Chapter: 04. Mass Estimation

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Chapter: 04. Mass Estimation

04.01 Introduction

Mass estimation uses a variety of semi-empirical preliminary design techniques derived partly from unpublished industrial sources and partly from published texts. These methods are applicable to conventional modern aluminium structures. They have been calibrated with existing aircraft data as far as possible. Effects of composites or other advanced materials are not considered, but suitable user-controlled factors can be applied to individual weight components. Emphasis is placed on wing mass estimation, which is the most relevant contribution from the sizing viewpoint.

Strictly speaking Piano works in terms of mass rather than weight, but some traditional weight-style abbreviations such as MTOW, OEW, etc are used interchangeably for convenience.

A detailed report showing the mass breakdown can be produced via the 'Mass' item under the 'Report' menu.

04.02 Maximum Takeoff Mass

The maximum takeoff mass or weight (MTOW) is given by the parameter mto-mass (kg or lb). This is a 'vital' (red) parameter. When modelling an existing aircraft, mto-mass should be the value quoted by the manufacturer. During a design exercise, several possibilities exist: You can keep the mto-mass constant, or iterate it automatically to match a specific design range, or choose it indirectly after a traditional parametric study, or calculate it through a multivariate optimisation process so as to minimise a nominal goal subject to constraints.

The MTOW is, by definition, the sum of the Operating Empty Weight (OEW), the nominal design payload, and the corresponding design fuel mass. The OEW is built up by calculation from the various component mass estimation methods described in this chapter. It reflects your choice of many design parameters, including the MTOW itself. For existing aircraft, this calculated OEW can be adjusted to match a known value precisely. The design payload is effectively a direct input, as shown below. Therefore the design fuel mass will be a 'fall-out' at any given MTOW.

04.03 Payload Mass

The nominal design payload is given by:

( number-of-pax * mass-per-pax ) + cargo-mass

The number-of-pax or total number of passengers is a 'vital' parameter. The mass-per-pax is the average mass of a passenger including luggage and defaults to 95 kg/pax. (Standards vary, e.g. Airbus may use 91 kg/pax for short haul and Boeing tend towards 200 lb/pax for 2-class seating configurations or 210 lb/pax for 3-class seating). The cargo-mass defaults to zero.

Maximum payload is influenced by detailed stressing and volumetric restrictions that are not known at the early design stages. It is specified in terms of the design payload via the parameter max-payload/design-payload (default value = 1). For the purposes of Piano the maximum payload is used to determine the Maximum Zero Fuel Weight (as MZFW = OEW + maximum payload) and to set the upper boundary for payload-range diagrams.

04.04 Design Conditions and Limits

Piano initially requires two 'vital' parameters to provide a baseline point for the calibrated mass equations: The design-cruise-mach and design-cruise-altitude . Your choice of design-cruise-mach should represent the fastest anticipated cruise under normal operating conditions (at, or near, the 'maximum operating mach number' or Mmo for certificated aircraft). The design-cruise-altitude should correspond roughly to an average altitude during normal cruise (not necessarily the highest certificated altitude). Typical values would be of the order of 25,000 ft for turboprops, 35,000 ft for commercial jets, or 40,000 ft for business jets. The selection of these parameters does not need to be overly precise. Pick your best estimates and stick with them: Making unnecessary minor refinements at a later stage is not recommended, as it would change the structural mass as well as some aerodynamic drag calculations, in the calibration of which these parameters are also used.

The max-operating-altitude is a 'calculable' parameter related to pressurisation. If you don't supply a value, it is nominally set equal to the design-cruise-altitude , but the aircraft is still allowed to climb to any altitude provided there is enough performance available. If, however, you do supply a value, this will also act as a limiting altitude in all performance calculations.

You can optionally specify the design-dive-mach or MD, another 'calculable' parameter. Otherwise this is set to the current design-cruise-mach + 0.05. Statistical correlations are used to derive other approximate values for the design cruise speed VC and the dive speed VD based on these Mach numbers.

