Cranfield University Blended Wing Design

1. Blended wing body airframe mass prediction
D Howe¤
College of Aeronautics, Cranfield University, Cranfield, Bedfordshire, UK
Abstract: The blended wing body (BWB) concept is one in which the payload is carried within the inner
wing of the aircraft, the local aerofoil sections being deepened to accommodate it. Difficulties, both in
design and mass prediction, arise when the payload requires the pressurization of the non-circular cross-
sections of the blended wing region. The paper presents a method by which the mass of the BWB airframe
may be predicted using an empirically weighted theoretical approach. The ideal wing structure mass is
modified by introducing penalties for the secondary structure and, in particular, the payload carrying
function. Absolute validation of the method is not possible as no full-size aircraft of this category has been
built and flown. Nevertheless, application of the method to several design studies gives reason to believe
that it is acceptable for preliminary design purposes.
Keywords: mass prediction, blended wing body
NOTATION
A wing aspect ratio
A material allowable compressive stress factor
b wing span (m)
B maximum breadth of the fuselage section (m)
BF width of the floor (m)
c chord of the wing section (m)
d diameter of the arc of the fuselage section (m)
D ideal mass of the wing box covers and spar webs
(kg)
e ratio of the width of the structural box in the line
of flight to the wing aerodynamic chord
fa allowable compressive stress (N=m2
)
·fa ratio of the allowable compressive stress to the
upper limiting value
ft allowable working hoop tensile stress (N=m2
)
·ft ratio of the allowable working hoop tensile stress
to 108
N=m2
F penalty allowance for the secondary and payload
structure (kg)
k12 factor in the formula for the mass of tip fins
·l ratio of the length of the weapon bay to the
centre-line chord length
L effective rib pitch at the inboard end of a wing
component (m)
M mass (kg)
N ultimate design normal acceleration factor
P concentrated local mass
Q proportion of the total fuel load that is carried by
a component
r wing bending relief factor
·r ratio of the centre-line relief factor to that at the
inner end of the outer wing
R design range of the aircraft (km)
S wing planform area, both sides (m2
)
S9o planform area of the outer wing, based on the
idealized geometry (m2
)
VD design (diving) speed (m=s)
w end-load resultant in the cover of the structural
box (N=m)
y distance of the concentrated mass out from the
centre-line (m)
Y ratio (2y=b)
ç sweep of the mid-chord of the structural box
äP pressure cabin working differential pressure
(bar)
ì taper ratio, the ratio of the outer to the inner
chord lengths of a wing component
r density of the structural material (kg=m3
)
ô maximum aerofoil thickness–chord ratio
ô thickness–chord ratio, inner wing outer to inner
end
j sweep of the quarter-chord line
Subscripts
c centre-line value
i relating to inner wing
j indicating one of a number of items
319
The MS was received on 16 February 2001 and was accepted after revision
for publication on 10 September 2001.
¤Corresponding address: 57 Brecon Way, Bedford, Bedfordshire, MK41
8DE, UK.
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part Gby guest on January 7, 2016pig.sagepub.comDownloaded from

2. k kink station value
o relating to outer wing
R root (centre-line) value
T tip or total value
Note. Where a term is without subscript it refers to an
overall wing value; eo is based on a mean value across the
outer wing, but ei is the value at the kink station and
(ôk)o ˆ (ôk)i(ck)i=(ck)o.
1 INTRODUCTION
Considerable interest has been shown recently in the
blended wing body (BWB) configuration. The BWB
concept is a particular class of tail-less aircraft where the
payload-carrying volume is located across a significant
portion of the inner wing. This part of the wing is
characterized by relatively thick aerofoil sections and often,
partly as a consequence of this, by substantially greater
sweep than is employed on the outer wing. The region
between the payload-carrying volume and the outer wing is
blended to handle the transition from the thicker aerofoil
sections inboard to the more conventional outer ones. The
tail-less configuration is usually completed by the addition
of wing tip fins to provide directional control and stability.
It has been suggested that the BWB layout may confer
substantial overall advantages when applied to a transport
aircraft in the ultra-high-capacity category. A number of
designs for such an aircraft have been proposed, for
example the Cranfield University, College of Aeronautics
BW-98 project illustrated in Fig. 1 [1]. In some designs the
powerplants are buried in the rear of the wing, it being
proposed that the over-wing air intakes may be used to
provide a degree of laminar flow, thereby reducing the
parasitic drag. The BWB concept is not new as there were
several proposals for BWB supersonic airliners over four
decades ago, for example the Cranfield A-60 project shown
in Fig. 2 [2].
Tail-less designs have always been of interest to
aerodynamicists since they consist only of the one essential
component, namely the wing. They therefore make it
possible to design an aircraft having low zero lift drag. The
recent resurgence of interest is, at least in part, due to the
success of the Northrop-Grumman B2 stealth bomber.
Although this aircraft has similar features to some BWB
designs, such as buried powerplants, it is not a true BWB
aircraft since it has a discrete fuselage. Some large models
of BWB configurations have flown, but as far as is known
no full-size aircraft has been built. Therefore, all design
predictions have to be based on the results obtained from
free flight and wind-tunnel models and from the analysis of
the design proposals. This is of special significance in
relation to the prediction of airframe mass, where tradi-
tional estimating techniques place heavy reliance on the
availability of empirical data derived from previous air-
craft.
