Configuration

Layout and Loft

• T h e a ctu a l confi g u ration geometry i s the h e a rt a n d s o u l of a i rcraft concept u a l design .

• I n i ti a l a i rcraft layout is a ski l l l ea rned over m a ny yea rs (and it isn't j ust CAD) .
• A wel l-done layout " m i ra c u l o usly" g oes through s u bseq uent a n a lysis a nd d eta i l
desig n-th i n g s fit. t h e drag i s low, a n d t h e struct u re i s l i g htweight. This i s not a n
accident!
• Good l oft i n g i s n ecess a ry but not s ufficient.

I ntrod uction

T
he Advanced Design Department of a major aircraft company is a
busy place. Project managers are planning and supervising current
design projects and trying to win the next one. Performance and
sizing specialists are loading design data into massive computer programs
and attempting to understand and explain the results. Experts in aero­
dynamics, structure, weights, propulsion, stability, control, and operations
are making calculations of the latest configuration, looking for potential
problems and looking for ways to make it better. And over in the corner,
hunched over drafting tables or huddled in front of CAD scopes, you will
find a handful of designers making the new configuration layouts.
All of these activities are important. The airplane won't fly unless they're
all done and done well. But in the end, the only thing that gets built is the
aircraft as defined by the layout geometry. The only thing that actually
"flies" is the drawing. This obvious fact is sometimes lost in the noise, even
though the purpose of all that "noise" is to make the design layout better.
This should be foremost in the minds of the project managers. All of
the activities that they plan must be planned around the drawing. Wind­
tunnel tests aren't simply to verify that everything works-they are also to

1 65
1 66 A i rc raft Desi g n : A C o n c e p t u a l A p p r oa c h

uncover and fix problems and to find ways to improve the design. There must
be enough time in the plan, after the test, to take what was learned and revise
the design layout. This isn't a matter of a few days of CAD work. The new
version of the design must be carefully studied to make sure that the
changes don't introduce new problems. If they do, yet another revision
to the design must be made. The same thing is true for design trade
studies and structural or systems studies-it takes time after those studies
to incorporate lessons learned into a revised design.
This author once saw a major aircraft development project in which a
number of design trade studies ("scout configurations") were to be per­
formed. Good idea. However, the program plan only allowed a few wee ks
for the designers to integrate the best results into a final baseline for configur­
ation freeze. It actually took several months. Although it is a great plane
today, one can still see several clumsy design "fixes" that could have been
solved more elegantly during a well-planned configuration layout process.*
So the heart of the design process is the actual layout: the aircraft
configuration geometry that will be taken into detail design and fabrication.
It has to be expertly done and is not a job to assign to someone based just
upon CAD skills. In the past, a person needed about 10 years of experience
in other areas, usually aerodynamics and structures, before he or she
would be allowed to join the configuration layout group. Even then, that
person would serve an apprenticeship within the group before being
trusted with the next "blank sheet of paper" design.
Simply put, the very first initial design layout has to be good. The layout
geometry has to provide a smooth aerodynamic shape around the internal
components, with neither excess nor inadequate internal volume. Those
internal components-payload, passengers, engines, landing gear, and
other subsystems-have to be cleverly arranged and well-enough defined
that major changes to them will not be required, thus invalidating the
design layout. Usually that initial definition is done by the configuration
designer, not the company's specialists in those areas. There isn't enough
time, and those specialists always need more information than is available
at the start of a project. The layout geometry also has to properly reflect a
number of design requirements and "good practices" such as pilot outside
vision, compatibility with airports, maintenance access, and others.
Those considerations are discussed in Chapters
8 - 1 1 . Essentially these are the things that the desig­ Never forget: the
ner should be thinking about while the designer's end product of
fingers are creating the actual layout. The "mechan­ design is the
ical" but crucial task of creating the layout geometry design layout!
is the subject of this chapter.

* No, I won't identify the airplane. That would annoy its supporters and provide ammunition to its
opponents. It is a great airplane, and I wish it a long and successful operational life. Besides, all air­
planes wind up with such "fixes."
 CHAPTER 7 Confi g u ration Layout a n d Loft 1 67

End Products of Configuration Layout

The outputs of the configuration layout effort will be design drawings or
C AD files, plus geometric information required for further analysis.
The design layout process generally begins with a number of conceptual
sketches. Figure 7.1 shows the actual sketch that started the conceptual
design of Rockwell North American Aviation's entry into the Air Force
Advanced Tactical Fighter competition. l20l As can be seen, these sketches
are often crudely done, but depict the major ideas that the designer intends
to incorporate into the actual design layout. Sketches aren't normally shown
to anybody outside of Advanced Design. They are used to help us organize
our thoughts and discuss the concept with others. As described in Chapter 3,
they can also be used to quickly estimate sizing parameters needed to begin
the "real" layout.
A good sketch will show the overall aerodynamic arrangement including
fuselage, wings, and tails and will indicate the locations of the major internal
components. These should include the landing gear, crew station, payload or
passenger compartment, propulsion system, fuel tanks, and any unique
internal components such as a large radar.
The actual design layout is developed from the sketch using the
techniques discussed below. Figure 7.2 shows the design developed from

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Fig. 7 . 1 Design sketch.

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Fig. 7 . 2 Design layout on a CAD system .

 C HA PT E R 7 Config uration Layout a nd Loft 1 69

the sketch in Fig. 7.1, done on Rockwell's computer-aided conceptual design

l21l Figure 7.3 shows a typical drafting table design layout, being
software.
Rockwell's entry into the X-29 Forward Sweep Demonstrator competition.
The design techniques are similar whether a computer or a drafting board
is used .
A design layout such as those shown in Figs. 7.2 and 7.3 is the "input" into
the analysis and optimization tasks discussed in Chapters 12- 19. These later
analytical tasks require certain geometric values such as the trapezoidal
geometries of the wings and tails and various measured lengths, areas, and
volumes. To avoid confusion, it is better if the designer makes these
geometric measurements rather than simply passing the CAD file or
drawing to the analysts. Three other inputs should be prepared by the
designer: the wetted-area plot (Fig. 7.4), volume distribution plot (Fig. 7.5),
and fuel-volume plots for the fuel tanks. Preparation of the wetted-area
and volume plots is discussed later in this chapter; the fuel-volume determi­
nation is discussed in Chapter 10.
Once the design has been analyzed, optimized, and redrawn for a number
of iterations of the conceptual design process, a more detailed drawing can be
prepared. Called the "inboard profile" drawing, this depicts in much greater
detail the internal arrangement of the subsystems. Figure 7.6 illustrates the
inboard profile prepared for the design of Fig. 7.3. A companion drawing,
not shown, would depict the internal arrangement at 20-50 cross-sectional
locations.
The inboard profile is normally done during preliminary design and is far
more detailed than the initial layout. For example, while the initial layout
might merely indicate an avionics bay based upon a statistical estimate of
the required avionics volume, the inboard profile drawing will depict the
actual location of every piece of avionics (i.e., "black boxes") as well as the
required wire bundles and cooling ducts.
The inboard profile is generally a team project and takes many weeks.
During the preparation of the inboard profile, it is not uncommon to find
that the initial layout must be changed to provide enough room for every­
thing. As this can result in weeks of lost effort, it is imperative that the
initial layout be as well thought out as possible.
Figure 7.7 shows a side-view inboard profile prepared in 1942 for an early
variant of the P-5 1 . This detailed drawing shows virtually every internal
system, including control bellcranks, radio boxes, and fuel lines. Preparation
of such a detailed drawing goes beyond the scope of this book, but aspiring
designers should be aware of them.
At about the same time that the inboard profile drawing is being
prepared, a "lines control" drawing can be developed. This refines and
details the external geometry definition provided on the initial layout.
Again, such a detailed drawing goes beyond the scope of this book.
In today's design environment, the inboard profile development is usually
done on a three-dimensional CAD system. This greatly simplifies the actual
1 70 A i r c ra ft Desi g n : A C o n c eptu a l A p p roa c h

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 C H A PTE R 7 Confi g u ration Layout a n d Loft 1 71

Component Su rface
Fuselage 70344 . 8
Ve rt tail 26 1 65 . 3
Wing 1 02 6 3 6 . 7
Circular arc canopy 907 1 . 4
Nacelle 25462.9
Total 2 3 3 6 8 1 .0

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Fig. 7.4 Wetted area plot.

