INTERNATIONAL
SOCIETY OF ALLIED
WEIGHTS ENGINEERS, INC.
FUNCTIONAL
RECOMMENDED
PRACTICE
NUMBER
Serving the Aerospace - Shipbuilding - Land Vehicle
and Allied Industries
Date Issued
Executive Director
P.O. Box 60024, Terminal Annex
Los Angeles, CA 90060
Not yet Baselined
MASS PROPERTIES
ESTIMATION
Revision Letter
Prepared by
Government - Industry Workshop
Society of Allied Weight Engineers, Inc.
All SAWE technical reports, including standards applied and practices recommended, are advisory only. Their use by
anyone engaged in industry or trade is entirely voluntary. There is no agreement to adhere to any SAWE standard or
recommended practice, and no commitment to conform to or be guided by any technical report. In formulating and
approving technical reports, the SAWE will not investigate or consider patents that apply to the subject matter.
Prospective users of the report are responsible for protecting themselves against liability for infringement of patents.
Notwithstanding the above, if this recommended practice is incorporated into a contract, it shall be binding to the extent
specified in the contract.
SAWE RECOMMENDED PRACTICE
___________________
___________________
PAGE AND REVISION LOG
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Latest
Revision
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Latest
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Latest
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Estimating System Mass Properties ---------------------------------------------------------------- 4
1. Scope ------------------------------------------------------------------------------------------ 4
2. Purpose ---------------------------------------------------------------------------------------- 4
3. Reference Documents ----------------------------------------------------------------------- 4
3.1.
General ---------------------------------------------------------------------------------- 4
3.2.
Land ------------------------------------------------------------------------------------- 4
3.3.
Sea --------------------------------------------------------------------------------------- 4
3.4.
Air and Space -------------------------------------------------------------------------- 5
3.5.
Additional Reference Publications -------------------------------------------------- 5
4. Definitions, Abbreviations, Acronyms --------------------------------------------------- 5
5. General Requirements----------------------------------------------------------------------- 5
5.1.
Mass Properties to be Estimated -------------------------------------------------------- 5
5.2.
Implications of the Product Life Cycle ------------------------------------------------ 6
5.3.
Utilization of Mass Properties Breakdown Structures ------------------------------ 7
5.4.
Other Considerations --------------------------------------------------------------------- 8
6. Detailed Requirements -------------------------------------------------------------------- 10
6.1.
Basic Mass Estimation Equation ----------------------------------------------------- 11
6.2.
Process Flow ---------------------------------------------------------------------------- 11
6.3.
Estimation Methods -------------------------------------------------------------------- 12
7. Summarization ----------------------------------------------------------------------------- 14
8. ANNEX A – Mass Estimating Tools Library ----------------------------------------- 14
(purchase/obtain from SAWE)----------------------------------------------------------------- 14
(COTS) -------------------------------------------------------------------------------------------- 14
Estimating System Mass Properties
1. Scope
This document defines recommended practices regarding estimation of transportation
system mass properties. All modes of transportation such as by land, sea, air, and exoatmospheric are addressed in a consistent manner. Mass properties discipline analysis
procedures are appropriately indicated from within this document. Industry specific
recommended practices and procedures are also indicated from within this document.
2. Purpose
The purpose of this document is to present general mass properties estimation concepts
and techniques for transportation systems at a hierarchy level where all modes of
transportation are incorporated. The functional processes which should occur to estimate
transportation system mass properties throughout a product life cycle are described. The
document also refers to lower level hierarchy analysis standards and publications for each
discipline. By following the standards of this document and references to discipline and
industry specific lower level documents mass properties engineers can communicate
across all transportation regimes and facilitate development of a high quality final
product.
3. Reference Documents
Standards and Recommended Practices: This recommended practice shall be used in
conjunction with the following publications. When the following specifications are
superseded by an approved revision, the revision shall apply.
3.1.
General
1. SAWE Weight Engineers Handbook
3.2.
Land
2. SAWE RP No. X: Mass Properties Control System for Wheeled and Tracked
Vehicles, May 13, 1986.
3.3.
