Calculation of Wing Loads
Calculation of Wing Loads
Calculation of Wing Loads
Kharkiv, 2015
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 of
the 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 all
geometrical sizes of the plane: the wing area, wing span, swept-back wing, chords of
a wing, position of engines, the landing gear, etc.
The given home task should be included into your course project and after your
course project should be included into your baccalaureate project.
For all students we give critical loading condition C - flight on cruise speed VC
on cruise altitude HC with maximal maneuvering load factor nl and 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 the
illustrated variable (not literal expression of the variable).
2. All diagrams should be built to some scale (the scale should be the same for
all diagrams illustrated at one figure). The shape of the curves should
correspond 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 down
result with units.
8. You should not rewrite reference data, drawings from manual, and
explanations.
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.
Airplane category
Take-off mass (kg)-Mt
Design cruise airspeed (km/h) - VC
Design airspeed (km/h) - V
Design cruise altitude of flight (m) - H
Wing mass (kg) - mw
Total fuel mass (kg) - mf
Mass of engine (kg)- me
Mass of main leg of landing gear (kg)- mml
Wing area (m2) - Sw
Wing span (m) (for swept wing) - Lw
Wing 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
(1.2.1)
5
The received value of the area must coincide with the area of the airplane with
swept-back wing for mid-wing and high-wing airplanes. For convenience of realization
of the further calculations figures of a wing (see fig. 1.2.1, 1.2.2 and 1.2.3) should
contain maximum quantity of the information. So, on the top view of a half-wing
following characteristic lines are put by dotted, a stroke dotted or by light lines: a
center-of-pressure line, the center of gravity (c.g.) line of cross sections of a wing and
lines of spars.
The locations of aggregate's centers of gravity (landing gears, engines, fuel tanks
etc.) are indicated by the sign, and value and direction of the appropriate mass
concentrated forces - by vectors. The areas are occupied by fuel tanks, on both
projections are shaded. Centers of tanks weight are also indicated by the sign. In
figures the geometrical sizes and numerical values of the concentrated forces are put
down.
The explanatory book should contain geometrical and aerodynamic characteristics
of the chosen airfoil. In the final development it is supposed, that all wing cross
sections 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, C and D it is
calculated) - the appropriate angle of attack (see ap. 1) - relative coordinate of
center-of-pressure line cp.
The wing's gravity center in cross section is located approximately on distance of
40 - 45 % of a chord from the leading edge.
Gravity centers coordinates of aggregates are made out from the description of
the airplane - prototype or chosen independently, being guided by the knowledge
acquired in another subject matters of aggregate's design features. For example, the
center of gravity for a turbojet is placed in area of the turbine compressor, but not in
area of a jet nozzle.
At gravity center positions estimation of landing gear primary struts if the ones
are 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 Lw is a wing span, the b is a wing
chord; the ll - is the landing gear base, the bl - is a distance from the leading edge
wing to gravity center of the primary strut in the retracted position.
engine
fuel tank
front spar
leading edge
reduced axis
bt
br
Lw/2
rear spar
rear
spar
center of gravity
qt
0
qa
qf
Q
Qc
0
Qt
Qd
Mc
Z
Mtot
Md
M, kNm
mz, kN
Mz, kNm
Mz, c
Z
Mz,t
Mz, d
X
equivalent straight wing
axis of
stiffnes
s
ck
rk
center of
pressure
swept wing
e
reduced axis
h
Z
center of
wing gravity
stiffness axis
center of fuel
gravity
center of gravity
for k-th aggregate
Fig. 1.2.3. Plotting of equivalent straight wihg.
10886
;
M t 4536
where Mt is the design maximum takeoff mass in kilograms; except that
l
n y max man may not be less than 2.5 and need not be greater than 3.8.
(2.1)
Table 3.1.
Assemblages and payloads relative mass in the percent share from transport airplane
take-off mass
t
w
l
pp
pp
tl
10
12.2
4.5
12.3
16.4
43.3
150
200
9.1
8.8
3.7
3.6
10.2
10.0
15.1
15.0
61.4
67.6
Note: the total load Mtl is 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 tanksection 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 cross
section 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 with Scut area,
located on the right of the 1-1 cross section. Considering approximately, that air
loading is constant on all wing area, we can write down:
S
S
(3.1)
Py M t g cut Gt cut
Sw
Sw
where Gt M t 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:
S
(3.2)
0 = Gt cut z0 G* ( z z1 ) .
