributed aerodynamic forceby yw.

For distributed load we have next sign convention - if distributed load isdirected upward it has positive sign, if distributed load is directed downward ithas negative sign.

The function )z( depends from many factors, from which in the given work

you should take into account only the dependence from wing taper and sweepback.Relative circulation in this case is determined by the formula:

)z( = )z(f + )z(

, (4.1.2)

where )z(

is amendment on the wing sweep, )z(f function values for flat

straight trapezoidal center-section-less wing are reduced in Appendix 3.This amendment is calculated by the formulas:

)()(

4545

, (4.1.3)

where the

is the designing wing sweep on the chords fourth, angle in degree,(45)is amendment for wing sweep on the chords fourth which is equal 45. This

amendment was given in Appendix 4.

For calculation )z(f you should know wing taper which is designated through

and is equal to:

tr b/b ,

where br is root chord of wing, bt tip chord.


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4.2. THE WING STRUCTURE MASS LOAD ALLOCATION.

In approximate calculations it is possible to consider, that load per unit of wingspan mass forces is proportional to chords. Then in wing frame of reference the nextformula is used:

, (4.2.1)

where the b(z) is the wing chord, Mw the wing mass, - distributed inertialforce from wing mass.

The length of wing chord (see column 3 in table 4.3.1) is computed by formulas:

r r tb( z ) b ( b b )z . (4.2.2)

where br is root chord of wing, bt tip chord, - relative coordinate of cross

section (column 2).After the component calculations it is possible to compute the total distributed

wing load qt acting in the direction of the axis yw in the wing coordinate system.Calculations are put into the tab. 4.3.1. At this action the coordinates origin is put intothe wing root cross section. Cross sections are enumerated from the wing root in thewing tip direction beginning from the i = 0.The letter accentuates relative coordinate

wL/z2z . Since on the site = 1 0.9cross sections the qaydiagram is moved

away from straight line, it is necessary to introduce the cross section with the= 0.95coordinate.

4.3. CALCULATION OF THE TOTAL DISTRIBUTED LOAD ON A WING

Table 4.3.1The, ,and qtdistributed loads calculations scheme

i b( z ),m

f

m

kN,q

a

y

m

kN,q

w

y

,tkN

qm

1 2 3 4 5 6 7 8 9

0 0

1 0.1

2 0.2

3 0.34 0.4

5 0.5

6 0.6

7 0.7

8 0.8

9 0.9

10 0.95

11 1.0 0 0 0 0


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The total distributed wing load is calculated by the formula:a w

t y yq q q . (4.3.1)

It is also necessary to plot the , and qtfunctions in the same coordinatesystem and in the same scale (see fig. 1.2.1).

In this formula you should summarize in algebraic sense with account of sign.The concentrated mass forces from aggregates Ppw(4.5) also put on figure of a

wing (see fig. 1.2.1). Thus it is convenient to show forces by vectors and to put downa value of these forces.

4.4. THE CHEAR FORCES, BENDING AND REDUCED MOMENTS DIAGRAMSPLOTTING

In the beginning functions shear force )z(Qd and bending moment )z(Md

from the total distributed load qt(z) are found on the wing span. For this purposeintegrals are calculated by tabulated way with trapezoids method.

z

L5.0 w

dz)z(qQ ,

w

z

L2

M Q( z )dz

(4.4.1)

You must yourself to determine signs for q, Q, Maccording to sign conventionfrom mechanic of materials see fig. 4.4.1.

The calculation scheme is given in the tab. 4.4.1, which includes the following values:i 1 ii w

z 0.5( z z )L ; z11=0,(i =10, 9... 1, 0),

, . , , , Q11= 0, (i =10, 9... 1, 0),QQQ iii 1 . Q11= 0; (i = 10, 9... 1, 0),

. , M11=0, (i =10, 9 1, 0)MMM iii 1 ., M11= 0; (i = 10, 9 1, 0) (4.4.2)

where z10 is distance between cross-section number 10 and cross-section number11 and so on; accordingly Q11=0 is increment of shear force in cross-sectionnumber 11 from distributed loads out tip wing. Q10- is increment of shear force incross-section number 10 from distributed loads on site between 10 and 11 cross-sections and so on; Q11=0 is shear force in cross-section number 11 fromdistributed loads out tip wing.Q10 - is shear force in cross-section number 10 fromdistributed loads on site between 10 and 11 cross-sections and so on; M11=0 - isincrement of bending moment in cross-section number 11 from distributed loads outtip wing. M10 - is increment of bending moment in cross-section number 10 fromdistributed loads on site between 10 and 11 cross-sections and so on; M11=0 isbending moment in cross-section number 11 from distributed loads out tip wing; M10-is bending moment in cross-section number 10 from distributed loads on site between

10 and 11 cross-sections and so on.


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Fig. 4.4.1. Sign convention for a shear force Qand bending moment M.

The table 4.4.1 is constructed in the assumption that integration implements bythe trapezoids method. The origin is placed in the wing root section. Cross sectionsare numbered from a wing root to a wing tip sincei=0. You can rewrite from previoustable columns 1, 2, 9 in columns 1, 2, 4 accordingly.

After filling of tab. 4.4.1 by the calculated shear forces Qand bending momentsM (on fig.1.2.1 is shown Q and on fig. 1.2.2 is shown M) diagrams are plotted.Diagrams of bending moments are plotted on tension fibers of a wing. Also it is

necessary to result the shear forces and bending moments affected by the Py,agrconcentrated mass forces (in the same coordinate systems that Qand M. and in thesame scale) diagrams. However the sign of these diagrams is opposite to one ofdiagrams Qand M. On fig.1.2.1 diagram Qcfrom concentrated forces is shown (table4.4.2) and on fig. 1.2.2 is shown Mc.

In concentrated mass forces you must include all aggregates of wing engines,landing gears, fuel tanks and so on.

The calculation scheme is given in the tab. 4.4.2, which includes the following

values: Qic= Pw,agr,ifrom (4.7) where i - is number of cross section in which this unit

is placed; in any cross sections Qic = 0. In table 4.4.2 for example concentratedforce is given only in cross section i= 9. You can rewrite columns 1, 2 and 3 fromprevious table.