Component Vol ume

Fuselage 847 1 24.4
Vert tail 42903.5
Wing 287005.5
Circ u l ar arc canopy 460 1 4.0
Nacelle 95 1 49 . 8
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Fig. 7 .5 Volume distribution plot.

1 72 A i r c raft Desi g n : A C o n c e p t u a l A p p r o a c h
 C HAPT E R 7 Confi g u ration Layout a n d Loft 1 73

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 CHAPT E R 7 Config u ration Layout a n d Loft 1 75

layout work, but the designers still must obtain and model the detailed
geo metry of the aircraft's internal components and subsystems. Such
CAD systems do not require a separate lines control drawing. Instead, at
th e appropriate phase during design, a production-quality "solid model"
geo metry that defines the aircraft surfaces in great detail and accuracy will
be prepared. This, too, is a far-from-trivial task.
After the inboard profile drawing has been prepared, an "inboard
isometric" drawing (Fig. 7.8) can be prepared. These are usually prepared
by the art group for illustration only, used in briefings and proposals.
Isometrics are often published by aviation magazines, and theirs are
usually better than those prepared by the aircraft companies!

Con ic Lofting
"Lofting" is the process of defining the external geometry of the aircraft.
The word itself apparently comes from old shipyards, where the drawings
would be made in a loft over the worl�shop. "Those drawings made in the
loft" became the "loft" of the ship.
"Production lofting," the most detailed form of lofting, provides an exact,
mathematical definition of the entire aircraft including such minor details
as the intake and exhaust ducts for the air conditioning. A production-loft
definition is expected to be accurate to within a few hundredths of an inch
(or less) over the entire aircraft. This allows the different parts of the aircraft
to be designed and fabricated at different plant sites yet fit together perfectly
during final assembly.
Most aircraft companies now use computer-aided design systems that
incorporate methods discussed in [22l . These systems are so accurate that
different parts of the aircraft can be designed and built in different locations,
yet will fit together perfectly.
For an initial layout it is not necessary to go into as much detail. However,
the overall lofting of the fuselage, wing, tails, and nacelles must be defined
sufficiently to show that these major components will properly enclose the
required internal components and fuel tanks while providing a smooth
aerodynamic contour.
Lofting for ship hulls was done using enormous drawings. To provide a
smooth longitudinal contour, points taken from the desired cross sections
were connected longitudinally on the drawing by flexible "splines," long,
thin wood or plastic rulers held down at certain points by lead "ducks"
(pointed weights-see Fig. 7.9).
This technique was used for early aircraft lofting but suffers from two
disadvantages. First, it requires a lot of trial and error to achieve a smooth
surface both in cross section and longitudinally. Second, and perhaps
more important, this method does not provide a unique mathematical
definition of the surface. To create a new cross section requires a
tremendous amount of drafting effort, especially for a canted cross section
1 76 A i rc raft Desig n : A C o n c e pt u a l A p p ro a c h

Lead "d ucks"

Fig. 7 . 9 Spline lofting.

(i.e., a cross-sectional cut at some angle other than perpendicular to the

centerline of the aircraft). In addition to the time involved, this method is
prone to mismatch errors. Quite simply, there is too much "art" involved.
A new method of lofting was developed and used for the first time on the
North American Aviation P-51 Mustang. l23l This method, now considered
traditional, is based upon a mathematical curve form known as the "conic."
The great advantage of the conic method is that it is in fact a mathematically
defined curve, so that it can be plotted with great accuracy for production
lofting, but it is also easy to construct on the drafting table.
Up until roughly the 1 980s, conic lofting was used almost exclusively
for aircraft design. Today, modern three-dimensional CAD systems use
more sophisticated mathematical curves that are plotted on the screen
by laborious point-at-a-time calculations-computers are good at that.
However, this author firmly believes that a good understanding of traditional
conic lofting is a necessary foundation for understanding the process of
aircraft surface design and will help the designer learn to properly use even
the best of modern CAD systems.
A conic is a second-degree curve whose family includes the circle, ellipse,
parabola, and hyperbola. The conic is best visualized as a slanted cut through
a right circular cone (Fig. 7.10). The shape of the conic depends upon the
angle of the cut through the cone. If the cut is flat (i.e., perpendicular to
the axis of the cone), then the resulting curve will be a circle; if somewhat
slanted, an ellipse; if exactly parallel to the opposite side, a parabola. A
greater cut angle yields a hyperbola.
The generalized mathematical form of the conic is given in Eq. (7. 1). This
form of the equation is never used directly. A number of specialized conic
equations are provided in [22l .
 C HA P T E R 7 Configu ration Layout a n d loft 1 77

On a drafting table, the conic curve is constructed from the desired start
an end points (A and B) and the desired tangent angles at those points.
d
These tangent angles intersect at point C. The shape of the conic between
the points A and B is defined by some shoulder point S. (The points
labeled E in Fig. 7.10 are a special type of shoulder point, discussed later.)
figure 7. 1 1 illustrates the rapid graphical layout of a conic curve.
The first illustration in Fig. 7. 1 1 shows the given points A, B, C, and S.
In the second illustration, lines have been drawn from A and B, passing
through S.
The remaining illustrations show the generation of one point on the
conic. In the third illustration a line is drawn from point C at an arbitrary
angle. Note the points where this line intersects the A-S and B-S lines.
Lines are now drawn from A and B through the points found in the last
step. The intersection of these lines is a point P, which is on the desired
conic curve.

E l l i pse Pa ra bola Hyperbola

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Fig. 7 . 1 0 Conic geometry definition.

1 78 A i rc raft D e s i g n : A C o n c e p t u a l A p p roa c h

A c A c

s
•

G iven A, B, C, S
S is any s h o u l d e r point
B B

A c A c

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Fig. 7 . 1 1 Conic loyout.

B
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Fig. 7 . 1 2 Conic layout example.

 C H A PT E R 7 Confi g u ration Layout and Loft 1 79

To generate additional points, the last two steps are repeated. Another
C
line is drawn from point at another arbitrary angle, and then the lines
from A and B are drawn and their intersection is found. When enough
points have been generated, a French curve is used to draw the conic.
While this procedure seems complicated at first, with a little practice a
good designer can construct an accurate conic in less than a minute.
Figure 7. 12 illustrates a conic curve generated in this manner. Note that
it is not necessary to completely draw the various lines, as it is only their
intersections that are of interest.

Conic Fuselage Development

To create a smoothly lofted fuselage using conics, the points A, B, C,

and S
in each of the various cross sections are connected longitudinally by smooth
lines. Figure 7.13 shows the upper half of a simple fuselage, in which the A, B,
c, and s points in three cross sections are connected by smooth longitudinal
lines. These are called "longitudinal control lines" because they control the
shapes of the conic cross sections.
Figure 7.14 shows the side and top views of these longitudinal control
lines. Because the cross sections are tangent to horizontal at the top of the
fuselage, the A C
and lines are identical in side view. Similarly, the cross

Fig. 7 . 1 3 Longitudinal control lines.

