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Aircraft geometry is based on Conventional, Subsonic, Commercial configurations. This implies a distinct wing and fuselage (as opposed to blended body), some form of nacelles (on the wing, fuselage, or fin), and aft-mounted horizontal and vertical tails (stabiliser and fin). Piano does not consider canards, tandem wings, or other unusual multi-surface configurations.
You define the basic geometric characteristics through parameters such as wing-area , fuse-width , etc. Arbitrary shapes can be used for the fuselage and nacelles. Piano automatically derives all the dimensions, areas and volumes that are needed in aerodynamic and mass calculations. Detailed outputs are produced via the 'Geometry' item under the 'Report' menu.
The basic wing planform is specified as a simple trapezoid via the parameters wing-area , aspect-ratio (or alternatively span ), sweep-deg and taper . It is important to remember that these parameters refer to trapezoidal values. You can specify an optional planform break (and thickness break) separately.
The taper ratio is defined as (tip chord) / (notional trapezoidal chord at the centreline). The wing-area refers to the entire trapezoid including the portion buried inside the fuselage. You can provide either the aspect-ratio or the span , but not both. (In the unlikely event that neither is supplied, Piano picks a typical aspect ratio from statistical trends of structural cantilever ratios). Sweepback angle ( sweep-deg ) is normally specified at the quarter-chord line. (You could use the parameter xi-sweep to change this chordwise fraction). The wing span does not include any winglets. These are treated as separate items.
The wing is mounted on the fuselage in a high, low, or mid configuration according to wing-mounting , at a dihedral angle of dihedral-deg . Its longitudinal placement along the fuselage is determined by the aircraft balancing procedure described in Chapter#08section13 unless it is fixed by the user via wing-apex-fuse-fraction .
Source codes: The basic function is wing-geometry .
A single planform break can be added to the wing. This forms an extra triangular area along the inboard trailing edge, sometimes called a 'Yehudi'. Its size is dictated by the parameters planform-break-fraction and planform-break-t.e.-adjustment . Such a break provides a suitable location for mounting the undercarriage, and it also permits a local increase in chord and structural thickness near the root. Normally the planform-break-fraction is specified as a fraction of the exposed semispan. (You can change that by setting the parameter break-fraction-definition to :overall-semispan). The trailing edge inboard of the breakpoint will be unswept (i.e. at right angles to the fuselage), unless you specify otherwise via the parameter planform-break-t.e.-adjustment .
The thickness/chord ratio at the wing root is given by t/c-root . ('Root' here means the wing-fuselage junction or 'side-of-body', not the centreline). The t/c ratio at other spanwise stations is then defined as a fraction of this 'root' value, as follows:
At the wing tip, the t/c is the product of the parameter t/c-tip/root (default = 1) and the t/c-root . Similarly, if there is a 'thickness break', the t/c at that location is the product of t/c-break/root (default = 1) and t/c-root .
You can specify the spanwise location of the 'thickness break' (if any) via the calculable parameter thickness-break-fraction . If not supplied, this coincides with the value of planform-break-fraction .
During internal calculations, the physical thickness of the wing at intermediate stations is assumed to vary linearly from the root to the breakpoint and from the breakpoint to the tip. Inboard of any planform break, all t/c ratios naturally refer to the complete local aerofoil, not to the local trapezoidal chord.
There exists no unique, universally accepted definition of wing area. Brochure numbers are often quoted without explanation or consistency, leading to misinterpretation and gross errors. It's therefore important to be aware of any treatment of wing area:
The basic reference area used in Piano is wing-area , the trapezoidal area. All relevant input parameters and coefficients are based on it. Internal aerodynamic calculations also use this reference area, making suitable corrections for any planform break.
Starting from the trapezoidal wing plus an optional planform break as outlined in the previous sections, Piano also calculates the following alternative area definitions:
Airbus (or 'Airbus Gross') definition: = exposed wing area + (area of rectangle inside the fuselage between the leading and trailing edges at the root).
Boeing (or 'Wimpress') definition: = trapezoidal area + (exposed 'yehudi' break area) + (covered 'yehudi' break area) * (fraction of exposed span at the break).
ESDU definition: = the area of a notional trapezoid having the same exposed area as the actual exposed wing, and with the same tip chord and span. (This notional trapezoid is intended as a rough aerodynamic equivalent to the entire wing. It differs from the basic trapezoidal wing).