2 APPROACH TO THE PROBLEM
The approach to the problem of the mass prediction of the
airframe of BWB layouts that is adopted in this paper is
based on a theoretical procedure substantially modified by
the incorporation of empirical data derived from relevant
constructional details of other, existing, aircraft. The
Cranfield BW-98 design [1] has been used both as a basis
for making assumptions to simplify the analysis and for a
partial validation of the technique. However, in the absence
of any actual BWB aircraft, it is not possible to make a
complete validation.
The procedure is based on the assumption that the
airframe mass may be treated primarily as a wing mass
problem upon which can be superimposed corrections to
cover the use of the central region of the wing as a payload
volume. The theoretical approach is derived from that
developed previously by the author [3], where it is referred
Fig. 1 Cranfield BW-98 study
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
320 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

3. to as the ‘F’ method. In this approach, the mass of the
covers and spar webs of the structural box is dealt with by
estimating the material required to resist the spanwise
bending moment, allowance being made for inertial relief
effects. The mass of the ribs in the structural box is
estimated from a consideration of the stiffness needed to
preclude overall compression failure of the covers. Penal-
ties are added to this ideal box mass to make allowance for
departures from the ideal and the presence of secondary
structure such as high lift devices. Inevitably these
penalties are largely based on empirical data and, inasmuch
as they apply to the basic wing, may be read across to the
BWB configuration. The additional penalties due to the
carriage of the payload in the wing of the BWB are derived
from both relevant theoretical considerations and empirical
data appropriate to the fuselages of conventional aircraft.
Some of the data used have been extracted from a
published source (Addendum 4 in reference [4]), but they
have been supplemented as necessary.
3 WING GEOMETRY IDEALIZATION AND
ASSUMPTIONS
3.1 Idealization
The basic ‘F’ method [3], assumes that the wing planform
can be represented by a simple straight tapered wing. This
has proved to be adequate for the majority of wing
planforms, but it is not sufficient for the highly kinked
geometry and variable aerofoil thickness adopted for most
BWB layouts. It is therefore necessary to employ the more
complex idealization shown in Fig. 3. The outlined actual
geometry is representative of the Cranfield BW-98 project,
and the idealization is shown by the heavy dotted lines. The
fore and aft limits of the structural box are indicated by the
light dotted lines. In defining the idealization,the following
must be noted:
1. It is necessary specifically to define an inner wing,
identified by subscript i, and an outer wing, identified
by subscript o.
2. The choice of the spanwise location of the ‘kink’
position which defines the limits of the inner and outer
wings is important. Due regard must be given to the
actual planform geometry, but the inner wing must also
define the region that contains the payload.
3. The trailing edge at the kink may be discontinuous, but
the leading edge and the front and rear spars must be
continuous.
4. The idealized wing area should be as near to the actual
gross wing area as possible, but it need not be identical.
5. The wing span should be the true value exclusive of any
wing tip fins.
3.2 Overall assumptions
A number of overall assumptions are made in adapting the
‘F’ method for the BWB configuration:
1. The spanwise airload distribution is essentially semi-
elliptic in shape, the variations in the planform shape
being compensated for by local changes in aerofoil
section camber. For simplicity, in the application of the
method, the airload distribution is idealized to one of
trapezoidal form having the same semi-span centre of
pressure location as that of the semi-ellipse.
2. The payload is distributed across the span of the inner
wing in proportion to the length of the local chord. This
may appear to be a considerable simplification, but
observation of proposed designs indicates that it is
reasonably justified for the purpose of estimating the
inertial relief effect.
3. The powerplants and the main landing gear units are
attached only to the inner wing, and the nose landing
gear unit to the nose component, as indicated in Fig. 3.
If required, it is possible to allow for powerplants placed
Fig. 2 Cranfield A-60 supersonic airliner study
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 321
by guest on January 7, 2016pig.sagepub.comDownloaded from

4. on the outer wing by using the relevant information
given in Appendix 2 in reference [3].
4. A fin or winglet may be attached to the tip of the outer
wing and can be treated as a discrete item.
3.3 Procedure
The mass prediction procedure consists of six separate
phases of calculation:
1. Outer wing mass. This includes the secondary structure
such as the trailing edge and other devices and the tip
fin attachment penalty where relevant.
2. Mass of tip fins when present.
3. Inner wing mass as a ‘wing’ function. This includes
penalties for such items as the landing gear and power-
plant attachments and any controls or high lift devices.
4. Nose section mass including the nose landing gear
penalty. This item will usually include the accommoda-
tion for the crew.
5. Specific provision for the carriage of the payload within
the inner wing, in reality a ‘fuselage’ function. This will
include such items as the floors and bulkheads but must
also allow for the internal pressurization of the wing
section when this is required.
6. Penalties in the inner wing owing to the fuselage/
payload function such as doors, windows, emergency
exits and access panels generally.
4 MATERIAL PROPERTIES
4.1 General comments
Following the previous work [3], the material properties are
primarily based on a definition of the allowable overall
buckling stress in the upper, compressive, covers of the
structural box. For simplicity, the allowable tensile stress in
the lower covers is assumed to be the same as the
compressive value. This assumption is intended to make
allowance for fatigue requirements, but it is somewhat
optimistic when the compressive stress approaches an upper
limiting value, say the 0.2 per cent proof stress. Neverthe-
less, the assumption has been found to provide acceptable
results when applied to light alloy construction. The
allowable shear stress in the spar and rib webs is taken to be
50 per cent of the compressive value on the assumption that
the buckling characteristics are generally similar. In the
case of the BWB concept it is also necessary to define an
allowable hoop tensile stress, or the equivalent, when the
‘fuselage’ function requires the use of pressurization.