Sw
At the G* loads dropping the force is decreased by the value
S
(3.3)
Py ( Gt 2G* ) cut .
Sw
Thats why the * loads post dropping bending moment in 1-1 section is equal
to
* = Gt
Scut
2 Scut
z0 G *
z0 .
Sw
Sw
11
Front
spar
xf
c.g.
c.g.
1-st fuel
tank
2-nd fuel
tank
c.g.
Z
3-rd fuel
tank
Rear spar
z z* z1 z0 ( 2Scut / S w ) .
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 gravity
centers coordinates exceed the z* is more dangerous. At this stage the calculations
12
are necessary to perform for the Gfl flight mass which can be received, subtracting
from the Gt take-off weight the dropped freights and burnt out fuel. Mass of the
dropped freights and burnt out fuel in the further calculations is not taken into
account.
The z0 parameter is defined from the geometrical construction (fig.3.3) or by the
formula
l 0 b 2a
z0
.
3 b a
For all student designing cross section is assigned under z =0.2. In this case
designing flight mass Mfl is equal:
M fl M t 0.2M f ,
(3.4)
where Mf is total fuel mass.
13
In speed (aerodynamic) coordinate system the resultant air force R has two
components: 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 plane xp and body axis for wing xw (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 of
reference for plane:
HV 2
l
l
n M fl g n G fl C y
Sw .
2
In the SI we have from this formula:
2n l M fl g
,
Cy
HV 2 S w
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 Cy you can estimate the angle of attack with accuracy within 1o,
drag coefficient Cx and the relative coordinate of pressure center Ccp from
aerodynamic characteristic of airfoil (Appendix 1).
The angle between the resultant air force R and Y lift force (fig. 4.1) is
equal:
C
C
X
(4.1)
arctg a arctg x tg 1 x
Cy
Cy
Y
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 from
statistic take mean value a=2.
By those values we can calculate resultant air force R (see fig. 4.1):
(4.2)
where 2 =- - is angle between resultant air force R and lift force Yw in wing
frame of reference (see fig. 4.1).
Drag force in wing frame of reference Xw is equal to:
(4.3)
14
,
(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)
15
where the Yw, Pww are resultant air force and resultant inertial force in wing frame of
reference.
Load components acting along the yw axis from effect of a concentrated mass
of 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 relative
circulation low, i.e.
.
z
, z
,
(4.1.1)
0.5 Lw
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 force
by yw.
For distributed load we have next sign convention - if distributed load is
directed upward it has positive sign, if distributed load is directed downward it
has 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:
(4.1.2)
( z ) = f ( z ) + ( z ) ,
where ( z ) is amendment on the wing sweep, f ( z ) function values for flat
straight trapezoidal center-section-less wing are reduced in Appendix 3.
This amendment is calculated by the formulas:
( ) ( 45 )
,
(4.1.3)
45
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 f ( z ) you should know wing taper which is designated through
16
,
(4.2.1)
- distributed inertial
where the b(z) is the wing chord, Mw the wing mass,
force from wing mass.
The length of wing chord (see column 3 in table 4.3.1) is computed by formulas:
(4.2.2)
b( z ) br ( br bt )z .
where br is root chord of wing, bt tip chord, z - 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 into
the wing root cross section. Cross sections are enumerated from the wing root in the
wing tip direction beginning from the i = 0. The letter accentuates relative coordinate
z 2 z / Lw . Since on the site = 1 0.9 cross sections the qay diagram is moved
away from straight line, it is necessary to introduce the cross section with the
= 0.95 coordinate.
4.3. CALCULATION OF THE TOTAL DISTRIBUTED LOAD ON A WING
Table 4.3.1
The ,
b( z ), f
i
1
0
1
2
3
4
5
6
7
8
9
10
11
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
1.0
m
3
q ,
,
q ,
qy
17
(4.3.1)
q( z )dz ,
0.5 Lw
Lw
Q( z )dz
(4.4.1)
.