Piano Gross definition: = the total area encompassed when extending the leading and trailing edge lines through the fuselage to the centreline.
The calculated values of all these areas are shown in the 'Geometry' report.
When you construct a model of an existing aircraft you may know the manufacturer's quoted value for one of the above areas. If so, use the 'Re-Size Wing' facility (under the 'Plane' menu) to find the corresponding trapezoidal wing-area . This avoids the need for hand calculations or sketching. In such an exercise, you should first assign values to planform-break-fraction , taper , and sweep-deg based on available drawings or using your best estimates. Give an arbitrary initial value to wing-area and then use the 'Re-Size Wing' dialog to choose the desired definition and set the known area. You will need to specify either the span or a matching aspect ratio definition in the dialog (this aspect ratio may of course differ from the trapezoidal aspect-ratio ).
Reality check!: Some wing planforms are very complex, with subtle multiple breaks. You will invariably have to use some judgement in reducing such intricate shapes to a trapezoid with a single planform break. Piano's methods for calculating mass and drag are in any case based on this most common configuration. It would be pointless and also misleading to introduce extra detailed definition options that do not match the methodology limitations.
Some more comments on wing areas in the context of aerodynamic calculations can be found in Chapter#05section03 .
Finally, it could be said that confusion over wing areas is an established tradition in Aeronautics. Historically, major players such as Airbus, Douglas, and Boeing all chose different reference definitions (Douglas was trapezoidal, Boeing switched to 'Wimpress' in the era of the 747), and even different departments within the same company could conflict. When early-model 737s received an increase in wing area, the old area seems to have been retained for aero reference purposes. Such examples point to a simple truth: Each choice has minor pluses and minuses in terms of usability, but ultimately any single one is fine as long as you are consistent in its usage.
Fuselages are split into three separate segments (front, mid, and rear). Total fuselage length is the sum of the parameters front-fuse-length , mid-fuse-length , and rear-fuse-length .
The mid-segment is defined as a parallel tube of constant cross-section (not necessarily circular). It has an external width given by fuse-width , and its external depth is the product of fuse-depth/width (default value = 1) and fuse-width . Several choices for the shape of the cross-section are provided by the parameter fuse-xsection-type .
Arbitrary shapes can be assigned to the front and rear fuselage segments. These are the shapes seen in plan and elevation in 3-view drawings. Whenever you change the dimensions of a fuselage segment, the corresponding shapes are automatically scaled ('rubberised') to match the new length, width, or depth.
Source codes: The relevant function is fuse-geometry .
You can choose from a multitude of predefined shapes, or you can input your own arbitrary shapes for the front and rear fuselage segments, as well as for any nacelles. Shapes are kept as individual files in the 'shapes' folder, separately from planes. If you do not explicitly specify a shape when you create a new plane, the files named "default" will be used.
Use the 'Shape Editor' under the 'Misc' menu to create a new shape or to edit an existing one. You can also preview the shape and derive its wetted and projected areas. (Note: editing a shape is a separate process from loading it into the current plane).
A shape consists of a number of longitudinal stations, with each station having a corresponding value for the local height of the upper contour, the lower contour, and for the local width. Shapes are therefore symmetrical when viewed from above, but not necessarily from the side.
Stations are measured from left to right (as shown in 3-views). You can use any units (metres, mm, feet, inches) because a shape's dimensions are in any case 'rubberisable'. The first station must always be zero, but spacing between stations need not be regular. For front fuselages, start from the nosecone and move aft. For nacelles, start at the front (the intake) and move aft. For rear fuselages, start at the end of the mid-fuselage (max. diameter) and move aft. Heights (for upper or lower contours) can be measured relative to any arbitrary horizontal level, usually the bottom of the shape. No negative values are allowed. Widths may be either total widths or half-widths. One restriction is that the shape must be nominally open-ended at both ends, i.e. the gap between the upper and lower contours can be very small, but not zero.
When saving a shape (via the 'Shape Editor'), be sure to select the appropriate folder from amongst 'front fuselages', 'rear fuselages', 'nacelles', or 'nacelles on fin' (all of which are in turn located inside the 'shapes' folder). Piano will not be able to find any shapes that have been saved outside their assigned folders.