Apart from some general comments concerning the use
of carbon fibre reinforced plastic construction, the previous
work was based on the use of light alloy materials. However,
it is very likely that significant components of a BWB
aircraft would utilize carbon fibre reinforced plastic mater-
ials, and therefore it is desirable to make provision for this
in the developed mass prediction procedure. The datum
allowable compressive stress is defined in terms of the stress
resultant and the rib pitch at the inboard end of the wing for
both classes of material with an upper bound defined by the
Fig. 3 Idealizationof BWB geometry
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
322 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

5. equivalent of the 0.2 per cent proof value. Simplification of
the analysis is possible if it can be assumed that everywhere
the allowable stress is less than the limiting value, and an
analysis of a few BWB designs suggests that this may be the
case. This is discussed further in Section 5.2.1.
The allowable compressive stress is then defined as (cf.
equation (4) in reference [3])
fa ˆ A(w=L)1=2
3 105
N=m2
(1)
where
A ˆ constant for a given material
w ˆ end-load per unit width of the cover (N=m)
L ˆ rib pitch at the root of the box (or the kink station of
the outer wing of a BWB layout) (m)
General observation of light alloy wings suggests that a
typical value for L, from equation (10) in reference [3], is
L ˆ 0:55(ccô)1=2
m (2)
where
cc ˆ length of the root (centre-line) chord of the wing
(m)
ô ˆ thickness–chord ratio of the wing root aerofoil
section
In the absence of better information, equation (2) is
assumed to apply also to carbon fibre reinforced plastic
construction. Should better data become available, it can be
accommodated by appropriate modification of A, see
Section 4.3.
A typical value of w=L is given by equation (11) in
reference [3]. However, the simplifications made in deriv-
ing this equation are not applicable to the BWB where, by
implication, the ratio of the body width to wing span, â, is
zero. Use is therefore made of the previous equation for
w=L in reference [3] with â set to zero. It is also necessary
to correct for the approximation made to cover a range â
and ô, the variation in the thickness–chord ratio across the
span. This results in a change in the coefficient of the
equation from 0.59 to 0.55. Then
w
L
ˆ
0:55N MT Ar(1 ‡ ì) sec j sec ç
Leccô
(3)
where
N ˆ effective ultimate design factor (see Appendix 1 in
reference [3])
MT ˆ all-up mass of the aircraft (kg)
A ˆ aspect ratio of the wing
ì ˆ ratio of the tip to root chords; the taper ratio
j ˆ sweep of the quarter-chord line of the wing
ç ˆ sweep of the mid-chord line of the structural box
e ˆ ratio of the chordwise width of the structural box to
the overall chord
r ˆ factor to allow for the inertial relief (see Appendix 2
in reference [3]); note that, the greater the relief
load, the lower is the value of r
Substituting for L from equation (2)
w
L
ˆ
N MT rA(1 ‡ ì) sec j sec ç
e(ccô)1:5
(4)
and hence, from equation (1)
fa ˆ A
N MT rA(1 ‡ ì) sec j sec ç
e(ccô)1:5
" #1=2
3 105
N=m2
(5)
4.2 Light alloy
From equation (9) in reference [3] for a light alloy:
A ˆ 1:38 but fa < 352 3 106
N=m2
. The allowable hoop
tensile stress under pressure loading depends to some
extent upon the design philosophy adopted with regard to
crack stopping. For the purposes of mass prediction,
Addendum 4 in reference [4] suggests that the following
values may be assumed:
For: 0 < B < 2, ·ft ˆ 0:8
2 < B < 6, ·ft ˆ 0:8 ‡ 0:05(B ¡ 2)
B > 6, ·ft ˆ 1:0
where B is the maximum diameter (or width) of the
pressure cell (m) and ·ft is the ratio of the allowable
working stress to 100 3 106
N=m2
.
4.3 Carbon fibre reinforced plastic
Representation of the allowable stresses of carbon rein-
forced plastics is complicated by the many possible
variations in the lay-up of the laminate. To reduce the
problem to one that is suitable for the purposes of mass
prediction, the overall compressive buckling characteristics
of three specific laminates can be derived and then used to
deduce a typical overall value. The properties are based on
high-strength carbon fibres in a lay-up having a 60 per cent
volume fraction. Allowance has been made for the typical
effects of temperature and moisture.
Past experience suggests that the combination of loading
in a pressurized fuselage indicates the use of a quasi-
isotropic laminate lay-up. Although there is some depen-
dence upon the method of manufacture, this is a reasonable
assumption for mass prediction.
4.3.1 Quasi-isotropic lay-up
This lay-up has equal numbers of plies in each of the 0,
‡45, ¡45 and 908 directions. For this case A ˆ 1:5 but
fa < 360 3 106
N=m2
. The allowable working hoop tensile
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 323
by guest on January 7, 2016pig.sagepub.comDownloaded from

6. stress may be assumed to be given by ·ft ˆ 1:4, where ·ft is
defined in Section 4.2.
4.3.2 Predominantly 08 directional fibres
This lay-up has 50, 19, 19 and 12 per cent plies in the 0,
‡45, ¡45 and 908 directions respectively. For this case
A ˆ 1:85 but fa < 450 3 106
N=m2
.
