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COMPANY CONFIDENTIAL β DO NOT DUPLICATE OR DISTRIBUTEΒ© 2018 TRU Simulation + Training Inc. All Rights Reserved.
WATER HANDLING MODELING
SIMULATION OF SEAPLANES AND AMPHIBIOUS AIRCRAFT ROBERT LIEGL
June 11-12 THE FUTURE REALITY OF FLIGHT SIMULATION
COMPANY CONFIDENTIAL β DO NOT DUPLICATE OR DISTRIBUTEΒ© 2018 TRU Simulation + Training Inc. All Rights Reserved.
Intro
The Water Handling Model was
initially developed for, and is
Intellectual Property of
Pacific Sky Aviation Inc.
Used on two FFS Level D* simulators
β’ Viking Twin Otter Series 400
β’ Viking CL-415
*no regulatory QTG coverage available yet for the water handling
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Simulation Context
The Water Handling Model is to provide a Force Vector and a Moment Vector adding
to the Forces and Moments produced by the usual Aerodynamic, Propulsion and
Ground Handling Models
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Modeling approach vs. Relevant Literature
For an extensive coverage of the planing hull theory applicable in real watercraft design a good reference is the work of
Daniel Savitsky, but the approach in this model development addresses simulation modeling needs rather than design.
While providing good instruction on marine craft engineering, the literature reference below did not serve as a source
for modeling equations. FAA and Transport Canada documents helped gaining a perspective on seaplane pilot training.
A few useful titles, with no attempt to provide an exhaustive list could include:
1. Hydrodynamic Design of Planing Hulls, Daniel Savitsky, 1964
2. On the Subject of High-Speed Monohulls, Daniel Savitsky, 2003
3. The Dynamics of Marine Craft, Edward M. Lewandowski, 2008 (2004)
4. Sea Loads on Ships and Offshore Structures, O. M. Faltinsen, 1998 (1990)
5. Seaplane, Skiplane, and Float/Ski-Equipped Helicopter Operations Handbook: FAA-H-8083-23, 2004
6. Instructor Guide, Seaplane Rating, Transport Canada, TP 12668E, 1996
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Keep it as simple as possible, make it as complex as needed
Modeling approach, Simple vs. Complex
When developing a model from scratch, start by considering the big picture
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Modeling approach, Overview
β’ Observe the physics & describe it in equations, rather than relying on a βblack boxβ data fitting
o When analyzing test data try to understand causation rather than merely noting correlation
β’ Geometry to reasonably imitate the real float, without becoming too expensive
β’ Interaction with water geometrically quantified through 3 elements of an immersed float section
o immersed volumes
o immersed volume differentials and
o wetted surfaces
o Plus extra lumped articles (e.g. landing gear units, water scoops, other gear) treated separately
β’ Static interaction: float displaces water, water buoys float, easy to model but with a catch*
β’ Dynamic interaction: float deflects water, own wave making, water pushes against float
β’ Immersion: measured against an equivalent waterline projected in the float symmetry plane and composed of the natural water state (including sea waves) + the own wave
* How much buoyancy is left on a moving float?
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Waves on the Surface of Deep* Water
π circular frequency
π wave number
π wave length
π phase velocity
π =2π
π=π2
π
Given the gravitational acceleration, the phase velocity (or celerity)
of a wave will be proportional to sqrt of wave length; the longer the
wavelength, the faster the wave will travel.
When applied to the own wave, which borrows the speed of the
ship, this implies that the own wave wavelength will be increasing
with ship speed
(*) βdeepβ water, i.e. h > 0.5 π, at least
π =π
π=π
π=
π
2ππ
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Watercraft Own Wave
Illustration adapted from D. Savitsky [2]
π ππΏ Speed-Length Ratio
π
πΏπ€π
speed of craft on water
length of load waterline
π ππΏ =πΉππ
πΉπ =π
ππΏπ€π
πΉπ Froude number
π =2π
ππ2
π ππΏ =π
πΏπ€π
π wave length
For π[kts] and πΏπ€π[ft] π ππΏ = 1.34 at βhull speedβ
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Float Geometry, Real Hardware Components
Illustration adapted from FAA Handbook [5]
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Float Geometry, Model, Stations & Segments
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Waterline Natural State, Sampling
The water surface produced by the visual system is sampled in a number of sampling points.
With the model running at higher frequency than the visual system (e.g. 240 Hz vs. 60 Hz), βnavigationβ room is provided in front of the float. Between one visual frame and the next, the watercraft navigates in the frozen, last received frame. Then the water info is refreshed with the next visual frame and the cycle repeats.