Sea
3. SAWE RP No. 12 Issue C, Weight Control Technical Requirements for Surface
Ships, May 22 , 2002.
4. SAWE RP No. 13, Standard Coordinate System for Reporting Mass Properties for
Surface Ships and Submarines, June 5, 1996.
5. SAWE RP No. 14, Weight Estimating and Margin Manual for Marine Vehicles, May
22, 2001.
6. SAWE RP No. 15, Vendor Weight Control for the Marine Industry, May 18 2004.
3.4.
Air and Space
7. SAWE RP No. 6, Standard Coordinate Systems for Reporting the Mass Properties of
Flight Vehicles, Sept. 1, 1999.
8. SAWE RP No. 7, Mass Properties Management and Control For Military Aircraft,
May 18 2004.
9. SAWE RP No. 8, Weight and Balance Data Reporting Forms for Aircraft (including
Rotorcraft), June 1 1997.
10. SAWE RP No. 11, Mass Properties Control for Space Vehicles, June 3 2000.
3.5.
Additional Reference Publications
11. A. Schuster and R. Aasen: Marine System Weight Estimating Methods, Class Notes
SAWE training course 24th September 2005, Valencia CA.
12. SAE-J1100 Jul 79 - Motor Vehicle Dimensions, SAE Recommended Practice
13. SAE-J874 Apr 80 - Center of Gravity Test Code
14. L.L. Yang, W.E. Kruse and R.T. Sugiyama; Mass Properties Control Standard for
Space Vehicles, Aerospace Corporation, Report No. TOR-2005(8583)-3970, 20-July2005.
15. American Institute of Aeronautics and Astronautics: Recommended Practice for Mass
Properties Control for Satellites, Missiles, and Launch Vehicles, AIAA/ANSI R020A-1999.
16. International Council on Systems Engineering (INCOSE): Systems Engineering
Handbook, A “What To” Guide For All Se Practitioners, INCOSE-TP-2003-016-02,
Version 2a, 1 June 2004.
4. Definitions, Abbreviations, Acronyms
General terminology for Mass Properties Estimation is provided in SAWE FRP No. x
“Top level document name”, additional terms pertinent to mass estimation are:
Term
yyyyyyyy
Definition
ssssssssssssssssssssssssssssssssssssssss
5. General Requirements
5.1. Mass Properties to be Estimated
Mass properties for an entity are fundamentally characterized by the three terms, Mass,
Center of Gravity, and Inertia.
Mass – Basic quantity, units of mass (slug, kg)
Center of Gravity - a position vector (x,y,z) relative to a reference coordinate
system, units of length (in, ft, m)
Inertia – specifically the symmetric inertia tensor defined by 6 terms:
Three diagonal tensor terms representing the entity’s Moment of Inertia
MOI, derived units of (mass*length^2):
Ixx – Moment of Inertia about the reference X axis
Iyy – Moment of Inertia about the reference Y axis
Izz – Moment of Inertia about the reference Z axis
Three off diagonal tensor terms representing the entity’s Product of Inertia
POI (unbalance in a plane), derived units of (mass*length^2):
Ixz – Product of Inertia in the XZ plane
Ixy – Product of Inertia in the XY plane
Izy – Product of Inertia in the ZY plane
More complete definitions of these basic mass properties terms and the inter-relationships
of inertia terms to entity principal axes can be found in references [SAWE Handbook],
and [RP 6]. It is most typical to desire estimation for entity mass and nearly as often,
center of gravity. Estimation of Inertial terms is less common in early phases of product
design but becomes necessary as stability and dynamic motion performance
characteristics are required. Distribution of single entity and multiple entity masses across
a larger element (vehicle) become important when vehicle loading and strength analyses
are being performed. Often within a particular transportation industry, derived mass
properties terms are standard and of particular importance to that industry. For example,
in the building of large marine vehicles the term KG is routinely estimated and tracked
throughout the ships product lifecycle. KG represents the product of the ships mass times
the vertical distance of that masses center of gravity to the bottom, keel, of the ship. In
aerospace design the distance from an aircrafts center of lift to its center of gravity (Xw
[Nicolai]) may be tracked as another of these estimated mass properties derived from
design configuration data in conjunction with the primary mass property values. It is
useful, for a complex system design to track design pertinent basic and derived mass
property information as Technical Performance Measures (TPMs). Often these TPMs
will be evaluated, tracked and controlled through use of a program’s formal Continuous
Risk Management Process []. Table of sample industry specific Derived Mass TPM’s?