4.3.3 All shear lay-up
There are equal numbers of ‡45 and ¡458 plies but no 0 or
908 plies. For this case A ˆ 1:35 but fa < 100 3
106
N=m2
.
4.3.4 Overall value
In any particular wing component, use is likely to be made
of several different laminate lay-ups. It is not possible at
the level of the present analysis to distinguish between
these, and it is necessary to derive a conservative overall
value, based on the above results, for use in the mass
prediction equations. For this reason it is suggested that, in
the absence of more specific information, the data to be
used should be A ˆ 1:5 but fa < 350 3 106
N=m2
.
4.4 Density
The density of light alloy construction may be taken as
2700 kg=m3
. The basic material density of a 60 per cent
volume fraction high-strength carbon fibre epoxy resin
component is about 1650 kg=m3
, but in a practical
application there will almost certainly be metallic fittings
which will cause this value to be increased. It is suggested
that, to allow for this and other practical limitations, the
density used for overall mass prediction should be taken as
1900 kg=m3
.
5 MASS REQUIRED FOR THE ‘WING’
FUNCTION
5.1 General
Equation (3) in the previous work [3] expresses the
structural mass of the wing as
Mw ˆ D ‡ Mr ‡ F (6)
where
D ˆ mass of the covers and shear webs of the structural
box
Mr ˆ mass of the ribs in the structural box
F ˆ penalty due to the departures of the box from the
ideal and allowance for the secondary structure
Equation (6) applies also to the BWB layout except that the
inner and outer portions of the wing have to be dealt with
separately and the values of F allocated appropriately.
5.1.1 Ideal mass of the covers and webs
The first of equations (8) in reference [3] gives
D ˆ
0:71N MTbrA(1 ‡ ì) sec j sec çr
faô
kg (7)
where
b ˆ wing span (m)
r ˆ density of the material (kg=m3
)
Substituting for fa, from equation (5)
D ˆ (N MTb3
re sec j sec ç)1=2
3
r
A
´
cc
ô
´0:25
310¡5
kg (8)
where use has been made of
A(1 ‡ ì) ˆ
2b
cc
It should be noted that D is based on the assumption that
the maximum value of w=L occurs at the side of the
fuselage or centre-line as appropriate. This is usually true
for a conventional wing layout and, although in some cases
the maximum value is at a kink station, the assumption has
proved to be satisfactory for the purposes of mass
prediction.
5.1.2 Rib mass
The ribs within the inner wing of a BWB layout are very
deep, possibly being of the order of 8 m for an ultrahigh-
capacity airliner. Therefore, they make an unusually large
contribution to the mass of the wing. Equations (12) and
(13) in reference [3] were developed for conventional
wings of up to about 2 m deep, and the approximations
included are not appropriate for much deeper components.
To overcome this difficulty, the evaluation of the rib mass
has been revised. As previously, the mass is based on the
rib stiffness required to provide overall support to the
covers, but the necessary empirical corrections have been
based on the need to ensure that the material thicknesses
have a practical value. The revised formula, which is
applicable to shallow as well as deep ribs, is
Mr ˆ 4:4Se(ccô)1=2
(1 ‡ 0:35ì)r 3 10¡3
kg (9)
The similarity to equation (12) in reference [3] will be
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
324 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

7. noted, although there is considerable simplification of the
terms which include the taper ratio, ì.
5.1.3 Penalties—F values
The values of the penalty factors, F, quoted in Table 2 of
reference [3] are applicable to the ‘wing’ function of the
BWB aircraft but must be allocated in proportion to the
relative wing spans of the inner and outer wing compo-
nents. There is an additional outer wing penalty which is
that due to the attachment of a tip fin when it is present. It
is suggested that this allowance should be
¢FV
MT
ˆ 0:1
2Sv
So
´
(10)
where
Sv ˆ area of one fin (m2
)
So ˆ reference area of both sides of the outer wing (m2
)
Equation (10) does not include the mass of the fin itself
(see below).
5.1.4 Mass of wing tip fins
Equation (AD4.9) in reference [4] gives the mass of a
vertical empennage as
Mv ˆ 0:065k12VDSv
1:15
kg
where
VD ˆ design speed for the aircraft (m=s)
k12 ˆ factor which is unity for a low mounted tail and
1.5 for a ‘T’ tail
In view of the special attachment difficulty of a tip fin, it is
suggested that the 1.5 factor applies in this case, and hence
for each fin
Mv ˆ 0:1VDSv
1:15
kg (11)
5.2 Outer wing mass
5.2.1 Mass of covers and webs
Equation (7) may be applied to the outer wing by treating
the kink station at its inboard end as equivalent to the
centre-line condition, providing that:
1. The spanwise bending moment due to the airload is
adjusted to the value at the kink station rather than the
centre-line value. Applying assumption 1 of Section 3.2
yields the ratio of these two bending moments as
Moment ratio ˆ 0:727y2
k(1 ‡ 0:375yk) (12)
where yk is the ratio of the outer wing span, bo, to the
total span, b.
2. A correction is introduced to compensate for any
difference between the idealized area of the outer wing,
S9o, and the actual reference area, So.
