ESDU 99031:2009

INTRODUCTION

Details are provided of a program, ESDUpac A9931, which
calculates the maximum lift coefficient, the lift coefficient at
zero angle of attack and the lift curve of aerofoil sections and
straight-tapered wings with high-lift devices deployed at low
speeds. The basic wing (no devices deployed) may have camber and
twist. The program includes methods that allow for the presence of
a fuselage. For completeness, calculations can be made for the
aerofoil and wing when there are no high-lift devices deployed but
the prediction of the shape of the non-linear part of the lift
curve should be treated with caution because it employs a technique
developed for use when high-lift devices are deployed*. The method
is intended for use only for free-stream Mach numbers up to about
M = 0.25. No allowance is made for ground effect.

An auxiliary program, ESDUpac B9931, allows the prior
calculation of the spanwise position of the section of the basic
wing that has the peak loading due to angle of attack. It is
necessary to know that section because full runs of the main
program for wings and wing-fuselage combinations require its
geometry.

A companion program described in Item No. 93015 allows
calculations of the maximum lift coefficient to be made for a basic
wing for subcritical Mach numbers. The program introduced in Item
No. 93015 also permits aerofoil characteristics to be calculated
for Mach numbers up to 0.4. However, neither the lift coefficient
at zero angle of attack nor the general shape of the lift curve is
estimated.

The methods employed within the program to determine the maximum
lift coefficient and the lift coefficient at zero angle of attack
are those given in Item Nos 84026 and 94027 to 94031 for aerofoils
with and without high-lift devices and in Item Nos 89034 and 91014,
92031, 93019, 95021, 96032, 97009 and 97011 for wings with and
without high-lift devices. The method of Item No. 96003 is used to
calculate the lift curve. The calculation of the zero-lift
incidence, the lift-curve slope and the lift coefficient at zero
angle of attack for a basic aerofoil or wing section are made using
Item Nos 72024, 97020 and 98011, in preference to using the more
approximate methods given in other Items before Item Nos 97020 and
98011 were available. This provides greater consistency throughout
the program although the changes in magnitude are small and of
little consequence in the overall construction of the lift curve.
Some Items employ a two-dimensional lift-curve slope from Item No.
Aero W.01.01.05 in the estimation of device effectiveness and the
method of that Item is retained in such cases to preserve the
integrity of the original correlations.

The presence of a fuselage is modelled via its effect on the
zero-lift angle of attack, using the method of Item No. 89042, and
through its influence on the performance of high-lift devices if
they are fitted close to the fuselage side. The method of Item No.
97003 is used to determine the fuselage effect on trailing-edge
flaps. The influence of the fuselage on the performance of
leading-edge devices is treated by assuming that they extend to the
fuselage centre-line. For the fuselage effect on maximum lift
coefficient the user must enter an increment derived from
experiment or based on experience as there is no Data Item method
for the prediction of that contribution, which is thought to be
small.

Section 3 highlights some particular features of the programs.
Section 4 describes the input files required by the programs A9931
and B9931 and Section 5 discusses the output. Section 7 provides
examples of input and output files for specific cases. Section 6
lists the Derivation and References. Appendix A presents a flow
chart that gives an alternative description of the construction of
input files for A9931.

* For basic aerofoils and wings the angle of attack for the
onset of non-linear behaviour may be obtained from Item No. 88030
and is dependent on section geometry and, for wings, planform
geometry. At present there is no Data Item that addresses the lift
curve beyond that angle of attack, but it is likely that the
subsequent non-linear behaviour up to maximum lift is also
dependent on section and planform geometry. These effects are
masked by the additional effects associated with high-lift devices
when they are deployed and are not represented in the simple
fairing that models the lift curve as the maximum lift coefficient
is approached. However, comparisons with a few data have shown that
the use of the fairing developed for cases where devices are
deployed gives an improvement over a linear assumption and, in the
absence of a more detailed alternative, this is used for basic
aerofoils and wings to provide an initial estimate of the curve in
the non-linear range.