, M11 =0, (i =10, 9 1, 0)
(4.4.2)
M i M i M i 1 ., M11 = 0; (i = 10, 9 1, 0)
where z10 is distance between cross-section number 10 and cross-section number
11 and so on; accordingly Q11=0 is increment of shear force in cross-section
number 11 from distributed loads out tip wing. Q10 - is increment of shear force in
cross-section number 10 from distributed loads on site between 10 and 11 crosssections and so on; Q11=0 is shear force in cross-section number 11 from
distributed loads out tip wing. Q10 - is shear force in cross-section number 10 from
distributed loads on site between 10 and 11 cross-sections and so on; M11=0 - is
increment of bending moment in cross-section number 11 from distributed loads out
tip wing. M10 - is increment of bending moment in cross-section number 10 from
distributed loads on site between 10 and 11 cross-sections and so on; M11=0 is
bending 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.
18
Q>0
M>0
Fig. 4.4.1. Sign convention for a shear force Q and bending moment M.
The table 4.4.1 is constructed in the assumption that integration implements by
the trapezoids method. The origin is placed in the wing root section. Cross sections
are numbered from a wing root to a wing tip since i=0. You can rewrite from previous
table columns 1, 2, 9 in columns 1, 2, 4 accordingly.
After filling of tab. 4.4.1 by the calculated shear forces Q and bending moments
M (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,agr
concentrated mass forces (in the same coordinate systems that Q and M. and in the
same scale) diagrams. However the sign of these diagrams is opposite to one of
diagrams Q and M. On fig.1.2.1 diagram Qc from concentrated forces is shown (table
4.4.2) 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,i from (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 concentrated
force is given only in cross section i= 9. You can rewrite columns 1, 2 and 3 from
previous table.
,
,
, , (i = 10, 9... 1, 0),
. ,
.
, M11c =0, (i =10, 9... 1, 0),
4.4.3)
,
,
M i , M i 1 , M i 1 , . M11, = 0; (i = 10, 9... 1, 0)
where Q11,c=0 is shear force in cross-section number 11 from concentrated loads in
the tip wing. Q10,c - is shear force in cross-section number 10 from concentrated
loads. 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 - 0 and new value
19
1
0
1
2
3
4
5
6
7
8
9
2
0
4
qt0
5
Q0
6
Q0
7
M0
8
M0
...
0.9
z9
qt9
10
0.95
z10
11
1.0
Q9
qt10
Q 9
Q 10
Q 10 = Q 10
M 9
M 10
M 10 = M 10
qt11
M9
20
Table 4.4.2
The Qic(z) shear forces and the ic(z) bending moment are affected by the
concentrated load.
i
zi,.
zi
Q i .
Q i .
M i .
M i .
m
kN m
kNm
kN
kN
1
2
3
4
5
6
7
M0
0
0
0
Q0
M0
1
2
3
4
5
6
...
7
Q7=Q9
8
...
Q8=Q9
M8
M8 =M8
0
0
9
0.9
z9
Q9
Q9 = Q9 /0
10
0.95
z10
0
0
0
0
11
1.0
0
0
0
0
0
Table 4.4.3
The total Qtot(z) shear forces and the total itot(z) bending moment are affected
by all forces.
Qic.
Qitot.
Mid.
Mic.
Mitot.
i
Qid.
kN
kN
kN
kN*m
KN*m
kNm
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
8
9
10
11
Those bending moment and shear forces were calculated in the wing system
coordinate yw, xw, zw (see fig. 4.1).
An origin is placed in the gravity centre of wing cross section on longitudinal axes
of wing cross section xw. According to fig. 4.1 it is possible to write down:
21
,
,
(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 Qtot and Mtot are shear force and
bending moment in the design cross sections in wing coordinate system, taken from
the table 4.4.3; the Qyw
,is normal shear force which acts by axes yw in the wing
coordinate system and Qxw is shear forces which acts by axes xw in the wing
coordinate system; the Myw is bending moment in the design cross sections in the
wing coordinate system relative axes yw and Mtot = Mxw is bending moment in the
design cross sections in the wing coordinate system relative axes xw.
If <, which is usual for the A critical loading condition, than 2= - <0 and
hence the Qxw and Myw vectors change their direction to the opposite one.
You should calculate values Qyw, Qxw, Mxw and Myw only for your design cross
section and write down in table of result.
At plotting of the diagram of the reduced moments in the beginning we set a
position of an axis of reduction (fig. 1.2.1). This axis is parallel to an axis z (strictly
speaking the axis of reduction should be a parallel axis of stiffness centers of a wing).