3. The allowable compressive stress, fa, at the kink station
is no greater than the upper limiting value for the
appropriate material given in Sections 4.2 and 4.3. As it
happens, this is the spanwise station where the greatest
value of w=L may be anticipated, since inboard the
cross-section of the structural box and the inertial relief
are both greater. Adapting equation (5) and using
equation (12) gives
( fa)k ˆ A 0:727N MT Ao ro(1‡ìo)secjo secço y2
k
"
3
(1‡0:375yk)
eo(ckôk)1:5
o
#1=2
3 10¡5
N=m2
(13)
where subscript o indicates the outer wing and subscript
k the kink station value. See equation (16) for the
definition of ro. The correction required is
·fa ˆ
( fa)k
( fa)limit
(14)
but ·fa > 1.
Using equations (12) and (14) with equation (7), the outer
wing geometry and correcting for the actual reference area
gives
Do ˆ 0:85[N MTb3
ro eo sec jo sec ço y4
k(1 ‡ 0:375yk)]1=2
3
S9o
So
´
ro f
A
´
ck
ôk
´0:25
o
310¡5
kg (15)
In order to evaluate the the inertial relief effect, ro, it is
assumed that the mass of the structure and systems in the
outer wing is a nominal 5 per cent of MT, and that this and
the fuel load act at 37 per cent of the outer wing span out
from the kink station. From assumption 3 of Section 3.2
there are no powerplants or landing gear units attached to
the outer wing. Following the method of Appendix 2 in
reference [3], the relief factor is
ro ˆ 1¡ 0:042 ‡ 0:84Qo(0:1 ‡ 2R 3 10¡5
)
µ
‡
4:55Mv
MT
¶
yk (16)
where Qo is the ratio of the fuel carried in the outer wing to
the total fuel mass and R is the design range of the aircraft
(km).
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 325
by guest on January 7, 2016pig.sagepub.comDownloaded from

8. 5.2.2 Mass of the ribs
The mass of the box ribs in the outer wing is derived
directly from equation (9) by using the geometric values
for the outer wing:
Mr ˆ 4:4Soeo(ckôk)1=2
o (1 ‡ 0:35ìo)ro 3 10¡3
kg (17)
5.2.3 Penalty factor
Using the values of F given in Table 2 in reference [3], the
mass of the secondary structure is
Fo ˆ (0:02MT ‡ ¢FLE ‡ ¢FTE ‡ ¢FS ‡ ¢FCF)yk
‡ ¢FTIP (18)
where
¢FLE=MT ˆ 0.007 when leading edge devices are
present
¢FTE=MT ˆ 0.003 when single-slotted trailing edge
flaps are used OR
ˆ 0.006 when Fowler or double-slotted flaps
are used OR
ˆ 0.012 when triple-slotted flaps are used
¢FS=MT ˆ 0.0015 when spoilers/airbrakes are present
¢FCF=MT ˆ ¡0.005 when the auxiliary surfaces are of
carbon fibre reinforced plastic
construction
¢FTIP=MT ˆ 0.002 when there are no tip fins but
equation (10) when they are present
5.2.4 Total mass of the outer wing
The total mass of the outer wing including the tip fins
when present is
(Mw)o ˆ Do ‡ (Mr)o ‡ Fo ‡ 2Mv kg (19)
from equations (15), (17), (18) and (11) respectively.
5.3 Inner wing mass
5.3.1 Mass of covers and webs (‘wing’ function)
It is not possible to make direct use of equation (8) for the
evaluation of the mass of the covers and spar webs of the
inner wing structural box. The equation is adequate to
represent the effect of the shear forces and bending
moments due to the airload, providing appropriate modifi-
cation is made to allow for the reduced span inboard of the
kink station. The relief factor, r, deduced from Appendix 2
in reference [3], and used by implication in equations (8)
and (15), is based on the assumption that all the relief effect
may be represented by an equivalent moment at the inboard
end of the wing as it is assumed that this is the station
where w=L is greatest. This assumption is inadequate for
the inner wing of a BWB aircraft owing to the large,
distributed, inertial relief effect of the payload and the
considerable variation in the geometric properties of the
cross-section. The consequence of these effects is that the
maximum value of w=L is most unlikely to occur at the
centre-line of the aircraft. Indeed, as commented upon in
Section 5.2.1, it is likely that it will occur at the outer end
of the inner wing, the kink station.
To overcome this difficulty, it is assumed that the inertial
relief factor, r, varies linearly across the inner wing,
decreasing from a maximum value ro at the kink station to
ri at the centre-line of the aircraft. Using the spanwise
airload distribution and the box geometry with this
assumed variation in r enables the value of w=L to be
stated at any given spanwise location. The local allowable
stress and the thicknesses of the covers and webs follow.
Integration of these thicknesses across the inner wing span
enables the value of Di to be derived. The integration is
numerically complex but after some simplification yields
Di ˆ 1:52
N MTb3
roei sec ji sec çi
ô ‡ 1
´1=2
3 [(1 ¡ yk) ¡ 0:46(1 ¡ yk)2:5
](1 ‡ 0:53r)
3
cR
ôR
´0:25 ri
A
´
3 10¡5
kg (20)
where ô is the ratio of the kink to centre-line values of the
thickness–chord ratio and r is the ratio of the centre-line
relief factor, ri, to ro [equation (10)]. Subscript i represents
the inner wing values, and subscript R the centre-line (root)
values.
