water handling modeling

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WATER HANDLING MODELING

SIMULATION OF SEAPLANES AND AMPHIBIOUS AIRCRAFT ROBERT LIEGL

June 11-12 THE FUTURE REALITY OF FLIGHT SIMULATION


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

• Viking Twin Otter Series 400

• Viking CL-415

*no regulatory QTG coverage available yet for the water handling


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


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


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


Modeling approach, Overview

• Observe the physics & describe it in equations, rather than relying on a “black box” data fitting

o When analyzing test data try to understand causation rather than merely noting correlation

• Geometry to reasonably imitate the real float, without becoming too expensive

• 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

• Static interaction: float displaces water, water buoys float, easy to model but with a catch*

• Dynamic interaction: float deflects water, own wave making, water pushes against float

• 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?


Waves on the Surface of Deep* Water

𝜔 circular frequency

𝑘 wave number

𝜆 wave length

𝑐 phase velocity

𝑘 =2𝜋

𝜆=𝜔2

𝑔

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

(*) “deep” water, i.e. h > 0.5 𝜆, at least

𝑐 =𝜆

𝑇=𝜔

𝑘=

𝑔

2𝜋𝜆


Watercraft Own Wave

Illustration adapted from D. Savitsky [2]

𝑅𝑆𝐿 Speed-Length Ratio

𝑉

𝐿𝑤𝑙

speed of craft on water

length of load waterline

𝑅𝑆𝐿 =𝐹𝑁𝑔

𝐹𝑁 =𝑉

𝑔𝐿𝑤𝑙

𝐹𝑁 Froude number

𝜆 =2𝜋

𝑔𝑐2

𝑅𝑆𝐿 =𝑉

𝐿𝑤𝑙

𝜆 wave length

For 𝑉[kts] and 𝐿𝑤𝑙[ft] 𝑅𝑆𝐿 = 1.34 at “hull speed”


Float Geometry, Real Hardware Components

Illustration adapted from FAA Handbook [5]


Float Geometry, Model, Stations & Segments


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), “navigation” 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.


Waterline, Deflections

any segment [𝑖] in front of a

station [𝑘], if touching water,

will cause a deflection at the

station behind; the sum will

position the waterline at [𝑘]

𝑖=1

𝑘−1

𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠

Deflection magnitudes depend

on the intensity of segment-

water interaction (through

volume differentials) and the lag

of the affected station behind a

given segment

𝜑 =𝑔 𝑥𝑙𝑎𝑔𝑉2


Waterline, Own Wave

The sum of deflections caused by all “wet” (active, touching water) segments in

front of each station will induce an overall waterline reposition from its natural

state

𝑖=1

𝑘−1

𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠


Hydrostatics, Buoyancy

An immersed segment volume [𝑖]will float with a force

𝐹𝑖𝑏𝑢𝑜𝑦

= 𝐶𝑏𝑢𝑜𝑦 ∙ 𝜌 ∙ 𝑉𝑜𝑙𝑖 ∙ 𝑔

hydrostatic assumption: 𝐶𝑏𝑢𝑜𝑦 = 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 “water tanks” (preferably empty…) in the mass properties

model; water level in “tank” will slowly equalize the immersion level, through simulated leaking in/out


Hydrodynamics, Reference Forces

a steady state variation of immersed volume as the water flows past the float at segment [𝑖] can be derived as:

∆𝑉𝑜𝑙

∆𝑡𝑖

=∆𝑉𝑜𝑙 𝑖

𝑙𝑖𝑉𝑥 where ∆𝑡 =

𝑙𝑖

𝑉𝑥(not the simulation timestep), and 𝑙𝑖 the segment length

a volume differential reference force can be written as:

𝐹𝑟𝑒𝑓𝑉𝑜𝑙

𝑖= 𝜌 𝑉𝑥

∆𝑉𝑜𝑙

∆𝑡𝑖

a wetted surface reference force can be producedby reference to local dynamic pressure:

𝐹𝑟𝑒𝑓𝑆𝑢𝑟𝑓

𝑖=

1

2𝜌 𝑉𝑖

2 ∙ 𝑆𝑖 where 𝑆𝑖 is the wetted surface area of float segment [𝑖]

where 𝜌 is water density


Hydrodynamics, actual Forces

𝐹𝑛𝑜𝑟𝑚𝑎𝑙[𝑖] = 𝐶𝑛𝑜𝑟𝑚𝑎𝑙 ∙ 𝐹𝑟𝑒𝑓𝑉𝑜𝑙

𝑖

𝐹𝑙𝑜𝑛𝑔[𝑖] = 𝐶𝑙𝑜𝑛𝑔 ∙ 𝐹𝑟𝑒𝑓𝑉𝑜𝑙

𝑖

𝐶𝑛𝑜𝑟𝑚𝑎𝑙 = 𝐶𝑛𝑜𝑟𝑚𝑎𝑙 𝑖, 𝑉𝑘𝑡𝑠 and 𝐶𝑙𝑜𝑛𝑔 = 𝐶𝑙𝑜𝑛𝑔(𝑖, 𝑉𝑘𝑡𝑠)

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

𝐹𝑙𝑜𝑛𝑔 𝑖 += 𝐹𝑠𝑘𝑖𝑛 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 + 𝐹𝑔𝑒𝑎𝑟 + 𝐹𝑠𝑐𝑜𝑜𝑝 + … with 𝐹𝑠𝑘𝑖𝑛 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝐶𝑠𝑘𝑖𝑛 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 ∙ 𝐹𝑟𝑒𝑓𝑆𝑢𝑟𝑓

𝑖

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

𝐹𝑙𝑎𝑡 𝑖 = 𝐶𝑙𝑎𝑡 ∙ 𝐹𝑟𝑒𝑓𝑆𝑢𝑟𝑓

𝑖൯𝐶𝑙𝑎𝑡 = 𝐶𝑙𝑎𝑡(𝑎𝑡𝑎𝑛2(𝑉𝑦 , 𝑉𝑥), 𝑖


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 “ground” 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


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:

• Displacement, static or very low speed, below “hull speed”

• Plowing, (“semi-displacement”, “semi-planing”)

• (On) Step, planing

Relevant test inputs

• power setting

• elevator (pitch control), at relevant airspeeds

Output parameters to watch closely, likely under tolerance constraints:

• on water speed (“ground” speed) & air speed (if high enough to be relevant / reliable*)

• pitch angle


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


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

• 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

• 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 360° 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]


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.

water handling modeling

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