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DESCRIPTION OF ESDU 95010
COMPUTER PROGRAM FOR ESTIMATION OF SPANWISE
LOADING OF WINGS WITH CAMBER AND TWIST IN SUBSONIC
ATTACHED FLOW
Introduction:
ESDUpac A9510 uses steady lifting-surface theory based on the Multhopp-Richardson
solution to provide the spanwise loading of wings with camber and twist in subsonic attached
flow.
The program calculates the spanwise loading distributions of local lift and pitching moment
due to incidence, due to camber at zero incidence, and due to twist at zero incidence. The
loadings can be obtained individually or simultaneously. The overall loading distribution can
be calculated for a specified incidence or total lift coefficient.
The program allows for either the input of a straight-tapered planform defined simply via
aspect ratio, taper ratio and nth-chord line sweep or the input of a cranked planform with
straight leading-edge and trailing-edge segments.
Planform geometry
1- For a straight-tapered planform the number of cranks Nk is entered as zero and the
program requires a definition of the wing planform in terms of aspect ratio A, taper
ratio  , and the sweep of the chosen nth chord line  n together with the value of n.
o
2- For a wing with Nk cranks, the planform is divided into Nk + 1
panels. Those panels are defined in dimensional terms, following the input of an
integer that specifies the units system, 1 for SI, 2 for British, by
(Note: root and tip is does not count as a crank)
a) the spanwise positions of the root chord, of each crank and of the wing tip,
si for i = 0 to Nk + 1, ( s0=0, sNk+1=s)
b) the streamwise co-ordinates of the wing leading edge at the spanwise stations si , measured
positive aft from some transverse datum,
xi for i = 0 to Nk + 1 ,
c) the root chord, the chord at each crank and the tip chord,
ci for i = 0 to Nk + 1 .
The program outputs a wing lift-curve slope, a1 .
All the loading distributions and force and moment coefficients that are output by ESDUpac
A9510 have been factored by the ratio of lift-curve slopes to incorporate this improvement in
accuracy.
SAMPLE INPUT FILE PREPARATION
TEXT1
At the top of the file there is provision for the user to enter three lines of text to
TEXT2
describe any run. In each case a blank line must be entered if there is no text.
TEXT3
straight wing EXAMPLE
NMs, NMc: 33 3 (spanwise and chordwise collocation points-used by steady lifting surface
theory Multhopp Ric.solution)
NL: 2
(number of loading type: can be 1,2 ,3)
Lm: 1 3 (loading types; 1: loading due to incidence, 3: loading due to camber at zero
incidence, 4: loading due to twist at zero incidence)
NM: 1 (number of Mach numbers)
Ml: 0.35184 (values of Mach numbers- if more than one written side by side)
No: 13 (number of spanwise stations- less than equal to 40)
 oi : 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.98 0.9999 (dimensionless values of spanwise
stations for output; leave one or more space between the numbers)
P: 1 (selects calculation mode; 0: separate spanwise loadings (incidence, camber, twist),1:
also calculates total loading for specified angles of incidence, 2: total lift coefficients (CL) are
specified and corresponding values of incidence are calculated)
1 (if the above value P is 1, then number of incidences (  ), if 2 number of overall lift
coefficients (CL) is given)
2.0 (incidence angle in degrees is given; (  ))
Nk: 0 (number of cranks in the wing is given, 0 in this example. O implies straight tapred
wing)
A: 6.0 ( aspect ratio of the wing)
 : 1.0 (taper ratio of the wing; 1 for rectangular wing)
 n : 0.0 (sweep of nth chord line)
n: 0 (chord line identifier- Sketch 3.1 on page 6)
If LM contains 3 which means camber data
NsC: 3 (number of spanwise stations  Ci where camber is defined; 2  NsC  20)
 Ci :1 (dimensionless value of spanwise stations for camber input from tip to root; 1 is the
wing tip)
NcCi: 18 (number of chordwise stations for camber input; 2  NcCi  20)
0
0.00000
0.0125 0.00123
0.025 0.00242
0.05 0.00469
.
.
.
.
.
.
(meanline data for the NACA airfoil, yc data)
(1st column gives dimensionless values of chordwise stations)
(2nd column gives camber ordinates as fraction of chord)
( from leading edge to trailing edge; 0: leading, 1: trailing)
0.4 (dimensionless value of spanwise stations for camber input from tip to root)
18 (number of chordwise stations for camber input)
0 (dimensionless value of spanwise stations for camber input from tip to root; 0 is the wing
root)
18 (number of chordwise stations for camber input)
TYPICAL OUTPUT FILES
Refer to AE 462 Wing Design Project document.
LOCAL LIFT AND MOMENT COEFFICIENT CALCULATION
a1: lift curve slope is in term of per radian.
 : angle of attack is in term of degrees.
Therefore, we have the factor 57.3.