Further you should plot a diagram of the distributed reduced moments mz affected by
and . For the moment mz the formula is received writing
the distributed loads
down the moment from the specified loads concerning an axis of reduction. At
calculation mz it is necessary to mean, that the adduced moments are calculated in
wing frame of reference. Thus assume that frontal components lay in a plane xw0zw
and, hence, moment about axis of reduction does not give (fig. 4.4.2).
qa
reduced
axis
qw
and
22
(4.4.5)
where the e and the d are distances from load points
and to the reduction axis.
The moment is considered like positive if it acts on pitching relative to the
reduction axis. The and d values are taken from the fig. 1.2.3.
You can compute their by formulas:
d i zi tg x c .g bi 0.5 Lw z i x c .g bi .
.
,
.
.
0.8( br bt )
,
tg
Lw
where z i - is the relative coordinate z for i-th cross section (column 2 from table
4.4.2). x c .g - 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 which
designations is entered:
M zid 0.5( m zi 1 m z ,i )z i M z ,11 M z ,11 0 ;
23
Table 4.4.4
Reduced moments calculation scheme from distributed loads
i
1
0
zi, . ,
m kN /m
2
3
,
1
2
3
4
5
6
7
8
9
10 z10
11 z11
ei
m
4
e0
kN /m
5
,
e10
e11
,
,
di
m
6
d0
d 10
d 11
mz i
M zid
kN
7
kN m
8
mz 0
M z id
kN m
9
M z 0d
m z 10 M z 10d
0
m z 11
M z 10 d
Table 4.4.5
Calculation scheme of reduced moment from concentrated loads and from all loads.
I
1
0
1
2
3
4
5
6
7
8
9
10
11
Pw.ag.i
kN
2
ri
m
3
Mz.c .i
kN*m
4
Mz.c.i
kN*m
5
Mzdi
kN*m
6
Mztoti
kN*m
7
It is also necessary to plot the M z ,tot total reduced moment diagram (on fig.
1.2.2 it is shown by the solid line).
24
,
, , [kN],
. .
, [kNm],
,
,
. .
(4.5.1)
, ,
,
Here Mfl is designing flight mass of plane from (3.4). Mw the wing mass. is
the distance from root section to the air resultant load point; ck - is the distance from
root section to the k-th aggregate's gravity center and fuel tanks; e and d are
distances from the axis of reduction to points of interception of a plane z=c with the
center-of-pressure line and with the c.g. line; rk - is the distance from an axis of
reduction to the k-th aggregate centre of gravity and fuel tanks. In list of aggregates
you should include all aggregates of wing engines, landing gears, fuel tanks and so
on. Value C is found with the help of geometrical construction or by the formula:
Lw 2
.
6 1
(4.5.2)
where the is the wing taper. Values ck. and rk are taken from fig.1.2.3 and
parameters e and d values from drawing (see fig.1.2.3) in the z = c cross section.
Summation in the right parts of adduced formulas is distributed to all
concentrated masses located in one half-wing. Error of calculation of values , ,
should not exceed value 1, 10 and 15 % accordingly in relation to
, , and
, ,
the appropriate values taken from tables in root cross section.
4.6. CALCULATION OF SHEAR FORCES POSITION IN THE DESIGN CROSS
SECTION
By values of shear force and the reduced moment it is possible to find out
point of application for shear force on a wing chord in design cross section:
, ,
(4.6.1)
,
,
The xr coordinate 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). You
should calculate this value only for your design cross section i=2.
25
Table 4.6.1
Results of calculations
Design loading condition
Design flight mass (kg) - Mfl
Limit load factor - nl
Safety factor - f
Ultimate 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
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 of
resultant shear force , (m, form. 4.6.1)
The angle of attack (degree)
The angle between resultant air force and lift force (degree)
0.2
Comment.
a. Masses in integer kg.