5.2. Implications of the Product Life Cycle
Mass properties estimation can be important to all phases of a product’s life cycle.
Organizations define different types of product life cycle phases which encompass a
product’s status from Needs Identification through Operational Life to Disposal. We will
refer in this document to four product life cycle phases based upon those in the
International Council of Systems Engineers Handbook [INCOSE HDBK]. The four
phases of interest to us are: Concept Exploration, Product Definition, Engineering
Manufacturing and Development, and Production/Deployment/Operation. SAWE Paper
#3300[] is also a general reference to the Mass Properties product deliverables which
support Mass Properties Engineering for general product development. Further details on
Mass Properties Control are available in SAWE Functional Recommended Practice
(FRP) XXX.
Mass property estimation is required early on in product development, ie: during Concept
Exploration and Product Definition phases, to assist System Engineering Architecture
trade studies and to assure appropriate values are used to assess vehicle performance and
develop vehicle design loads. After a typical Contract Authority to Proceed date for
vehicle fabrication (ATP) the Mass Properties Control process becomes very rigorous
and more formally documented. Program Mass Properties are typically stated to be at one
of three defined levels of fidelity.
Estimated – Mass Determined by historical data, and theoretical analysis
Calculated – Mass calculated from engineering data (CAD, Drawings) of
designed elements.
Actual
– Mass determined by obtaining Metrological (measured) data of a
component.
This document is concerned only with methods used to create Estimated Mass Properties
Data. Note that estimated mass properties may still be required during the Manufacturing
and Development phase of a product where for example masses of all elements are not
yet at the calculated state. Mass estimations may similarly be required during the
Operational use of a product, for example to determine acceptable values for uncertain
loading like variations in passenger and payload weights and positions.
5.3. Utilization of Mass Properties Breakdown Structures
Transportation vehicles are complex systems that are comprised of components from
multiple disciplines which must function together in the single final product. To track
mass of the single vehicle requires that vehicle mass be broken down into sub-categories
based typically upon the masses functional requirement. Systems Engineers and Project
Managers often refer to the Work Breakdown Structure (WBS) to track product
development. Mass properties engineers use this breakdown or those of a more
Functional basis, Functional Breakdown Structure (FBS) to track all masses which make
up the whole vehicle. Mass estimation for the vehicle becomes an integration of mass
estimation for each element of the vehicle’s FBS. Some standard breakdown structures
for various transportation vehicles are given below: (place in appendix, or ref to a website
?)
Vehicle Breakdown Structures
Marine Systems
Military Aircraft
EWBS[]
WBS[]
MarAd[]
Commercial Aircraft
Missles and Spacecraft
Automotive
Military Land Vehicles
[]
FBS[]
[]
[]
As mass properties encompass all systems which make up a vehicle the mass properties
engineer must be cognizant of the status of work from each of the systems groups which
comprise the total vehicle. This need typically places the mass properties engineering
function on a team which is cognizant of total vehicle design/development status such as
a Systems Engineering and Integration group. Mass properties are often captured as
Technical Performance Measures (TPM’s) [][][]. In a large project where mass is critical,
as is often the case in high performance or energy conscious design, mass properties as a
TPM are formally tracked in the Systems Engineering and Integrations Risk Management
Process. [Schuster weight as a TPM].
5.4. Other Considerations
A good mass properties engineer
A good mass properties engineer is essential to obtain good mass properties estimations.
General qualifications include:





Knowledge of the estimation system he is using
Good knowledge of the historical database he is using, and of similar product line
data.
