06.0_Batman_Math
Team <skype>
Qiuyang Zhou <qiuyangskype>
Etienne Gernez <el_tieno>
Gonzalo Tampier <gonzalotampier>
Julia Cerrud <amorphica>
Sebastian Neitsch <kleinneitsch>
Josh Updyke <josh.updyke>
The mathematical model consists of mathematical equations obtained by studying the physical phenomena around Protei.
It is the virtual equivalent of the mechanical model.
The simulation consist in solving these equations using computer programs.
To simulate an articulated sailing vessel pulling an articulated tail with changing mass, exposed to the influence of wind, currents and waves, manoeuvring in an oil spill.
We will split the problem in 3 sub parts, and aim at 3 sub goals for each part.
May 1st 2011 to June 1st 2011: preparation for Protei prototyping
June 1st to September 1st: Protei v6 prototyping, combining experiment with the mechanical and the mathematical model
September 2011 to september 2016: deep research on the flow around articulated hulls, inflatable membranes,...within the fields of fluid-structure interaction and bio-mimicry.
The physical forces acting on the sails and the hull can be explicited, based on the classical description of a yacht, available in Larsson or "real world physics problem".
Aerodynamic side force (ASF) and Driving force (ADF) are directly depending on the Lift and Drag forces of the sail. The direction and intensity of the Lift and Drag depend on the angle of the boat to the wind (Apparent Wind Angle AWA), the Speed of the boat with respect to the wind (Apparent Wind Speed AWS) and the performance of the sails. Such wind versus sail performance plots are called Sail Polar Plots.
The Hydrodynamic Side Force (HDS) and the upright Resistance (R) depend on the hull shape and its appendages (rudder, keel, fins,...): every object that is under the water, in the way of the ship.
The rudder, keel and fins are modeled exactly like a sail or a wing, i.e like a lifting object, with a Lift and Drag, which direction and intensity depend on their orientation to the water flow and the velocity of this inflow. So the HDS depend on the appendages Lift and Drag.
The upright resistance R has basically two components: viscous resistance (Rv) and wave resistance (Rw). Rv is due to the friction of water on the outer part of the hull in contact with the water: Rv depends on the wet surface of the hull. Rw is due to the volume of water put in movement by the ship when moving forward. At low speeds, the Rv is the most important. The fastest the boat, the more Rw kicks in. In our case, Protei should sail quite slowly, so Rv should be predominant.
PK---> Can we put values (quantify) at what ship speeds for a given vessel size and shape Rw begins to dominate Rv?
Yes, we can try, looking at the Froude number and the Reynolds number.
The Froude (Fn) number depends on the boat length, speed and gravity. It relates to the wave resistance Rw.
The Reynolds (Rn) number depends on the boat length, speed, and fluid viscosity. It relates to Rv.
Both are non dimensional coefficients, so that all kind of ship hull/sail/wing resistances/drag can be compared for different speed in different fluids (air, fresh water, sea water).
Once given the value for Fn and Rn, you can have an idea of how much Rw and Rv contribute to the overall resistance.
The weight of the ship pulls the ship down. On the other hand, the volume of water it displaces pushes it up: that´s the buoyancy force.
The ship is trying to reach an equilibrium between the aerodynamic forces (sails) and hydrodynamic forces, as well as weight and bouyancy. In trying to find this equilibrium, the ship can:
-
heel/roll: rotate around its longitudinal axis
-
pitch: rotate around its transverse axis
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yaw: rotate around its vertical axis (around the mast for example)
- 3 additional translating movements: heave, sway, surge respectively along the longitudinal, transverse and vertical axes
By projecting the all forces acting on the ship we get can get the equations governing the movement of the ship in all the 6 directions.
A. the upright resistance:
we can estimate the friction part Rv from the Protei wet surface, using the ITTC 1978 formula. ITCC means International Towing Tank Conference: all the ship designers using model testing in a towing tank have agreed on a formula enabling to calculate the resistance of a ship based on the resistance of the same ship at small scale. A flat plate with the same area as the ship hull wet surface is towed in a tank and its resistance measured. The resistance of the ship is derived from the resistance measurement and a "form" factor which converts the plate resistance into ship resistance.
To get the full resistance, we need to estimate the form factor (k) and the wave resistance (Rw).
B. the hydrodynamic forces from the appendages.
If we are using one good old rudder, then the hydrodynamic forces can be known by looking at the section of the rudder and finding the most look alike NACA profile (wing profiles extensively tested in wind tunnels).
If we are not using a rudder, and that the whole hull act as a rudder, then it will require model testing and more fluid dynamics calculations.