Once a shape has been defined, you load it using 'Load Shape' (under the 'Misc' menu). It will be automatically scaled to the dimensions of the current plane. If you then save the plane using 'Store Plane...', the shape becomes permanently linked to it. The linkage of a shape file to a plane is achieved via the parameters front-fuse-name , rear-fuse-name , nac-name , and nac<fin>-name . These simply hold the corresponding shape's filename. Clicking on such parameters is an alternative way to load shapes.
A given shape may be used by several planes, scaled to different dimensions for each. It is important to remember this if you decide to modify an existing shape: You may be affecting more than just your current plane!
Source codes: Relevant functions are load-all-solids , setup-front-fuse , setup-rear-fuse , setup-nac , setup-nac<fin> .
Engine nacelles can be wing-mounted, fuselage-mounted, or fin-mounted (e.g. as in the MD-11). It is also possible to place engines internally within the fuselage.
The primary dimension of a nacelle is its maximum width, given by nac-width . Depth and length are then specified as fractions of this width, by nac-depth/width (default = 1) and nac-length/width (default = 2). These dimensions apply to all wing-mounted and/or fuselage-mounted nacelles. If a fin-mounted nacelle exists, its dimensions are specified in relation to the main nacelles by the parameters nac<fin>-width-proportion , nac<fin>-depth-proportion , and nac<fin>-length-proportion . Since parameters are defined in such relative terms, it is easy to scale the entire nacelle shape uniformly by changing the nac-width alone.
The spanwise locations of wing-mounted nacelles (and, implicitly, their number) are specified via the single parameter nacs-mounted-on-wing . In the fore-and-aft direction, nacelle position is adjusted by nac-location-ahead-of-wing , and in the vertical direction by nac-location-below-wing .
The number and lateral locations of rear fuselage-mounted nacelles are specified by the parameter nacs-mounted-on-fuse . Their position in the fore-and-aft direction is controlled by nac-location-on-fuse . (In the vertical direction, fuselage-mounted nacelles are approximately placed with their axis passing through the end of the fuselage tailcone).
A single fin-mounted nacelle (MD-11 style) is specified by the parameter nac-mounted-on-fin , and its position controlled by nac<fin>-longitudinal-location and nac<fin>-vertical-location .
If there are engines mounted internally in the fuselage, they can be specified via the parameter nacs-mounted-internally . This dictates both the number and longitudinal placement of such engine(s). Nacelle dimensions are obviously not relevant in this case.
Source codes: Relevant functions are nac-geometry , nac<fin>-geometry .
By default, the areas of the stabiliser (horizontal tail) and fin (vertical tail) are determined during the aircraft balancing procedure described in Chapter#08section13 . When modelling an existing aircraft, you can input any known tail areas quoted by the manufacturer directly through the 'Set Tail Areas' feature (under the 'Plane' menu). Alternatively, you can set the areas indirectly through the 'tail volume coefficient' parameters required-stab-vol-coeff and required-fin-vol-coeff .
Both the stabiliser and the fin are modelled as simple trapezoidal surfaces with a constant thickness/chord ratio across their entire span. The basic geometric parameters are stab-aspect-ratio , stab-taper , stab-sweep-deg , stab-t/c , fin-aspect-ratio , fin-taper , fin-sweep-deg , and fin-t/c . By definition, the stabiliser area is a gross value including any portion buried in the fuselage. (An exposed stabiliser area is of course also estimated by Piano and used during drag calculations). The fin area is assumed to be exposed in its entirety (total area = exposed area). In 3-views, the fin is simply drawn as a separate trapezoid attached to the upper contours of the fuselage at the quarter-chord root point.
The stabiliser and fin are located just before the end of the fuselage. You can move them fore and aft through stab-tailcone-gap and fin-tailcone-gap . These represent a typical length of tailcone that remains aft of the root trailing edge of the tail surfaces.
In the vertical direction, stabiliser placement is determined by the stab-mounting . Low-mounted stabilisers are positioned at the same level as the end of the tailcone. Mid- or High-mounted stabilisers (cruciform or T-tails) are positioned along the fin so that their quarter-chord point at the root coincides with the quarter-chord of the fin (in which case incidentally the value of stab-tailcone-gap becomes irrelevant).