, , ,, (i = 10, 9... 1, 0),., . , , , M11c=0, (i =10, 9... 1, 0), 4.4.3)

MMM ,1i,1i,i . M11,= 0; (i = 10, 9... 1, 0)where Q11,c=0 is shear force in cross-section number 11 from concentrated loads inthe tip wing. Q10,c - is shear force in cross-section number 10 from concentratedloads. Q9,c- is shear force in cross-section number 9 from concentrated loads which

has jump in this cross-section and two values one previous value - 0and new value

Q>0

M>0


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Q9,cand so on; M11,c=0- is increment of bending moment in cross-section number11 from concentrated loads out tip wing. M10,c- is increment of bending moment incross-section number 10 from concentrated loads on site between 10 and 11 cross-sections and so on; M11,c=0 is bending moment in cross-section number 11 fromconcentrated loads out tip wing. M

10,c - is bending moment in cross-section number

10 from concentrated loads on site between 10 and 11 cross-sections and so on. Youmust know that increment of bending moment from concentrated force and bendingmoment from concentrated force you can calculate for next cross-section with numberi-1=8 in our examplesee fig. 1.2.2 and table 4.4.2.

Folding appropriate diagrams algebraically (table 4.4.3), you should plot totaldiagrams Qtotand Mtot(on fig. 1.2.2 are shown by continuous lines). The calculationscheme is given in the tab. 4.4.3, which includes the following values:Qid-is shear force from distributed loads from table 4.4.1;Qic- is shear force from concentrated loads from table 4.4.2;

Qitot=Qid+ Qicwith account signs;Mid- is bending moment from distributed loads from table 4.4.1;Mic- is bending moment from concentrated loads from table 4.4.2;Mtot= Mid+ Micwith account signs.

Table 4.4.1The Qd(z)shear forces and the d(z)bending moment are affected by the qt(z)

distributed load.

ii zi,.

m

,tq

kN

m

Q

id.

kN

Qid

.

kN

Mid.

kNm

Mid.kN m

1 2 3 4 5 6 7 8

0 0 qt0

Q0 Q0 M0 M01

2

34

5

6

78 ...

9 0.9 z9 qt9

Q9 Q

9 M9 M9

10 0.95 z10 qt10

Q10

Q10

=Q10

M10 M10 =M1011 1.0 0 q t11

0 0 0 0


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Table 4.4.2The Qic(z)shear forces and the ic(z)bending moment are affected by the

concentrated load.

ii zi,.

m

Qi

.

kN

Qi

.

kN

Mi .

kNm

Mi .

kN m1 2 3 4 5 6 7

0 0 0 Q0 M0 M0

1

2

3

4

5

...

7 Q7=Q9 8 ... Q8=Q9 M8 M8=M89 0.9 z9 Q9 Q9=Q9/0 0 0

10 0.95 z10 0 0 0 0

11 1.0 0 0 0 0 0

Table 4.4.3The total Qtot(z)shear forces and the total itot(z)bending moment are affected

by all forces.

i Qid.kN

Qic.kN

Qitot.kN

Mid.kN*m

Mic.KN*m

Mitot.kNm

1 2 3 4 5 6 7

0

1

2

3

4

5

67

8

9

1011

Those bending moment and shear forces were calculated in the wing systemcoordinate yw, xw, zw(see fig. 4.1).

An origin is placed in the gravity centre of wing cross section on longitudinal axesof wing cross section xw. According to fig. 4.1 it is possible to write down:


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, , (4.4.4) ,

.where the 2=- is the angle between total aerodynamic force R and lift

force Yw in wing frame of reference (see 4.1), the Qtotand Mtotare shear force andbending moment in the design cross sections in wing coordinate system, taken fromthe table 4.4.3; the Qyw ,is normal shear force which acts by axes ywin the wingcoordinate system and Qxw is shear forces which acts by axes xw in the wingcoordinate system; the Myw is bending moment in the design cross sections in thewing coordinate system relative axes yw and Mtot = Mxw is bending moment in thedesign cross sections in the wing coordinate system relative axesxw.

If


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The distributed reduced moment mzaffected by the distributed loads andis equal:

(4.4.5)where the eand the dare distances from load points andto the reduction axis.

The moment is considered like positive if it acts on pitching relative to thereduction axis. The and dvalues are taken from the fig. 1.2.3.

You can compute their by formulas:

c .g c .g ii i i w i d z tg x b 0.5L z x b .

. . . . ,r t

w

0.8( b b )tg

L

,

where i - is the relative coordinate z for i-thcross section (column 2 from table

4.4.2). c .gx - is relative coordinate of wing center of gravity.Integrating the diagram mz we receive the reduced moments Mzd affected by

the distributed loads. The scheme of calculation is shown in tab. 4.4.4 in whichdesignations is entered:

ii,z1zizid z)mm(5.0M 01111 ,z,z MM ;

z ,i ,d z ,i 1,d z ,i ,dM M M

, (i = 10, 9....., 0).

In the explanatory book you should plot diagrams mzandMz (a diagram Mz isshown on fig.1.2.2 by a dashed line). In a coordinate system for the moments Mzalsoit is necessary to result a diagram of the reduced moments affected by concentrated

masses (on fig. 1.2.2 it is shown by a light line).Affected by a concentrated mass of the i-th aggregate the increment of the

moment z ,c ,i

M is found out by the formula:

,, ,, (4.4.7)where the ri is the distance from the i-th concentrated mass gravity center toreduction axis (it is measured on the drawing). Pw,ag,i is design inertia force by

formula (4.7). The momentz ,,c ,i

M is positive if it acts on pitching. This increment you

have only in point where you have aggregates. In any points this increment is equalzero. Reduced momentMz.c.iis calculated by the formula:

z ,c ,11 z ,c ,11M M 0

;

z ,c ,i z ,c ,i 1 z ,c ,iM M M

. (i = 10, 9.....,0). (4.4.8)

In the point with aggregates we have jumps of reduced moment (see fig. 1.2.2).For this table we take Mz i d from table 4.4.4 and total reduced moment you

should compute with account of signs by the formula:Mz tot= Mz d+ Mz c (4.4.9)


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Table 4.4.4Reduced moments calculation scheme from distributed loads

i zi,

m

.,

kN /m

ie

m

,

kN /m

id

m

m iz

kN

zidM

kN

m

M idz

kN m1 2 3 4 5 6 7 8 9

0 , e0 , d0 m 0z M dz01

2

3

4

5

6

78

9

10 z10 , e10 , d10 m 10z M dz10 M dz1011 z11 , e11 , d11 m 11z 0 0

Table 4.4.5Calculation scheme of reduced moment from concentrated loads and from all loads.

I Pw.ag.ikN

rim

Mz.c .ikN*m

Mz.c.ikN*m

MzdikN*m

MztotikN*m

1 2 3 4 5 6 7

0

1

23

4

56

7

8

9

10

11

It is also necessary to plot thez ,tot

M total reduced moment diagram (on fig.

1.2.2 it is shown by the solid line).


