Chapter: 06. External Aerodynamic Inputs

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Chapter: 06. External Aerodynamic Inputs

06.01 External-Source Aerodynamics

You can override Piano's aerodynamic calculations and use instead alternative Lift/Drag polars supplied by any external sources. For the clean ('high speed') configuration, such data can be provided in a 'fixed polar' file. Clearly, this option should be restricted to 'frozen' designs or models of existing aircraft. It is not meaningful to change the design whilst keeping the same aerodynamics.

Another possibility is to continue using Piano's own polar, but modify it by adding a data-matrix of corrections. This 'polar mod' approach also lets you match a known polar precisely, whilst simultaneously retaining some valid design capability. Piano can generate the necessary matrix of corrections by comparing its own calculated polar with any fixed polar provided by you. The resulting 'polar mod' file can then be linked to the plane file.

Finally, you can specify the low-speed aerodynamics separately, for various flaps-down configurations. A 'lowspeed aero' file can contain both the low-speed polar and the variation of maximum lift (CLmax) with flap deflection.

06.02 Fixed Polar Files

External polars are manipulated via the 'Fixed Polars...' item (see 'Misc' menu). Each polar comprises a simple text file. Such files must be placed inside the 'fixed polars' folder found within the Piano folder. You can edit files manually via 'Edit Fixed Polar...', or through the general-purpose 'Open' item under the 'File' menu.

To permanently link a fixed polar to a plane, you must first load the polar ('Load Fixed Polar...') and then store the plane. The connection is established via the parameter fixed-polar-name . If you alter any of Piano's design parameters while a fixed polar is in use, you will be cautioned about the fact that your changes will not be reflected in the aerodynamics until the fixed polar is cleared ('Clear Fixed Polar...').

There are many different ways of specifying aerodynamic characteristics. Piano caters for most of the formats commonly found in Industry. It is possible to provide basic parabolic polars, complete tabulations of data showing the variation of Cd with CL and Mach number, correction tables for Altitude and Mach number to cater for Reynolds effects, or a style of corrections used by Boeing and other manufacturers. In all cases, the file contains a number of key parameter identifiers, each followed by the corresponding data. Key parameters are explained below and can be specified in any order. They are not related to any of Piano's standard design parameters.

To generate your own polar, you could start by duplicating and re-naming one of the example files provided in the 'fixed polars' folder, then using it as a template to work with. You can add comments to the file by preceding them with the semicolon ( ; ) character.

It is also possible to generate a new fixed polar file automatically, from the calculated aerodynamics of the current plane, through the 'Show Calculated' item. You can then edit and save this file (in the 'fixed polars' folder) as necessary. This is particularly useful when you don't have a complete polar to input, but you do have one or two known datapoints and would like to adjust Piano's own polar slightly to pass near or through these.

06.03 - Basic Polar Data

Piano recognises the following key parameters within fixed polar files. Each name should be followed by matching data.


This is the arbitrary reference area for all subsequent CL and Cd values given in the fixed polar. It must always be in square feet. It is not necessary for this area to match any of the wing areas calculated by Piano. Whenever you produce any drag output reports or pictures, all aerodynamic coefficients will be automatically adjusted to the reference wing area of the current plane (see Chapter#05section03 ). This ensures consistency when you compare calculated and fixed-input aerodynamics.


The basic zero-lift drag coefficient. It can be set to zero if you choose instead to incorporate Cd0 in subsequent data representing Cd as a function of CL and Mach.


The induced drag constant (lambda) in the standard parabolic polar representation (Cdi = lambda * CL ^ 2). It too can be set to zero if you prefer instead to incorporate the induced drag in subsequent data representing Cd as a function of CL and Mach.

The three parameters described sofar must always form part of any fixed polar file. On their own, they specify a simple parabolic 'low-subsonic' polar. The remaining parameters outlined below are optional, although normally necessary for accurate representations. They cover compressibility corrections and Reynolds-number related corrections.

06.04 - Compressibility-Related Data

The following parameter is used to represent compressibility drag, although you may also choose to include Cd0 and Cdi in it by setting basic-cd0 and induced-lambda to zero, as described above.