Note: If not supplied, the values of stab-sweep-deg , fin-sweep-deg , fin-aspect-ratio and fin-taper are chosen from statistical correlations with the wing's sweep-deg and the stab-mounting .
A small 'dorsal fin' can be specified through dorsal-fin-height-fraction and dorsal-fin-length-fraction . Dorsals are often added to prevent fin stall or buffeting at high sideslip angles, and Piano merely treats them as an extra drag and mass item, not as part of the fin area.
Source codes: Relevant functions are stab-geometry , fin-geometry .
Traditional-style winglets are specified via the parameter exist-winglets . Their size relative to the wing is set by winglet-span/wing-halfspan and winglet-root-chord/wing-tip-chord . The outward cant angle winglet-cant-deg is only included for aesthetic reasons. Note that the parameter span refers to the wing alone and does not include the winglets. However the overall span including winglets is shown in geometry reports and 3-views.
Source codes: See function winglet-geometry .
Undercarriage length is determined by the (calculable) parameter u/c-length-below-fuse . This length is used in u/c mass estimates and also to derive approximate rotation limits during the takeoff run (see Chapter#10section08). The main undercarriage is mounted either on the fuselage or on the wing, according to u/c-mounted-on , at a spanwise location given by eta-u/c . If not supplied, a typical value for u/c-length-below-fuse is chosen from a rough correlation with fuselage size. Because of the large variety of possible configurations, it is generally best to input this parameter directly.
Source codes: See function u/c-geometry , variables main-u/c-length , nose-u/c-length .
For the purposes of area calculations and 3-views, trailing edge flaps are assumed to extend from the wing root to a spanwise location given by eta-flap . Their chordwise extent is dictated by flap-chord-fraction . This fraction applies outboard of any planform break. The inboard flap is presumed to have a constant chord equal to its value at the breakpoint.
If there are any slats (depending on exist-slats ), they occupy a (trapezoidal) chord fraction given by slat-chord-fraction and a fraction of the exposed span given by slat-exp-span-fraction . If the latter is less than 1, slats start at the tip and extend inboard.
Spoilers are simply rectangles whose size is set by spoiler-exp-span-fraction (zero if there are no spoilers) and spoiler-chord-fraction (a nominal value at the mean chord).
The windscreen is used for a minor correction in the calculation of fuselage drag. Normally Piano draws a windscreen at the point where the front fuselage shape first shows a 'kink'. This can be changed by windscreen-top-fraction . A frontal area is calculated according to windscreen-depth and windscreen-width-fraction . Windows are placed along the cabin according to number-of-windows (normally determined by the number-of-pax and seats-abreast ). Their size is set by window-depth and window-width (assumed to be elliptical or circular).
Cabin layout and seating configuration details are beyond the scope of Piano. However, some checks are done to ensure that the fuselage geometry can (at least in principle) accommodate the specified number-of-pax and the number of seats-abreast . A uniform single-class layout is examined, according to the values of cabin-seat-pitch , cabin-seat-width , and cabin-aisle-width . By default, the cabin occupies the mid-fuselage segment (constant cross-section). It can also intrude in the front and rear fuselage segments as specified by cabin-in-front-fuse-fraction and cabin-in-rear-fuse-fraction . The vertical location of the cabin floor is given by cabin-floor-location . If a full second deck exists (such as in the A380) , this should be specified by exist-2nd-deck . (Note: the B747's small upper deck is unusual and this aircraft is treated as a single-decker). These geometric safety checks can be overridden via the parameter ignore-seating-checks .
Source codes: See function cabin-geometry .
A variety of wetted areas are needed in the calculation of skin friction drag. The wetted area of the mid-fuselage segment depends on its cross-section type, dictated by the parameter fuse-xsection-type .The wetted areas of the front fuselage, rear fuselage, and nacelle shapes (see the 'Shape Editor') are derived according to procedures [data not available online]. It is assumed that the local cross-sections of such shapes are roughly elliptical along the entire length, scaled to the given width and depth at each station. To join the different shapes smoothly, some form of shape-blending is, by implication, presumed to occur along the fuselage axis near the junctions of individual segments. This method gives extremely good accuracy in area calculations whilst avoiding any need for complex meshes of 3-Dimensional surface specifications.