26
APPENDIXIES
27
Appendix 1
Characteristic of airfoil
The airfoil NACA 0009
Geometric characteristic of airfoil
(in % from chord)
Aerodynamic characteristic of
airfoil
Yt
Yb
Cy
Ccp
-4
-0.30
0.014
2.5
1.96
-1.96
3.92
-2
-0.16
0.008
2.67
-2.67
5.34
0.00
0.0064
7.5
3.15
-3.15
6.30
0.16
0.008
0.240
10
3.51
-3.51
7.02
0.30
0.014
0.240
15
4.01
-4.01
8.02
0.45
0.020
0.240
20
4.30
-4.30
8.60
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
0.324
90
1.09
-1.09
2.18
22
0.96
0.340
0.362
100
24
0.91
0.392
0.383
28
Aerodynamic characteristic of
airfoil
Yt
Yb
Cy
Ccp
-4
-0.30
0.015
2.5
2.62
-2.62
5.24
-2
-0.15
0.009
3.56
-3.56
0.00
0.00
0.007
7.5
4.20
-4.20
8.40
0.15
0.009
0.244
10
4.68
-4.68
9.36
0.30
0.015
0.244
15
5.34
-5.34
10.68
0.445
0.020
0.244
20
5.74
-5.74
11.48
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
24
1.09
0.322
0.335
29
Cy
Ccp
-4
-0.30
0.014
2.5
3.27
-3.27
6.54
-2
-0.15
0.009
4.44
-4.44
8.88
0.00
0.007
0.238
7.5
5.25
-5.25
10.50
0.15
0.009
0.238
10
5.85
-5.85
11.70
0.30
0.014
0.238
15
6.68
-6.68
13.36
0.45
0.020
0.238
20
7.17
-7.17
14.34
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
24
1.21
0.269
0.300
Aerodynamic characteristic of
airfoil
30
Yt
Yb
1.25
2.5
5
7.5
10
15
20
25
30
40
50
60
70
80
90
95
100
2.95
3.72
4.67
5.28
5.72
6.33
6.67
6.82
6.82
6.52
5.89
5.04
4.03
2.86
1.5757
0.87
0
-0.90
-1.45
-2.44
-.12
-3.64
-4.36
-4.80
-5.07
-5.18
-5.10
-4.71
-4.09
-3.30
-2.38
-1.32
-0.75
0
h
0
3.85
5.17
8.11
8.40
9.36
10.69
11.47
11.89
12.00
11.622
10.60
9.13
7.33
5.24
2.89
1.62
0
Cx
Cm
Ccp
-4
-0.26
0.014
-0.062
-2
0
2
4
6
8
10
12
14
16
18
20.8
21
21
22
24
26
30
-0.20
0.035
0.20
0.36
0.50
0.65
0.80
0.95
1.09
1.23
1.36
1.50
1.52
1.20
1.12
1.02
0.96
0.88
0.0095
0.0071
0.011
0.017
0.0225
0.034
0.047
0.065
0.083
0.114
0.128
0.160
0.182
0.252
0.281
0.341
0.392
0.464
-0.024
0.0072
0.046
0.0814
0.1165
0.152
0.187
0.222
0.255
0.288
0.319
0.352
0.354
0.352
0.353
0.360
0.346
0.347
--0.206
0.230
0.232
0.233
0.234
0.234
0.234
0.233
0.234
0.234
0.234
0.234
'0.293
0.315
0.353
0.360
0.394
31
Yt
Yb
Ym
0
h
0
-4
Cy
Cx
Cm
Ccp
-0.25 0.0092
-0.054
---
-0.019
---
1.25
2.84 -1.10
0.87
3.94
-2
-0.10 0.008
2.5
3.76 -1.60
1.08
5.36
0.05
0.0073
0.017
0.336
4.97 -2.17
1.40
7.14
0.20
0.009
0.052
0.260
7.5
5.71 -2.68
1.52
8.39
0.37
0.016
0.092
0.249
10
6.22 -3.15
1.54
9.37
0.50
0.022
0.123
0.246
15
6.80 -3.89
1.46
10.69
0.66
0.034
0.161
0.244
20
7.11 -4.38
1.37
11.49
10
0.80
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
0.082
0.268
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
30
0.94 0.454
0.372
0.395
100
0.048
32
Cy
Ccp
0.120
0.010
0.467
2.5
2.92
-1.52
0.70
4.44
0.262
0.013
0.339
4.02
-1.96
1.03
5.98
0.403
0.020
0.304
7.5
4.83
-2.17
1.33
7.00
0.545
0.029
0.291
10
5.51
-2.47
1.59
7.98
0.688
0.043
0.279
15
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
33
Cy
Ccp
-4
-0.17
0.0110
2.5
3.35
-1.96
5.31
-2
-0.01
0.0088
4.62
-2.55
7.17
0.13
0.0088
0.476
7.5
5.55
-2.89
8.44
0.29