Design load factors are determined according to FAR-25 rules. The limit manoeuvre load factor is calculated from Section 25.337 and the gust load factor from Section 25.341. Conditions are examined at sea level, at 20,000 feet and at the given design-cruise-altitude , assuming standard prescribed gust speeds at airspeeds equal to VC and VD. You can override these calculations and input a limit load factor directly via design-n-lim , a 'calculable' parameter that is the greater of the manoeuvre and gust load values. The ultimate load factor will be 1.5 times that.

Aircraft 'families' and derivatives of existing designs need some consideration. When, for example, mto-mass is reduced relative to some original design (say for a 'shrunk' derivative), many major structural components (and systems) often remain unchanged. To account for this, you can set the 'calculable' parameter mto-origin-mass to the MTOW of the parent aircraft, or to the MTOW of some heavier member of a family concept. Component mass calculations are then based on that instead of mto-mass . Values lower than mto-mass are excluded since that would violate stress limits. For heavier (say 'stretch') derivatives, increasing the mto-mass naturally yields higher component masses. This is normal procedure in Piano and does not involve mto-origin-mass .

Exactly how to use mto-origin-mass involves a judgement. It reflects the extremes in a vast spectrum of design possibilities: Modifications can be made to all components or to none. It is always possible to achieve reductions in structural mass, at the price of reduced commonality with the parent design. Whatever the situation, any component mass reductions due to changes in aircraft geometry (such as shortening the mid-fuse-length ) are still accounted for in the calculations.

'Stretches' tend to be more efficient than 'shrinks'. It may be argued that during the design of new aircraft 'families', a reasonable approach is to set mto-origin-mass to represent a middle member of the family. This avoids penalising the lightest members excessively. By the time the heaviest members of the family are developed, improved knowledge of the design usually makes these versions more efficient. They can be treated as point-designs at their own MTOW. Such aspects of structural design philosophy go beyond preliminary mass estimation.

Source codes: Relevant functions are find-design-limits , find-design-speeds , find-design-loadfactors , find-n-gust-limit , gust-fps , find-n-manoeuvre-limit .

04.05 Wing Structural Mass

Two major methods are available for the estimation of wing structural mass: One is the 'original' method derived from unpublished industrial sources using analytical-empirical equations. The other is the 'Torenbeek' method [data not online].

Use the parameter wing-mass-method to make a different choice for any given aircraft. The default setting is 'original'.

'Original' method

The original method gives good results over a broad range of aircraft designs, from the smallest aircraft considered by Piano up to the size of a B747-400. For the largest aircraft currently under development (600 pax+) the calibration is unproven and is suspected of underestimating the influence of extreme span values. The method is designed to be sensitive to all major geometric parameters such as sweep, thickness, span, taper and structural box size, to the load factor calculations, (as previously outlined) and to the MTOW. It does not explicitly account for the MZFW and is therefore not sensitive to the maximum payload case.

Source codes (original method): The basic function is find-box-mass-hsa . Bending moments are calculated by wing-bend-lbft and include load relief from engines and undercarriage through the function wing-bend2-lbft . The final value stored in the variable box-mass comes from the addition of 8 terms (w1...w8) accounting separately for span loading and thickness, min. gauge, taper, stiffness, internal structure, compressibility, fuel tank, and engine reinforcement. Data for a calibration line are stored in the list *wing-box-mass-calibration* .

'Torenbeek' method

Torenbeek's method is implemented in three separate versions, of which the most relevant is the 'modified' or 'tor-mod' method. This comprehensive, analytical method is based on an integration of the spanwise loads, with allowances for ribs, stiffness, minimum material, etc. Weights are calculated separately for the manoeuvre load case and the gust case, and the highest weight is then selected. A correction affecting this determination of the critical loading condition has been included in tor-mod following direct discussions with the author. The uncorrected method (as described in LR-693) is still implemented as tor-693, but this is included for reference purposes only and should not normally be used. The remaining option is called tor-mod-allev. This is similar to tor-mod but may be used instead when an active gust or manoeuvre load alleviation system is available, thereby allowing the less critical case to be chosen.

The Torenbeek method gives fairly good results for most sizes of aircraft, although the 'original' method was marginally closer to known wing weights. Nonetheless the Torenbeek method appears to be more sensitive to span effects for very large aircraft and is recommended for use with such projected (600 pax+) designs.