Knowledge in all discipline areas of the project
Analytical capability
Understanding of results feasibility, what ranges to expect in the results
Historical data
To be able to produce a successful estimation, historical mass property data must exist in
a structured form according to a breakdown structure. The historical data must be
reliable, quality assured and have a maturity status of ”actual”. Furthermore, parameter
information according to the methods to be used must exists for the historical projects, as
well as other essential project parameters, data and drawings.
Methods and tools for parametric estimation
Methods and tools which utilize historical mass properties data are very enabling towards
obtaining acceptable results. Estimation must be possible to execute according to the
mass property WBS of the historical data. Some characteristics of quality estimation
tools in recent use are:
 Interactive interface to the historical data
 Capability to filter information out of the historical data
 Quantification of uncertainty
 Report capabilities

Capability of extending the database by adding newly defined mass property
information and additional mass property estimating relationships
Use of result
When structuring the work of estimation one should consider who will use, and for what
purpose the results will be used. Level of effort in terms of estimation process complexity
must be balanced against schedule and design status constraints.
Consideration of the level of estimation detail
The level of estimation detail is determined by report requirement, data available for
estimation and properties estimated. I.e.: While the mass may be obtained at a relatively
low level detail, the need for accurate center of gravity may call for a more detailed
estimation.
Accepted uncertainty
One should define what level of uncertainty is accepted for the estimation.
Verification of results


Mass distribution curves: Do they harmonize with extension and center of
gravity?
Visualization of center of gravity of mass items in a reference
Reports and documentation
What documentation is needed. How results should be reported. Coordinate system
documentation.
50/50 estimate
Mass Properties estimates should be based on the 50/50 principle. The 50/50 principle
requires that there be an equal chance of the real value to be lower as higher than the
estimated value. Uncertainty analysis may be formally implemented to understand the
impact of deviation from 50/50 estimates. Mass Properties Control processes account for
appropriate margins, reserves, and growth factors. Early optimism or pessimism in mass
properties estimation is avoided by working from the 50/50 principle. The Mass
Properties Engineer’s familiarity with the particular system in development, his control
and documentation processes ensure that the 50/50 estimate is disseminated and
understood by other members of the product development/deployment and operations
teams.
Mass budget
The estimation result should be defined as a mass budget. A mass budget should be
frozen and not changed. A copy of the mass budget may serve as a starting point for
mass tracking, but the original mass estimation should not be changed and serve as the
values to compare to. The time of freezing is normally when a contract is entered that
refers to mass properties. [refer more to mp control plan here]
Handling margins
It is very important to distinguish between different margins. Margins added for
uncertainty in the estimate as a “security factor” or other margin containing undefined
weights violates the 50/50 principle and should not be introduced until a complete 50/50
estimate is finished. At that time additional mass may be included with associated
documentation as to its purpose. Each transportation discipline utilizes specific
nomenclature to define various portions which make up a full component mass estimate.
(place table here?) [refer to mp control plan here][uncertainty/risk analysis]
The mass estimations prescribed in section 6 are used to arrive at typically “Basic Mass”
values. Basic Mass estimates should be adjusted with appropriate margin and
contingency allowances to represent the mass property required for program purposes.
6. Detailed Requirements
Mass Estimation for the different transportation disciplines involves similar data, and
data processing which will be generalized in this section. References [SAWE RP 14],
[Marine System Mass Est Class] and [SAWE Aircraft Weight Engineering] were
instrumental in the development of this Recommended Practice. Those interested in more
detailed extensions to the techniques used for Mass Estimation should also become
familiar with the Society of Allied Weight Engineers collection of Technical Papers,
particularly those of the following Highlighted listed categories.
