1. SECTION 3. AERODYNAMICS OF AN AIRPLANE
THEME 14. AN INTERFERENCE OF AN AIRPLANE PARTS
After assembling the aircraft separate parts into the whole their streamlining and
aerodynamic characteristics change. It is caused by mutual influence of these parts i.e.
interference. We can distinguish the interference of three types: 1) between the lifting
and poorly lifting elements (wing and fuselage, tail-plane and fuselage, nacelle and
wing and others); 2) between the lifting elements (wing and tail-plane); 3) between jets
of engines or props and parts of the aircraft. Let's find out physics of the interference of
the aircraft various parts.
14.1. Geometrical characteristics of an aircraft
The external shapes of an aircraft and its parts, their sizes and mutual arrangement
providing the obtaining of necessary aerodynamic characteristics are called as
aerodynamic configuration.
The aircraft aerodynamic configuration is characterized by presence of some
separate parts, their mutual arrangement and geometrical features. The following
aerodynamic configurations of the aircraft are the most widespread.
Aircraft are distinguished by number of wings as biplanes and monoplanes. The
biplane configuration contains two wings located one above another. This structure was
widely used at the beginning of aircraft development. Now the majority of airplanes are
constructed by the monoplane scheme, i.e. with one wing.
There distinguish the normal airplane configuration, canard configuration,
configuration “tailless” and “a flying wing” by presence and location of horizontal tail
unit.
Horizontal tail of normal configuration is located behind the wing. This
configuration provides the favorable conditions for flow about wing, however
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2. horizontal tail is in the zone of disturbed flow caused by wing and on some modes can
lose the efficiency.
In the canard configuration the horizontal unit is placed ahead of a wing and
works in an undisturbed flow, but it effects the flow about wing. This influence can be
both negative and positive depending on the horizontal tail shape both wing and their
mutual arrangement.
The airplanes of the configuration “tailless” have no horizontal tail and the
configuration “flying wing” besides actually has no fuselage and vertical tail.
For monoplanes one differs three configurations depending on wing installation
by fuselage altitude: low-wing monoplane, mid-wing monoplane and high-wing
monoplane.
Vertical tail, as a rule, is installed in a tail part of the airplane. Depending on the
number of fins the aircraft can be designed on single-finned, twice-finned and multi-
finned configurations, and on the number of fuselages the aircraft can be designed on
the single-fuselage and twice-fuselage configurations.
The power plant essentially influences external shape of modern aircraft. The
engines can be mounted in a wing, on a wing, under a wing, under a wing on pylons, in
a fuselage, under a fuselage, on a horizontal tail unit, in a fin.
In the aircraft aerodynamic configuration its separate elements (wing, fuselage,
horizontal tail, vertical tail, engine nacelles etc.) influence each other. Therefore, the
aerodynamic characteristics of these elements will vary in aircraft system and at the
isolated streamlining.
One distinguishes a positive and negative interference, depending on whether
total aerodynamic characteristics are improved (in certain sense) or became worse. This
circumstance is necessary for taking into account while aerodynamic designing.
Physical features of interaction of lifting surfaces (such as wing, horizontal tail)
with a fuselage, engine nacelles with a wing and fuselage, wing and horizontal tail will
be considered below. There are other kinds of interaction, for example, jets of the air
prop or turbo-prop engines with elements of the aircraft, influence of the cargo plane
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3. onto dropped freights, influence of ground or water surfaces onto the aircraft
aerodynamic characteristics etc.
14.2. Coefficient of flow deceleration.
Generally wing, horizontal and vertical tail installed a fuselage will be flown with
speed different from speed of incoming flow V∞ . It occurs due to the influence of
viscosity and to the appearance of head shock waves at M∞ > M* . Coefficient of flow
deceleration is used for the account of this effect, which is a ratio of mean dynamic
pressure before a considered aircraft element to dynamic pressure of undisturbed
flow q∞ :
kd wing = q w q∞ ; kd h.t . = q h.t . q∞ ; kd v .t . = qv .t . q∞ , (14.1)
2 2
where q∞ = 0 .5 ρ ∞V∞ = 0 .7 p∞ M ∞ is the dynamic pressure of undisturbed flow;
(
q w = 0 .5 ρV 2 ) w
(
, q h.t . = 0 .5 ρV 2 ) h.t .
