1. Notation and Units

Sketch 1.1 Aerofoil Geometry

Sketch 1.2 Wing Notation

Sketch 1.3 Wing Notation with Devices Undeployed (Single Panel)

Sketch 1.4 Plain leading-edge flaps and drooped leading edges (see explanatory notes below)

From the sketch,

Equations (1.1) and (1.2) relate to the specific type of device shown in the sketch, i.e. a device deployed by rotation around a lower-surface hinge. Many variations in design are possible and the corresponding values of c_l´ and c´ appropriate to any other arrangement used would have to be determined.

Sketch 1.5 Krueger flaps and sealed slats (see explanatory notes below)

Krüger flaps and sealed slats have no slot and are therefore quite similar, in terms of their operation, to plain leading-edge flaps; the method for predicting ΔC_L0l is likewise similar. Care is, however, required for the definition of equivalent flap chord, c_l´ and deflection angle, δ_l. Sketches 1.5(a) to 1.5(c) show how they are defined for sealed slats and two forms of Krüger flap, termed upper-surface and lower-surface Krüger flaps.

For the sealed slat and upper-surface Krüger flap the equivalent leading-edge flap is taken to be related to that part of the aerofoil and flap forward of the point at which the section first departs from the original upper-surface profile due to the deployment of the flap, i.e. points A on Sketches 1.5(a) and 1.5(b). The flap chord and deflection consistent with this are shown on those sketches. There is of necessity a small difference in the definitions for the case of the lower-surface Krüger flap, see Sketch 1.5(c).

Sealed slats and upper-surface Krüger flaps (Sketches 1.5(a) and 1.5(b))

For sealed slats and upper-surface Krüger flaps the values of c_l´ and δ_l for the equivalent plain flap are obtained as follows. A straight line is drawn from the leading edge, passing through the centre of the flap leading-edge radius to point A, the point of departure from the original aerofoil surface. A circle centred on the mid-point of this line intersects the basic aerofoil chord at point B. The straight line joining B to the flap leading edge and passing through the centre of the flap leading-edge radius defines the equivalent plain flap chord, c_l´. The angle between that chord and the aerofoil chord defines δ_l.

Lower-surface Krüger flap (Sketch 1.5(c))

For a lower-surface Krüger flap, where the flap trailing-edge is on the aerofoil lower surface, the chord c_l´ is taken as the length of the line drawn from A to the leading edge of the flap, passing through the centre of the flap leading-edge radius. The angle between that chord and the aerofoil chord defines δ_l.

In Sketches 1.5(a) to 1.5(c)

	c´ = c + Δcl	= c + cl´ − xτ	(1.3)

Sketch 1.6 Slats and vented Krueger flaps (see explanatory notes below)

The deflection, δ_l, of both slats and vented Krüger flaps is defined using the angle between the datum chords of the slat (or flap) and the aerofoil. The slat (or flap) datum chord is defined using the line passing through the centre of the leading-edge radius and the slat (or flap) trailing edge. The extended chord, c´, and the chord extension, Δc_l, are defined by rotating the slat (or flap) about the intersection of the slat (or flap) and aerofoil datum chords, as shown in the sketch.

In Sketches 1.6(a) and 1.6(b), for a slat and vented Krüger flap

For a slat, the geometry in Sketch 1.6(a) gives

For a vented Krüger flap, the geometry in Sketch 1.6(b) gives

Sketch 1.7 Plain trailing-edge flap

Sketch 1.8 Split flap

Sketch 1.9 Slotted flaps

Sketch 1.10 Wing-fuselage geometry

2. Introduction

Details are provided of a program, originally released as ESDUpac A9931 and here reissued incorporating a modern graphical UI as the ESDU Lift Curve Aerodynamics suite (LiCrA). The program 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 module to the original version of the 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. When using the LiCrA UI, since the spanwise peak loading position calculation is seamlessly incorporated there is no need for it to be run separately.

A companion program described in ESDU 93015⁸ allows calculations of the maximum lift coefficient to be made for a basic wing for subcritical Mach numbers. The program introduced in ESDU 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 ESDU 84026³ and ESDU 94027¹⁰ to ESDU 94031¹⁴ for aerofoils with and without high-lift devices and in ESDU 89034⁴ and ESDU 91014⁶, ESDU 92031⁷, ESDU 93019⁹, ESDU 95021¹⁵, ESDU 96032¹⁷, ESDU 97009¹⁹ and ESDU 97011²⁰ for wings with and without high-lift devices. The method of ESDU 96003¹⁶ 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 ESDU 72024², ESDU 97020²¹ and ESDU 98011²², in preference to using the more approximate methods given in other Items before ESDU 97020 and ESDU 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 ESDU Aero W.01.01.05¹ 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 ESDU 89042⁵, and through its influence on the performance of high-lift devices if they are fitted close to the fuselage side. The method of ESDU 97003¹⁸ 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 ESDU 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 6 lists the Derivation and References. In the printed Data Item, Section 7 provides examples of input and output files for specific cases and Appendix A presents a flow chart that gives an alternative description of the construction of input files for A9931.