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4.5. LOAD CHECKING FOR WING ROOT CROSS SECTION

Shear forces, bending and reduced moments values are checked in the rootcross section by the formulas:

,

. . ,,[kN],

, . . , , [kNm],,, . . , (4.5.1)

Here Mflis designing flight mass of plane from (3.4). Mw the wing mass. isthe distance from root section to the air resultant load point; ck- is the distance fromroot section to the k-th aggregate's gravity center and fuel tanks; e and d aredistances from the axis of reduction to points of interception of a plane z=cwith thecenter-of-pressure line and with the c.g. line; rk - is the distance from an axis ofreduction to the k-thaggregate centre of gravity and fuel tanks. In list of aggregatesyou should include all aggregates of wing engines, landing gears, fuel tanks and so

on. Value Cis found with the help of geometrical construction or by the formula:

wL 2

6 1

. (4.5.2)

where the is the wing taper. Values ck.andrkare taken from fig.1.2.3 andparameters eand dvaluesfrom drawing (see fig.1.2.3) in the z = ccross section.

Summation in the right parts of adduced formulas is distributed to allconcentrated masses located in one half-wing. Error of calculation of values,,,,and ,,should not exceed value 1, 10 and 15 % accordingly in relation tothe appropriate values taken from tables in root cross section.

4.6. CALCULATION OF SHEAR FORCES POSITION IN THE DESIGN CROSSSECTION

By values of shear force and the reduced moment it is possible to find outpoint of application for shear force on a wing chord in design cross section:

, ,,, (4.6.1)Thexrcoordinate is count off from the reduction axis. The resultant position is

necessary to be shown by an asterisk on the wings top view (see fig. 1.2.1). Youshould calculate this value only for your design cross section i=2.


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Table 4.6.1Results of calculations

Design loading condition C

Design flight mass (kg) - Mfl

Limit load factor - n

l

Safety factor - fUltimate load factor - nu

Fuel mass in 1-st fuel tank (kg) - mf1

Fuel mass in 2-nd fuel tank (kg) ) - mf2

Fuel mass in 3-rd fuel tank (kg) - mf3

Wing span (m) (for equivalent wing)- Lwe

Wing taper

(for equivalent wing)

Wing aspect ratio

(for equivalent wing)

Root wing chord (m) (for equivalent wing) - br

Tip wing chord (m) (for equivalent wing) - bt

Relative thickness of airfoil (%) - c

Number of airfoil

Designing cross section z 0.2

The bending moment for designing cross section (kN*m,form. 4.4.4)

The bending moment for designing cross section (kN*m,form. 4.4.4)

The shear force for designing cross section (kN, form.4.4.4)The shear force for designing cross section (kN, form.4.4.4)

The distance from reduced axis up to application point ofresultant shear force ,(m, form. 4.6.1)The angle of attack

(degree)

The angle between resultant air force and lift force (degree)

Comment.a. Masses in integer kg.


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APPENDIXIES


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Appendix 1Characteristic of airfoil

The airfoil NACA 0009

Geometric characteristic of airfoil(in %from chord)

Aerodynamic characteristic ofairfoil

X Yt Yb h Cy Ccp

0 0 0 0 -4 -0.30 0.014 -

2.5 1.96 -1.96 3.92 -2 -0.16 0.008 -

5 2.67 -2.67 5.34 0 0.00 0.0064 -

7.5 3.15 -3.15 6.30 2 0.16 0.008 0.240

10 3.51 -3.51 7.02 4 0.30 0.014 0.240

15 4.01 -4.01 8.02 6 0.45 0.020 0.240

20 4.30 -4.30 8.60 8 0.60 0.032 0.240

25 4.46 -4.46 8.92 10 0.74 0.042 0.240

30 4.50 -4.50 9.00 12 0.90 0.059 0.240

40 4.35 -4.35 8.70 14 1.05 0.077 0.240

50 3.97 -3.97 7.94 16 1.19 0.098 0.240

60 3.42 -3.42 6.84 18 1.30 0.120 0.24

70 2.75 -2.75 5.50 20 1.17 0.165 0.266

80 1.97 -1.97 3.94 21 1.06 0.280 0.32490 1.09 -1.09 2.18 22 0.96 0.340 0.362

100 0 0 0 24 0.91 0.392 0.383


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Aerodynamic characteristic of

airfoil

X Yt Yb h Cy Ccp

0 0 0 0 -4 -0.30 0.015 -

2.5 2.62 -2.62 5.24 -2 -0.15 0.009 -

5 3.56 -3.56 0.00 0 0.00 0.007 -

7.5 4.20 -4.20 8.40 2 0.15 0.009 0.244

10 4.68 -4.68 9.36 4 0.30 0.015 0.244

15 5.34 -5.34 10.68 6 0.445 0.020 0.244

20 5.74 -5.74 11.48 8 0.60 0.033 0.244

25 5.94 -5.94 11.88 10 0.745 0.041 0.244

30 6.00 -6.00 12.00 12 0.90 0.059 0.244

40 5.80 -5.80 11.60 14 1.045 0.075 0.244

50 5.29 -5.29 10.58 16 1.20 0.096 0.244

60 4.56 -4.56 9.12 18 1.32 0.119 0.244

70 3.66 -3.66 7.32 20 1.46 0.142 0.244

80 2.62 -2.62 5.24 21 1.55 0.173 0.244

90 1.45 -1.45 2.90 22 1.20 0.262 0.301

100 0 0 0 24 1.09 0.322 0.335


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Geometric characteristic ofairfoil

(in %from chord)


X Yt Yb h Cy Ccp

0 0 0 0 -4 -0.30 0.014 -

2.5 3.27 -3.27 6.54 -2 -0.15 0.009 -

5 4.44 -4.44 8.88 0 0.00 0.007 0.238

7.5 5.25 -5.25 10.50 2 0.15 0.009 0.238

10 5.85 -5.85 11.70 4 0.30 0.014 0.238

15 6.68 -6.68 13.36 6 0.45 0.020 0.238

20 7.17 -7.17 14.34 8 0.60 0.031 0.238

25 7.43 -7.43 14.86 10 0.74 0.042 0.238

30 7.50 -7.50 15.00 12 0.89 0.060 0.238

40 7.25 -7.25 14.50 14 1.02 0.075 0.233

50 6.62 -6.62 13.24 16 1.17 0.095 0.238

60 5.70 -5.70 11.40 18 1.30 0.119 0.238

70 4.58 -4.58 9.16 20 1.42 0.140 0.238

80 3.28 -3.28 6.56 21 1.55 0.178 0.238

90 1.81 -1.81 3.62 22 1.29 0.210 0.284

100 0 0 0 24 1.21 0.269 0.300


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The airfoil NACA-21012

Geometric characteristic of airfoil(in %from chord) Aerodynamic characteristic of airfoil