1 80 A i rc raft Des i g n : A C o n c e p t u a l A p proa c h

B, C
s

Fig. 7 . 1 4 Cross-section development from longitudinal control lines.

sections are tangent to vertical at the side of the fuselage, so that the B and C
lines are identical in top view. This is common, but not required.
In Fig. 7. 14, the longitudinal control lines are used to create a new cross
section, in between the second and third cross sections already defined. This
new cross section is created by measuring, from the longitudinal control
lines, the positions of the A,
B, C, and S points at the desired location of
the new cross section.
A,
As is shown for point each point is defined by two measurements, one
from side view and one from top view. From these points the new cross
section can be drawn using the conic layout procedure illustrated in Fig. 7. 1 1 .
The original cross sections that are used to develop the longitudinal
control lines are called the "control cross sections" or "control stations."
These cross sections are drawn to enclose the various internal components,
such as the cockpit or engine.
Control stations can also be drawn to match some required shape. For
example, the last cross section of a single-engine jet fighter with a conven­
tional round nozzle would have to be a circle of the diameter of the nozzle.
Typically, some 5 - 10 control stations will be required to develop a
fuselage that meets all geometric requirements. The remaining cross sec­
tions of the fuselage can then be drawn from the longitudinal control lines
developed from these control stations.
 CHAPTE R 7 Confi g u ration Layout a n d Loft 181

-8 Fuselage Lofting Example

Figure 7.15 illustrates a common application of conic lofting to define
a fighter fuselage for an initial layout. Five control stations are required
fo r this example. Station 0 is the nose, which is a single point. All of the
longitudinal control lines must originate there.
Station 120 is established for this example by the requirements for the
cockpit (Chapter 9). This station is approximately circular in shape and is
defined using two conics (upper and lower) . Each conic has its own A, B,
C, B
and S points. Note that the (end) point of the upper conic is identical
A
to the (start) point of the lower conic.
Station 240 has a flat side to provide for a side-mounted inlet as can be
seen on the F-4, the MiG-23, the SAAB Gripen, and many other aircraft.
At this station, the end points of the upper and lower conics are moved
apart vertically, with the area between them defined as a straight line. Note
in side view that the longitudinal control lines separate smoothly, not
suddenly. This is to ensure a smooth l c:mgitudinal contour.
Station 370 is similar to station 240, with a relatively square cross­
sectional shape. This could allow room for the landing gear or perhaps to
attach a low wing to the side of the fuselage, without a drag-producing
acute angle.

0 1 20 240 370 500

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Fuselage

� 290

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Fig. 7 . 1 5 Typical fuselage lofting.

1 82 A i rc raft Des i g n : A C o n c e p t u a l A p p roa c h

Station 500 is a circular cross section, to allow for a connection with a

round exhaust nozzle. The longitudinal control lines come back together
in a smooth fashion, as shown.
These five control stations are then used to create the longitudinal
control lines. From those lines, additional cross sections can be created as
desired. Section 290 was created in such a fashion, by measuring the conic
control points from the longitudinal control lines and then drawing the
conics as described earlier.
Figure 7. 1 5 shows only the fuselage lofting. The canopy, inlet duct, and
inlet duct fairing would be lofted in a similar fashion, using longitudinal
control lines through a few control stations.

MIJ Conic Shape Parameter

One problem arises with this method of initial lofting. The locations of
the shoulder points S can be difficult to control, creating conics either too
square (shoulder point too close to point C ) or too flat (shoulder point too
far away from point C ). An alternate technique using conics involves a par­
ameter that directly controls the shoulder point's distance from the point C.
The points labeled E in Fig. 7.10 are conic shoulder points that happen
to lie upon the line D-C. D is the point exactly midway between A and B.
Such a shoulder point E determines the conic shape parameter p, as
defined in the following equation:
p= I DE l / I D C I (7.2)
where

IAD I = I BD I (7.3)
Referring to Fig. 7.10, the shoulder points labeled E are based upon the p
values required to obtain the ellipse, parabola, or hyperbola forms of the
conic. These are given below, along with the p value that defines a circle
(a special form of the ellipse):
Hyperbola:
p > 0.5
Parabola:
p = 0.5
Ellipse:
p < 0.5
Circle:

p = 0.4142 and IA C I = I B C I (7.4)

 C HAP T E R 7 Config u ration Layout a n d Loft 1 83

The conic shape parameter allows the designer to specify the conic
c urve's C.
distance from the point A conic with a large p value (approaching
1.0) will be nearly square, with the shoulder point almost touching the
p C.
oint A conic with a small p value (approaching 0.0) will nearly resemble
the straight line from A-B. The parameter p can be used to control the
longitudinal fairing of a fuselage more easily.
Figure 7.16 shows the use of the conic shape parameter p to lay out a
conic. Points A, B, and C are known, but the shoulder point S is not
known. However, the value of p is given.
In the illustration on the right side of Fig. 7.16, the line has been A-B
drawn and bisected to find the point D.
The shoulder point S is found by
measuring along line D- C, starting at D,
by a distance equal to p times the
total length of line D- C. Once the shoulder point is found, the conic can
be drawn as illustrated in Fig. 7. 1 1 .
By using this approach, a fuselage can b e lofted without the use o f a
longitudinal control line to control the location of the shoulder points. If p
is specified to be some constant value (or all of the cross sections, then the
designer need only control the conic endpoints and tangent intersection
points. To permit the fuselage ends to be circular in shape, the value of p
would be fixed at 0.4142.
Greater flexibility can be attained by allowing p to vary longitudinally. For
example, the fuselage of Fig. 7.15 requires a p value of 0.4142 at both ends to
allow a circular shape, but the values of p at the middle of the fuselage are
higher, perhaps around 0.7.
An "auxiliary control line" can be used to coi;itrol the value of p graphi­
cally, as shown in Fig. 7.17. Note the auxiliary control line for p at the

Given control
c
poi nts a n d p

B
A

A I DS I = p l D C I
I AD I = I DB I

Fig. 7 . 1 6 Conic layout using p.

1 84 Ai rc raft D e s i g n : A C o n c e p t u a l A p p ro a c h

bottom. If the value of p varies smoothly from nose to tail, and the conic
endpoints and tangent intersection point are controlled with smooth
longitudinal lines, then the resulting fuselage surface will be smooth.
In Fig. 7.17 the upper conic has a constant p value of 0.4142, while the
lower conic has a p value varying from 0.4142 at the nose and tail to about
0.6 at the middle of the fuselage. This has the effect of "squaring" the
lower fuselage to provide more room for the landing gear.
Figure 7.18 shows the use of p to develop the cross sections labeled A
and B. Observe the development of the upper and lower conics by the
method shown in Fig. 7.16 and the use of different p values for the upper
and lower conics.
Thus far, no mention has been made of the method for developing the
longitudinal control lines and auxiliary control lines. During production
lofting, these control lines would be defined mathematically, using conics
or some form of polynomial.
For initial layouts, sufficient accuracy can be obtained graphically through
the use of the flexible splines discussed earlier. Points are taken from the

Top view

(Radome) Section A Section B (Nozzle)

Side view

-1 I

---\ - 1
- Lower conic
p _
/
0.5

r
p 0 0.4142

-� p-Control l i nes
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- -

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Fig. 7 . 1 7 Conic fuselage development using p.

 CHAPTER 7 Configu ration Layout a n d Loft 1 85

p = 0.4142 p = 0.4142

p = 0.595 p = 0.610

Section A Section B

Fig. 7 . 1 8 Cross-section development using p.

control cross sections and plotted in side and top view and then connected
longitudinally using a spline to draft a smooth line. In fact, a designer with
a "good eye" can obtain sufficient smoothness using a French curve if
spline and ducks are not available.
Figure 7.19 shows an illustrative example of the conic-developed loft
lines for an exotically shaped aircraft, the sup�rsonic SAAB J-35 Draken
(Dragon). In this isometric view you can see the longitudinal control
scheme for fuselage, nacelle, canopy, and inlet duct, and you can also see
the lines definition for wing and tail. Such a detailed loft definition is not
normally done until sometime in preliminary design. But, a good designer
will consider the overall loft definition even from the earliest conceptual
design layout.

Flat-Wrap Fuselage Lofting

An important cost driver for aircraft fabrication is the amount of
compound curvature used in lofting the aircraft. Compound curvature
implies the existence of surface curvature in all directions for some point
on the surface.
For example, a ball is entirely composed of compound-curvature surfaces.
A flat sheet has no curvature, compound or otherwise. A cylinder is curved,
b ut only in one direction, so it does not have any compound curvature.
Instead, a cylinder or any other surface with curvature in only one direction
is said to be "flat-wrapped."
If a surface is flat-wrapped, it can be constructed by "wrapping" a flat
sheet around its cross sections. This is mathematically known as a
1 86 A i rc raft Des ig n : A C o n c e p t u a l A p p r o a c h

;1ii
!flt! !ft! 1t1 11r 1r:n:
. I • 1 /Jll!ilf!f!!H!1

>,
... > ,.,,.,. -.,_>l.;:..
� .. ....