Note 1: Unlike the 'original' method which is only based on the MTOW case, Torenbeek's methodology is also sensitive to the MZFW case and therefore to maximum payload.

Note 2: In Torenbeek's approach, load factors are determined within the manoeuvre and gust-dependent weight equations. By the nature of the logic, a simple direct input for design-n-lim cannot meaningfully override these calculations. Piano checks the input status of this parameter to avoid any conflict.

Source codes (Torenbeek method): The main function is find-wing-mass-torenbeek . Structural box mass is calculated by find-box-mass-torenbeek , which includes annotations referencing the corresponding equations in LR-693. Structural weight itself contributes some load relief, potentially creating a need for iteration, but by using simple statistical functions like guess-structural-fraction and guess-max-zero-fuel-mass this unnecessary complication is avoided.

04.06 Winglets Mass

If winglets are used (see exist-winglets ), a simple correction is applied to the wing weight. This consists of two terms, one accounting for the winglet mass itself, and the other for the increased wing root bending moment caused by the change in spanwise load distribution. They are empirical linear functions of winglet-span/wing-halfspan only, based on limited data for the original Whitcomb-type winglets.

Source codes: See winglet-bending-moment-factor , winglets-mass .

04.07 Mass of Flaps, Slats, etc.

Flap mass is derived from modified empirical equations [data not online]. It is sensitive to (amongst other things) the flap-type , the flap proportions relative to the wing ( eta-flap and flap-chord-fraction ), and to the maximum deflection ( landing-flap-deg ). Slats, ailerons, and spoiler masses use simple empirical equations from similar sources. The term 'slats' covers all types of leading-edge high-lift devices; there are no reliable data for differentiating between these.

Source codes: The relevant functions are find-flap-mass , find-slat-mass , find-aileron-mass , and find-spoiler-mass . These are used in common by all wing mass estimation methods (see wing-mass-method ) with the single exception of the unmodified tor-693 method, which, as originally published, relies on simple estimates implemented under the function find-secondary-wing-mass-torenbeek .

04.08 Fuselage Mass

The two methods that can be used to determine fuselage mass are the 'torenbeek' and 'affdl' methods. Selection is via the parameter fuse-mass-method .

The 'torenbeek' method is the default and recommended choice. It is implemented according to Torenbeek's textbook 'Synthesis of subsonic airplane design', Appendix D, (Delft University Press), and consists of a sequence of terms accounting for the mass of the shell skin, stringers, bulkheads, supports and floor. It is sensitive to pressurisation levels (dictated by cabin-altitude and max-operating-altitude when cabin-is-pressurised ) and to design load factors.

The 'affdl' method derives [data not online] and is a slightly more detailed method with explicit allowances for cutouts due to doors and windows. To account for doors it requires inputs from the parameters pax-doors-area and cargo-doors-area . It also allows for the design-floor-loading (and the floor area, calculated according to cabin-floor-location ). Despite the added complexity, it is generally less accurate than the 'torenbeek' method, and its calibration for purely civil aircraft is uncertain, so using the 'affdl' option is not normally recommended.

Both methods are sensitive to the proportion of the fuselage length that lies aft of the wing, and therefore fuselage mass can vary during aircraft balancing procedures.

Source codes: Relevant functions are find-fuse-mass , find-fuse-mass-torenbeek , and find-fuse-mass-affdl .

04.09 Tail Mass

Three empirical methods are available for estimating the masses of the stabiliser and fin. Selection is via tail-mass-method . The default 'piano' method is calibrated against known data, accounts for all the basic geometric parameters (tail area, aspect ratio, sweep, taper, t/c) and should normally be preferred. It originates [data not online]. The alternative methods ('torenbeek' and 'nicolai') are less detailed: The simple 'torenbeek' equation (from 'Synthesis of subsonic airplane design') does not explicitly cater for the geometry except in terms of tail areas, and the 'nicolai' method (L.M. Nicolai, 'Fundamentals of Aircraft Design') is an uncalibrated example.

Source codes: See find-stab-mass , find-stab-mass-vdep , find-fin-mass , find-fin-mass-vdep .

