ESDU Toolbox

ESDU provides essential design methods and software for the aerospace, defence, transportation, energy and related industries. These methods and software are produced and rigorously validated in concert with the collective knowledge of hundreds of engineers from around the world.

Listed below are the ESDU 'Toolbox Apps'. These provide user friendly web-based interfaces to some ESDU programs. Some Toolbox Apps are only available to subscribers, others are freely available to subscribers and non-subscribers alike.

Subscriber Toolbox Apps

ESDU 95009: Calculation of effect of wing height on lift and aerodynamic centre for a slender wing-body combination

From Data Item ESDU 95009.

This app implements the method of ESDU 95009, in ESDUpac A9509, for estimating the change in lift and aerodynamic centre position resulting from moving a wing from a centrally-mounted position to one above (or below) the centre line of a forebody-cylinder combination.

The method generally applies to a plane wing with sweptback leading edge, local span increasing (and then possibly constant) streamwise, and an unswept trailing edge. The body has a constant diameter circular section over the wing root chord and the wing may be set at an angle to the body centre line. The particular case of a rectangular wing is also considered.

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ESDU ASTEROID: Excrescence drag calculation tool


Utilising Data Items ESDU 75031, ESDU 75028 and ESDU 74036.


The ASTEROID program brings together the various ESDU methods for the calculation of excrescence drag due to steps, ridges, grooves and cavities on the external surfaces of aircraft. The app provides a simple interface that enables users to define the excrescences and then calculate the drag increments within a few minutes.

ASTEROID integrates the programs associated with ESDU 75031, ESDU 75028 and ESDU 74036 within the context of a specified and predetermined aircraft flow field. Multiple excrescence geometries can be specified on selected aircraft major components (i.e. a wing upper or lower surface, fuselage, nacelle, horizontal tail or fin). The app first asks the user to select an aircraft type (e.g. single-aisle transonic airliner, low-speed commuter airliner, etc) from a list and to choose an appropriate cruise Mach number for consideration. The app then allocates the appropriate pre-generated local flow field so that typical flow conditions (including flow direction) at each excrescence can be determined. The flow data for the single-aisle and low-speed commuter aircraft are presented for the whole airframe, together with a range of wings representative of short-, medium- and long- range jet transports, and a blended-wing body design.

Excrescence geometries are then specified either as circular cavities or as multi-node excrescences, which can be closed (e.g. to model a repair plate or cover) or open (e.g. to model a control surface gap). The edges of the excrescence can be characterised as steps (with or without edge treatments), rectangular or square ridges, grooves or gaps (with or without sealing).

When the excrescences have been defined, the app automatically selects the method from the appropriate Data Item and calculates the drag coefficients based on both the excrescence and aircraft reference areas. The aircraft drag coefficient penalty summed for all excrescences is also calculated.



ASTEROID fp (flat plate) is a version of the ASTEROID drag prediction tool that uses the graphical and calculation modules (and data management capabilities) offered by the original program, but the user is freed from having to select one of the flow-fields for specific aircraft or generic wings in the current database. Instead, all flow conditions are specified by the user, thereby extending ASTEROID's applicability, not only to aircraft whose airframes or components are not presently represented within the flow-field library, but also missiles, rockets, drones and non-aeronautical applications such as rail and road transports and wind engineering.

The designation 'fp' relates to the 'flat plate' condition, which is that addressed in all the excrescence drag calculation methods in the Aerodynamics Series' Data Items relating to specific excrescence types. Most of the wind-tunnel data were indeed for excrescence models mounted on flat plates but, in the wider context of applying such data to drag prediction, this should be interpreted as the drag in the absence of a pressure gradient. Therefore, no allowance is made in ASTEROID fp for any drag magnification that may be present, so that, in effect, the drag magnification factor is set to unity. The subject of excrescence drag magnification is discussed in detail in ESDU 90029.

Note that the use of ASTEROID fp is, in most respects, identical to ASTEROID, so the help files and instructional videos are applicable; the exception, of course, being references to the flow-field data library.

ESDU Aero A.02.03.02: Optimum area distribution and associated minimum theoretical transonic drag-rise for aircraft at zero lift

From Data Item ESDU Aero A.02.03.02.

This app determines the optimum area distribution and corresponding minimum theoretical transonic drag-rise at zero lift. The program implements the method of ESDU Aero A.02.03.02, accessing the graphical data by use of the equations provided in the Data Item.

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ESDU 74036: Drag due to a circular cavity in a plate with a turbulent boundary layer at subsonic, transonic and supersonic speeds

From Data Item ESDU 74036.

This app implements ESDUpac A7436, which, in turn, is based correlations of experimental results obtained on a plate at zero incidence, for predicting the increment in drag for Mach numbers less than 3. The methods apply to a cavity with sharp edges, walls normal to the plate, flat bottom and no through-flow; no information is available on rounding or chamfering of the corners, but such edge modifications should not be assumed to be beneficial. The depth/diameter ratio varied from 0.04 to 1.5 but a method of dealing with a cavity in which the ratio is less than 0.04 and based on the method of ESDU 75031 is utilised. The data apply strictly in zero pressure gradient flows, but guidance on their use where there is a pressure gradient is given in the Data Item.