Fig. 7 . 1 9 Isometric view of SAAB Draken major loft lines (courtesy SAAB Aircraft).

"developable surface" and is not necessarily the same as the "ruled surface"
available on most CAD systems.
For aircraft fabrication, flat-wrap lofting allows the skins to be cut from
flat sheets and bent to the desired skin contours. This is far cheaper than
the construction technique for a surface with compound curvature.
Compound curvature requires that the skins be shaped by a stretching or
stamping operation, which entails expensive tools and extra fabrication
steps.
 C H A PT E R 7 Confi g u ration Layout a n d Loft 1 87

The advantage of flat wrap was seen during the design and fabrication of
th e X-31 Enhanced Fighter Maneuver demonstrator. Rockwell's manufactur­
ing personnel pointed out a problem: the compound curves of the aft fuselage
would require hot die forming. Because the material around the engine was
titanium, the die itself would cost about $400,000 (1999 dollars) and be the
pacing item in the fabrication schedule. By changing the last 30 in. {76 cm}
of the aft fuselage to a flat-wrap loft, titanium sheet could be bent to shape
with no forming required.
Aircraft applications of flat-wrap lofting must be defined in the initial loft
definition used for the conceptual layout. There are several ways of lofting a
surface so that it is flat-wrapped. The simplest technique uses a constant
cross section. For example, a commercial airliner usually has the identical
circular-cross-sectional shape over most of its length. In fact, any cross­
section shape will produce a flat-wrap surface if it is held constant in the
longitudinal direction.
If the same cross-sectional shape is maintained but linearly scaled in size,
a flat-wrap contour is produced. For example, a cone is a flat-wrap surface
produced by linearly scaling a circular cross section.
Many aircraft have a tailcone that, although not circular in cross section,
is linearly scaled to produce a flat-wrap surface. This can be accomplished
with conics by maintaining identical tangent angles and p value, using
straight longitudinal control lines, and maintaining the lengths AC and BC
in constant proportion.
Sometimes it is necessary to vary the shape of the cross sections other
than by scaling. Flat wrap cannot be exactly maintained in such cases using
conics. A more sophisticated technique (beyond the scope of this book)
must be used.
However, flat wrap can be closely approximated in most such cases on
two conditions. First, the longitudinal control lines must be straight. This
includes the line controlling the shoulder point S. If the conic shape
parameter p is used instead of a shoulder-point control line, then the p
value must be either constant or linearly varied. Second, the tangent angles
of the conics must not change longitudinally. If the tangent angles are all
either horizontal or vertical, as in Figs. 7.15 and 7.17, this condition can
easily be met.
Figure 7.20 shows such a complex flat-wrapped surface. The fuselage is
defined by five conics plus a straight-line, flat underside. The "bump" on
top could represent the back of the canopy and grows smaller toward the
rear of the fuselage. While the conics change shape and size, their endpoints
hold the same tangent angles.
The use of flat-wrap lofting for a fuselage represents a compromise.
While flat-wrap surfaces are easier and cheaper to fabricate, they are less
desirable from an aerodynamic viewpoint. For example, a smoothly con­
toured teardrop shape will have less drag than a flat-wrap cylinder with a
nosecone and tailcone.
1 88 A i r c ra ft Desig n : A C o n ceptua l A p p ro a c h

Fig. 7 .20 Complex flat-wrapped surface.

Circle-to-Square Adapter
A common problem in lofting is the "circle-to-square adapter." For
example, the inlet duct of many supersonic j et aircraft is approximately
square at the air inlet, yet must attain a circular shape at the engine front-face.
Modern, two-dimensional nozzles also require a circle-to-square adapter.
Flat-wrap can be attained for a circle-to-square adapter by constructing
the adapter of interlocking, V-shaped segments, each of which is itself
flat-wrapped (Fig. 7.21). The flat sides of the square section taper to points

Section A-A

Fig. 7 . 2 1 Circle-to-square adopter.

 CHAPTER 7 Confi g u ration Layout and Loft 1 89

that just touch the circular section. Similarly, the cone-shaped sides of the
circular section taper to points that touch the corners of the square
section. Note the "rounded-off square" shape of the intermediate sections.
The connecting surfaces must be straight longitudinally for a flat-wrap
surface to be maintained.

Loft Verification via Buttock-Plane Cuts

If conic lofting is properly done with smooth longitudinal control
lines, the resulting shape should be smooth. Sometimes, though, it is wise
to check the surface contours. Perhaps part of the fuselage is flat-wrapped
or oddly shaped for some other reason, or perhaps a designer is asked to
evaluate a design created by someone else.
Surface contours can be visualized and evaluated using an ancient
technique borrowed from shipbuilding. Hull contours are checked for
smoothness by laying out the "waterlines." If a ship is floating in the water,
the line around the hull where the surface of the water intersects the hull
is a waterline. For good ship performance, this waterline should be smooth
in the longitudinal direction.
If the hull is raised partly out of the water some arbitrary distance, a new
waterline is formed. Hull designers check for hull smoothness by laying
out a large number of these waterlines, each separated in height by some
arbitrary distance. If all of the waterlines have smooth contours, then the
hull is smooth.
Such horizontal waterline cuts can be used for evaluation of the smooth­
ness of an aircraft fuselage, but it is more common to use vertically oriented
cuts known as "buttock-plane cuts" (Fig. 7.22).
Buttock-plane ("butt-plane") cuts form the intersection of the aircraft
with vertical planes defined by their distance from the aircraft centerline.

Airfoil is a butt-plane cut of the wing

Fig. 7 .22 Buttock-plane cut.

1 90 Ai rcraft D e s i g n : A Conceptu a l Approach

Cut fuselage with vertical planes

p a ra l l e l to centerl i n e

cl

I
I I I
I
Top view
I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I
Cross- I
I I section I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I I I
I

FRP

Fig. 7 .23 Buttock-plane cut layout.

For example, "butt-plane 30" is the contour created by intersecting a vertical

plane with the fuselage at a distance of 30 in. from the centerline. Note
in Fig. 7.22 that the butt-plane cuts are oriented such that the airfoil is a
butt-plane cut of the wing. It is for this reason that butt-plane cuts are
more commonly used for aircraft than waterlines.
Figure 7.23 illustrates the development of butt-plane cuts. Vertical lines
are drawn on each cross section, indicating the locations of the arbitrarily
selected butt-planes. The points where these vertical lines intersect the
cross sections are transferred to the side-view drawing and connected
longitudinally. If the fuselage surface is smooth, then these longitudinal
lines for the different butt-planes will all be smooth.
Buttock-plane cuts can also be used to generate new cross sections. Once
the butt-plane cuts are developed as in Fig. 7.23, a new cross section can be
developed by transferring the vertical locations of the butt-plane cuts to the
cross section desired and then drawing a smooth cross-sectional contour
using those points.
 C HAPTE R 7 Confi g u ration Layout a n d Loft 191

Sometimes this archaic method is actually easier than developing the

longitudinal control lines for conic fuselage lofting. This is most likely
when the surface is highly irregular, such as the forebody of a blended wing­
b ody aircraft like the B- lB.