(
, qv .t . = 0 .5 ρV 2 ) v .t .
is the dynamic pressure
before a wing, horizontal and vertical tail-plane.
One assumes, that density ρ = ρ∞ = const and pressure p = p∞ = const , we shall
record:
2 2 2
2
Vw ⎛ Mw ⎞ Vh .t . ⎛ M h . t . ⎞
2
Vv2t . ⎛ M v .t . ⎞
kd wing = =⎜
⎜ ⎟ , k d h.t . =
⎟ =⎜ ⎟ , k d v .t . = . = ⎜
⎜ M ⎟ .
⎟
2
V∞ ⎝ M∞ ⎠ V∞ 2 ⎜ M ⎟ V∞ 2
⎝ ∞ ⎠
⎝ ∞ ⎠
At known coefficient of flow deceleration the Mach number M before an aircraft
element is determined by the following formulas:
M w = M ∞ k d w , M h . t . = M ∞ k d h . t . , M v . t . = M ∞ k d v .t . .
These numbers M are necessary for taking into account at calculating the
aerodynamic characteristics of the isolated parts.
For example, lift of a wing and its drag depend on M w = M ∞ kd w
Сα λ = f ⎛
⎜ M w − 1 , λ tgχ , η ⎞ , С xв λ c 2 = f ⎛ M w − 1 , λtgχ , η ⎞ .
2
⎟ ⎜ 2 ⎟
ya ⎝ ⎠ ⎝ ⎠
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4. Let's consider the process of flow deceleration. At the beginning we shall study
flow about a wing (horizontal tail), located on a fuselage. In a subsonic flow
( M∞ < M* ) speed deceleration before a wing for the normal configuration and before
horizontal tail for the canard configuration occurs only in a boundary layer on a part of a
fuselage located ahead of a wing or horizontal tail. Taking into account that the
thickness of a boundary layer δ * is much less than wing span or tail span, it is possible
to assume
kd wing = 1 , kd h.t . = 1 , kd v .t . = 1 .
Shock wave occurs before a
fuselage nose in a supersonic flow
M∞ > 1 (Fig. 14.1). Flow rate
decreases behind the shock wave. The
amount of flow deceleration
coefficient depends on intensity of the
Fig. 14.1. shock wave. In turn, intensity of the
shock wave depends on wave drag of the fuselage nose and number M ∞ .
Approximately it is possible to adopt that:
{kd wing , kd h.t . , kd v .t .} ≈ 1 − 0 .02( M∞ − 1)C x
2
nose
.
It is necessary to take into
account a capability of shock wave
getting onto a wing surface
(horizontal tail). At that the external
parts will be streamlined by an
undisturbed flow (Fig. 14.2).
Fig. 14.2. Let's consider the case, when
the wing and horizontal tail are located on the fuselage. For such configuration the
leading lifting surface can effect flow deceleration before the trailing lifting surface.
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5. Deceleration occurs due to the viscosity (trailing lifting surface getting into the
aerodynamic trail) at M∞ < M* and, in addition, behind the shock wave from the
trailing lifting surface at M∞ > M* (Fig. 14.3). Here it is necessary to distinguish the
aircraft normal configuration and canard configuration.
Fig. 14.3. Influence of trailing lifting surface:
a) - normal configuration; b) - canard configuration;
c) - field of speeds behind the wing.
Let's determine thickness of a boundary layer in the aerodynamic trail behind the
wing for the normal configuration
( 2
H = 0 .86 1 + 0 .2 M ∞ ) C x p w ( x 1 + 0 .5 ) b1 , x 1 = x1 b1
where x1 and b1 are the geometrical parameters of the semispan of horizontal tail
(Fig. 14.3).