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ESDU 75028: Drag due to grooves in a flat plate with turbulent boundary layer, at subsonic and supersonic speeds

From Data Item ESDU 75028.

ESDU 75028 is derived from a correlation of experimental data that enable the drag increment to be predicted due to a groove of planform aspect ratio greater than 8 normal to the flow. For grooves inclined at angles to the flow exceeding 60 degrees the data for the grooves normal to the flow apply, while for grooves inclined between 0 degrees (parallel to the flow) and 60 degrees a method for obtaining the maximum increment is suggested based on the use of ESDU 75031 to predict the increments due to the forward- and rearward-facing steps together with an appropriate skin friction allowance.

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ESDU 75031: Drag of two-dimensional steps and ridges immersed in a turbulent boundary layer for Mach numbers up to 3

From Data Item ESDU 75031.

ESDU 75031 gives an empirical method for the prediction of the drag increment due to a variety of two-dimensional excrescences, each mounted normal to the flow direction on a flat plate, and immersed in a turbulent boundary layer for Mach numbers up to 3. The excrescence types are (1) a forward-facing step, ramp (chamfered step), or a radiused step, (2) a rearward-facing step, ramp (chamfered step), or a radiused step, and (3) a square section ridge or a rectangular section ridge (of height/length ratio 2), with or without radii to the top corners.

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ESDU 20003: Crack Resistance Curves

From Data Item ESDU 20003.

ESDU 20003 provides crack resistance curves (R-curves) for several aluminium, steel and titanium aerospace sheet materials in SI and British (lbf, in) units. The curves are indexed by alloy specification, details of which are given, together with relevant test conditions, in the Data Item. The Data Item includes a full description of the resistance curve concept, its application, advantages and limitations. The use of data determined from wide panel specimens is discussed. Two fully worked examples illustrate the use of the data to determine the onset of fast fracture. This Item supersedes ESDU 85031.

This Toolbox App is provided to interrogate the database of R-curves according to material type, specification, heat treatment, orientation and additional criteria such as thickness and width. The output from the Toolbox App consists of a summary of the input data and a plot of the chosen R-curve. The Δa' versus KR co-ordinates of the R-curve may be saved as either a CSV or a JSON file.

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Free Toolbox Apps

International Standard Atmosphere app

This app determines, at a specified pressure altitude in the International Standard Atmosphere (ISA), absolute and relative values of pressure, temperature and density together with the absolute values of the speed of sound, kinematic and dynamic viscosity and thermal conductivity. It also determines VTAS, VEAS, kinetic pressure and unit Reynolds number for a specified Mach number at the given pressure altitude. Calculations are limited to the troposphere and stratosphere.

Section 4, of the ESDU Aerodynamics Series contains additional information on Atmospheres. In particular, for calculations at greater altitudes and for further details of the ISA consult ESDU 77021. A range of 'design' atmospheres that differ from the ISA is given in ESDU 78008.

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Wing lift-curve slope app from ESDU TM 169

This app employs a modified version of the Helmbold-Diederich equation (described in ESDU TM 169) to estimate the lift-curve slope of a wing of trapezoidal planform. In order for the method to be applicable the wing must be thin and employ only moderate camber and twist, and the flow must remain both attached and wholly subcritical. Compressibility effects are catered for by means of the classic Prantl-Glauert factor. The original Helmbold-Diederich equation was often used before there was general access to more soundly based methods such as the lifting-surface theory (which is the basis of ESDU 70011). However, the improved and modified version of the equation used in this app provides estimates accurate to within a few per cent of those obtained by ESDU 70011, which itself has been assessed as providing estimates to within around 5% of wind-tunnel test data. The limits of applicability in terms of flow and geometric parameters for which the app produces results have been restricted to those cited for the method from ESDU 70011.

The full background to this method, and that of ESDU 70011, is given in ESDU TM 169 in the ESDU Aerodynamics Series.

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Skin friction coefficient on a flat plate

This app uses the semi-empirical method of Spalding and Chi to obtain the local and mean skin friction coefficients for a turbulent boundary layer on a smooth flat plate with zero pressure gradient and zero heat transfer.

The data are applicable to flows with Reynolds numbers based on streamwise distance over the range 100 thousand to 1000 million and for Mach numbers up to 5.

The equations used are taken from Appendix A of ESDU 78019, which itself is based on the method described in ESDU 68020. Both of these Items are to be found in the Aerodynamics Series.

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Inelastic stress-strain curves from ESDU 89052

This app provides a method of estimating the stress-strain behaviour of a metallic material within the assumptions that this behaviour may be represented by a smooth continuous generalised curve. The method is valid for both tensile and compressive stress-strain data.

The curve is derived using the Young's modulus and two data points in the inelastic region (the tensile strength is used solely to limit the extent of the curve). The curve follows the modulus in the elastic region and in the inelastic region the greatest accuracy is in the region of the two data points used to derive the curve.

The two data points in the inelastic region may be given as either (a) two proof stresses and the corresponding permanent strains, or (b) two stresses and the corresponding total strains.

The theoretical basis for the generalised stress-strain form used by the app is detailed in ESDU 89052, 'Construction of inelastic stress-strain curves from minimal materials data', and ESDU 76016, 'Generalisation of smooth continuous stress-strain curves for metallic materials'.

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