estimating the oswald factor from basic aircraft ......aero –aircraft design and systems group...
Post on 26-Mar-2020
48 Views
Preview:
TRANSCRIPT
AERO – AIRCRAFT DESIGN AND SYSTEMS GROUP
Hochschule für Angewandte Wissenschaften Hamburg
Hamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR
FROM BASIC AIRCRAFT GEOMETRICAL
PARAMETERS
Mihaela Niță Hamburg University of Applied Sciences
Dieter Scholz Hamburg University of Applied Sciences
Deutscher Luft- und Raumfahrtkongress 2012
German Aerospace Congress 2012
Berlin, Germany, 10.-12.09.2012 DLRK 2012
e
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 2
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Introduction
Airplane drag
zero-lift drag
drag due to lift
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
)++=+=+= δππ
1(2
0,
2
0,,0, A
CC
Ae
CCCCC L
DL
DiDDD
Oswald factor e
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 3
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1:
Oswald Factor e Calculated without Input of CDo
Application: Preliminary Sizing
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
MeDeFetheo kkkee ,,, 0⋅⋅⋅=
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 4
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1: Calculate Oswald Factor e without Input of CDo
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
MeDeFetheo kkkee ,,, 0⋅⋅⋅=
Me
De
Fe
theo
k
k
k
e
e
,
,
,
0
Oswald factor:
correction factor for the aspect ratio to calculate drag due to lift
theoretical Oswald factor, invisid drag due to lift only
correction factor: losses due to the fuselage
correction factor: viscous drag due to lift
correction factor: compressibility effects on induced drag
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 5
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1: Oswald Factor e without Input of CDo
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
MeDeFetheo kkkee ,,, 0⋅⋅⋅=
2
, 21
−=b
dk F
Fe
1;0
1,
=<
+
−=
ee
e
b
compeMe
ca
cM
Mak
e
3.0
1
82.10
00152.0
===
−=
comp
e
e
e
M
c
b
a
Aircraft category
All 0.114 0.974 -
Jet 0.116 0.973 0.873
Business Jet 0.120 0.971 0.864
Turboprop 0.102 0.979 0.804
General Aviation
0.119 0.971 0.804
bdF / Fek , 0,Dek
theoe see next pages
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 6
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Literature Study: HÖRNER
Corrections to induced drag for unswept wings as a function of taper ratio λ
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Α/=) kf λ(
δ+=
1
1theoe
δ=k
)λ(f
λ Afetheo ⋅+
=)(1
1
λ
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 7
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating a Theoretical Oswald Factor
� Approximation of Hörner‘s function:
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Method 1: etheo for unswept Wings
0119.00706.01659.015.00524.0)( 234 +−+−= λλλλλf
From the derivative of thefunction f(λ), the optimumtaper ratio for unsweptwings is λopt = 0.357
λopt = 0.357
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 8
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Literature Study: NACA Report 921
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 9
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1: etheo
Optimum Combination of Taper Ratio and Sweep Angle
� For each sweep, there is an optimal taper ratio that minimizes the induced drag.
� NASA Report 921 delivers a curve that relates the taper ratio to sweep for an approximate elliptical loading
� An equation that approximates this curve is
� The optimum taper ratio for an unswept wing is(this is not quite the value from Hörner)
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
250375.045.0 ϕλ ⋅−⋅= eopt
45.0=optλ
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 10
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1: etheo for swept Wings
Shifting Hörners curve to a minimum as given by NASA
� The difference in the minimum between Hörner and NASA (sweep angle in degrees):
� Calculating the theoretical Oswald Factor from Hörner‘s now shifted curve:
Hörner‘s equation now applied as:
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
250375.045.0357.0 ϕλ ⋅−⋅+−=∆ e