If supplied, this must be followed by a list of data enclosed in parentheses ( ). The format consists of pairs of CL and Cd at different Mach numbers, as in this sample:


 ( Mach 0.70
   0.20      0.00000
   0.40      0.00000
   0.49      0.00100
   0.52      0.00178
   0.63      0.00515

   Mach 0.76 
   0.00      0.00000
   0.15      0.00002
   ....  etc ....... ) 
As shown above, the list of CL values can differ at each Mach number. If however your data are 'square' (same CLs at all Mach numbers), you may instead prefer to use the following equivalent parameter:


This must be followed by a table of data. The first row indicates the Mach number, the first column the CL, and the rest are Cd values, as in the following example:


      .60    .70    .75    .80    .82    .85    .87
 .25  .00000 .00000 .00000 .00000 .00000 .00000 .00000
 .35  .00000 .00000 .00000 .00000 .00000 .00027 .00053 
 .40  .00000 .00000 .00008 .00031 .00054 .00097 .00169 
 .56  .00005 .00024 .00054 .00137 .00205 .00278 .00357 
 .60  .00026 .00068 .00143 .00265 .00336 .00420 .00519 
Unlike the previous parameter, tables must not be surrounded by any parentheses, but must be followed by at least one blank line.

Whichever format you choose to represent Cd = f (Mach, CL), the following rules apply:

- 1. Interpolation in the direction of CL is smooth (a spline fit). Outside the range of data, the final slope at the extreme points is used to provide linear extrapolation.

- 2. Interpolation in the direction of Mach number is linear, because Mach-related effects can be very uneven. Any attempt at smoothing is almost guaranteed to cause oscillations. It is advisable to provide reasonably 'dense' data in the Mach direction, say in steps of 0.02 Mach or less near cruise conditions. Extrapolation is not attempted. Piano assumes that the polar remains unchanged below the lowest quoted Mach, and that the drag is effectively infinite above the highest quoted Mach.

To check your input visually, use the 'Plot Cd (Mach,CL)' item in 'Fixed Polars'.

06.05 - Reynolds-Related Data

There are three ways of accounting for Reynolds-number effects: You can provide a full set of corrections, use a simple method adjusted to a single reference condition, or apply a specific style of adjustment used by manufacturers for flight test data. If you don't provide any of the following parameters, Reynolds effects are ignored.

- Full Reynolds Correction:


If supplied, this must be followed by a list of data enclosed in parentheses ( ). The format consists of pairs of altitude (always in feet) and delta-Cd, at different Mach numbers. Delta-Cd is the correction (+ or -) to the total drag coefficient. For example:


( Mach 0.4 5000 -0.00030 20000 0.00017 36000 0.00064 45000 0.00084 Mach 0.6 5000 -0.00065 20000 -0.00022 36000 0.00032 .... etc ..... )

Reynolds corrections tend to be well behaved, so these data can be fairly sparse. Smooth (spline) interpolation is used in both directions. Altitude extrapolation is allowed, and Machs outside the range of data are set to the nearest quoted Mach. To check your data, you can plot them via the 'Plot Cd (Mach,H)' item.

As you might expect, the equivalent 'tabular' format is available as an alternative:


This is similar to the format shown previously for table-cd-vs-mach&cl, except that instead of CLs you must specify altitudes (in feet).

- Simplified Reynolds Correction:

As a simple alternative to full data matrices, you can use Piano's built-in method to correct for Reynolds effects. To do this, you only need to specify a reference flight condition for the basic-cd0 (already discussed) through the following parameter:


This is followed by the reference altitude (in feet) and Mach number, enclosed in parentheses as in this example:

 altitude&mach-for-basic-cd0   ( 35000  0.82 ) 
- Manufacturers' Reynolds Correction:

A particular style of Reynolds corrections is occasionally used by Boeing and other manufacturers. This is a specialised method: It presupposes that you have a given flight-tested polar in terms of CL and Mach, plus a matching correction for (W/delta), where W is the aircraft test weight in pounds and delta is the atmospheric pressure ratio (p/p0). You will need the following:


A number of the order of 0.004. It represents the constant k in the equation:

delta-Cd = k log10 ( [Re/ft/Mach]actual / [Re/ft/Mach]nominal ).


A list of numbers representing alternately the (W/delta) in pounds and the corresponding altitude in feet. The list must be enclosed in parentheses ( ).

06.06 Polar 'Modification' Files

Polar modifications ('polar mods') let you adjust Piano's own aerodynamic calculations incrementally. They are handled via the 'Modify Polar' item (under the 'Misc' menu). Each mod consists of a simple text file. This must be placed inside the 'polar mods' folder found within the Piano folder. Files can be edited manually via 'Edit Polar Mod...' (or by choosing 'Open' from the 'File' menu).

To permanently link a 'polar mod' to a plane, first load it ('Load Polar Mod...') and then store the plane. The connection is established via the parameter polar-mod-name .

The format of a polar mod file consists simply of pairs of CL and delta-Cd (positive or negative adjustments to the total Cd) at different Mach numbers, as in this example:

 Mach 0.72
 0.3    0.00140
 0.4    0.00058
 0.5   -0.00007
 0.55  -0.00018
 0.6    0.00013

 Mach 0.76
 0.3    0.00162
 0.35   0.00122
 0.4    0.00080
 .... etc ..... 
The reference area for 'polar mods' is always the wing-area parameter. You can visually check your data via the 'Plot Polar Mod' item.