The value of the relief factor on the centre-line is
ri ˆ 1¡
µ
0:12 ‡ 0:114(1 ¡ 0:63yk)
‡ 2:27(1 ¡ 0:63yk)(Qo ‡ Qi)(0:1 ‡ 2R 3 10¡5
)
‡ 4:55
Mv
MT
‡ 0:76
MPAY
MT
´
cR ‡ 2(ck)i
cR ‡ (ck)i
µ ¶
‡ 4:55
ªPjYj
MT
´¶
(21)
but
ri > 0:1
where
MPAY ˆ mass of the payload distributed across the inner
wing (kg)
Pj ˆ concentrated local mass such as a powerplant or
landing gear unit (kg)
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
326 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

9. Yj ˆ 2yj=b, where yj is the distance of the mass out from
the centre-line (m)
(ck)i ˆ inner wing kink chord, which may differ from
(ck)o (m)
Qi ˆ ratio of the fuel mass located in the inner wing,
away from the centre-line, to the total fuel mass
The simplifications made in the derivation of equation (20)
result in less than §5 per cent error for 0:4 , yk , 0:7 and
no more than about §10 per cent error for 0:25 ,
yk , 0:9.
5.3.2 Mass of ribs
The mass of the ribs in the structural box of the inner wing
is derived directly from equation (9) using the relevant
inner wing geometry:
(Mr)i ˆ 4:4Siei(cRôR)1=2
(1 ‡ 0:35ìi)ri 3 10¡3
kg (22)
5.3.3 Penalty factor (‘wing’ function)
From Table 2 in reference [3] the penalty factor for the
inner wing relevant to the ‘wing’ function is
(Fi)w ˆ (0:02MT ‡ ¢FLE ‡ ¢FTE ‡ ¢FS ‡ ¢FCF)
3 (1 ¡ yk) ‡ ¢FPP ‡ ¢FMG kg (23)
where ¢FPP=MT ˆ (0:0005 ‡ 0:00025NPP) for 2 < NPP <
4, NPP being the number of wing-mounted powerplants,
and ¢FMG=MT ˆ 0:004NMG, NMG being the number of
wing-mounted main landing gear units. All the other terms
are defined after equation (18).
5.3.4 Total mass of the inner wing (‘wing’ function)
The total mass of the inner wing in its ‘wing’ function only
is
(Mw)i ˆ Di ‡ (Mr)i ‡ (Fi)w kg (24)
from equations (20), (22) and (24) respectively. The mass
required to meet the payload/fuselage function has to be
added to equation (24) (see Section 6).
6 MASS REQUIRED FOR THE ‘FUSELAGE’
FUNCTION
6.1 General approach
The additional mass associated with the ‘fuselage’ function
of the inner wing of the BWB concept is handled by
evaluating a specific penalty factor (Fi)f. However, unlike
the outer and inner wing penalty factors, Fo and (Fi)w
respectively, which are based on empirical data, the
derivation of (Fi)f uses a theoretical basis as far as is
possible.
The following sections deal with specific items, and, for
ease of application, typical numerical values of individual
penalty factors are given in Table 1. For convenience, the
‘fuselage’ function is treated as three separate items:
1. The nose fuselage. This is defined as being the structure
forward of the front spar at the root, as indicated in Fig.
3. The component is presumed to include the crew
accommodation, attachment of the nose landing gear
unit, inboard wing leading edge fairings and, in the case
of transport aircraft, secondary payload provision such
as an entrance foyer. It is assumed that this is a
pressurized region, although this would not be correct
for an uninhabited aircraft.
2. The main payload volume. This is the region bounded
by the front and rear spars of the inner wing and the
kink stations on either side of the aircraft. For simplicity
it is assumed that the volume aft of the rear spar is not
appropriate for primary payload use. In the case of a
transport aircraft the volume is pressurized, and this
represents one of the main design and mass prediction
challenges of the BWB concept. Apart from the main
outer shell, the component includes floors and bulk-
heads. For other classes of aircraft, such as an
uninhabited offensive design, there are comparable
penalties due to such items as weapons bays.
3. Secondary structural penalties. These are mainly con-
cerned with the allowances needed to cover departures
from the ideal structural form used to derive the mass of
item 2 above. In this respect they are comparable with
the ‘wing’ function F values. The items covered include
entry and freight doors, emergency exits, windows,
general access panels and cut-outs/bays other than for
the main landing gear units which have already been
included in equation (23).
Table 1 Typical fuselage function values of ¢F=MT
Component/item Light alloy Carbon fibre
Fuselage nose 0.01 0.008
Payload
Pressure membrane 0.01 0.007
Bulkheads 0.007 0.005
Passenger floors 0.017 0.014
Freight aircraft floors 0.023 0.019
Total for passenger aircraft 0.034 0.026
Total for freight aircraft 0.04 0.03
Weapons bay aircraft 0.02 0.031
Apertures
Windows 0.003 0.003
Doors, panels, etc. 0.010 0.01
Total 0.013 0.013
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 327
by guest on January 7, 2016pig.sagepub.comDownloaded from

10. 6.2 Nose fuselage
6.2.1 Outer shell
It is assumed that when it is pressurized the nose fuselage
component has either a circular cross-section or one made
up of circular arcs with ties across the points of change in
curvature. In this case
¢FNP ˆ
1:2BSPRESäPr
·ft
´
3 10¡3
kg (25)
where ·ft is defined in Sections 4.2 and 4.3, B is the
maximum width (diameter) of the section (m), äP is the
working differential pressure (bar) and SPRES is the total
surface area of the pressure cell, including the front
bulkhead (m2
).