3. Program Features

For aerofoil calculations, the original version of the program, A9931, reads in all the required geometric and flow data from a single directed input file. When using A9931 for the case of a wing or a wing-fuselage combination, it is usually necessary to run the auxiliary program B9931 first in order to determine η_p, the spanwise location of the peak loading due to angle of attack for the basic wing. When using the LiCrA UI, this extra step is not necessary. Strictly, η_p varies with Mach number, but for M ≤ 0.25 the movement is sufficiently small to be neglected. It is suggested that users initially adopt a Mach number in the middle of their range of interest. With η_p known, the user can then identify the section geometry at that station and enter it as program input in the UI.

There is one special feature in the entry of the basic-section geometry in that the user may specify whether the section is of ‘conventional’ or ‘modern’ type, the latter description denoting rear-loaded sections which terminate with a small trailing-edge base thickness, incorporate large rear camber, and have a higher maximum lift coefficient than ‘conventional’ sections with the same (z_u / c)_1.25 and tan τ_u, see ESDU 84026³. Alternatively, the program can be set to make the decision automatically through a test based on the geometry over the rear 10% of the section chord. If, at x / c = 0.9, (z_u - z_l) / z_u > 0.64 and if, at the trailing-edge, t_b / c > 0.004, the section is taken as ‘modern’. (These criteria were adopted in ESDU 93015⁸.) If the user selects the category a warning message is output should the choice be contrary to that which the program would have made.

Where geometric details of the aerofoil, wing, fuselage or high-lift system are required the user is referred to sketches that identify the necessary parameters. The sketches identify the source Data Item(s) from which they have been reproduced, with additional annotation in some cases.

For the basic wing, linear and non-linear spanwise variations of geometric twist and camber are allowable, provided that the twist variation and the spanwise variation of section zero-lift angle due to camber are monotonic and give a modest effective tip twist angle, of less than 10° say. For such cases, geometric data are required only for the wing root (centre-line) section and the wing section at η = 2/3, see ESDU 89034⁴.

Calculations may be made at a number of Mach number and Reynolds number pairs. At each pair there may be one or more settings of the leading-edge device. At each leading-edge device setting (or group of device settings) there may be one or more trailing-edge flap settings.

The user is allowed to select from a number of different types of run. Instead of calculating the whole lift curve, a run may be restricted to the calculation of the lift coefficient at zero angle of attack or to the calculation of the increment in the lift coefficient at zero angle of attack due to the deployment of high-lift devices, with or without the calculation of the increment in maximum lift coefficient. There is also a provision for user-defined lift coefficients to be used for the basic aerofoil, wing or wing-fuselage combination in place of the calculated values. Table 3.1 associates each type of run with an integer value of the Calc parameter, which is used as a switch in the program. The flow chart in Sketch 3.1 guides the user through the run selection process.

For wing and wing-fuselage combinations, calculations of the increments due to device deployment require section data at the mid-span of each device panel, see Sketch 1.3. Where needed in the calculation of the increments in maximum lift coefficient, the program automatically converts section properties and leading-edge device deflection angles to those normal to the leading edge and converts trailing-edge flap deflection angles to those normal to the flap hinge-line. For calculations that do not include the estimation of increments in maximum lift coefficient fewer section data are required.

Sketch 3.1 Calculation Types

The different types of high-lift devices that may be selected are given in Table 3.2, together with the integers N_l or (N_l)_j and N_t or (N_t)_j that are used to identify them in the program input. In the new UI, devices are selected from a drop-down list in which they are identified by name.

4. Input

Table 4.1 below provides detail of the inputs required for the various calculation types. Numerical values may be entered singly or, where appropriate, as comma-delimited lists.

5. Output

The main equations evaluated in the program are as follows:

For Aerofoils

For Wings

For Wing-fuselage Combinations

Lift Curve

From the values of lift coefficient at zero angle of attack, the maximum lift coefficient and the initial linear value of the lift-curve slope the program uses the method of ESDU 96003¹⁶ to construct the non-linear lift curve from C_L = 0 at the appropriate zero-lift angle up to maximum lift coefficient at the angle of attack for maximum lift, at quarter-degree intervals. The case for a wing-fuselage combination is illustrated in Sketch 5.1. It is possible that the constructed curve will extend to large negative angles of attack when trailing-edge flaps are deployed and values of C_L for α < −5°, say, may not represent achievable conditions. Therefore the program outputs a warning in such cases and no values of lift coefficient are output between zero and the value at α = −10°.

Sketch 5.1 Lift Curve

6. Derivation and References

Derivation

The Derivation lists sources of information that have assisted in the preparation of this Guide.

References

The References are sources of information supplementary to that in this Guide.