Afetheo ⋅∆−+
=)(1
1
λλ
0119.0)(0706.0)(1659.0)(15.0)(0524.0)( 234 +∆−−∆−+∆−−∆−=∆− λλλλλλλλλλf
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 11
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Literature Study: KROO
Losses due to the Fuselage
� If the flow were axially symmetric and the fuselage were long, then mass conservation leads to
� Aspect ratio A = b²/S is kept constant by convention, so the losses are included into the span efficiency e. The reduction in e is expressed by the factor ke,F . So the factor on the span efficiency ke,F is
� In practice losses are bigger and experience has shown that induced drag increment is about twice the simple theoretical value, so
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
222Fdbb −=′
2
2
22
, 1
−=−=b
d
b
dbk FF
Fe
2
, 21
−=b
dk F
Fe
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 12
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
� Fuselage correction factor
for the Oswald factor e
to correct missing or reduced
lift due to presents of fuselage
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
2
, 21
⋅−=b
dk F
Fe
ke,F
ke,F
2
, 1
−=b
dk F
Fe
Method 1: ke,F Fuselage Correction
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 13
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Method 1: Influence of Mach Number: B737 and MPC75
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 14
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
k_e,M_PG
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,40 0,50 0,60 0,70 0,80 0,90
k_e,M
M
ke_M
� Mach number correction for Oswald factor - from Prandtl-Glauert (ke,M,PG) comparedwith own factor ke,M (using data for the A320)
� ke,M fits the data better than Prandtl-Glauert (ke,M,PG) (see next page)
2,, 1 Mk PGMe −=
1;0
1,
=<
+
−=
ee
e
b
compeMe
ca
cM
Mak
e
Method 1: Influence of Mach Number - Comparison with Prandtl-Glauert-Correction
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 15
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Oswald factor – A320 data and own method. Own Mach number correction ke,M
Method 1: Influence of Mach Number and Results for A320
0,5
0,6
0,7
0,8
0,9
1,0
0,40 0,50 0,60 0,70 0,80 0,90
e, k
_e
,M
M
e_A320,DBD
e_calc_A320
ke_M
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 16
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
MeDeFetheo kkkee ,,, 0⋅⋅⋅=
Method 1: Summary: Influence of Parameters
> 0,9 . Driven by wing parameters: taper, sweep, aspect ratio. Small influence!
> 0,9 . Driven by fuselage diameter to span
around 0,85 . Influenced by zero lift drag of the aircraft, but CD0 not required
0,5 … 1,0. Strongest influence on final result of e for cruise of jet aircraft !
theoe
Fek ,
0,Dek
Mek ,
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 17
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 1: Results: The Polar of the Boeing 737-800
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Aircraft Flight Manual Calculated
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 18
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Method 2:
Oswald Factor e Calculated with Input of CDo and Twist
Application: Conceptual Design
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
APQ
ke Me
π+= ,
Fetheo keQ
,
1
⋅= K = 0,380,DKCP =
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 19
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Method 2: Oswald Factor e Calculated with Input of CDo and Twist
APQ
ke Me
π+= ,
0,2
2)(D
L
L
L
L KCC
wC
C
vCP +
⋅+
⋅=
θθαα
Fetheo keQ
,
1
⋅=
Twist θ = iW,o – iW,i (is generally negative)v and w from DUBSK = 0,38
For A > 4:
( ) 4tan12
22
5022 +−+⋅+
=MA
ACL
ϕπ
α
K = 0,380,DKCP =
Including the Effect of Twist:
( )( ) ( )22
2
0006.010051.00088.0
0037.03.00134.0
Aw
v
−⋅−=
−−=
λλλλ
v gets negative when λ< 0.33
from Method 1
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 20
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
The lift-dependent drag term has two components:
� an inviscid part, also called vortex drag
� a viscous part
The term Q covers the inviscidpart of the induced coefficient,
The term P is used to express the viscous part of induced drag coefficient.