X Yt Yb h Cx Cm Ccp

0 0 0 0 -4 -0.26 0.014 -0.062

1.25 2.95 -0.90 3.85 -2 -0.20 0.0095 -0.024 ---

2.5 3.72 -1.45 5.17 0 0.035 0.0071 0.0072 0.206

5 4.67 -2.44 8.11 2 0.20 0.011 0.046 0.230

7.5 5.28 -.12 8.40 4 0.36 0.017 0.0814 0.232

10 5.72 -3.64 9.36 6 0.50 0.0225 0.1165 0.233

15 6.33 -4.36 10.69 8 0.65 0.034 0.152 0.23420 6.67 -4.80 11.47 10 0.80 0.047 0.187 0.234

25 6.82 -5.07 11.89 12 0.95 0.065 0.222 0.234

30 6.82 -5.18 12.00 14 1.09 0.083 0.255 0.233

40 6.52 -5.10 11.622 16 1.23 0.114 0.288 0.234

50 5.89 -4.71 10.60 18 1.36 0.128 0.319 0.234

60 5.04 -4.09 9.13 20.8 1.50 0.160 0.352 0.234

70 4.03 -3.30 7.33 21 1.52 0.182 0.354 0.234

80 2.86 -2.38 5.24 21 1.20 0.252 0.352 '0.293

90 1.5757 -1.32 2.89 22 1.12 0.281 0.353 0.31595 0.87 -0.75 1.62 24 1.02 0.341 0.360 0.353

100 0 0 0 26 0.96 0.392 0.346 0.360

30 0.88 0.464 0.347 0.394


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Geometrical characteristic of airfoil(in % from chord)

Aerodynamic characteristic of airfoil

X Yt Yb Ym h Cy Cx Cm Ccp

0 0 0 0 0 -4 -0.25 0.0092 -0.054 ---

1.25 2.84 -1.10 0.87 3.94 -2 -0.10 0.008 -0.019 ---

2.5 3.76 -1.60 1.08 5.36 0 0.05 0.0073 0.017 0.336

5 4.97 -2.17 1.40 7.14 2 0.20 0.009 0.052 0.260

7.5 5.71 -2.68 1.52 8.39 4 0.37 0.016 0.092 0.249

10 6.22 -3.15 1.54 9.37 6 0.50 0.022 0.123 0.246

15 6.80 -3.89 1.46 10.69 8 0.66 0.034 0.161 0.244

20 7.11 -4.38 1.37 11.49 10 0.80 0.048 0.195 0.244

25 7.23 -4.66 1.29 11.89 12 0.97 0.063 0.237 0.244

30 7.22 -4.80 1.21 12.02 14 1.10 0.0820.268

0.244

40 6.85 -4.76 1.05 11.61 16 1.24 0.105 0.300 0.244

50 6.17 -4.42 0.88 10.59 18 1.38 0.130 0.337 0.244

60 5.27 -3.85 0.71 9.12 20 1.50 0.156 0.366 0.244

70 4.19 -3.14 0.53 7.33 22 1.60 0.180 0.389 0.245

80 2.99 -2.26 0.37 5.25 22 1.26 0.252 0.368 0.292

90 1.63 -1.26 0.19 2.89 24 1.13 0.320 0.378 0.334

95 0.89 -0.71 0.09 1.60 26 1.04 0.372 0.377 0.363

100 0 0 0 0 30 0.94 0.454 0.372 0.395


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The airfoil NACA - 2210



X Yt Yb Ym h Cy Ccp

0 0 0 0 0 0.120 0.010 0.467

2.5 2.92 -1.52 0.70 4.44 2 0.262 0.013 0.339

5 4.02 -1.96 1.03 5.98 4 0.403 0.020 0.304

7.5 4.83 -2.17 1.33 7.00 6 0.545 0.029 0.291

10 5.51 -2.47 1.59 7.98 8 0.688 0.043 0.27915 6.40 -2.50 1.96 9.00 10 0.827 0.058 0.273

20 6.78 -2.78 2.00 9.56 12 0.960 0.074 0.267

25 6.94 -2.96 1.99 9.90 14 1.080 0.094 0.264

30 6.97 -3.03 1.97 10.00 16 1.195 0.114 0.260

40 6.75 -2.95 1.90 9.70 18 1.250 0.130 0.257

50 6.16 -2.72 1.72 8.88 20 1.162 0.163 0.283

60 5.34 -2.30 1.52 7.64 21 1.158 0.207 0.299

70 4.29 -1.81 1.24 6.10 22 1.130 0.278 0.317

80 3.19 -1.41 0.89 4.60

90 1.60 -0.74 0.43 2.34

100 0 0 0 0


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The airfoil NACA -2212



X Yt Yb h Cy

Ccp

0 0 0 0 -4 -0.17 0.0110

2.5 3.35 -1.96 5.31 -2 -0.01 0.0088

5 4.62 -2.55 7.17 0 0.13 0.0088 0.476

7.5 5.55 -2.89 8.44 2 0.29 0.0135 0.348

10 6.27 -3.11 9.38 4 0.43 0.0195 0.316

15 7.25 -3.44 10.69 6 0.59 0.028 0.300

20 7.74 -3.74 11.48 8 0.73 0.040 0.289

25 7.93 -3.94 11.87 10 0.88 0.055 0.283

30 7.97 -4.03 12.00 12 1.02 0.072 0.278

40 7.68 -3.92 11.60 14 1.16 0.092 0.275

50 7.02 -3.56 10.58 16 1.30 0.113 0.272

60 6.07 -3.05 9.12 18 1.42 0.139 0.270

70 4.90 -2.43 7.33 20 1.54 0.162 0.269

80 3.52 -1.74 5.26 21 1.60 0.203 0.268

90 1.93 -0.97 2.90 22 1.40 0.240 0.300

100 0 0 0 24 1.31 0.310 0.327


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X Yt Yb h Cy

Ccp

0 0 0 0 -5.12 -0.229 0.0162 0.104

2.5 3.8 -2.41 6.21 -3.27 -0.106 0.0131 -

5 5.21 -3.15 8.36 -1.51 0.017 0.0116 -

7.5 6.23 -3.58 9.81 0.3 0.139 0.0127 0.418

10 7.06 -3.90 10.96 2.14 0.264 0.0165 0.327

15 8.20 -4.28 12.48 4.01 0.396 0.0235 0.299

20 8.69 -4.69 13.38 5.79 0.535 0.0325 0.285

25 8.92 -4.94 13.86 7.65 0.678 0.0446 0.279

30 8.97 -5.03 14.00 9.5 0.825 0.0596 0.275

40 8.68 -4.89 13.57 11.39 0.943 0.0764 0.275

50 7.88 -4.44 12.32 13.15 1.057 0.0923 0.261

60 6.05 -3.71 10.66 14.99 1.154 0.110 0.261

70 5.5 -3.02 8.52 16.94 1.226 0.1302 0.260

80 3.96 -2.18 6.44 18.65 1.257 0.1672 0.263

90 2.07 -1.21 3.28 20.43 1.214 0.2041 0.285

100 0 0 0 22.22 1.190 0.2359 0.302


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Geometric characteristic of airfoil(in % from chord)