0.0135
0.348
10
6.27
-3.11
9.38
0.43
0.0195
0.316
15
7.25
-3.44
10.69
0.59
0.028
0.300
20
7.74
-3.74
11.48
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
24
1.31
0.310
0.327
34
Cy
Ccp
-5.12
-0.229
0.0162
0.104
2.5
3.8
-2.41
6.21
-3.27
-0.106
0.0131
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
22.22
1.190
0.2359
0.302
35
Yt
Yb
Ym
0
2.67
3.61
4.91
5.80
6.43
7.19
7.50
7.60
7.55
7.14
6.41
5.47
4.36
3.08
1.68
0.92
0
0
-1.23
-1.71
-2.26
-2.61
-2.92
-3.50
-3.97
-4.28
-4.46
-4.48
-4.17
-3.67
-3.00
-2.16
-1.23
-0.70
0
0
0.77
0.95
1.33
1.60
1.76
1.85
1.77
1.66
1.54
1.33
1.12
0.90
0.68
0.46
0.23
0.11
0
0
3.90
5.32
7.17
8.41
9.35
10.69
11.47
11.88
12.01
11.62
10.58
9.14
7.36
5.24
2.71
1.62
0
-4
-2
0
2
4
6
8
10
12
14
16
18
20
22
22
24
26
30
Cy
-0.22 0.013
-0.08 0.00955
0.085 0.0071
0.24 0.012
0.385 0.018
0.53 0.025
0.68 0.035
0.835 0.050
0.98 0.067
1.12 0.088
1.28 0.108
1.40 0.130
1.53 0.159
1.63 0.186
1.31 0.255
1.19 0.317
1.045
0.98
Cm
0.046
-0.011
0.028
0.065
0.099
0.134
0.169
0.206
0.242
0.275
0.313
0.342
0.372
0.396
0.382
0.394
0.390
0.393
Ccp
0.330
0.270
0.257
0.253
0.248
0.247
0.247
0.245
0.244
0.245
0.243
0.243
0.292
0.331
0.375
0.400
36
Cy
Ccp
-2
0.00
0.009
2.5
2.39
-1.58
0.405
3.97
0.15
0.008
0.490
3.36
-2.01
0.675
5.37
0.30
0.012
0.370
7.5
4.09
-2.24
0.925
6.33
0.45
0.020
0.331
10
4.67
-2.38
1.145
7.05
0.60
0.028
0.310
15
5.54
-2.50
1.52
8.04
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
37
Aerodynamic characteristic
of airfoil
Cy
Ccp
-2
0.00
0.003
2.5
3.11
-2.16
0.475
5.27
0.13
0.011
0.527
4.31
-2.85
0.73
7.16
0.30
0.014
0.377
7.5
5.18
-3.26
0.96
8.14
0.44
0.020
0.338
10
5.86
-3.52
1.17
9.38
0.58
0.028
0.310
15
6.89
-3.82
1.535 10.71
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
26
1.24
0.360
0.351
38
Cy
Ccp
-4
-0.19
0.013
2.5
3.85
-2.74
6.59
-2
-0.01
0.010
5.26
-3.66
8.92
0.13
0.011
0.510
7.5
6.28
-4.25
10.74
0.30
0.014
0.357
10
7.08
-4.66
11.74
0.42
0.020
0.324
15
8.25
-5.13
13.38
0.53
0.030
0.302
20
8.97
-5.38
14.35
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
26
1.34
0.340
0.324
39
Yt
Yb
Ym
Cy
Cm
Ccp
-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
0.13
0.010
0.076
0.588
4.13
-3.01
0.56
7.14
0.29
0.0128
0.119
0.397
7.5
4.96
-3.46
0.75
8.42
0.42
0.020
0.150
0.355
10
5.63
-3.75
0.94
9.38
0.58
0.030
0.189
0.326
15
6.61
-4.10
1.255
10.71
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
1.10
0.414
0.377
100
28
40
Aerodynamic characteristic of
airfoil
Yt
Yb
Ym
Cy
-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
5.07
0.62 8.91
7.5
6.06
-4.47
0.80 10.53
10
6.83 -4.90
0.87 11.73
15
7.97 -5.42
1.28
13.39
20
8.70 -5.66
1.52
14.36
10
25
9.17 -5.70
1.74 14.87
12
30
9.38 -5.62
1.88 15.00
14
40
9.25 -5.25
2.00 14.50
16
50
8.57 -4.67
1.95 13.24
18
60
7.50 -3.90
1.80 11.40
20
70
6.10 -3.05
1.53 9.15
22
80
4.41 -2.15
1.13 6.56
24
90
2.45 -1.17
0.64 3.62
26
95
1.34 -0.68
0.33 2.02
28
30
1.10
100
-3.84
Cx
Cm
Ccp
0.415 0.378
41
Yt
Yb
Ym