The wing is split into a number of spanwise panels and the wetted area of each is calculated, with an empirical 'form factor' correction for the local thickness/chord ratio of the aerofoil. Stabiliser, fin, and winglet (if any) wetted areas are treated similarly, using single panels. The portion of the stabiliser that is buried in the fuselage is subtracted.
The effects of the wing-fuselage junction on wetted area are complex and dependent on 3-D contour details. On the one hand some of the fuselage area is covered by the root aerofoil, on the other hand additional area is introduced by the root fairing and by portions of the wing inboard of the side-of-body position. An empirical allowance for these contributions uses the parameter fairing-type , which offers a choice of common fairing configurations. This is based on limited data and represents a token adjustment. For large or unusual fairings it may be appropriate to apply a further factor to the fuselage drag ( user-factor-on-fuse-drag ).
Nacelle wetted areas are derived from the relevant shapes in a similar way to fuselage sections. There is no attempt to explicitly cater for the pylon's geometry or wetted area. Instead, typical corrections are made directly to the nacelle drag calculations (see Chapter#05section09 ).
Adjustments are also made to the total wetted area to cater for any area covered by the fin-mounted nacelle, the winglet areas, and the dorsal fin area (if applicable). The stand-alone values for individual components and the overall wetted area which includes all adjustments are quoted under the 'Geometry' report.
Source codes: Relevant functions are plane-swet , wing-swet-between-etas , fairing-geometry , fuse-perim , and other functions given in previous geometry sections.
Piano derives the available fuel volume (also called the 'fuel capacity') directly from the aircraft's geometry and according to the following criteria:
The structural wing box is assumed to be 'wet' (i.e. capable of holding fuel) between the front and rear wing spars. Spar locations are defined at the wing root and tip stations by xi-front-spar-root , xi-front-spar-tip , xi-rear-spar-root , and xi-rear-spar-tip , as fractions of local trapezoidal chord. Positions at intermediate stations are interpolated linearly. In the spanwise direction, the wet region extends from the wing root to a position eta-wet-wing . The box centresection (treated as a straight carry-through of the root section for the whole fuse-width ) may be either wet or dry, depending on the parameter centresection-is-wet (default value = true).
The region covered by the wing planform break (if any) is normally assumed to be dry, because its purpose is in any case to provide storage space for the undercarriage. This can be changed through the parameter planform-break-is-wet (default value = false).
The stabiliser and fin are also usually dry, unless you specify otherwise through the parameters stab-is-wet and fin-is-wet .
A total available capacity is calculated from the above considerations. It can then be adjusted through the parameter fuel-vol-adjustment . Such a correction may be positive or negative, and could reflect the existence of dry bays, additional fuselage-mounted tanks, etc. Alternatively it can be used to match the quoted fuel capacity of an existing aircraft. To do this, select the 'Set Fuel Capacity' feature under the 'Plane' menu and input the known capacity, whereupon Piano will calculate the corresponding value of fuel-vol-adjustment . (Note however that if you subsequently modify the aircraft geometry the capacity could change again).
Available fuel capacity is shown under the 'Geometry' report, where it is also compared to the 'required' volume (needed to accommodate the design fuel mass, see Chapter#04section14 ), depending on the value of fuel-density .
Reality check!: As is the case for the whole wing, the detailed geometry of the structural box may include complex planform breaks and will be influenced by aerofoil contours. Ribs and other internal structure and fixed equipment will occupy some of the available volume. Tail fuel capacities could be liable to variations due to uncertainties in control surface geometry. Various statistical factors are included in the calculations to allow for these effects, and the total capacity value is of necessity approximate.
Source codes: See functions box-geometry , tank-geometry , find-fin-vol , find-stab-vol , box-vol-in-web , box-csa-at-eta , final-fuel-checks .
Aircraft drawings are generated via the '3-View' item (under the 'Report' menu).
A '3-View' provides a visual check of the input geometry and can help spot gross errors or potential conflicts. These drawings are compact technical outlines, not marketing-style presentations. All information is derived directly from the current input parameters. Piano does not use any finite-element or CFD methods, and there is no attempt to generate potentially misleading 3-dimensional models.
It is a good idea to use '3-View' (or its keyboard equivalent Command-3) as a convenient way of 'redesigning' the aircraft after you modify any geometric parameters. Of course, any other request for output after a modification will also force a 'redesign', but without this visual check.