X Yt Yb Ym h Cy Cm Ccp

0 0 0 0 0 -4 -0.22 0.013 0.046 -

1.25 2.67 -1.23 0.77 3.90 -2 -0.08 0.00955 -0.011 -

2.5 3.61 -1.71 0.95 5.32 0 0.085 0.0071 0.028 0.330

5 4.91 -2.26 1.33 7.17 2 0.24 0.012 0.065 0.270

7.5 5.80 -2.61 1.60 8.41 4 0.385 0.018 0.099 0.257

10 6.43 -2.92 1.76 9.35 6 0.53 0.025 0.134 0.253

15 7.19 -3.50 1.85 10.69 8 0.68 0.035 0.169 0.248

20 7.50 -3.97 1.77 11.47 10 0.835 0.050 0.206 0.24725 7.60 -4.28 1.66 11.88 12 0.98 0.067 0.242 0.247

30 7.55 -4.46 1.54 12.01 14 1.12 0.088 0.275 0.245

40 7.14 -4.48 1.33 11.62 16 1.28 0.108 0.313 0.244

50 6.41 -4.17 1.12 10.58 18 1.40 0.130 0.342 0.245

60 5.47 -3.67 0.90 9.14 20 1.53 0.159 0.372 0.243

70 4.36 -3.00 0.68 7.36 22 1.63 0.186 0.396 0.243

80 3.08 -2.16 0.46 5.24 22 1.31 0.255 0.382 0.292

90 1.68 -1.23 0.23 2.71 24 1.19 0.317 0.394 0.33195 0.92 -0.70 0.11 1.62 26 1.045 0.390 0.375

100 0 0 0 0 30 0.98 0.393 0.400


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The airfoil NACA - 2309



X Yt Yb Ym h Cy Ccp

0 0 0 0 -2 0.00 0.009 -

2.5 2.39 -1.58 0.405 3.97 0 0.15 0.008 0.490

5 3.36 -2.01 0.675 5.37 2 0.30 0.012 0.370

7.5 4.09 -2.24 0.925 6.33 4 0.45 0.020 0.331

10 4.67 -2.38 1.145 7.05 6 0.60 0.028 0.310

15 5.54 -2.50 1.52 8.04 8 0.75 0.040 0.299

20 6.08 -2.52 1.78 8.60 10 0.90 0.054 0.290

25 6.37 -2.51 1.93 8.88 12 1.06 0.074 0.285

30 6.50 -2.50 2.00 9.00 14 1.20 0.094 0.282

40 6.32 -2.39 1.965 8.71 16 1.34 0.120 0.279

50 5.82 -2.13 1.845 7.95 18 1.44 0.142 0.278

60 5.07 -1.78 1.645 6.85 20 1.51 0.188 0.277

70 4.11 -1.38 1.365 5.49 21 1.40 0.238 0.307

80 2.96 -0.97 0.995 3.93 22 1.30 0.310 0.342

90 1.64 -0.54 0.55 2.18 24 1.20 0.380 0.375

100 0 0 0 0


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Geometric characteristic of airfoil

(in %from chord)

Aerodynamic characteristic

of airfoilX Yt Yb Ym h Cy Ccp

0 0 0 0 0 -2 0.00 0.003 -

2.5 3.11 -2.16 0.475 5.27 0 0.13 0.011 0.527

5 4.31 -2.85 0.73 7.16 2 0.30 0.014 0.377

7.5 5.18 -3.26 0.96 8.14 4 0.44 0.020 0.338

10 5.86 -3.52 1.17 9.38 6 0.58 0.028 0.310

15 6.89 -3.82 1.535 10.71 8 0.74 0.040 0.297

20 7.54 -3.94 1.80 11.48 10 0.90 0.056 0.289

25 7.88 -3.99 1.945 11.87 12 1.04 0.064 0.284

30 8.00 -4.10 2.00 12.00 14 1.18 0.090 0.273

40 7.77 -3.84 1.965 11.61 16 1.30 0.114 0.279

50 7.14 -3.45 1.845 10.59 18 1.42 0.140 0.276

60 6.21 -2.92 1.645 9.13 20 1.54 0.164 0.276

70 5.02 -2.31 1.355 7.33 21 1.61 0.200 0.276

80 3.62 -1.63 0.995 5.25 22 1.47 0.247 0.302

90 2.00 -1.91 0.545 2 91 24 1.36 0.300 0.316

100 0 0 0 0 26 1.24 0.360 0.351


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X Yt Yb h Cy

Ccp

0 0 0 0 -4 -0.19 0.013

2.5 3.85 -2.74 6.59 -2 -0.01 0.010

5 5.26 -3.66 8.92 0 0.13 0.011 0.510

7.5 6.28 -4.25 10.74 2 0.30 0.014 0.357

10 7.08 -4.66 11.74 4 0.42 0.020 0.324

15 8.25 -5.13 13.38 6 0.53 0.030 0.302

20 8.97 -5.38 14.35 8 0.72 0.040 0.292

25 9.36 -5.48 14.84 10 0.86 0.054 0.285

30 9.50 -5.50 15.00 12 1.01 0.072 0.279

40 9.22 -5.29 14.51 14 1.10 0.090 0.277

50 8.47 -4.77 13.24 16 1.30 0.110 0.273

60 7.66 -4.06 11.42 18 1.40 0.140 0.274

70 5.95 -3.22 9.17 20 1.53 0.162 0.274

80 4.29 -2.28 6.57 21 1.54 0.172 0.275

90 2.39 -1.26 3.62 22 1.44 0.230 0.297

95 1.30 -0.72 2.02 24 1.40 0.280 0.314

100 0 0 0 26 1.34 0.340 0.324


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X Yt Yb Ym h Cy C Cm Ccp

0 0 0 0 0 -4 -0.18 0.012 0.001 --

1.25 2.15 -1.65 0.25 3.80 -2 0.00 0.0088 0.044 __

2.5 2.99 -2.27 0.36 5.26 0 0.13 0.010 0.076 0.588

5 4.13 -3.01 0.56 7.14 2 0.29 0.0128 0.119 0.397

7.5 4.96 -3.46 0.75 8.42 4 0.42 0.020 0.150 0.35510 5.63 -3.75 0.94 9.38 6 0.58 0.030 0.189 0.326