Wi ng/Ta i l Layout and Loft

� Reference Wing /Tai l Layout
Chapter 4 described the selection of the basic geometric parameters for
the wing and tails. These parameters include the aspect ratio taper ratio A,
A, sweep, dihedral, and thickness. Also, the selection of an appropriate
airfo il was considered. In Chapter 6, the actual sizes for the wing, tails, and
fuselage were defined, based upon an initial estimate for the takeoff
gross weight.
From these parameters, the geometric dimensions necessary for layout of
the reference (trapezoidal) wing or tail �an be obtained, as shown in Fig. 7.24
and defined by the following equations:

b = v'AS (7.5)
Croot =
2S (7.6)
b ( l + A)
Ctip = ACroot (7.7)

.._-- Croat ---io--

t
y

i c hord ( C )
Mean aerodyna m i c

b/2

j
Fig. 7 . 24 Reference (trapezoidal) wing/tail.
 ( ) Croot 1
1 92 A i rc raft Desi g n : A C o n c e p t u a l A p p r o a c h

- 2 + A + A2
C= 3 (7.8)

(�) (11: :)
l+A

y= 2
(7.9)

The mean aerodynamic chord (MAC or C, pronounced "C-bar") is the

wing chord that acts like all of the area of the wing is compressed there.
Recall that the wing subsonic pitching moments do not change with angle
of attack if measured about a point 25% of chord back from the leading
edge of the MAC. Y (" Y-bar") is the spanwise location of C-bar.
For a vertical tail, the Y-bar value calculated in Eq. (7.9) must be doubled.
This occurs because the total area is half the value obtained if the vertical
tail were to be laid flat and converted to a symmetrical wing. All other
calculations are the same as for a wing or horizontal tail.
Figure 7.24 also shows a quick method of determining C-bar and Y-bar
from a trapezoidal wing. Y-bar is found as the intersection of the
50%-chord line and a line drawn from a point located at the tip chord
length behind the root chord, to a point at the root chord length ahead of
the tip chord. C-bar is found simply by drawing it at that location.
As mentioned in Chapter 4, the elliptically shaped wing has less drag than
the trapezoidal wing already assumed, and if modern composite construction
is used, it might no longer have the historically expected cost penalty. When
designing an elliptical wing the span is found as usual from Eq. (7.5). The root
chord Croot is found from Eq. (7. lOa). Then the chord length is found as a
function of distance Y from the centerline as in Eq. (7. lOb). The MAC is
84.9% of Croot • and Y-bar is equal to 52.9% of the semispan.

Croot = 7Tb
45
(7 . l Oa)

(7 . lOb)

Note that total area is 'TT/ 4 times the product of span and root chord. Also,
it is common for the chords of elliptical wings to be "slid" in the chordwise X
direction so that the 25% of chord line is straight and unswept. This has no
effect on the above calculations, but does move the 25% of MAC location a
bit forward .

.a Wing Location with Respect to the Fuselage

The location and length of the MAC are important because the designer
locates the wing on the aircraft so that some selected percent of the MAC
is aligned with the aircraft center of gravity. This provides a first estimate
of the wing position to attain the required stability characteristics.
 C HAPTE R 7 Confi g u ration Layout a n d Loft 1 93

If the airplane is a pure flying wing, with no other components than a

wing of trapezoidal shape, it will be neutrally stable if its center of gravity
is at that 25% of C-bar location. The pitching moment doesn't change
around that point so that if the angle of attack changes, the moments do
not change. This is the very definition of neutral stability.
An aft tail adds to the stability. For a stable aircraft with an aft tail, the
wing should be initially located such that the aircraft center of gravity is at
about 30% of the mean aerodynamic chord. When the combined effects of
the fuselage and tail are considered, this gives a reasonable level of stability.
When designing an unstable aircraft with an aft tail such as the F-22,
the wing must be farther forward. A good first approximation is to locate
the wing such that the center of gravity is at about 40% of the mean
aerodynamic chord.
For a canard aircraft, such rules of thumb are less reliable due to the
canard downwash and its influence upon the wing. For a control-type
canard with a computerized flight control system (i.e., an unstable aircraft),
the wing can initially be placed such t�at the aircraft center of gravity is at
about 15-20% of the wing's mean aerodynamic chord.
For a lifting-type canard, the mean aerodynamic chords of the wing and
canard should both be determined, and a point at about the 15% MAC
for each should be identified (20-25% for an unstable aircraft). Then
the combined MAC location can be determined as the average of these
percentage MAC locations for the wing and canard, weighted by their
respective areas. Note that this is a very crude estimate!
After the initial layout is completed and analyzed using the methods of
Chapters 12- 19, the wing will probably need to be moved and the tails
resized to meet all required stability and control characteristics. Hopefully
the initial estimates will be close enough so that major changes will not
be needed.

8IJ Wing/Ta i l Lofting

After positioning and drawing the trapezoidal wing and tails, the actual
exposed wing and tails are designed. As changes are made, those original plan­
forms should be retained on the drawing or as components in the CAD file,
to facilitate their use in aerodynamic calculations. Recall that the trapezoidal
wing is used as the reference wing for aerodynamic coefficients-don't forget
what it is!
The trapezoidal wing is defined to the aircraft centerline and is based
upon the projected area (i.e., dihedral does not affect the top view of the
reference wing). The actual, exposed wing begins at the side of the fuselage
and includes the effect of the dihedral upon the true-view area. The dihedral
angle increases the actual wing area equivalent to dividing by the cosine of
the dihedral angle.
1 94 A i rc raft D e s i g n : A Conceptu a l A p proach

a) Rounded wingtip b) Tra i l i ng-edge "kick" or "bat"

d) Cu rved

Fig. 7.25 Nontrapezoidal wings.

Also, the actual wing planform might not be trapezoidal. Figure 7.25
illustrates several of the many nontrapezoidal wing variations. A typical
rounded wing tip is shown in Fig. 7.25a. This and other wing-tip shapes
have already been discussed. The straightened-out trailing edge shown in
Fig. 7.25b increases the flap chord and provides increased wing thickness
for the landing gear.
Figure 7.25c illustrates a "leading-edge extension" (LEX), which increases
lift for combat maneuvering (see Chapter 12). A highly blended wing/body
is shown in Fig. 7.25d, in which the actual wing looks very little like the
reference wing.* This type of wing is used to minimize the transonic and
supersonic shocks.
Once the designer has settled upon the actual wing and tail planforms,
their surfaces must be lofted to provide accurate cross sections. These are
required to verify that there is sufficient room for the fuel tanks, landing
gear, spars, and other internal components. During production design, this
lofting would be done using conics or some other mathematical surface
definition in a modern CAD system.
For initial design, simpler methods of wing and tail lofting can be used.
These rely upon the assumption that the airfoil coordinates themselves are

* Be careful: if the actual wing looks almost nothing like the original trapezoidal wing, classical
analysis methods based on the original wing parameters may give a poor result. Computational
aerodynamics analysis methods are not so affected.
 CHAPTER 7 Confi g u ratio n Layout a n d Loft 1 95

smoothly lofted. This is an excellent assumption-otherwise the airfoil

performance would be poor.
If the wing or tail uses the identical airfoil section and thickness ratio at all
span stations and is without twist, the airfoils can be drawn simply by scaling
the airfoil coordinates to fit the chord lengths of the selected spanwise
locations.
It is customary to lightly draw the airfoils on the top view of the wing,
superimposing them on their chordline (Fig. 7.26). This layout procedure
simplifies the generation of cross sections, as will be discussed later. For
initial design purposes the airfoils can be quickly drawn using only a few
scaled coordinate points for the top and bottom surfaces.
If twist is incorporated, the incidence at each span station must be deter­
mined and the chord line rotated accordingly before the airfoil is drawn.
Because the chord length is defined in top view, the chord length at each
spanwise station must be increased equivalent to dividing by the cosine of
the appropriate incidence angle.
For a complicated twist distribution, an auxiliary twist control line can be
constructed behind the wing. The airfoil incidence at each span station can
then be read from the control line (Fig. 7.27).
A wing with a complicated aerodynamic design might have the twist,
camber, and thickness all varying from root to tip. These spanwise variations
can be lofted by using a separate auxiliary control line for each, as shown
in Fig. 7.28. The airfoil coordinate points must be calculated by separating
the airfoil into its camber line and thickness distribution, scaling them as
indicated by the auxiliary control lines, and recombining them. Such a
complicated wing design is not normally accomplished until later in the
design process. In fact, the latest computational wing design methods directly
reshape the wing surfaces in the CAD model so that these methods may not
b e needed. Still, it is useful to understand the classical methods.