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Waterline, Deflections
any segment [π] in front of a
station [π], if touching water,
will cause a deflection at the
station behind; the sum will
position the waterline at [π]
π=1
πβ1
πππππππ‘ππππ
Deflection magnitudes depend
on the intensity of segment-
water interaction (through
volume differentials) and the lag
of the affected station behind a
given segment
π =π π₯ππππ2
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Waterline, Own Wave
The sum of deflections caused by all βwetβ (active, touching water) segments in
front of each station will induce an overall waterline reposition from its natural
state
π=1
πβ1
πππππππ‘ππππ
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Hydrostatics, Buoyancy
An immersed segment volume [π]will float with a force
πΉπππ’ππ¦
= πΆππ’ππ¦ β π β ππππ β π
hydrostatic assumption: πΆππ’ππ¦ = 1
On a side note, malfunctions like flooded float compartment will not* reduce the immersed volume (the float is still
displacing water, albeit containing some water itself)
*hint : add water mass, i.e. treat the float compartments as βwater tanksβ (preferably emptyβ¦) in the mass properties
model; water level in βtankβ will slowly equalize the immersion level, through simulated leaking in/out
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Hydrodynamics, Reference Forces
a steady state variation of immersed volume as the water flows past the float at segment [π] can be derived as:
βπππ
βπ‘π
=βπππ π
ππππ₯ where βπ‘ =
ππ
ππ₯(not the simulation timestep), and ππ the segment length
a volume differential reference force can be written as:
πΉππππππ
π= π ππ₯
βπππ
βπ‘π
a wetted surface reference force can be producedby reference to local dynamic pressure:
πΉπππππ’ππ
π=
1
2π ππ
2 β ππ where ππ is the wetted surface area of float segment [π]
where π is water density
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Hydrodynamics, actual Forces
πΉππππππ[π] = πΆππππππ β πΉππππππ
π
πΉππππ[π] = πΆππππ β πΉππππππ
π
πΆππππππ = πΆππππππ π, πππ‘π and πΆππππ = πΆππππ(π, πππ‘π )
lookup table parameters to identify
The longitudinal force will add wetted wall skin friction and, depending on specific model needs can add float-borne landing gear, water scooping probe or other drag components
πΉππππ π += πΉπ πππ πππππ‘πππ + πΉππππ + πΉπ ππππ + β¦ with πΉπ πππ πππππ‘πππ = πΆπ πππ πππππ‘πππ β πΉπππππ’ππ
π
The lateral force can conveniently use the wetted area reference force affected by a lateral coefficient to be identified as function of local speed components and segment position
πΉπππ‘ π = πΆπππ‘ β πΉπππππ’ππ
πΰ΅―πΆπππ‘ = πΆπππ‘(ππ‘ππ2(ππ¦ , ππ₯), π
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QTG & Validation, Where to Start?
Some tests as defined for a land plane lend themselves for a quick adaptation, e.g.
1b TAKEOFF
could adapt as a minimum at least βgroundβ acceleration and normal takeoff
other takeoff tests could be discussed case by case, e.g. VMU, critical engine failure on takeoff, crosswind takeoff
1e STOPPING
could show reverse thrust and free (idle) deceleration tests
1a TAXI
this section would need to be larger for on water taxi, addressing longitudinal aspects irrelevant for a land plane
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QTG, 1a TAXI, Longitudinal Aspects
Land plane tests cover mainly directional aspects, turn radius (1a1), yaw rate vs. steering control (1a2)
For on water taxi, need to include a section explicitly testing all relevant longitudinal performance aspects
3 distinct forward moving modes to validate:
β’ Displacement, static or very low speed, below βhull speedβ
β’ Plowing, (βsemi-displacementβ, βsemi-planingβ)
β’ (On) Step, planing
Relevant test inputs
β’ power setting
β’ elevator (pitch control), at relevant airspeeds
Output parameters to watch closely, likely under tolerance constraints:
β’ on water speed (βgroundβ speed) & air speed (if high enough to be relevant / reliable*)
β’ pitch angle
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QTG, 1a TAXI, Lateral-Directional Aspects
For planes with a low speed water rudder (small single engines more likely to have one), 1a1, 1a2 tests could find
quick equivalents, with the water rudder replacing nose wheel input.
For two engine sea planes, differential thrust allows for turns to be executed while moving forward, backward or
virtually on the spot, if thrust is controlled closely around the zero-thrust level; 1a2 equivalent tests could be
used to validate yaw rate response to power input. Yaw rate likely a parameter to bear a tolerance, as it does in
the on-runway landplane taxi tests
In low speed taxi, wind could be a validation problem
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Sailing, Wind, Air Data, Model Integration
Sea planes never really sit still, unless a low tide left you stranded on a beach
A few points to consider
β’ Flight test air data is known to break down at low speeds, with
air speed, flow angles and wind reconstruction not reliable;
find ways to circumvent this technology limitation
β’ Water handling model cannot be validated in isolation, but
integrated with the aero model under wind, and even ground
handling model (in scenarios including ramping, beaching,
docking); this begets enhancements in all models; to name a
few
o 360Β° sideslip aerodynamic envelope and sailing aerodynamic
effects, including response to control surface inputs under wind
o Ground handling model extensions to treat immersed ground
(beach, ramp) and vertical walls (docks)Illustration adapted from FAA Handbook [5]
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Thank you!
National Research Council Canada
Kohlman Systems Research
Pacific Sky Aviation
TRU Simulation + Training
Viking Air
Ansett Aviation Training
Acknowledgments owed to all testing crews, both in
real aircraft flight testing and in simulator testing.