Path: Airships/Mass
% Generate a distributed mass model for an axisymmetric airship.
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Form:
[body,comp] = BuildAirshipMassModel( name, h, xon, bvf );
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Inputs
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name (:) Name of airship design file.
h (1) Altitude (meters)
xon (1) x-location of origin, measured back from nose
(optional, default is to put origin at CV)
bvf (1) Ballonet volume fraction, optional (default: 1)
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Outputs
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body (.) Body mass data structure with fields:
.mass Total mass of the airship
.inertia Moment of inertia about CV
.cM Center of mass position wrt CV
comp (.) Component mass data structures with fields:
.mass Mass of the component
.inertia Inertia of the component about
the local origin
.cM Center of mass position wrt the
origin of the local frame
.r0 Position of the local frame
origin wrt the CV
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DESCRIPTION:
The airship hull is modelled as 2 axi-symmetric ellpsoids. It has 4
symmetric tailfins, and a hanging empennage that supports the payload and
2 engines / propellers.
The total mass is given as:
m = mS + mF + mP + mH + mA
where the individual mass components are
mS: structure and all systems
mF: external fabric
mP: payload
mH: Helium
mA: air in ballonets (varies with altitude)
In order to compute the CG and the moment of inertia, we approximate the
mass distribution of the airship. Several steps and assumptions are taken
to develop the model.
* The structure/system mass (mS) includes the engines, internal
structure, and tail-fins. Solar cells are ignored.
The engine mass is assumed to be 60% mS. The tail-fins are assumed to
be 10% mS. This leaves 30% mS for support structure.
* Each tail-fin is treated as a point-mass, with the CG located at the
centroid of the surface area.
* The support structure is assumed to be distributed uniformly
across the hull surface.
* The air in the ballonets occupies the bottom portion of the hull.
The volume of air (and the mass) changes with altitude. We assume two
ballonets, fore and aft, are used. Each is modeled as a
half-ellipsoid, and they are centered at the CV location of the hull,
which is also the center of buoyancy (CB). This is done so that, when
the ballonets have equal volumes, the center of mass of the air lies
directly beneath the CB, creating no moment.
* The payload is treated as a point mass, located at [xP;0;zP], which
is the center point of the hanging empennage. A separate function can
be used (BalanceAirshipPayload) to find the "xP" value that give zero
moment when the ballonets are empty. The airship should be designed
so that this value fits within the x-range of the empennage.
* The right/left engines are treated as two point-masses, located at
[xE;+/-yE;zE]. To be practical, xE and zE should lie within the area
occupied by the hanging empennage.
Given these assumptions, the model is composed of 7 point masses (4 fins,
2 engines, 1 payload), and 4 continuum masses (fabric shell, Helium, air,
structure). Each continuum mass is split into front and rear components.
This gives a total of 15 components. When the airship is above the
pressure altitude, the ballonets are empty and are thus not included,
leaving 13 components.
The "IntegrateMassProps" function is called to compute the mass, CG and
inertia of the complete airship in body-frame coordinates. The body-frame
is an orthoganal frame with x pointing through the nose, z pointing down,
and y completing the right-handed system. The origin of the body-frame
may be specified as an input. If not provided, it is placed at the CV.
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AerospaceUtils: AeroData/AtmData Airships: Mass/IntegrateMassProps Airships: Modeling/AirshipCV Airships: Modeling/GondolaGeometry Airships: Modeling/HalfEllipsoid Common: Atmosphere/StdAtm Common: CommonData/SwooshWatermark Common: General/CellToMat Common: General/MatToCell Common: General/Watermark Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PltStyle Common: Transform/IConvP Math: Linear/SkewSq
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