15 6.61 -4.10 1.255 10.71 8 0.72 0.040 0.224 0.311

20 7.26 -4.23 1.515 11.49 10 0.88 0.052 0.264 0.300

25 7.67 -4.22 1.725 11.89 12 1.00 0.074 0.294 0.294

30 7.88 -4.12 1.88 12.00 14 1.16 0.090 0.334 0.288

40 7.80 -3.80 2.00 11.60 16 1.30 0.112 0.370 0.281

50 7.24 -3.34 1.95 10.58 18 1.40 0.140 0.392 0.281

60 6.36 -2.76 1.80 9.12 20 1.52 0.160 0.424 0.279

70 5.18 -2.14 1.52 7.32 22 1.60 0.192 0.444 0.278

80 3.75 -1.50 1.125 5.25 24 1.34 0.300 0.436 0.325

90 2.08 -0.82 0.63 2.90 26 1.20 0.360 0.428 0.355

95 1.14 -0.48 0.33 1.62 28 1.10 0.414 0.377

100 0 0 0 0


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Geometric characteristic of airfoil (in% from chord)



0 0 0 0 0 -4 -0.18 0.013 -0.050

1.25 2.71 -2.06 0.33 4.77 -2 -0.02 0.010 0.035

2.5 3.71 -2.86 0.43 6.57 0 0.13 0.012 0.0735 0.557

5 5.07 -3.84 0.62 8.91 2 0.28 0.016 0.110 0.392

7.5 6.06 -4.47 0.80 10.53 4 0.42 0.020 0.145 0.345

10 6.83 -4.90 0.87 11.73 6 0.57 0.030 0.182 0.320

15 7.97 -5.42 1.28 13.39 8 0.71 0.042 0.218 0.307

20 8.70 -5.66 1.52 14.36 10 0.86 0.056 0.255 0.297

25 9.17 -5.70 1.74 14.87 12 1.00 0.071 0.288 0.288

30 9.38 -5.62 1.88 15.00 14 1.15 0.090 0.326 0.283

40 9.25 -5.25 2.00 14.50 16 1.28 0.112 0.360 0.281

50 8.57 -4.67 1.95 13.24 18 1.40 0.136 0.390 0.278

60 7.50 -3.90 1.80 11.40 20 1.50 0.160 0.415 0.276

70 6.10 -3.05 1.53 9.15 22 1.54 0.192 0.425 0.276

80 4.41 -2.15 1.13 6.56 24 1.41 0.280 0.441 0.313

90 2.45 -1.17 0.64 3.62 26 1.31 0.332 0.439 0.335

95 1.34 -0.68 0.33 2.02 28 1.20 0.383 0.425 0.354

100 0 0 0 0 30 1.10 0.415 0.378


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42





0 0 0 0 0

1.25 1.62 -1.23 0.195 2.85 -4 -0.192 0.012 -0.004

2.5 2.27 -1.66 0.305 3.93 -2 0.00 0.008 0.044

5 3.2 -2.15 0.525 5.35 0 0.13 0.008 0.076 0.588

7.5 3.87 -2.44 0.715 6.31 2 0.29 0.0128 0.118 0.39710 4.43 -2.60 0.915 7.03 4 0.43 0.020 0.150 0.352

15 5.25 -2.77 1.24 8.02 6 0.58 0.028 0.188 0.326

20 5.81 -2.79 1.51 8.60 8 0.72 0.040 0.224 0.311

25 6.18 -2.74 1.72 8.92 10 0.88 0.054 0.264 0.300

30 6.38 -2.62 1.88 9.00 12 1.02 0.070 0.298 0.293

40 6.35 -2.35 2.00 8.70 14 1.18 0.090 0.336 0.287

50 5.92 -2.02 1.95 7.94 16 1.30 0.112 0.370 0.284

60 5.22 -1.63 1.795 6.85 18 1.43 0.140 0.402 0.281

70 4.27 -1.24 1.515 5.51 20 1.50 0.180 0.416 0.277

80 3.10 -0.85 1.125 3.95 22 1.30 0.270 0.444 0.342

90 1.72 -0.47 0.625 2.19 24 1.16 0.370 0.430 0.371

95 0.94 -0.28 0.33 1.22 26 1.08 0.420 0.389

100 0 0 0 0 28 1.00 0.410 0.410


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43


Geometric characteristic of airfoil

(in % from chord)

Aerodynamic characteristic of

airfoilX Yt Yb Ym h Cy Cx Cm Ccp

0 0 0 0 -4 -0.21 0.014 -0.042

1.25 3.34 -1.54 0.90 4.90 -2 -0.06 0.011 -0.006

2.5 4.44 -2.25 1.095 6.69 0 0.09 0.0082 0.029 0.332

5 5.89 -3.04 1.425 8.93 2 0.23 0.014 0.063 0.274

7.5 6.91 -3.61 1.65 10.52 4 0.39 0.018 0.101 0.259

10 7.64 -4.09 1.78 11.73 6 0.53 0.027 0.135 0.255

15 8.52 -4.84 1.84 13.36 8 0.69 0.038 0.173 0.251

20 8.92 -5.41 1.76 14.33 10 0.83 0.051 0.206 0.248

25 9.08 -5.78 1.65 14.86 12 0.98 0.068 0.242 0.247

30 9.05 -5.96 1.55 15.01 14 1.13 0.088 0.278 0.246

40 8.59 -5.92 1.34 14.51 16 1.27 0.108 0.312 0.246

50 7.74 -5.50 1.12 13.24 18 1.40 0.132 0.343 0.245

60 6.61 -4.81 0.90 11.42 20 1.52 0.158 0.372 0.244

70 5.25 -3.91 0.67 9.16 22.2 1.61 0.190 0.393 0.244

80 3.73 -2.83 0.45 6.56 22.2 1.36 0.245 0.375 0.275

90 2.04 -1.59 0.23 3.63 24 1.27 0.288 0.379 0.298

95 1.12 -0.90 0.12 2.02 26 1.18 0.338 0.382 0.324

100 0 0 0 0 30 1.01 0.372 0.368


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44





0 0 0 0 -4 -0.22 0.012 -0.0415

1.25 2.04 -0.91 0.07 2.95 -2 -0.09 0.009 -0.013

2.5 2.83 -1.19 0.82 4.02 0 0.09 0.0066 0.031 0.344

5 3.93 -1.44 1.25 5.37 2 0.225 0.011 0.063 0.280

7.5 4.70 -1.63 1.54 6.33 4 0.39 0.0165 0.103 0.26410 5.26 -1.79 1.74 7.05 6 0.53 0.023 0.137 0.258