Interpolation in the direction of CL is smooth (a spline fit). Outside the given data, the final slope is used for extrapolation. Mach interpolation is linear, because these effects are more uneven. It is best to provide fairly dense Mach values, and a minimum of 3 Machs are required. Outside the range of data, Mach is set to the nearest quoted value.

Piano can calculate a 'polar mod' directly from a 'fixed polar'. To do that, first load the fixed polar and then use the 'Difference Table' item under 'Fixed Polars'. This produces a tabulation of the difference:

Delta-Cd = (Cd from the fixed polar file) - (Cd from Piano's own calculations)

The output is in the standard format for polar mod files and can be saved directly in the 'polar mods' folder.

Note: The comparison between fixed and calculated polars is done at a nominal altitude to cater for Reynolds effects. This altitude is taken from the standard dialog for 'Lift/Drag Polar...' plots. You can use the 'Overlay Polars...' item to check in advance how the fixed and calculated data compare, and fix the nominal altitude in the process.

06.07 Simplified Polar Adjustments

If you need to create a polar adjustment that depends on either CL or Mach number, but not on both at the same time, you can do it without using a 'polar mod' file:

Simply input your corrections directly through either user-adjust-cl-cd-curve or user-adjust-mach-cd-curve , as appropriate. These are 'data curve' type parameters. The user-adjust-cl-cd-curve can hold a list of paired numbers representing alternately a CL and the corresponding Cd increment, whereas user-adjust-mach-cd-curve similarly holds pairs of Mach and Cd increments. If you use these parameters and load a 'polar mod' file at the same time, all the adjustments are added up.

The parameters' dialogs include a 'plot data' button. Data are interpolated smoothly (using spline fits).

06.08 Low-Speed Aerodynamics

Files containing user-specified low-speed aerodynamics are kept in the 'lowspeed aero' folder inside the Piano folder. You can manipulate them via the 'Lowspeed Aero' item ('Misc' menu).

To link a low-speed aero file to a plane, first load the file ('Load Lowspeed Aero...') and then store the plane. The connection is established via the parameter lowspeed-aero-name .

Piano recognises the following key parameter names within 'lowspeed aero' files:


Similar to the parameter used in the 'fixed polar' format described earlier, this is an arbitrary reference area (always in square feet) for all subsequent CL and Cd values. Normally these two reference areas will be the same, but this is not a requirement.


This must be followed by a list of data enclosed in parentheses ( ). The format consists of pairs of CL and total aircraft L/D at different flap deflections (in degrees, identified by the word 'flap-deg'), as in the following sample:


( flap-deg 0 
  0.00   0.00
  0.20   8.77
  ... etc ...
  2.60  10.00
  2.80   9.39

  flap-deg 5 
  0.00   0.00
  0.20   6.71
  ... etc ... ) 
Note that these data do not include the undercarriage drag (gear is 'up'). This drag is added whenever necessary according to the value of delta-cd-due-to-u/c , or as explained below.


This is followed by a simple list of data representing the flap deflection in degrees and a corresponding CLmax, surrounded by parentheses as in this example:


(  0    2.09
   5    2.25
  10    2.40
  ... etc ...
  35    3.11
  45    3.28 ) 
The following data are optional. You can supply them if you know the variation of the undercarriage drag coefficient with flap setting and CL. This drag is then added to the gear-up low-speed polar as required. It will override the value of delta-cd-due-to-u/c .


The format consists of pairs of CL and undercarriage Cd (based on reference-area) at different flap deflections, as shown:


( flap-deg 0
  0.0  0.030
  2.0  0.025

  flap-deg 50
  0.0  0.028
  2.0  0.018 ) 
Such variations in u/c drag with flap deflection are due to changes in the local flow field. (The u/c 'sees' less than free-stream conditions with the flaps down). However it is rare to have this information available, and there is no generic way of estimating the effect.

It is possible to generate a 'lowspeed aero' file automatically, from the calculated aerodynamics of the current plane, through the 'Show Calculated' item. This includes data for l/d-vs-flap&cl and clmax-vs-flap, but not u/c-cd-vs-flap&cl, as there is no built-in method for that. You can edit and save the file (in the 'lowspeed aero' folder) as necessary.

For verification, all of the above inputs can be plotted via the 'Plot L/D (CL,flap)', 'Plot CLmax (flap)' or 'Plot u/c Cd (CL,flap)' items under 'Lowspeed Aero'.

Note that when you load a fixed 'lowspeed aero' file, the following parameters will not be used:


Low-speed aerodynamics do not require separate adjustments for Reynolds or Mach number.

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