Aerodynamic characteristic of
airfoil
Cy
Cx
Cm
Ccp
-0.004
1.25
1.62
-1.23
0.195 2.85
2.5
2.27
-1.66
0.305 3.93 -2
0.00
0.008 0.044
3.2
-2.15
0.525 5.35
0.13
0.008
0.076 0.588
7.5
3.87
-2.44
0.715 6.31
0.29 0.0128
0.118 0.397
-4 -0.192 0.012
10
4.43
-2.60
0.915 7.03
0.43
0.020
0.150 0.352
15
5.25
-2.77
1.24
8.02
0.58
0.028
0.188
20
5.81
-2.79
1.51
8.60
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
28
1.00
0.410 0.410
0.326
42
Yt
Yb
Ym
Aerodynamic characteristic of
airfoil
Cy
-4
-0.21
0.014 -0.042
-0.06
0.011
Cx
Cm
Ccp
1.25
3.34
-1.54
0.90
4.90
-2
2.5
4.44
-2.25
1.095
6.69
5.89
-3.04
1.425
8.93
0.23 0.014
0.063 0.274
7.5
6.91
-3.61
1.65 10.52
0.39 0.018
0.101 0.259
-4.09
1.78 11.73
0.53 0.027
0.135 0.255
10
7.64
-0.006
0.332
15
8.52
-4.84 1.84
13.36
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
30
1.01
0.372
0.368
43
Yt
Yb
Ym
h
0
Cy
-4
-0.22
0.012 -0.0415
-0.09
0.009
Cx
Cm
Ccp
1.25
2.04
-0.91
0.07 2.95
-2
2.5
2.83
-1.19
0.82 4.02
3.93
-1.44
1.25 5.37
0.225 0.011
0.063 0.280
7.5
4.70
-1.63
1.54 6.33
0.39 0.0165
0.103 0.264
1.74 7.05
0.53
0.023
0.137 0.258
-0.013
0.344
10
5.26
-1.79
15
5.85
-2.17 1.84
9.02
0.69
0.035
0.175
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
30
0.95
0.389 0.409
0.254
44
Yt
Yb
Ym
Aerodynamic characteristic of
airfoil
Cy
-4
-0.20
0.012 -0.043
Cx
Cm
Ccp
1.25
3.32
-0.86
1.23
4.18
-2
2.5
4.36
-1.11
1.625
5.47
0.300
5.69
-1.50
2.095
7.19
0.26 0.0128
0.067 0.257
7.5
6.48
-1.91
2.29
8.39
0.40 0.018
0.100 0.250
2.31
9.37
0.55 0.027
0.137 0.249
10
6.99
-2.38
15
7.53
-3.18
2.18
10.71
0.70 0.038
0.173
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
30
1.97
0.392 0.404
0.247
45
Yt
Yb
Ym
Cy
-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
0.11 0.008
0.0391 0.356
4.80
-2.37
1.22 7.17
0.28 0.013
0.079
0.282
7.5
5.74
-2.70
1.52 8.44
0.42 0.019
0.125
0.298
10
6.44 -2.95
1.75 9.39
0.57 0.027
0.148
0.259
15
7.37 -3.34
2.015 10.71
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
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
30
1.00
0.461 0.387
0.387
100
1.10
Cx
Cm
Ccp
46
Cy
Ccp
--16
-0.596
0.203
0.356
2.5
3.10
-2.03
5.13
-12
-0.562
0.095
0.264
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
0.130
0.013
0.493
20
8.33
-3.25
11.58
0.266
0.023
0.330
30
8.85
-3.14
11.99
0.400
0.072
0.278
40
8.66
-3.00
11.66
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
47
Cy
Ccp
-2
0.034
0.0110
2.5
1.80
-0.98
2.78
0.168
0.012
0.619
2.78
-1.23
4.01
0.294
0.016
0.470
7.5
3.62
-1.32
4.94
0.428
0.022
0.298
10
4.29
-1.34
5.63
0.562
0.032
0.359
15
5.26
-1.34
6.60
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
48
Cy
Ccp
--3
-0.208
0.009
----
2.5
1.36
-1.36
2.72
1.5
-0.104
0.008
---
1.8
-1.8
3.6
-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
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
0.458
0.020
0.240
30
3.05
-3.05
6.1
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
49
Appendix 2
THE STANDARD ATMOSPHERE IN SYSTEM SI.