'
' A i rcraft top view
'
'

Fig. 7 .26 Airfoil layout on wing planform .

1 96 Aircraft Des i g n : A Conceptua l Approach

A i rfoi l incidence (deg)

+ 2 +l 0 -1 -2

_f_ _
-� - -
1 .0 deg

I
O deg�

{
- 1 .0 deg

- - - - �::=;;�
-�
- - - - - -

-2.0 deg
Ang les a re exaggerated for i l l u stration

Fig. 7 . 2 7 Airfoil layout with twist.

Auxiliary control l i nes

( +J ___,-+---4-'--.-+-�-- H

L
J
Ca m ber _} Twist

Th ickness (tic)

Fig. 7 .28 Wing airfoi l layout-nonlinear variations.

 C HA PT E R 7 Confi g u ration Layout and Loft 1 97

U n rigged Rigged

I
This section moved down
- Note T.E.

Fig. 7 . 29 Wing airfoil rigging.

For a wing such as shown in Fig. 7.28, the complex curvatures of the wing
su rface can present difficulties. A spar running from root to tip might be
so curved that it is structurally undesirable. Even worse, the hinge lines for
the ailerons and flaps might not lie in a straight line. Curved hinge lines
are impossible, so the ailerons and flaps might have to be broken into a
shorter segments unless the wing surface can be modified to straighten the
hinge line.
This is done by "wing rigging" (not to be confused with the rigging of a
b iplane wing)-the process of vertically shifting the airfoil sections until
some desired spanwise line is straight.
Figure 7.29 illustrates a complex wing in which the aileron hinge line,
Section A-A, is curved. On the right side of the figure is the same wing
with the midspan airfoil moved downward a few inches. This provides a
straight hinge line shown as Section B-B.

aJ)JJ Airfoil Linear Interpolation

Wings are often initially defined by a root airfoil and a tip airfoil, plus
their incidence angles or relative twist. Frequently the tip airfoil will be
selected for gentle stall characteristics whereas the root airfoil is selected
for best performance. The resulting wing has good overall performance
with good stall characteristics because the tip will stall after the root. The
airfoils between the root and tip can be quickly developed by one of
two methods.
Linear interpolation, the easiest method, is depicted in Fig. 7.30. Here
the new airfoils are created as "weighted averages" of the root and tip airfoils.
Linearly interpolated cross sections are also known as "ruled surfaces" and
are so called in many CAD programs.
1 98 A i rc raft Desi g n : A C o n c e p t u a l A p p r o a c h

\ (3)

\
\

\
\ (5) \
\ (6)
\ • •
• •
• \ •
\

\
\4)
\
(2)

(3)

Graphic i nterpolation between d iffering root and tip a i rfoils

1 -S u perim pose root a n d tip a i rfoils o n pla nform
2-Draw line at some constant percent of chord
3-Swi ng a i rfoi l point down onto chord reference l i n e
4-Con nect root a n d tip poi nts from 3
5-Swi ng point u p to new a i rfoi l location
6-Repeat for other perce nt chord l i n es

Fig. 7 .30 Wing airfoil layout-linear interpolation .

The intermediate airfoils are linearly interpolated by a five-step process.

The root and tip airfoils are drawn (step 1). A constant percent-chord line
is drawn connecting the root and tip airfoil, and vertical lines are drawn
from the intersection of that line with the chord lines (step 2). The airfoil
points found at those vertical lines are "swung down" to the chord line,
using an arc centered at the intersection of the chord line and the vertical
line (step 3). These swung-down points for the root and tip airfoils are
then connected by a straight line (step 4).
At the desired location of an interpolated airfoil, a chord line is drawn.
The intersection of that chord line with the line drawn in step 4 defines
the chordwise location of a point on the interpolated airfoil. In step 5 this
point is "swung up" to its thickness location by an arc centered at the inter­
section of the chord line and the spanwise percent-chord line from step 2.
 CHAPTER 7 Confi g u ration Layout a n d Loft 1 99

This process is repeated for as many points as are needed to draw

th e new airfoil. Then the process is repeated to draw other airfoils.
While it seems complicated, a wing can be developed using this method
in about 15 min by an experienced designer. A CAD system does this
instantly.
Linearly interpolated airfoils have section properties that are approxi­
mately the interpolation of the section properties of the root and tip airfoils.
Note that interpolated section properties may not be correct for modern
laminar airfoils.

al:J Airfoil Flat-Wrap Interpolation

The linear-interpolation method (ruled surface) doesn't necessarily
provide a flat-wrap surface, instead possibly yielding a slight amount of
compound curvature. This is especially true if the wing is twisted or the
airfoil shapes are dissimilar. This requires a modification to the method
just described.
In laying out a fuselage for flat-wrap, it was necessary to hold the same
tangent angle for the conics in the different cross sections. The same is
true for wings. To provide a proper flat-wrap lofted wing, linear interpolation
must be done between airfoil coordinates with the same slope (i.e., tangent
angle) rather than the equal-percent-of-chord method above.
Figure 7.31 illustrates this modification. The only difference is in step 2.
Previously a spanwise line was drawn connecting constant percent chord
locations on the chord line. To obtain a flat-wrap surface this spanwise
line must be drawn connecting locations on the chord line that have
the same surface slope. Note in the figure how the tip chord has the indi­
cated slope at a more-aft percent location of the chord than does the
root chord.
Is this really important? Many composite homebuilts are fabricated by
a method long used for model airplanes. A large block of foam is cut to
the desired wing shape using a hot-wire cutter that is guided by root and
tip airfoil templates attached to the foam block. The templates have tic-marks
that are numbered. The wire is guided around the templates by two home­
builders, one of whom calls out the numbers of the tic-marks.
If the tic-marks are at constant percent-chord locations, and the wing has
dissimilar airfoils or appreciable twist, this method will produce a linearly
interpolated instead of flat-wrap surface. For a wing covered by fiberglass,
this will pose no problem as the fiberglass cloth will easily conform to the
slight amount of compound curvature present.
However, if the wing is to be covered by sheet metal or plywood, the
linearly interpolated foam surface will be depressed relative to the flat­
wrapped skin. This could reduce the strength of the skin bonding. It is
conceivable that such a wing could fail in flight for this simple reason.
Who said lofting is not important?
200 A i rcraft Des i g n : A Conceptu a l A p p ro a c h

l2f'..)

� (3) (1 )

-?,0" " '\\ '

'\ '

'\
'\
\
'\ (5) (6)
'\
. '\ ,, . .
'\ '\\ . .

(1 )

Flat-wra p i n terpolation between d iffering root a n d tip a i rfoi l s

1 -S u perimpose root a n d tip a i rfoils on planform
2A-For a point on the root a i rfoil, fi n d the slope
2 8 - F i n d the point o n the tip a i rfoi l with the same slope
2C-Con nect the percent chord points from (2A) a n d (28)
3-At root a n d tip, swing points down onto chord reference l i n e
4-Con n ect the points from ( 3 )
5-Swing p o i n t u p t o n e w a i rfoi l location
6-Repeat for other points

Fig. 7 . 3 1 Wing airfoi l layout-flat-wrap.

MlJ Wing/Ta i l Cross-Section Layout

One of the important tasks during configuration design is to make sure
that the fuel tanks, landing gear, and other internal components all fit
within the wing contours. The wing shape is defined by airfoils, but this fit
verification is better done using wing and tail cross sections, which are
oriented perpendicular to the aircraft centerline. Such cross sections can
be easily developed once the airfoils are drawn onto the top view of the
wing. Figure 7.32 illustrates the development of one such cross section.
To develop a wing or tail cross-section cut, vertical lines are drawn on the
cross section at the spanwise location of the airfoils shown on the wing top
view. Also, the wing reference plane is shown at the appropriate wing
dihedral angle. Then the airfoil upper and lower points are measured relative
 CHAPTER 7 Configuration Layout a nd Loft 20 1

to th e plane of the wing and drawn accordingly on the cross section. The
cross -section shape can then be drawn using French curves.
The same procedure can be used to develop section cuts at angles other
th perpendicular to the aircraft centerline. The sections of Fig. 7.29
an
labeled A-A and B-B were developed in this manner.
A modern CAD system can easily create these cross-section cuts. Ideally,
those cuts are readily superimposed upon the internal components allowing
either them to be redesigned or relocated as appropriate.