If y h.t . > H , then tail-plane (wing) does not fall into the aerodynamic trail caused
by wing (horizontal tail). In this case, for the normal configuration we receive
kd h.t . = 1 at M∞ ≤ M* , kd h.t . = k 2 at M∞ > M* ,
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6. where k 2 is the coefficient of flow deceleration behind a system of shock waves from
(
the fuselage nose and wing, k 2 = f C x nose , C xw wing , M ∞ , x 1 . )
At horizontal tail falling into the aerodynamic trail from a wing ( y h.t . < H ) we
shall have
kd h.t . = k12 at M∞ ≤ M* , kd h.t . = k12 k 2 at M∞ ≥ M* .
(
k12 = f C xp wing , M ∞ , x 1 ) where k12 is the factor, which characterizes flow
deceleration in the aerodynamic trail behind the wing.
In the canard configuration the coefficient of flow deceleration before a wing is
determined under the formula
kd w = k* k1 , k* = 1−
(1 − k12 ) S*
12 12
Sw
where factor ( )
k12 = f C xp h.t . , M ∞ , x 1 . Multiplier k1 = 1 at M∞ < M* and
( )
k1 = f C x nose , C xw h.t . , M ∞ , x 1 at M∞ > M* .
14.3. Wing downwash
As it is known, the vortex sheet is formed behind a lifting surface which creates a
downwash. This downwash reduces true angle of attack of a lifting surface located back
that should be taken into account at calculating its lift and moment characteristics.
Let's consider the case of the normal
configuration, when the tail unit is located
behind the wing. The wing repels air
downwards with some speed Vi at creation of
lift. Due to it, flow incoming onto horizontal
Fig. 14.4 Wing downwash tail downwashes downwards at some angle
ε ≅ Vi V∞ , which is called the angle of downwash (Fig. 14.4). The downwash behind a
wing influences the aerodynamic characteristics of all aircraft parts located behind the
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7. wing. First of all wing downwash influences the aerodynamic characteristics of
horizontal tail, because downwash reduces the angle of attack of horizontal tail. If the
aircraft angle of attack α , an angle of attack of horizontal tail with taking into account
an angle of downwash ε will be
α г .о . = α − ε . (14.2)
The value of angle of downwash depends on the wing plan form, angle of its
setting, wing and fuselage interference, angle of attack, number M ∞ , and coordinates of
the considered point. The significant influence on the angle of downwash is paid by
vortexes forming at flow about wing on its lateral and leading edges.
Disturbances are distributed in all parties at subsonic speeds, therefore tail unit
effects the flow about the wing, located before it. However this influence, as a rule, is
insignificant in comparison with wing influence onto flow about tail unit located
behind. The wing downwash also reduces an angle of attack of that fuselage part which
is located behind a wing.
Disturbances are not distributed forward against flow at supersonic speeds, the
area of their propagation is limited by cones of disturbances and shock waves. That is
why there can be zones in which there is no downwash at supersonic speeds.
The angle of downwash depends on
wing lift, therefore, on an angle of attack. For
linear site this dependence can be written as
ε = ε0 + ε α α . (14.3)
The derivative ε α of downwash by the
Fig. 14.5. Dependence of derivative of angle of attack depends on number M ∞ , as it
downwash ε α on number M ∞ is shown in fig. 14.5. At subsonic speeds the
lifting properties of the wing grow at
increasing of number M ∞ , the derivative ε α also increases. They drop at supersonic
speeds with the increasing of number M ∞ , besides, the zones of disturbances
propagation are narrowing, therefore derivative ε α reduces.
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8. If the mean angle of downwash is known, then the angle of attack of horizontal
( )
tail is calculated under the formula α h.t . = α 1 − ε α − ε 0 . For the aircraft of the
normal configuration the parameter (1 − ε α ) is called the factor of tail-plane
effectiveness. The angle of downwash ε0 is determined by aerodynamic and
geometrical twist of wing.
The configuration of horse-shoe vortex is used as the basis for calculation of
downwash that is right, because the vortex sheet is unstable and at some distance is
turned off in two tip vortexes.