Height.
,
m
Temperature Pressure
PH,
tH,
0
C
Pa
kg/m3
Relative
density,
=/0
Density
Acoustic
speed
m/s
km/h
-1000
21.5
113920
1.347
1.099
344.1
1238
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
1168
5000
-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
50
Appendix 3
RELATIVE CIRCULATION BY WINGSPAN STRAIGHT TRAPEZOIDAL
CENTER-SECTION-LESS FLAT WING
f (5 10)
z =2z/l
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
1
= 1
1.1225
1.1261
1.1196
1.1096
1.0961
1.0765
1.0457
0.9954
0.9138
0.7597
0.6599
0
= 2
1.2721
1.2624
1.2363
1.1890
1.1299
1.0590
0.9814
0.8988
0.8032
0.6513
0.5151
0
= 3
1.3435
1.3298
1.2908
1.2228
1.1484
1.0570
0.9571
0.8538
0.7430
0.6090
0.4593
0
= 4
1.3859
1.3701
1.3245
1.2524
1.1601
1.0543
0.9419
0.8271
0.7051
0.5434
0.4092
0
= 5
1.4157
1.3987
1.3490
1.2711
1.1703
1.0561
0.9343
0.8098
0.6784
0.5115
0.3798
0
Comment.
1. Wing has not center-section (2 lc = 0).
2. Wing is flat.
2
3. Wing aspect ratio is equal to Lw S w .
4. Wing taper is equal to b0 / bt .
5. For low-wing monoplane f is given from board rib, for mid-wing and high-wing f
is given from axial rib.
6. If wing taper differentiates from table data then valises f are calculated by linear
interpolation.
51
Appendix 4
THE (45) AMENDMENT FOR WING SWEEP ON THE CHORDS FOURTH
WHICH IS EQUAL 45.
2z/l
0
0.1
0.2
0.3
0.4
0.5
s (45)
-0.235
-0.175
-0.123
-0.072
-0.025
0.025
2z/l
0.6
0.7
0.8
0.9
0.95
1.00
s (45)
0.073
0.111
0.135
0.140
0.125
0
52
Appendix 5
MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE
National Aerospace University
Kharkiv Aviation Institute
Strength Department
Explanatory book
(ALL THE WAY-0000-0000LEB)
Fulfilled by:
Checked up by:
Kharkiv 2015
53
REFERENCES
1.
2.
3.
. .
. . . 1985.
. .
. . . 1992.
. .. . .
. . 1978.
54
CONTENTS
INTRODUCTION....3
1. AIRPLAIN GENERAL DATA4
1. 1. WINGS GENERAL DATA5
1.2. WINGS GEOMETRICAL DATA..5
2. DETERMINATION OF LIMIT LOAD FACTOR...10
3. WINGS MASS DATA 10
4. WINGS LOADS CALCULATION ....13
4.1. AIR LOADS ALLOCATION BY THE WINGS SPAN. 16
4.2. THE WING STRUCTURE MASS LOAD ALLOCATION....17
4.3. CALCULATION OF THE TOTAL DISTRIBUTED LOAD ON A WING.17
4.4. THE CHEAR FORCES. BENDING AND REDUCED MOMENTS DIAGRAMS
PLOTTING 18
4.5. LOAD CHECKING FOR WING ROOT CROSS SECTION25
4.6. CALCULATION OF SHEAR FORCES POSITION IN THE DESIGN CROSS
SECTION...25
APPENDIXIES..27
APPENDIX 1.CHARACTERISTIC OF AIRFOIL..28
APPENDIX 2. THE STANDARD ATMOSPHERE IN SYSTEM SI .......50
APPENDIX 3. RELATIVE CIRCULATION BY WINGSPAN51
APPENDIX 4. THE (45) AMENDMENT FOR WING SWEEP 52
APPENDIX 5. THE COVER PAGE ....53
REFERENCES54