6.2.2 Leading edge extension
The inner wing leading edges forward of the front spar
datum at the centre-line are assumed to be constructed as
fairings attached to the sides of the nose pressure cell (see
Fig. 3):
¢FLE ˆ 0:0025SLEr kg (26)
where SLE is the total surface area of the extensions outside
the pressure cell (m2
).
6.2.3 Nose landing gear attachment and bay
Empirical data suggest that a typical penalty for the nose
landing gear attachment is
¢FNG
MT
ˆ 0:003 (27)
6.2.4 Windscreen
The mass of the windscreen is a function of the size and
performance of the aircraft. Past designs suggest that
¢FWS ˆ 0:75SWSVDäP kg (28)
where SWS is the surface area of the windscreen panels
(m2
). A typical value for a large transport aircraft is
320 kg.
6.2.5 Crew floor
Empirical data for the crew floor give
¢FCF ˆ (7 ‡ 1:2B)SCF kg (29)
where SCF is the surface area of the floor (m2
).
6.2.6 Allowance for doors and miscellaneous items
The allowance for these items should be
¢FNMISC
MT
ˆ 0:002 (30)
6.2.7 Total nose fuselage penalty
The total nose fuselage penalty is the sum of the items
covered in Sections 6.2.1 to 6.2.6:
¢FNOSE ˆ ¢FNP ‡ ¢FLE ‡ ¢FWS ‡ ¢FCF
‡ (¢FNG ‡ FNMISC) kg (31)
See equations (25) to (30), noting that (¢FNG ‡ ¢FNMISC)
is equal to 0:005MT.
6.3 Payload volume—pressurized aircraft
6.3.1 Reaction of pressure loading
The cross-section of the payload volume of a BWB
layout is more nearly rectangular than circular in shape.
There are two fundamental methods for reacting pressure
loading:
(a) by designing the upper and lower covers of the inner
wing to be able to react the pressure load in bending
between the ribs;
(b) by providing an internal pressure membrane configura-
tion, also using the ribs to react the loads as shown in
Fig. 4.
The two approaches were investigated in the Cranfield
BW-98 study [1], and it was concluded that the membrane
approach offered a lighter solution. However, the difference
was marginal. It is reasonable to assume as a result of this
study that the mass of a membrane approach is an
acceptable indication of the penalty resulting from the need
to pressurize the external shell in the region of the payload
Fig. 4 Internal pressure membrane concept
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
328 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

11. volume. It so happens that it is also simpler to predict the
mass of the membrane configuration, providing that it is
assumed that the membrane and the outer covers have
separate structural functions.
6.3.2 Pressure membrane
As shown by Fig. 4, it is likely that the pressure membrane
will consist of a number of segments, not all of which will
have the same effective diameter. Thus, the mass penalty of
the pressure membrane only may be expressed as
¢FPM ˆ
0:6äPrªdj(SPM)j
·ft
µ ¶
3 10¡3
kg (32)
where dj is the effective diameter (m) of a given segment,
j, of the membrane which has a total surface area (SPM)j
(m2
), and äP and ·ft are as defined in previous sections.
Application of equation (32) to the Cranfield BW-98 design
suggests that ¢FPM=MT is about 0.01 for light alloy
construction and 0.007 for carbon fibre reinforced plastic.
6.3.3 Vertical ties between cells
The rib webs act as the vertical ties between the cells. An
investigation of the thicknesses implied by equation (22)
indicates that they are adequate to handle the tensile loads
without any further mass penalty.
6.3.4 Pressure bulkheads
Analysis of relevant data from existing aircraft gives the
following mass penalties for internal pressure bulkheads:
¢FPB ˆ 6:5hSPBäPr 3 10¡3
kg (33)
where SPB is the area of a bulkhead (m2
) and h is a factor
which has a value of 1.0 for domed bulkheads, 1.25 for
full-area flat bulkheads and 1.75 for partial flat bulkheads.
6.3.5 Passenger and freight floors
The following formulae for floor mass assume that the
floors are not subjected to normal loading owing to
pressurization. Should this be the case, as, for example, for
a floor over a wheel bay, they should be factored by 1.3.
For passenger and freight floors in passenger aircraft:
¢FPAXF ˆ 4SPAXFr 3 10¡3
kg (34a)
where SPAXF is the total surface area of the relevant floors
(m2
).
For freight floors in dedicated freight aircraft:
¢FFRF ˆ 2:6(1 ‡ 0:6BF)SFRFr 3 10¡3
kg (34b)
where BF is the floor width (m) and SFRF is the area of the
floor (m2
).
6.3.6 Weapons bay
The penalty due to the presence of a weapons bay may be
estimated from
¢FWB=MT ˆ 0:045·l (35)
where ·l is the ratio of the length of the weapons bay to the
overall length of the aircraft on the centre-line.
6.3.7 Total penalty due to the payload function
The total payload penalty is the sum of the relevant items
from Sections 6.3.2 and 6.3.4 to 6.3.6. In general
¢FPAY ˆ ¢FPM ‡ ¢FPB ‡ ¢FPAYF
‡ ¢FFRF ‡ ¢FWB kg (36)
[see equations (32) to (35)].
6.4 Secondary structure penalties
6.4.1 Windows
The mass penalty resulting from the provisionof windows is
¢FWIN ˆ 90äPSWIN kg (37)
where SWIN is the total glazed area of the windows (m2
).