The remarks:
1. Generally downwash is variable spanwise. However, at calculating the total
aerodynamic characteristics of the trailing lifting surface in the aerodynamic
configuration one takes the mean value of downwash spanwise. Obviously, the
downwash before a wing will be less in the canard configuration, as wing external parts
fall into the upwash.
2. In the aircraft system the components of downwash ε α and ε0 will also
depend on mutual arrangement of the leading and trailing lifting surfaces, shape and
geometry of cross section of the leading lifting surface with a fuselage, numbers M ∞ .
The fuselage influence onto downwash is taken into account by change of the
configuration of the horse-shoe vortex.
3. The additional sources of downwash can be the jets of the air prop and jet
engines which turbulent baffling and ejection properties create a field of speeds directed
to jet axis.
Using model of horse-shoe vortex it is possible to offer the following formula for
calculation of components of angle of downwash caused by system: lifting surface-
fuselage:
Cα
k x k y kc k f , ε 0 = − ε α α 0 k m
α ya
ε = (14.4)
πλ
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9. where λ and C α are aspect ratio and derivative of the lift coefficient of forward
ya
surface cantilevers. The multipliers k i which are included in (14.4), depend on
aerodynamic configuration of the aircraft and Mach number M ∞ .
The multiplier k x takes into account mutual arrangement of a wing and
horizontal tail fuselage lengthwise. The multiplier k y takes into account vertical
displacement of horizontal tail relatively to wing. The multiplier kc is connected to
aerodynamic configuration of the aircraft (for normal configuration kc = 1 ). The
multipliers k f and k m also take into account the influence of fuselage onto downwash
and depend on the shape of cross section a forward lifting surface - fuselage.
14.4. Interference of the engine nacelles with parts of an airplane
14.4.1. Nacelles location on the fuselage lateral area in its tail part
The convergent-dilative channel is formed between nacelle and fuselage
promoting separation of the boundary layer and growth of profile drag of the system
nacelle-fuselage (Fig. 14.6). At subsonic speeds with M∞ ≈ M* in
a channel it is possible to expect the appearance of shock waves
that causes further growth of drag. Obviously, the additional drag
caused by interference is conveniently taken into account into
nacelle drag with the help of introduction of the correction factor.
In particular, the nacelle profile drag in the system with
Fig. 14.6. fuselage is determined with taking into account an interference
factor
C xp e .n .( f) = nke .n .C xp is .e .n . S e .n . ,
where n is the nacelle quantity, C xp is .e .n . is the profile drag of one isolated nacelle
with midsection Se .n . ( S e .n. = Se .n. S , S - characteristic area).
The factor ke .n . takes into account an interference effect
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10. ke .n . = 1 + 0 .3 n , n = 1, 2 , 4 ; ke .n . = 1.8 , n = 3 .
It is necessary to point to one more effect - decreasing of nacelle lift in the
airplane system because of its falling in the wing downwash. This effect is increased at
lifting devices deflection.
14.4.2. Nacelle installation onto wing.
As well as in the previous case a source of additional drag is the formation of a
channel between nacelle and wing with increased flow rate in a channel and reduced
speed in the outgoing area of nacelle. Here increasing of the boundary layer happens
and the flow stalling is possible. In the channel at M∞ ≈ M* shock waves can occur. All
said concerns the nacelles located on pylons or directly under the wing.
Other reason is connected with features of flow
about swept wing at engine nacelle installation on it.
Disturbance of flow on the isolated wing takes place in
this case, the additional chamber of streamlines by nacelle
walls (Fig. 14.7) occurs. In area 1 nearby the wing leading
edge an additional rarefaction will occur due to increasing
of speed. In area 2 , on the contrary, decreasing speed
occurs nearby the wing leading edge with further
Fig. 14.7.
opportunity of increasing at the nacelle tip. Critical Mach
number M* of the nacelle-wing system decreases. Thus, the flow disturbance on the
wing connected with the nacelle installation (or pylon) causes an increase of drag.