SAWE Technical Paper – Categories
12.0 Weight Engineering Computer Applications
13.0 Weight Engineering Marine
14.0 Weight Engineering Missile Design
15.0 Weight Engineering Missile Estimation
23.0 Weight Engineering Structural Estimation
24.0 Weight Engineering System Design
25.0 Weight Engineering System Estimation
26.0 Weight Growth
5.0 Inertia Calculations
16.0 Weight Engineering Organization
27.0 Weight Reduction Materials
6.0 Inertia Measurement
17.0 Weight Engineering Procedures
18.0 Weight Engineering –
Spacecraft Design
19.0 Weight Engineering Spacecraft Estimation
20.0 Weight Engineering –
Specific Deisgn
21.0 Weight Engineering –
Statistical Studies
22.0 Weight Engineering –
Structural Design
28.0 Weight Reduction Processes
29.0 Weight Value of a
Pound
30.0 Miscellaneous
1.0 Aircraft Loading-General
2.0 Aircraft Loading-Payload
3.0 Center of Gravity
4.0 Electrical Transducers
7.0 Section Properties
8.0 Weighing
9.0 Weighing Equipment
10.0 Weight Engineering - Aircraft
Design
11.0 Weight Engineering Aircraft Estimation
31.0 Weight Engineering Surface Transportation
6.1. Basic Mass Estimation Equation
One may think of mass estimating as determining a number of system unit weights
multiplied by the no. of corresponding units which in summation then comprises the total
system. Without accounting for uncertainty of a known or unknown nature the basic mass
estimation technique is:
System Mass = ∑(No. of units * unit mass)
Hidden within this simple representation are the subtleties of defining a unit, and
determining the appropriate estimation and often design parameterization of that units
mass quantity. As an example, units can be specific subsystems, elements, parts etc. such
as avionics, propulsion, piping as fine grained as is permitted by program schedule
requirements and the mass properties database of information. This type of unit is
typically noted in the systems FBS. Units may also be geometrically based such as areal
unit masses (mass per unit surface area). Areal mass is typically used to represent skin
type structural weights or weights of systems spread across large surface areas. The term
areal is utilized in the composites industry to express the mass of a lamina per its unit
area. The shipping industry uses the term Deck Area Fraction to represent similar
quantities. Certain system masses may be better represented based upon a linear measure,
mass per unit length or volumetric measure, mass per unit volume. Another unit method
is obtained by defining the mass per unit cross-sectional area at a cross-section station in
a vehicle, and then estimating the systems mass by integrating this mass per unit crosssectional area along the full length of the system. This technique is useful for conceptual
work with fuselage and hull type structures in the marine and aeronautics industries. All
of the unit weight techniques benefit from having a good historical database covering the
unit values and pertinent design characteristics of the system they are derived from.
6.2. Process Flow
Mass estimations may be obtained in a Top-Down or Bottoms-Up fashion. This refers to
basing estimates primarily from the top of the FBS and working down as much as
necessary, or from determining system mass by integrating up from the bottom of the
FBS as is finally available in a finished product. In a Top-Down mass estimation
approach the starting unit weight may be that of the entire system in question and there
need only be one. That estimated mass is then allocated down through various elements
in the systems Functional Breakdown Structure for tracking at the subsystem levels. This
technique is particularly useful when a smaller amount of modification is being made to
create a new system based upon an existing operational one. An historical data approach
including mass allocation knowledge at the various FBS levels is necessary to accurately
employ the top down methodology. Bottoms-Up system mass estimation technique starts
with more information about each subsystem at much lower levels in the FBS, the
various unit weights times their employed number of units is factored and summed up
through the breakdown structure to arrive increasingly at component, part, sub-assembly,
assembly, and finally total system mass properties. These two methods can be mixed as
knowledge about certain systems permits. For example a completely new system may
employ a major subsystem which is already at the operational (actual mass) state of
maturity. It would certainly make no sense to use any type of parametric mass
estimations for the known subsystem. The Top-Down and Bottoms-Up process flows are
actually functions which occur in the natural systems engineering process. In Systems
Engineering program goals are defined in terms of requirements, requirements are broken
down into functional needs which are allocated to various system elements. The product
is thus “broken down” from the top to its smallest pieces. Re-Integration from this now
“bottoms –up” starting point occurs and in the end a fully integrated finished product is
created. Mass-Properties are defined and documented all along the path of this
breakdown and re-integration process [Ref: NASA SP6105 Vee Chart].