6.4.2 Apertures—doors, panels, etc.
The penalty for general apertures in respect of the
‘fuselage’ function may be taken as
¢FAPT ˆ 60SAPT kg (38)
where SAPT is the total area of the primary structure
removed for the provision of the apertures (m2
).
6.4.3 Ramp-type freight door
The penalty for a rear, ramp freight door is
¢FFD ˆ 10(1 ‡ 0:75BF)SDOOR kg (39)
where SDOOR is the area of the door opening (m).
6.4.4 Total secondary structure penalties
The total secondary structure penalty is the sum of the
items in the previous two sections:
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 329
by guest on January 7, 2016pig.sagepub.comDownloaded from

12. ¢FFSS ˆ ¢FWIN ‡ ¢FAPT ‡ ¢FFD kg (40)
where ¢FWIN, ¢FAPT and ¢FFD are given by equations
(37) to (39) respectively.
6.5 Total ‘fuselage’ function mass penalty
This is the sum of the items of Sections 6.2 to 6.4:
(Fi)f ˆ ¢FNOSE ‡ ¢FPAY ‡ ¢FFSS kg (41)
from equations (31), (36) and (40) respectively.
7 TOTAL AIRFRAME MASS
The total mass of the airframe, excluding the power-
plant structure and landing gear, is given by the sum
of the components given in Sections 5.2.4, 5.3.4 and
6.3:
MAIRFRAME ˆ (Mw)o ‡ (Mw)i ‡ (Fi)f kg (42)
from equations (19), (24) and (40) respectively.
8 APPLICATION
The method outlined in the previous sections has been
applied to several BWB concepts including offensive as
well as transport aircraft. Most of the data used are
unpublished and did not include specific statements of
mass breakdowns. Therefore, no real comparisons could be
made, but the method did yield believable answers in the
sense that the predicted airframe masses were similar to,
but somewhat less than, those of conventional aircraft.
In the case of the Cranfield BW-98 study, the originally
projected airframe mass was deduced by adapting the mass
equations given in Addendum 4 of reference [4] by
assuming a reduced fuselage mass to be added to a basic
wing value and by making allowance for the use of some
carbon fibre reinforced plastic items. This yielded an
airframe mass that was 18.5 per cent of the take-off value.
The results of applying the method of this paper, using the
equations rather than the approximate values of Table 1,
are shown in Table 2. It will be seen that to achieve an
airframe mass comparable with that originally predicted
requires a virtually complete carbon fibre reinforced plastic
airframe. As a matter of interest, the conceptual design
technique outlined in reference [4] has been used to
estimate the effect of employing a totally light alloy
airframe, and it was found that the take-off mass increased
by some 14 per cent, an effective growth factor of about
2.4.
9 CONCLUSIONS
A method has been developed that enables the airframe
mass of BWB designs to be predicted in detail. Although
the absence of any actual aircraft prevents a full validation,
the evidence available indicates that it forms an acceptable
basis for initial design purposes. No doubt, should actual
BWB aircraft be developed there would be a need for
refinement of some of the empirical data.
REFERENCES
1 Smith, H. Blended-wing-body preliminary design study BW-
98. College Aeronaut. Aerogram, 1999, 9(4).
2 Howe, D. Aeroplane design studies—Mach 2.2 and Mach 3
supersonic airliners.College of Aeronautics Report 181, 1965.
3 Howe, D. The prediction of aircraft wing mass. Proc. Instn
Mech. Engrs, Part G, Journal of Aerospace Engineering,
1996, 210(G3), 135–145.
4 Howe, D. Aircraft Conceptual Design Synthesis, 2000 (Profes-
sional Engineering Publications Limited, London and Bury St
Edmunds).
APPENDIX
Simplified method for prediction of the ideal
structure box mass
The possibility has been investigated of combining the
values of (D)o and (D)i, the masses of the outer and inner
wing covers and spar webs, given by equations (15) and
(20), and (Mr)o and (Mr)i, the box rib mass, given by
equations (17) and (22).The proposed equation for the total
mass of the covers and spar webs is
D ˆ 0:61(N MTb3
roei sec ji sec çi)1=2
(cRôR)0:25 r
A
´
3 10¡5
kg (43)
Table 2 Cranfield BW-98 study—predicted airframe mass as a
percentage of the take-off mass
Component/item Light alloy Carbon fibre
Structural box
Covers and spar webs 9.28 6.53
Ribs 5.45 3.83
Wing function secondary structure 3.89 3.39
Fuselage function
Nose 0.91 0.79
Payload provision 3.27 2.37
Apertures 1.3 1.3
Total 24.1 18.1
Proc Instn Mech Engrs Vol 215 Part G G00501 # IMechE 2001
330 D HOWE
by guest on January 7, 2016pig.sagepub.comDownloaded from

13. The above equation assumes that the aerofoil thickness–
chord ratio is constant across the inner wing (ô ˆ 1).
Comparison with the sum of the individual values from
equations (15) and (20) indicates that the simplification
yields errors of no more than §10 per cent for the
conditions shown in Fig. 5. The total mass of the box ribs is
Mr ˆ 4:4Sei(cRôR)1=2
(1 ‡ 0:35ì)r 3 10¡3
kg (44)
Fig. 5 Limitations of applicabilityof simplified approach
G00501 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part G
BLENDED WING BODY AIRFRAME MASS PREDICTION 331
by guest on January 7, 2016pig.sagepub.comDownloaded from