Normally all 3 views (plan, front and side) are shown together in a single drawing with some overlap. You can avoid any overlap by using the 'View Options...' sub-menu to show the 'Plan View Only' or the 'Front and Side View' separately.
The 'Set Up 3-View' option lets you control various aspects of the drawing such as scaling and annotations, as follows:
Each plane is normally scaled to fill the available drawing area, which is always square. You can, however, compare different aircraft at the same scale if you specify a fixed size in 'Set drawing dimensions' (metres or feet). For example, an 80-metre box will hold anything up to an A380. This is particularly effective if you set the 'Picture Modes' to 'retain' and then use the <Tab> key to flick between different drawings. For more details on this trick, see Chapter#13section03 .
You can pick any colors for the plan, front and side views. By default, the fuel tank is shown in black. Yellow ticks along the centreline mark the c.g. limits, and green marks the neutral point. A blue cross is the aerodynamic centre of a flying surface and the yellow cross on the wing is the c.g. of the fuel.
It's possible to create oversized drawings bigger than your screen (up to 175%), depending on your choice of 'Window Size'. You can move such drawings around the screen by using the arrow keys to see different portions. Oversized drawings are sometimes useful for producing better quality printouts without jagged lines.
Normally, only a few seat rows are shown in the plan view, to give a sense of spacing. You can choose instead to draw all of the seats, or none. A simple human figure and a scale ruler are also shown.
When you are happy with your setup, click on 'Save Prefs...' to make it your preference for whenever you start Piano.
Sample Geometric Report
GEOMETRY REPORT _______________ Wing Stabiliser Fin ---- ---------- --- Area, trapezoidal reference 112.15 31.00 21.50 sq.metres Area, piano gross 124.47 31.00 21.50 sq.metres Area, airbus gross 122.40 sq.metres Area, boeing wimpress 119.83 sq.metres Area, esdu 119.58 sq.metres Area, exposed 98.40 23.54 21.50 sq.metres Area, wetted 201.10 47.93 43.78 sq.metres Aspect Ratio, trapezoidal 10.25 5.00 1.60 Aspect Ratio, piano gross 9.24 5.00 1.60 Aspect Ratio, airbus gross 9.39 Aspect Ratio, boeing wimpress 9.60 Aspect Ratio, esdu 9.62 Span (excluding winglets) 33.91 12.45 5.87 metres Sweepback at 1/4-chord 25.00 28.50 35.00 degrees Taper Ratio (trapezoidal) 0.29 0.31 0.35 t/c at root 0.153 0.110 0.110 t/c at thickness break 0.115 t/c at tip 0.108 0.110 0.110 Volume Coefficient (V-bar) 1.319 0.093 Mean Aerodynamic Chord 3.63 2.72 3.95 metres Arm between MAC 1/4 chords 17.34 16.39 metres Wing chord at tip 1.51 metres Wing chord at planform break 3.76 metres Wing chord at root (gross) 6.02 metres Wing chord at c/line (gross) 7.05 metres Wing chord at c/line (notional trapezoidal) 5.11 metres Planform break location 0.290 (fraction of exposed semispan) Thickness break location 0.290 (fraction of exposed semispan) Wing location (station of extended leading edge at c/line): 12.02 metres (32.0 % of fuse.length) Spar locations (fractions of local trapez.chord): Wing root: 0.14, 0.64 Wing tip: 0.14, 0.64 Fuel capacity avail/reqrd = 1.030 ------------- centresection is wet Available: 23.86 cu.metres (geometric capacity) Required : 23.18 cu.metres (at mtow & design payload) Fuselage geometry ----------------- fuselage max. width 3.99 metres fuselage max. depth 3.95 metres length, total fuselage 37.57 metres length, front section 6.40 metres length, mid section 17.47 metres length, rear section 13.70 metres wetted area, total fuselage 400.65 sq.metres wetted area, front section 59.75 sq.metres wetted area, mid section 217.74 sq.metres wetted area, rear section 123.16 sq.metres Nacelle geometry ---------------- nacelle length 3.67 metres nacelle max. width 2.25 metres nacelle max. depth 2.51 metres wetted area per nac. 25.88 sq.metres Overall dimensions ------------------ Span over winglets 33.91 metres Overall aircraft length 37.57 metres Height at top of fin 12.00 metres Overall aircraft wetted area 748.34 sq.metres
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