MJll Wing Fillets

For improved aerodynamic efficiency, the wing-fuselage intersection of
many aircraft is smoothly blended using a "wing fillet" (Fig. 7.33). A wing
fillet is usually defined by a circular arc of varying radius, tangent to both
the wing and fuselage. Typically, a wing fillet has a radius of about 10% of
the root-chord length.
The fillet arc radius can be constarrt or can be varied using an auxiliary
radius control line as shown in Fig. 7.33. The fillet radius usually increases
towards the rear of the aircraft to minimize airflow separation. Some aircraft
have a fillet only on the rear part of the wing. In this case the fillet starts, with
zero radius, at or near the wing's maximum thickness point.

'
'
'
'

//
"1
/I
/
/ I
Superim pose a i rfoils on pla nform I I
I I
transfer points to cross-section I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
\
-- Wing reference plane

Fig. 7 . 3 2 Wing/tail cross-section layout.

202 A i rc raft Desi g n : A C o n c e pt u a l A p p r o a c h

Wing fi l let
Lea d i n g-edge/
fi l let rad i u s

�
Arc Auxi l i a ry fi l let control l i n e
ra d I. U S
+
----1
i,
I

Fig. 7 .33 Wing fil let layout.

The fillet circular arc is defined perpendicular to the wing surface, so that
the arc is in a purely vertical plane only at the maximum thickness point of
the wing. At the leading edge, the arc is in a horizontal plane, that is, it is seen
in top view.
For initial layout purposes the fillet is frequently "eyeballed." Only a few of
the 10 or 15 aircraft cross sections developed for an initial layout will show
the wing fillet, so a fillet radius that "looks good" can be used.
Some airplanes have a fillet that is basically a straight and nearly vertical
line running from the maximum width point of the fuselage, down to the top
of the wing and extending towards the rear. While not as beautiful as the
circular fillet, it can work just as well.

MJjJ Winglet Design

Winglets were presented in Chapter 4 as devices to reduce induced drag,
especially for a wing with a fairly high span loading. They are now widely used
and are especially beneficial when an existing design is being recertified to a
higher takeoff weight. This increases span loading, which increases induced
drag unless the wing span is also increased. That is difficult and expensive.
Instead, winglets can be added to counteract the induced drag increase
without the need to extend the wing span.
Fundamentally, the winglet works by producing a side force (inward­
pointing "lift") that has a slight forward component because of the rotation
of the vortex over the top of the wing tip. If there is no side force, then
there is no winglet effect. Thus, the winglet must be wing-like (hence the
name), with both camber and angle of attack to the local flow.
 C HAPTER 7 Confi g u ration Layout and Loft 203

Another way to understand how a winglet works is this: it is a vertical

wing, lifting inwards. Like all lifting surfaces, it makes a "downwash"
behind itself, which in this case is an "outwash." This "blows" the wing's
tip vortices farther outward. In the far field, the effective span of a wing
depends on the separation between its tip vortices, so that the wing, in
effect, has greater span and hence less drag due to lift.
The winglet also acts as an endplate, resisting the tendency of the air to
flow arou nd the tip and therefore allowing the wing to generate more lift
near the tip.
There are many types, shapes, sizes, and geometries of winglets. Almost
every year, a new variation on the basic theme is proposed. Figure 7.34
illustrates what some call the "classic" winglet as defined by R. Whitco mb,
the original developer. The upper winglet should begin at the place where
the wing-tip airfoil has its maximum thickness, and it should be swept
about the same as the wing. It should be at least as tall as the tip chord of
the wing, and even taller is better because the drag reduction is roughly pro­
portional to the winglet height. The Caf!lber of the winglet should be greater
than that of the wing to ensure sufficient side force, and it should have a
4-deg leading-edge-out incidence angle. Typically, the winglet t/ c is about 8%.
The bottom winglet panel, seen o n the original winglet concept,
contributes less to the drag reduction. Because it sticks below the wing, it
threatens to scrape on the ground if the aircraft is rolled too much, so it is
not included on many winglet-equipped aircraft. If included, it should be
twisted with its root at a 7-deg incidence and its tip at 1 1 deg.

11 5 deg·
I

� ·'
I I

I
I
I
Height = c1 I

j
I

Dihedra l

Fig. 7 .34 Wing let design guidelines (after NASA N76-26 l 63, R. Whitcomb).
204 A i r c raft Desig n : A Conceptual A p p ro a c h

A further drag reduction can be obtained by smoothly curving the wing

tip upward to the winglet (when seen from the front) rather than having
the winglet be a separate piece attached to the top of the wing.
One danger with the winglet is that it is adding mass behind the elastic
axis of the wing. Flutter tendencies must always be considered, and a detailed
aeroelastic analysis should be performed to determine if structure stiffening
will be required. Because that will add weight, it can reduce the benefit of
the winglet.

Wetted-Area Determ i nation

Aircraft wetted area Swet , the total exposed surface area, can be visualized
as the area of the external parts of the aircraft that would get wet if it were
dipped into water. The wetted area must be calculated for drag estimation,
as it is the major contributor to friction drag.
The wing and tail wetted areas can be approximated from their plan ­
forms, as shown in Fig. 7.35. The wetted area is estimated by multiplying
the true-view exposed planform area Sex posed times a factor based upon
the wing or tail thickness ratio.
If a wing or tail were paper thin, then the wetted area would be exactly
twice the true planform area (i.e., top and bottom). The effect of finite
thickness is to increase the wetted area, as approximated by Eqs. (7.11) or
(7.12). Note that the true exposed planform area is the projected
(top-view) area divided by the cosine of the dihedral angle.
If t/ c < 0.05,
Swet = 2.003Sexposed (7. 1 1)
If t/ c > 0.05,
Swet = Sexposed [ l.977 + 0.52 (t/c)] (7.12)

---..,-��������-..,��������--..�����.-� cl
\
\
\
\

Fig. 7 . 35 Wing/tail wetted-area estimate.

 C HAPTE R 7 Config u ration Layout and Loft 205

A top

Fig. 7 .36 Quick fuselage wetted-area estimate.

The exposed area shown in Fig. 7.35 ·can be measured from the drawing in
several ways. A professional designer will have access to a "planimeter," a
mechanical device for measuring areas. Use of the planimeter is a dying art
as the computer replaces the drafting board. Alternatively, the area can be
measured by tracing onto graph paper and "counting squares."
The wetted area of the fuselage can be initially estimated using just the
side and top views of the aircraft by the method shown in Fig. 7.36. The
side- and top-view projected areas of the fuselage are measured from
the drawing, and the values are averaged.
For a long, thin body circular in cross section, this average projected area
times 1T will yield the surface wetted area. If the body is rectangular in cross
section, the wetted area will be four times the average projected area. For

)
typical aircraft, Eq. (7.13) provides a reasonable approximation.

Swet � 3.4 top : side

(
A A (7. 13)
A more accurate estimation of wetted area can be obtained by graphical
integration using a number of fuselage cross sections. If the perimeters of
the cross sections are measured and plotted vs longitudinal location, using
the same units on the graph, then the integrated area under the resulting
curve gives the wetted area (Fig. 7.37).
Perimeters can be measured using a professional's "map-measure" or
approximated using a piece of scrap paper. Simply follow around the
perimeter of the cross section making tic marks on the paper, and then
measure the total length using a ruler.
Note that the cross-sectional perimeter measurements should not
include the portions where components join, such as at the wing-fuselage
intersection. These areas are not "wetted."
206 A i rc raft Des i g n : A Conceptu a l A p p ro a c h

Cross-section
peri meter

Wetted a rea = a rea u n d e r cu rve

Fig. 7 .37 Fuselage wetted-area plot.