C. The aerodynamic forces.
We can use polar plots from tested sails. Usually the Lift and Drag forces are given as Lift and Drag coefficients, which enables to calculate the forces for any sail surface and apparent wind speeds.
A Velocity Program Prediction (VPP) is balancing these forces in all the 6 directions of movement, calculating the unknown forces from the known ones unknowns from the knowns.
Find the most appropriate yacht model, including:
sail Lift and Drag coefficient as a function of AWA
rudder Lift and Drag coeff as a function of angle with flow and inflow velocity
hull upright resistance
implement the model in a VPP in order to refine the above defined parameters
model the articulated hull and the articulated tail as deformable membranes. model the interaction between the sail and the hull as two deformable lifting surfaces acting in two different fluids with free surface.
The tail can be modeled as a floating cylinder, with an absorbing surface (oleophilic - aquaphobic). It can consist of several parts and be articulated. The volume of the cylinder gives buoyancy to the tail and can be completed by more volume underwater, to give more stability.
Like a ship, the tail has a resistance to movement in water: Tail Resistance or Tail Drag, both in the longitudinal and transverse direction. Obviously the resistance will depend a lot on the roughness of the tail surface, the oil viscosity, the quantity of oil absorbed, and the speed of the water along the tail (which is a combination of the ship speed + current speed).
--> In order to link the tail model to the ship model, we need to find
-
the buoyancy of the tail.
-
the longitudinal and transverse resistance of the tail.
with Gonzalo Tampier: propose a student project to measure the tail drag in a towing tank, using different length, roughness and sections for the tail.
with Gonzalo Tampier: start the tests in the towing tank. Technical and logistic issues: do not expect to be able the results directly for the prototyping. But experience and feedback can be exchanged between Rotterdam and Chile.
in Rotterdam: collect a number of tails and try them out on the sea, behind a motor boat if possible. We are working on finding a sail club in Rotterdam who could lends us a boat. With the boat towing the boom at different speeds the resistance of the boom can be measured using a load cell, and used as an input to the model.
propose an articulated model of the tail, based on the Dracone paper. Simulate its behaviour when exposed to current, wind and waves. Find out the best sailing patterns to collect as much oil as possible.
The oil spill is usually modeled as a point source pollution: 1 ship/ well/ etc leaking oil, turning into a plume under the effect of wind and surface currents. The inherent properties of the oil (density: weight compared to water, viscosity: easiness to mix with water, volatility: evaporation in air at certain temperature/pression) are modified when mixed with sea water under the action of waves. When a large volume of sea water is mixed with oil, the mix gets brownish, very heavy and sinks under the surface. Then it is subject to the currents acting at that depth, and Protei can not do much for it. This is what happened with the Erika oil spill.
Define the main characteristics of oil affecting the operability and performance of the booms we want to use.
Define the max sea state (wave height and wave frequency), wind speed, current speed in which Protei can operate.
Define the interaction of Protei with other available oil clean up technology
Define the successive operations of Protei in order to collect the oil in closed loop: all the collected oil has to be brought to the shore and handled properly.
--> Focus on how to deploy Protei from Fishing boats!! see http://nofo.no/modules/module_123/proxy.asp?D=2&C=39&I=432
Try out different non polluant liquid solvents simulating the behaviour of oil.
Fully simulate the oil spill collection using Protei.
--> See attached paper from Imedea in Spain: winds, waves and currents forecast for oil spill modeling, deployment of oil spill cleaning technology, communications between the different elements of the system (coastal witnesses, aerial observations, buoys for current and wave measurement, weather forecast model, oil clean up support vessel, oil clean up dirty vessels).
Work on the cost model developed by Etkin.
http://scoutbots.org/data/Protei/06.0_Batman/math/forces%20on%20a%20string.jpg
--> We need to indicate the symbols on the diagram above to match Elliason models According to Lars Larsson and Rolf E Eliassion, Principles of Yacht Design, List of Symbols, page Xiii.
Prof Lars Larsson is the Director of Graduate Studies,
Department of Shipping and Marine Technology, at Chalmers University, Göteborg, Sweden.
I met him once, and he is the nicest man on earth. That would be very nice to ask him his permission to use his book too!