15 5.85 -2.17 1.84 9.02 8 0.69 0.035 0.175 0.254

20 6.06 -2.55 2.26 8.61 10 0.83 0.050 0.209 0.252

25 6.11 -2.80 1.66 8.91 12 0.975 0.066 0.244 0.250

30 6.05 -2.96 1.55 9.01 14 1.12 0.088 0.279 0.249

40 5.69 -3.03 1.33 8.72 16 1.29 0.110 0.320 0.248

50 5.09 -2.86 1.12 7.95 18 1.40 0.133 0.347 0.247

60 4.32 -2.53 0.89 6.85 20.3 1.55 0.170 0.383 0.247

70 3.42 -2.08 0.72 5.50 20.3 1.30 0.232 0.383 0.295

80 2.41 -1.51 0.45 3.92 22 1.25 0.290 0.401 0.320

90 1.31 -0.86 0.23 2.17 24 1.16 0.360 0.420 0.362

95 0.72 -0.50 0.11 1.22 26 1.08 0.410 0.380

100 0 0 0 0 30 0.95 0.389 0.409


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45


Geometric characteristic of airfoil (in %from chord)



0 0 0 0 0 -4 -0.20 0.012 -0.043

1.25 3.32 -0.86 1.23 4.18 -2 -0.05 0.0078 -0.007

2.5 4.36 -1.11 1.625 5.47 0 0.10 0.0085 0.030 0.300

5 5.69 -1.50 2.095 7.19 2 0.26 0.0128 0.067 0.257

7.5 6.48 -1.91 2.29 8.39 4 0.40 0.018 0.100 0.250

10 6.99 -2.38 2.31 9.37 6 0.55 0.027 0.137 0.249

15 7.53 -3.18 2.18 10.71 8 0.70 0.038 0.173 0.247

20 7.80 -3.68 2.06 11.48 10 0.85 0.052 0.208 0.245

25 7.87 -4.00 1.94 11.87 12 1.00 0.070 0.249 0.244

30 7.81 -4.20 1.81 12.01 14 1.16 0.090 0.283 0.244

40 7.35 -4.26 1.55 11.61 16 1.30 0.112 0.318 0.244

50 6.59 -4.00 1.30 10.59 18 1.41 0.136 0.346 0.245

60 5.60 -3.51 1.05 9.11 20 1.54 0.161 0.378 0.245

70 4.46 -2.88 0.79 7.34 21.8 1.62 0.185 0.397 0.245

80 3.15 -2.10 0.53 5.25 21.8 1.26 0.266 0.370 0.302

90 1.71 -1.19 0.26 2.90 24 1.11 0.334 0.386 0.348

95 0.93 -0.69 0.12 1.62 28 1.00 0.379 0.379

100 0 0 0 0 30 1.97 0.392 0.404


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46


Geometric characteristic of airfoil (in

% from chord)