Volume Determ i nation

The aircraft internal volume can be used as a measure of the reason­
ableness of a new design. A conceptual design layout can't show all of the
internal components that will be packed inside by the time the airplane
flies. Many of them won't be designed until much later in the development
process. A statistical approach can be used to determine if there is enough
room in the design to accommodate all components. This should be done
by the designer as a check after the design layout is completed. It is also
commonly done by customer engineering groups to see if a design is
acceptable or if the designers have "cheated," making a layout that looks
good now due to its small size but will have to grow as the design
is matured.
This is done using statistical plots of total internal volume vs aircraft
takeoff gross weight for different classes of aircraft. An aircraft with
less-than-typical internal volume for its weight will probably experience
problems in development and will likely have poor maintainability in
service due to tight packaging. A more sophisticated density checking
method called net design volume is given in Chapter 19.
Aircraft internal volume can be quickly estimated in a similar fashion to
the wetted-area. Equation (7.14) uses the side- and top-view projected
areas as used in Eq. (7.13) to estimate volume. The 3.4 term assumes that
 CHAPTER 7 Confi g u ration Layout and Loft 207

the cross-section shape is intermediate between a square and a circle. L is

the fuselage length.

Vol � 3.4
(A top ) (A side ) (7. 14)
4L
An accurate estimate of internal volume can be found by a graphical
integration process much like that used for wetted-area determination.
The cross-section areas of a number of cross sections are measured and
plotted vs longitudinal location. The area under the resulting curve is the
volume, as shown in Fig. 7.38.
This "volume distribution plot" is also used predict and minimize
supersonic wave drag and transonic drag rise. In fact, its very shape
determines the supersonic drag. This will be discussed in Chapter 12.

Use of Computer-Aided Design (CAD)

in Conceptua l Design
Today, the previous discussion of drafting table techniques sounds
almost quaint. Everyone, from students to grizzled industry veterans, now
uses a CAD system of some sort for most design work.
Modern CAD systems are amazingly powerful and offer excellent graphi­
cal user interfaces, accurate surface definitions, realistic photo-like rendering
capabilities, and sophisticated data management systems, even on a personal

Cross-section
area

Vol u m e = a rea under curve

Fig. 7 .38 Aircraft volume plot.

208 Aircraft D e s i g n : A Con ceptu a l Approach

computer. Design capabilities allow creation of every imaginable type of

geometry, and various CAD systems have specific geometry creation tools
to simplify development of certain design components and features. The
best modern CAD systems have virtually automated design of certain
parts, such as hydraulic tubing and access doors. In one CAD program the
hydraulic system designer can simply indicate, in three dimensions, the
desired path of a hydraulic line, and the system will create the tubing at
the proper diameter, construct bends with diameters that can be fabricated
without cracking, and include the proper fittings, couplings, and brackets­
all automatically. The future will see more and more such automation of
the design of common parts and systems.
Furthermore, through the industry usage of modern CAD systems the
entire aircraft is being designed digitally, allowing the use of virtual rather
than actual mock-ups. T his saves time and money and does a better j ob of
identifying and fixing component interference problems and potential
difficulties in fabrication and maintenance of the aircraft. The digital
product definition also improves prototype fabrication and aircraft produc­
tion. Transference of the design data to computer-aided manufacturing
(CAM) becomes almost trivially easy, and the resulting parts fit together
perfectly. Altogether, the integrated use of CAD and CAM has been, in
this author's opinion, the single greatest improvement in cost and quality
that the aircraft industry has ever seen.
However, there can be problems with too great of a willingness to "let the
CAD system do it." First of all, with a CAD system there is a tendency to let
the computer lead you in the "easy" direction. If it is easy to retract the
landing gear directly inward with your CAD system, you may do so even if
a better design would result from having it retract inward and forward at
a difficult-to-construct oblique angle. If you can easily calculate the
volume of a square fuel tank, but don't know how to get the volume of a
complicated tank wrapped around the inlet duct, guess which one you are
likely to design!
Another problem is the actual calculation of the volumes, wetted areas,
and other dimensions critical to your analysis of your design. Sometimes a
CAD system may confidently display an incorrect answer! For example, we
might model the wing as a collection of airfoils connected by a mathematical
surface and might readily calculate the wetted area of the wing itself.
However, where that wing intersects the fuselage we must cut away the
surface of the wing where it penetrates the fuselage and cut away the fuselage
where the wing covers it. It is possible in many CAD systems to forget to
account for, or double-account for, the wing root airfoil "wetted area"
that must be removed from the fuselage and not included with the wing!
This potential problem is minimized if true "solid models" are (properly!)
employed. Other examples include the inlet front and the back end of a
fuselage or nacelle with a jet engine, or the front of a propeller nacelle,
where the exhaust or intake areas must not be included. Even a solid
 C HA PT E R 7 Configu ration Layout a n d Loft 209

model could accidentally give the wrong answer in this case, failing to
understand that the "hole" isn't there!
For this reason it is STRONGLY recommended that all CAD users start
by doing a trivially simple "aircraft design" consisting of a tube-plus-cone fuse­
lage and a simple wing, where the correct wetted areas and volumes can be
easily calculated by hand and compared with the answer from the CAD system.
Yet another problem for students is that the aircraft design course can
easily become the "learn how to use a certain CAD system" course. There
is not enough time in a semester course to really learn how to do conceptual
design, and ANY time spent learning which button produces which geometry
is time NOT spent learning the philosophy, methods, and techniques of
aircraft conceptual design.
In industry, a real but subtle problem is that, with a CAD system,
everybody's designs look good whether they are or are not! When everybody
was using a drafting table, you could usually tell from drafting technique that
a design was done by a beginner and therefore whether the design needed to
be reviewed extra carefully. Today, it "t�kes one to know one" -you must be a
pretty good designer yourself to know if a design you are looking at was
done properly.
CAD tools used during conceptual design should be tailored toward
the fluid environment and the unique tasks of aircraft conceptual design.
Quite simply, what is done during conceptual design, the things that are
critical, and the tasks that are boring and repetitive (and therefore ideal for
computerization) are different from those in other, later phases of aircraft
design.
A perfect example is the wing trapezoidal geometry. During detail part
design, it is out of the question to change the wing trapezoidal geometry,
no matter how much the design of, say, a certain wing rib would be improved
as a result. During conceptual design though, those parameters are constantly
being changed, almost every week in the early stages. Conceptual designers
need capabilities to change these instantly and to have the computer
automatically revise the wing's nontrapezoidal shaping to match the new
geometry and also revise the geometries of any parts made from the wing,
such as wing fuel tanks, flaps, ailerons, spars, ribs, and possibly even wing
carry-through structure and landing gear attachments. All that the designer
should have to do is to enter the revised geometric parameter (such as aspect
ratio).
Figure 7.39 shows such an automatic revision of the nontrapezoidal
geometry from changes to the geometric trapezoidal parameters, done with
the RDS-Professional program. l24l At the upper left is trapezoidal wing
geometry. To its right is the wing created from it, with a swept-back tip,
leading-edge strake, and trailing-edge kick. Below is the revised trapezoidal
geometry after the aspect ratio, taper ratio, and sweep are changed in
response to some optimization. To its right is the resulting wing geometry
including the same swept-back tip, leading-edge strake, and trailing-edge kick.
210 A i rc raft Des i g n : A C o n ceptu a l A p p roach

, - -
\
\
\
\

Fig. 7 .39 Automated revision of wing geometry.

Notional Design Layout: Advanced Technology Commuter/Cargo Jet (D. Raymer, courtesy
Conceptua l Research Corp.).
 CHAPTER 7 Confi g u ration Layout a n d Loft 21 1

C- 1 7 Globemaster (NASA photo by Jim Ross) .

What We've Learned

Configuration design layout i s the heart o f the design process: you build the
drawing. The fuselage and similar bodies should be designed using a deliberate
longitudinal control scheme, as illustrated by classic conic lofting. Wings and
tails should be designed using spanwise control lines to place and scale the
selected airfoils.
212 Airc raft D e s i g n : A C o n ceptu a l A p p roach