- AR aerodynamic driving force
- AS sail area or aerodynamic side force
- CL and CLmax lift coefficient and maximum lift coefficient, respectively
- Fn Froude number
- FR rudder side force
- H1/3 significant wave height
- R resistance, general
- RF frictional resistance
- RH heel resistance
- Rn Reynolds number
- RR residuary resistance
- SAF sail area, fore triangle
- SAM sail area, mainsail, triangular
- Sw wetted surface area
- V volume displacement, or yacht speed
- VPP velocity prediction program
Physics of one unit
- Basic Physics of boat : http://www.real-world-physics-problems.com/physics-of-sailing.html
- Physics of flight : http://www.grc.nasa.gov/WWW/k-12/UEET/StudentSite/dynamicsofflight.html
- Advanced mechanics of boat : http://scoutbots.org/data/Protei/06.0_Batman/mech/20110417Principles%20of%20yacht%20design%20-%20Larsson,%20Eliasson.pdf
courtesy of "real world physics problem"
Sailing simulation
Example of simulation : http://www.hangsim.com/vs/screen.php Commands on a boat: http://www.nauticexpo.com/prod/mi-simulators/boats-radar-simulators-26918-167485.html Multiple units
Example : http://www.poseysail.com/sts2000.htm
The VPP is an iteration calculation program that tries to find a stationary (i.e non transient, independent from the time) equilibrium between the forces of the sail, the hull and the boom, depending on:
the wind apparent angle, wind speed the hull velocity, leeway angle and heeling angle the hydro- and/or aerodynamic performance of the hull, the sails, the boom and any other appendage We will need 4 modules:
1 for the hull, 1 for the sorbent boom, 1 for the sail 1 that combines the 3 modules above into one VPP This is to evaluate the physics of Protei, now if we can integrate the physics of the oil moving on the water (depending on the wind), we would have a full model. Integrating the oil in the model, we may be able to evaluate how much oil we can collect.
We start with a simplified VPP to work out the main dimensions of Protei: the hull module gives the hull resistance at a fixed speed of 1 knot, as a function of ship length the sorbent boom drag is estimated to be the equivalent of 2 tonnes the sail module gives the sail force as a function of sail area, to be distributed into the number of sails we want You need an opensailing account to access the calculation spreadsheet
ITTC 1978 formula for the calm water hull resistance
Froude number, Reynolds number? Keep the flow laminar? When is the flow becoming to be turbulent? [image] Can the turbulence be of any help to collect more oil?
?? performance of the boom VS hull moving forward, pushing the oil away from the ship ??
The waves created by the hull when moving forward are moving at the same speed, at an angle of 19.5 degrees.
--> what is the best trajectory to concentrate the oil in one place?
--> can the local current direction and speed help to counter the spreading effect of the waves?
--> we can use lift and drag coefficients from the literature (Larson) to start with
WB-Sails from Finland looks very promising, let´s contact them! Macsail aerodynamics performance calculation in JAVA SailTrimSim sailing trim simulation in JAVA
Before we combine the 3 (hull + sail + boom), we must combine [Hull + Sail] and also [Hull + boom]. So two more test matrices.
At high speed the curvature of the hull creating lift, the natural curve of the boat indicates a trajectory that is opposed to the general motion of the vessel. That [camber + speed] creating lift must be described very precisely in the "Protei hull test matrix" since it will determine a limit and change in general behavior of the vessel.
5.1 Commercial VPP
There plenty of commercial VPPs available. Aerohydro´s AHVPP Wolfson Unit´s Windesign: brochure and explanation http://www.wumtia.soton.ac.uk/papers/SeahorseVPPArticle.pdf <-- a good reading!
While these are robust, widespread softwares, they cost quite some money (about 1000 USD for 1 license) and they are usually too "pretty" for us and we cannot manipulate their code source to turn a racing yacht into our inflatable articulated sailing vessel pulling a tail!!
5.2 Homemade VPP
So I suggest we instead look into homemade programs, which are a bit rough, but are just perfect for our DIY approach. Humberto Martinez´s SDN looks allright, but is not working on Mac OSX. M. Martinez has a great resource page of softwares for CFD + Hull design + Sail performance calculation + Hull performance prediction. It just needs some update...
Peter Schwenn´s Fast Yacht V++ looks intriguing
Gerard de Roy´s Boatarchitect is free, works in Windows and looks very good to me, very detailed documentation. I´m a Mac user, who can try it in Windows?
http://scoutbots.org/data/Protei/06.0_Batman/math/Protei%20Software%20Interoperability%20Matrix.xlsx
http://scoutbots.org/data/Protei/06.0_Batman/math/DevelopmentoftheAnacondaall-rubberWEC.pdf
http://scoutbots.org/data/Protei/06.0_Batman/math/TheearlydevelopmentoftheDraconeflexiblebarge.pdf
http://scoutbots.org/data/Protei/06.0_Batman/math/download.pdf
http://scoutbots.org/data/Protei/06.0_Batman/math/anaconda.pdf