The most unfavorable nacelle location is directly under a wing without offsetting.
In this case areas of minimum pressure on the wing surface and nacelle coincide, due to
that the positive pressure gradients grow and the conditions for earlier stalling of the
boundary layer are created.
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11. Nacelle displacement forward or back, its location on wing axis or on pylon
causes a decreasing of the interference drag. The least interference is received at nacelle
location wing chordwise.
As well as in case of the nacelle installation on the fuselage, an additional drag is
accounted by a factor ke .n . in nacelle drag, which depends on nacelle location relatively
to the wing:
k e .n . = k 1 k 2 k 3 ,
− 0 .5 ( a − 1)
2
0 .05 2
k1 = 1 + + 8 .6 h2 exp − 4 h , k 2 = 1 + 0 .8 exp ,
2
6h + 1
0 .6 λ e .n .
k3 = 1 + .
λ e .n . + 16 x 2
2
Here the factor k 1 takes into account nacelle displacement along perpendicular to the
wing plane h = H d e .n . ; k 2 - mutual influence of two nacelles located on one wing
cantilever a = a d e .n. ; k 3 - nacelle displacement along the wing chord x = x le .n. .
If one nacelle is located on the wing cantilever, then k 2 = 1 . The geometric parameters
H , a , x are shown in fig. 14.8.
Fig. 14.8. Engine nacelle location on a wing
The mutual influence of two nacelles installed on one wing cantilever causes
growth of drag, mainly, in an outcome of increase of flow rate between them and
growth of pressure gradient on the nacelles surface.
It is possible to reduce the interference drag of the wing-nacelle system if nacelle
axis is disposed with taking into account the direction of local flow rate.
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12. The positive effect of nacelle interference with the wing can be received at
M ∞ > 1 . In this case nacelles should be placed behind the line of wing maximum
thickness. The increased pressure induced by a shock wave from the nacelle creates a
component force of pressure directed forward (negative drag); there appears small lift.
14.4.3. Mutual influence of prop and airplane
It is convenient to divide study of mutual influence of prop and airplane into two
parts: influence of airplane parts onto prop and prop influence onto plane.
Axial speed component decreases under engine nacelle influence in the place of
prop installation. The flow becomes decelerated and radial speed component appears.
The wing influence onto prop located before the wing is similar to engine nacelle
influence or fuselage effect, but flow is decelerated before a wing much less, as a rule.
The wing influence onto prop located above the wing can be substantial and is
exhibited in increasing or reduction of flow velocity incoming on the prop, in
comparison with speed of undisturbed flow.
The prop influence onto the plane is shown, first of all, through a pressure rising
in jet directly behind the plane of rotation, where engine nacelle, wing and other parts of
the airplane are located. Besides, the jet behind the prop has speed exceeding speed of
the incoming undisturbed flow and distinguished from it by direction due to twist and
lack of coincidence of the prop axis with direction of the undisturbed flow or deflection
of jet from the prop by other parts of the airplane.
The pressure rising in jet behind the prop causes an additional pressure increasing
at nose sections of the airplane elements located in jet that is an additional drag.
The increasing of speed and change of flow direction in jet behind the prop
causes changes of forces of pressure and friction and their distributions. It results in
occurrence of additional drag and additional lift on parts of the airplane blown by jet
from the prop.
Influence of the prop on horizontal tail located behind the props is the same as on
the wing. However, the increasing of positive pitching moment occurs on the normal
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13. configuration airplanes at negative lift of horizontal tail which is necessary to counteract
by additional deflection of elevators for diving.
As the greatest effect from the airplane parts blown by props occurs at small
flight speeds , i. e. at takeoff modes, then it is necessary to take into account the
influence of ground proximity onto the airplane aerodynamic characteristics while props
activity.
The influence of ground proximity is shown first of all in decreasing of flow
downwash caused by the prop jet. It results in increasing of wing lift, reduction of its
induced drag, decreasing of horizontal tail negative lift and reduction of its pitching
moment.
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