0 0 0 0 0 -4 -0.20 0.012 -0.035

1.25 2.58 -1.34 0.62 3.92 -2 -0.04 0.0075 -0.0035

2.5 3.50 -1.85 0.83 5.35 0 0.11 0.008 0.0391 0.356

5 4.80 -2.37 1.22 7.172 0.28 0.013 0.079 0.282

7.5 5.74 -2.70 1.52 8.44 4 0.42 0.019 0.125 0.298

10 6.44 -2.95 1.75 9.39 6 0.57 0.027 0.148 0.259

15 7.37 -3.34 2.015 10.71 8 0.71 0.040 0.1815 0.255

20 7.82 -3.66 2.08 11.48 10 0.86 0.054 0.217 0.252

25 7.96 -3.92 2.02 11.88 12 1.01 0.072 0.252 0.250

30 7.89 -4.11 1.89 12.00 14 1.16 0.092 0.287 0.247

40 7.44 -4.17 1.64 11.61 16 1.30 0.113 0.321 0.246

50 6.66 -3.93 1.40 10.59 18 1.43 0.140 0.352 0.247

60 5.67 -3.47 1.10 9.14 20.8 1.59 0.175 0.390 0.245

70 4.48 -2.84 0.82 7.32 21.5 1.60 0.190 0.392 0.245

80 3.18 -2.07 0.56 5.25 21.5 1.38 0.235 0.387 0.280

90 1.73 -1.18 0.28 2.91 24 1.30 0.315 0.388 0.299

95 0.94 -0.67 0.14 1.61 26 1.18 0.368 0.400 0.339

100 0 0 0 0 30 1.00 0.461 0.387 0.387


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47

The airfoil CLARK-YH



X Yt Yb h Cy

Ccp

0 0 0 0 --16 -0.596 0.203 0.356

2.5 3.10 -2.03 5.13 -12 -0.562 0.095 0.264

5 4.59 -2.54 7.13 -8 -0.388 0.025 0.196

7.5 5.62 -2.81 8.43 -4 -0.130 0.013 -

10 6.42 -3.03 9.45 -2 0.000 0.012 -

15 7.57 -3.24 10.81 0 0.130 0.013 0.493

20 8.33 -3.25 11.58 2 0.266 0.023 0.330

30 8.85 -3.14 11.99 4 0.400 0.072 0.278

40 8.66 -3.00 11.66 8 0.656 0.043 0.308

50 7.91 -2.84 10.75 10 0.792 0.059 0.300

60 6.71 -2.69 9.40 12 0.924 0.077 0.294

70 5.07 -2.43 7.50 16 1.166 0.118 0.286

80 3.39 -1.98 5.37 18 1.258 0.146 0.286

90 1.73 -1.21 2.94 20 1.28 0.180 0.297

95 0.90 -0.69 1.59 22 1.24 0.239 0.316

100 0.08 -0.08 0.16 24 1.148 0.289 0.344


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48

The airfoil CAGI 6-8.3%



X Yt Yb h Cy

Ccp

0 0 0 0 -2 0.034 0.0110

2.5 1.80 -0.98 2.78 0 0.168 0.012 0.619

5 2.78 -1.23 4.01 2 0.294 0.016 0.470

7.5 3.62 -1.32 4.94 4 0.428 0.022 0.298

10 4.29 -1.34 5.63 6 0.562 0.032 0.359

15 5.26 -1.34 6.60 8 0.684 0.045 0.342

20 6.05 -1.28 7.33 10 0.808 0.061 0.322

30 7.20 -1.09 8.29 12 0.922 0.067 0.303

40 7.04 -0.90 7.94 14 1.004 0.122 0.298

50 6.63 -0.60 7.23 16 1.038 0.168 0.308

60 5.82 -0.35 6.17 18 1.024 0.231 0.346

70 4.52 -0.28 4.80

80 3.04 -0.16 3.20

90 1.51 -0.07 1.58

100 0 0 0


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49

The airfoil MUNK- 1



X Yt Yb h Cy

Ccp

0 0 0 0 --3 -0.208 0.009 ----

2.5 1.36 -1.36 2.72 1.5 -0.104 0.008 ---

5 1.8 -1.8 3.6 0 -0.006 0.007 ---

7.5 2.1 -2.1 4.2 1.5 0.120 0.008 0.158

10 2.34 -2.34 4.68 3 0.231 0.011 0.198

15 2.67 -2.67 5.34 4.5 0.341 0.014 0.237

20 2.88 -2.88 5.76 6 0.458 0.020 0.240

30 3.05 -3.05 6.1 9 0.667 0.034 0.264

40 2.85 -2.85 5.7 12 0.782 0.101 0.275

50 2.53 -2.53 5.06 15 0.805 0.196 0.2286

60 2.08 -2.08 4.16 18 0.788 0.257 0.312

70 1.54 -1.54 3.08 21 0.742 0.297 ---

80 0.91 -0.91 1.82

90 0.20 -0.20 0.40

100 0 0 0


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50

Appendix 2THE STANDARD ATMOSPHERE IN SYSTEM SI.

Height.

,m

Temperature

tH,0C

Pressure

PH,Pa

Density

,kg/m3

Relative

density,=/0

Acoustic

speedm/s km/h

-1000 21.5 113920 1.347 1.099 344.1 1238

0 15 101325 1.225 1.000 340.2 1225

1000 8.5 89860 1.11 0.907 336.4 1211

2000 2.0 79500 1.006 0.821 332.5 1197

3000 -4.5 70130 0.909 0.742 328.5 1183

4000 -11.0 61595 0.819 0.668 324.5 11685000 -17.5 54000 0.736 0.601 320.5 1154

6000 -24.0 47200 0.660 0.539 316.4 1139

7000 -30.5 41060 0.590 0.482 312.2 1124

8000 -37.0 35600 0.526 0.420 308 1109

9000 -43.5 30800 0.467 0.381 303.8 1093

10000 -50.0 26400 0.413 0.337 299.4 1078

11000 -56.5 22665 0.365 0.298 295 1062

12000 -56.5 19385 0.312 0.254 295 1062

13000 -56.5 16570 0.266 0.217 295 1062

14000 -56.5 14160 0.228 0.186 295 1062

16000 -56.5 10280 0.166 0.137 295 1062

18000 -56.5 7560 0.120 0.099 295 1062

20000 -56.5 5520 0.088 0.072 295 1062


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51

Appendix 3RELATIVE CIRCULATION BY WINGSPAN STRAIGHT TRAPEZOIDAL

CENTER-SECTION-LESS FLAT WING

f(5

10)=2z/l = 1 = 2 = 3 = 4 = 5

0.0 1.1225 1.2721 1.3435 1.3859 1.4157

0.1 1.1261 1.2624 1.3298 1.3701 1.3987

0.2 1.1196 1.2363 1.2908 1.3245 1.3490

0.3 1.1096 1.1890 1.2228 1.2524 1.2711

0.4 1.0961 1.1299 1.1484 1.1601 1.1703

0.5 1.0765 1.0590 1.0570 1.0543 1.0561

0.6 1.0457 0.9814 0.9571 0.9419 0.9343

0.7 0.9954 0.8988 0.8538 0.8271 0.8098

0.8 0.9138 0.8032 0.7430 0.7051 0.6784

0.9 0.7597 0.6513 0.6090 0.5434 0.5115

0.95 0.6599 0.5151 0.4593 0.4092 0.3798

1 0 0 0 0 0

Comment.

1. Wing has not center-section (2 lc= 0).2. Wing is flat.

3. Wing aspect ratio is equal to wSwL2

.

4. Wing taper is equal to tb/b0 .

5. For low-wing monoplane f is given from board rib, for mid-wing and high-wing fis given from axial rib.

6. If wing taper

differentiates from table data then valises f are calculated by linearinterpolation.


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52

Appendix 4

THE

(45)AMENDMENT FOR WING SWEEP ON THE CHORDS FOURTHWHICH IS EQUAL 45.

2z/l

s(45) 2z/l

s(45)0 -0.235 0.6 0.0730.1 -0.175 0.7 0.111

0.2 -0.123 0.8 0.135

0.3 -0.072 0.9 0.140

0.4 -0.025 0.95 0.125

0.5 0.025 1.00 0


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53

Appendix 5MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE

National Aerospace UniversityKharkiv Aviation Institute

Strength Department

CALCULATION OF WING LOADS

Explanatory book

(ALL THE WAY-0000-0000LEB)

Fulfilled by:

Checked up by:

Kharkiv 2015


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54

REFERENCES

1. . . . . . 1985.

2. . . . . . 1992.

3. . .. . . . . 1978.


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CONTENTS

INTRODUCTION....31. AIRPLAIN GENERAL DATA41. 1. WINGS GENERAL DATA51.2. WINGS GEOMETRICAL DATA..52. DETERMINATION OF LIMIT LOAD FACTOR...103. WINGS MASS DATA 104. WINGS LOADS CALCULATION ....134.1. AIR LOADS ALLOCATION BY THE WINGS SPAN. 164.2. THE WING STRUCTURE MASS LOAD ALLOCATION....174.3. CALCULATION OF THE TOTAL DISTRIBUTED LOAD ON A WING.174.4. THE CHEAR FORCES. BENDING AND REDUCED MOMENTS DIAGRAMSPLOTTING18

4.5. LOAD CHECKING FOR WING ROOT CROSS SECTION254.6. CALCULATION OF SHEAR FORCES POSITION IN THE DESIGN CROSSSECTION...25

APPENDIXIES..27APPENDIX 1.CHARACTERISTIC OF AIRFOIL..28APPENDIX 2. THE STANDARD ATMOSPHERE IN SYSTEM SI .......50APPENDIX 3. RELATIVE CIRCULATION BY WINGSPAN51

APPENDIX 4. THE

(45)AMENDMENT FOR WING SWEEP 52APPENDIX 5. THE COVER PAGE ....53

REFERENCES54

calculation of wing loads

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