6.3. Estimation Methods
6.3.1. Baseline
If the system being estimated differs in discrete areas from the definition of an existing
system the new systems mass estimations can be initiated from a Baseline comprised of
existing system data. Areas of difference can then be addressed by techniques which will
be described next. Note, here again the importance of having good historical information
broken out in a manner which supports the process of integrating derived masses into a
new system mass definition. Product databases, spreadsheets, CAD information and
general information now characterized in Product Data Management systems will assist
the mass properties engineer in arriving at credible weights for derived systems.
ref: (adjustment of a/c hdbk ch 11)(baseline rp14) (Mark Beyers Morphing Techniques?)
6.3.2. Mass Fractions
Historical data can also be processed to provide system Mass Fractions. A Mass Fraction
expresses the sub-systems mass in question as a percentage of another sub-system or of
the overall system mass. Mass fractions can be used in most lifecycle phases of product
development. Conceptually mass fractions may characterize items such as payload,
structure, life-support and other items as percentages of system gross, system dry, or
other subsystem masses. As the design progresses mass fractions may be brought online
for initial estimates of lower level FBS elements. Insulation as a fraction of surface skin
weight, or hydraulic component non-optimum items as a function of the hydraulic
systems total mass are possible applications at this design stage. Sample Wf tables for
various projects??
6.3.3. Ratiocination
Expression of a subsystem mass as proportional to the scaled value of a parent mass is
ratiocination. The derived mass equals the parent mass multiplied by a scale factor, or
factors, equivalent to some new system parameter divided by the value of that same
parameter for the parent system. A simple example might be expression of electrical
cable mass as equivalent to the parent systems electrical cable mass factored by the ratio
of the new systems cable running length to the cable running length of the parent system.
As an example of a technique which combines mass estimation techniques consider the
case where an areal weight, say aircraft fuselage areal mass is expressed as a
ratiocination. The new systems fuselage areal mass may be set by factoring the parent
systems fuselage areal mass by fuselage fineness ratio. New system fuselage mass is then
simply the now known fuselage areal mass times the new systems fuselage area. As
raciocination factors become more complex, typically by use of multiple factors each
controlled by a power law exponent we are at a point where regression analysis can be
utilized to help define the ratiocinations.
6.3.4. Historical Regression
A good historical database is of paramount importance in being able to supply the
information required to perform subsystem mass regression curve fits. Regressions may
be based upon vehicle design information such as structural loading, power requirements,
man-days of life support, provision requirements and innumerable other items as well as
the other system masses as we have commented on. This is why good mass properties
information includes these design parameters and vehicle arrangement definitions as well
as just FBS mass properties statements. (note: words about keeping track of what you are
regressing on, and is it consistent with the design variable you are modifying. Keeping
track also of the configuration aspects also to avoid utilization of inappropriate data
points in the regression, ex: lox fwd configuration used to predict mass of lox aft launch
vehicle concept)
6.3.5. Synthesis Equations
When a set of equations for mass properties estimation can be defined such that all
desired system mass properties are parameterized, the equations can be incorporated into
a parametric vehicle design process. Synthesis programs are computer programs which
include system mass properties equations in the iterative process of sizing a vehicle to
meet mission performance requirements in an overall optimal manner. Typically as
vehicle size grows, vehicle capability increases. However as vehicle size grows, fuel
consumption grows, structural load intensities grow and other subsystems are
increasingly taxed as well. This increase in overall vehicle mass as a function of a unit
mass increase is termed the vehicles growth factor. Growth factor may be considered
constant for small deviations about a vehicle baseline mass, but in more general terms the
growth factor itself, a measure of system mass sensitivity, is a function of vehicle size.
Figure x shows how different systems unit of vehicle payload capability requires a certain
mass increase in vehicle…………
Figure(s)
Companies utilize vehicle synthesis programs
synthesis programs – bottoms up, physics based
Implications of formal Modeling &Simulation, and Simulation Based Acquisition based
program management
Quasi-analytical vs Analytical (wt eng A/C ref)
7. Summarization
8. ANNEX A – Mass Estimating Tools Library
(purchase/obtain from SAWE)
0.2 John Nakai’s java classes
1.2 xl spreadsheets, Bob Zimmerman’s, …..
2.2 …
(COTS)
3.2 ShipWeight
4.2 DBMASS
5.2 Solicit other SAWE/Industry vendors……