Theoretical Background
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
2, LiD CP
A
QC ⋅
+=π
APQe
π+= 1
Qeinviscid /1=
+= PA
Q
Ae ππ1
PA
QAe
+=
π
π 1
wCCvCCKCCA
QC LLLLDLiD
220,
2, )( θθ
π αα+++=
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 21
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
( ) 20037.03.00134.0 λλ −−=v 22 0051.00088.0)0006.01/( λλ −=− Aw
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Literature Study: Including the Effects of Twist: v and w from DUBS
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 22
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Extension of Method 1 and 2:
Oswald Factor e for Nonplanar Configurations
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
2
,
,,
,,,,
,
21
0
+=
⋅+
=
⋅⋅⋅⋅=⋅=
b
h
kk
kAPQ
ke
kkkkee
kee
NPNPe
NPeMe
NP
NPeMeDeFetheoNP
NPeNP
π
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 23
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Wing with winglets
The following relations can be derived from geometry:
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
eb
be
A
Ae
Ae
C
eA
CC
Ae
CC
b
h
b
b
effeffWL
WL
L
eff
LWLiD
LiD
eff
⋅
=⋅=
==
=
+=
2
22
,,
2
,
21
ππ
π
eb
heWL ⋅
+=2
21
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 24
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configurations
Wing with wingletsCorrection of the simple geometrical consideration via the factor
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
WLk
WLeMeDeFetheoWLeWL
WL kkkkeekeb
h
ke ,,,,,
2
0
21 ⋅⋅⋅⋅=⋅=⋅
+=
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,0 0,1 0,2 0,3 0,4 0,5
h/b
1/k_
e,W
L
22
,2
1
==
+=
b
b
A
A
b
h
kk effeff
WLWLe
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 25
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Real wings with winglets: Boeing and Airbus data
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
ekeb
h
ke WLe
WLWL ⋅=⋅
+= ,
22
1
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 26
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Wing with dihedral
The following relations can be written:
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
( )
−Γ
=
+=⇒−=
Γ=⇒Γ⋅=
1cos
1
2
1
212
1
cos
1cos
22
b
hb
h
b
bbbh
b
bbb
effeff
effeffe
A
Ae eff ⋅=Γ
Γ⋅⋅⋅⋅= ,,,, 0 eMeDeFetheo kkkkee
22
, 1cos
111
21
−Γ
⋅+=
⋅+=Γ
WLWLe kb
h
kk
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 27
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Wing with dihedral
From the simple geometrical consideration:
A more accurate evaluation is achieved by penalizing the relation with the factor
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
22
, cos
121
Γ=
⋅+=Γ b
hke
WLk
22
, 1cos
111
21
−Γ
⋅+=
⋅+=Γ
WLWLe kb
h
kk
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 28
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Various Non-Planar Configurations
KROO
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Span efficiency for various optimally loaded non-planar systems (h/b = 0.2)
Literature Study: KROO
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 29
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Non-Planar Configurations in GeneralThe following relations can be written: (this time via a penalty factor called
The factor for wings with winglets and dihedral, investigated above, becomes now a
particular case of the factor kNP.
Having the from KROO, can be calculated for each configuration
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
NPk
ekeeb
h
ke NPeNP
NPNP ⋅=⇔⋅
+= ,
22
1
NPkNPek ,
1
12
, −⋅=
NPeNP
kb
hk
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 30
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
Non-Planar Configurations in General
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
NPeMeDeFetheo
NPeNP
NP
kkkke
ekeb
h
ke
,,,,
,
2
0
21
⋅⋅⋅⋅=
⋅=⋅
+=
h/b = 0.2 general
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 31
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
The Box-Wing Aircraft
; ;
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
ke
e
box
refD
D
refi
boxi ==,
,
bhkk
bhkk
e
e
e
e NP
ref
box
/
/
21
43
⋅+⋅+==
bhkk
bhkkk
D
D
refi
boxi
/
/
43
21
,
,
⋅+⋅+==
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 32
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configurations
The Box-Wing Aircraft
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
h/b
k
(c) k Prandtl
(d) k Rizzo
(a) k Prandtl (Biplane)
(b) k Prandtl (Biplane 2)
k from iDrag results fit to
"box wing equation" with
parameters from (f)k from iDrag results fit to
"winglet equation"
k DeYoung
k iDrag results
k from wind tunnel data
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 33
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Estimating the Oswald Factor for Non-Planar Configuratio ns
The Box-Wing Aircraft
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
h/b
e_bo
x / e
_ref
e_box / e_ref from iDrag results fit to'box wing equation' parameters from (f)
e_box / e_ref from iDrag results fit to 'winglet equation'
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 34
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Summary and Conclusions
� Simple, physics based method for both conventional and unconventionalconfigurations given
� Treats more in depth the special cases of wings with winglets, wings with dihedraland box wings
� Information provided to assist aircraft designers in making a sufficient accurate estimation of the span efficiency factor e during preliminary aircraft design and aircraft design optimization.
ESTIMATING THE OSWALD FACTOR FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
German Aerospace Congress
Berlin, 10-12.09.2012
Dr.-Ing. Mihaela Nita
Estimating the Oswald Factor from Basic Geometrical Parameters
10.09.2012, Page 35
Aero - Aircraft Design and Systems Group
Hochschule für Angewandte
Wissenschaften HamburgHamburg University of Applied Sciences
Thank you!
http://AERO.ProfScholz.de
ESTIMATING THE OSWALD FACTOR
FROM BASIC AIRCRAFT GEOMETRICAL PARAMETERS
Contact
Hochschule für Angewandte
Wissenschaften Hamburg
Hamburg University of Applied Sciences
top related