04.10 Undercarriage Mass

Undercarriage mass is a simple empirical function of the landing mass (see max-landing-mass-ratio ), the undercarriage length (see u/c-length-below-fuse ), and the number of wheels (see main-u/c-wheels-per-a/c and nose-u/c-wheels-per-a/c ). It is based on unpublished data contributed by an industrial customer.

Source codes: A spline fit is used, see the function find-u/c-mass .

04.11 Powerplants Mass

The 'powerplant mass' is the mass of an entire propulsion unit including the dry engine, nacelle, pylon, and propeller (if any). You can input it directly through the parameter mass-per-powerplant . Otherwise it will be calculated from reference-thrust-per-engine and other parameters. During design exercises, one option is to fix the 'calculable' parameter powerplant-thrust/weight ratio. Typical values for this vary widely (between say 2.5 and 4.5) depending on the engine configuration. Note that by definition, powerplant-thrust/weight = reference-thrust-per-engine / ( mass-per-powerplant * g ). It is not the T/W ratio of the entire aircraft.

If neither the mass-per-powerplant nor the powerplant-thrust/weight are specified, the powerplants' mass is calculated as the sum of engine, nacelles and pylon, as follows:

- The dry-engine-mass-curve is used to determine the dry engine mass as a function of the reference thrust. It can hold a list of numbers representing alternately the reference-thrust-per-engine (in lbf) and a corresponding engine mass (in lb). A built-in default curve is used if no data are supplied.

- The nac-specific-mass determines the mass of the nacelles (as a mass per unit of surface area). A simple internal correlation with nacelle dimensions is used unless you supply your own value.

- The mass of the pylons is determined by pylon-mass-ratio . This is the pylon mass per unit of 'suspended' mass (i.e. dry engine + nacelle). A simple internal correlation with nacelle position relative to the wing (or fuselage) will be used, unless you supply your own value.

04.12 Fixed Equipment Mass

The mass of 'fixed equipment' items can only be estimated in a broad statistical sense. Fixed equipment consists of furnishings, surface controls, fuel systems, hydraulics, electrics, avionics, auxiliary power unit, air conditioning, and miscellaneous other systems. The accuracy of each prediction may be poor, but their sum total tends to be reasonably accurate. (For example, one aircraft may rely on hydraulics, another on electric systems for similar tasks).

Furnishings mass is a significant contribution that depends entirely on the required passenger comfort. It is controlled via furnishings-mass-per-pax . This can be as low as 15 kg/pax for simple short-haul aircraft, or higher than 85 kg/pax for long-range aircraft with extensive amenities. Adjusting the furnishings-mass-per-pax can be a convenient way of 'tuning' a design to match a specific empty weight. In principle you can also adjust the remaining contributions individually via surface-controls-mass , fuel-systems-mass , hydraulic-systems-mass-fraction , electric-systems-mass-fraction , avionics-mass , apu-mass , air-condition-mass , and misc-systems-mass-fraction , but it is probably neither very meaningful nor necessary to do so.

All calculations are based on statistical data provided by industrial sources and are mostly simple functions of the MTOW, with the exception of the APU and air conditioning masses which are functions of the number of passengers.

Source codes: The basic function is find-fixed-equipment-mass .

04.13 Crew Mass

The number-of-flight-crew defaults to 2, and the number-of-cabin-crew (a 'calculable' parameter) is normally found by assuming at least 1 cabin attendant per 30 pax. These parameters together with mass-per-crew determine the total crew mass.

04.14 Mass Buildup and Adjustments

The 'buildup' format that is used for mass accounting purposes is shown in the 'Mass' reports produced via the 'Report' menu.


You can adjust the mass of major structural components via user-factor-on-box-mass (for the wing box), user-factor-on-flap-mass , user-factor-on-fuse-mass , user-factor-on-stab-mass , user-factor-on-fin-mass , and user-factor-on-u/c-mass .

The sum of the structural mass, powerplants, fixed equipment, and the parameter manufacturers-contingency-mass (which defaults to zero) equals the Manufacturer's Empty Weight or MEW.

The MEW plus the crew mass and the parameter operational-items-mass (which also defaults to zero) yield the Operator's Empty Weight or OEW.

When modelling an existing aircraft, individual component mass predictions cannot be (and do not need to be) exact. However, the correct value of OEW is obviously important and must be assigned prior to attempting meaningful performance calculations. You can do this by adjusting the operational-items-mass alone. Alternatively, the OEW itself can be specified through the 'Set Weight, OEW' feature (see 'Plane' menu), whereupon the corresponding value of operational-items-mass will be calculated. If you tick the option marked 'Freeze this OEW', the OEW will then be held constant, irrespective of any subsequent modifications to other parameters that would alter the weight. In this case the value of operational-items-mass is allowed to 'float' as necessary (and may even become negative in some cases).

The Maximum Zero Fuel Weight (MZFW) is equal to the OEW plus the maximum payload (determined by the parameter max-payload/design-payload as described earlier).

The Maximum Landing Weight (MLW) is determined from the max-landing-mass-ratio , as a fraction of either the MTOW or the MZFW, depending on whether the input value is less than 1 or greater than 1 respectively.

At a given MTOW, OEW, and design payload, the corresponding fuel mass is a 'fall-out'. Whether or not this 'required' fuel mass can be accommodated in the 'available' volume (fuel capacity) depends on the wing geometry and the fuel-density . The capacity issue is addressed in Chapter#03section16 . If the available volume is insufficient, suitable warnings will be shown under the 'Mass' and 'Geometry' reports.

On rare occasions, the nominal payload case quoted by the manufacturer is 'fuel capacity limited'. This makes that payload inconsistent with the MTOW, and is therefore a somewhat odd choice for a design case in an all-new aircraft. However, it may happen with modified versions of older aircraft or during developmental refinements. You can choose whether to treat fuel capacity restrictions as a 'soft' or 'hard' limit through the parameter ignore-fuel-vol-violations . If this is 'true', the capacity restriction will be ignored (a warning will still be issued). If it is 'false', the fuel mass will be reduced to match the available capacity and therefore the design range may be flown at less than MTOW.

The implication sofar has been that the 'required' fuel mass is given by ( MTOW - OEW - design payload ). This ignores possible minor differences between a startup ramp mass and the actual takeoff mass. You use the parameter ramp-fuel-allowance to match any quoted ramp values. (See also Chapter#09section09 ).

Sample Mass Report
 Design Limits

 Design cruise point is Mach 0.82 at 11278.metres 

 Design dive Mach     MD       0.87
 Design cruise speed  VC       177. m/s.EAS
 Design dive speed    VD       206. m/s.EAS
 Limit    load factor          2.55
 Ultimate load factor          3.83
 Cabin pressure differential  55.58 kn/m2 (limit) 

 Mass Report      (in kg. and % of MTOW)

 MTOW    73500.
 OEW     41310.     (56.2%)
 MZFW    60500.     (82.3%)
 MLW     64500.     (87.8%)

 Mass Breakdown            kg.    % MTOW
 wing group               7815.   10.63 %
  (    6345.)
  (flaps          761.)
  (slats          342.)
  (spoilers       171.)
  (ailerons        77.)
  (winglets       119.)
 fuselage group           7923.   10.78 %
 stabiliser                837.    1.14 %
 fin                       458.    0.62 %
 undercarriage            2913.    3.96 %
 _____________________  _______   _______
 basic structure total   19946.   27.14 %

 powerplants total        6906.    9.40 %

 furnishings              4830.    6.57 %
 surface controls         1035.    1.41 %
 fuel systems              286.    0.39 %
 hydraulics                551.    0.75 %
 electrics                 883.    1.20 %
 avionics                  566.    0.77 %
 APU                       430.    0.58 %
 air conditioning          657.    0.89 %
 misc. systems            1838.    2.50 %
 _____________________  _______   _______
 fixed equipment total   11076.   15.07 %

 manufact. contingency       0.    0.00 %
 _____________________  _______   _______
 Manufact. Empty Mass    37928.   51.60 %  = MEW

 crew                      700.    0.95 %
 operational items        2682.    3.65 %
 _____________________  _______   _______
 Operators Empty Mass    41310.   56.20 %  = OEW

 design payload          13650.   18.57 %
 design fuel             18540.   25.22 %
 _____________________  _______   _______
 Maximum Takeoff Mass    73500.   100   %  = MTOW

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