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Design by Modelling

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Hi fellow aficionados


Crazy as some who know me believe I am, I have decided to use 21st. century technology and tools to design, model, simulated and optimize my own system for sheet control as I am planing to use in my model sailboat, The Carina, of which a report is being maintained and developed in the build from scratch report forum. Some background information to the sheet control system, to its challenges and some pictures with it, so you know what i am talking about and why I have decided to embarque in this very major endeavour of design by modelling my sheet control system!




As can be seen in the photo from the original Endeavour the sheet goes 6 times from Deck to boom and back. Due to the size of my model this means I have to be able to change the available length of the sheet by 840 cm!





To achieve my goal I am going to use a stepper motor to implement the winch. The reason to use a stepper motor is that it has properties that support my goals. At YouTube and my channel Hellmut195612 you can see videos I recorded of my first round of experiments with the stepper motor with no load and in the report of the building also you find some data about it!


A stepper motor running with 256 microsteps per full step results in it making 51200 microsteps to make a full 360° turn and to achieve the change of length 0of 840 cm I am building a drum for the sheet that will have a length of its circumference of 40 cm, resulting in 21 360° turns or 51200 by 21 = 1.075.200 positions at which it can be placed. 




Here you see the drum in construction. The drum is as big as possible, so that the stepper motor can be turning as slow as possible. The slower a stepper motor runs, the higher the torque is, such being a counter effect to the radius of the drum that generates more load torque the bigger the radius is!




Here you see the stepper motor, of which i will have 2 in my sailboat with the drum mounted.



Here the link to one of my videos at youtube where you can appreciate how fast the stepper motor is capable to turn, still offering the tremendously high resolution. The control IC used in the electronics have the option to do the same angle turn per microstep, something which is usually not the case!


My goal is to have my system to only make that much sheet length available at any time that the boom needs.




Here you can see the sketch of how I track to angular position of the boom. The axis is connected to the boom in such a way that it rotates with the boom around the vertical axis and goes next to the deck surface. On the end next to the deck surface is an magnet and at the deck surface there is a plastic foil covering the opening on the deck, where the magnetic angular sensor is, so that the magnet turns with the axis as the boom turns, just 1-2 mm away form the sensor. The sensor has a resolution of 16 to 14 bits per absolute angle detection depending on the technological advances with the sensor IC at the time i decide to buy it. 16 bits means he detects 64*1024 angular positions, 14 bits 16*1024, only 25% of those or either 4096 or 16384 positions are required for the boom only turning to both sides of the hull centerline by 90°. This information is available by reading a register from the sensor. For tracking the relative angular position the sensor delivers 3 PWM signals, called "A, B and Z".




The microcontrollers used, ARM Cortex Mo or ARM Cortex M3 do have a peripheral integrated that decodes this signals and delivers valuable data. But the resolution is 2 bits lower than that of the absolute angular position available by reading the content of a register in the sensor. The additional "Z", also called "Index" signal takes place once per turn, so that full turns can be tracked!


So I have developed a graphic of the whole sheet control system, which will be just one of the few that I will implement. here the graphic:




As you can see form the first glance, the system looks pretty complex, but will be simple to adapt to other sailboat geometries making its reuse easy! as I will have a boom for the main and the fock sail, the subsystem to track the boom angular position is present twice. The 2 vertical branches represent the tracking of the boom position, which is fed to a very cheap and small board available from Embedded Artists for just 20.- Euros, the LPCXpresso1769. This board can that have the 3 PWM signal feed to its peripheral quadrature encoder and it can read the register from the sensor to get the absolute angular value. "stepRocker", or the follow-up board from Trinamic, the "motionCookie" ist the stepper motor control board. This controls the stepper motor which via the drum connected to it releases or collects the sheet as required by the boom position. This way the sheet will not block by any obstacle on the deck! At the drum will be a second magnet and next to it in the drum case an angular magnetic sensor that will monitor the stepper motor position to prevent step errors!




So whatever position the control stick on the R/C transmitter has is transmitted to the receiver in the model and there a PWM has a positive value of ta length that is proportional to the stick position on the transmitter.A LPCXpresso 1769 board measures the length of the pulse and here, for simplicity, I assume it gets 1024 different values representing the position of the control stick at the transmitter and so the command from the skipper. A table stored in the flash memory of the controller LPC1769 assign to each of the possible 1024 positions of the control stick an position for the stepper motor and as a result a certain sheet length. This value is passed to the LPCXpresso 1769 board that also receives the data from monitoring the boom angular position as soon as the value changes. This value tells the microcontroller up to which maximum position the boom af the sail is allowed to open, identical to what usually is done when operating s sailboat. As long as the sail is less open than this maximum value the electronic control will follow the boom position by releasing or collecting the proper amount of sheet.


Just reflecting over this system and its implementation I found the need for a mechanism to allow free movement of the boom when it is allowed to do so which required to define a scheme of 2 threshold values to allow the system to work.




With capital "X" I define the current angular position of the boom, monitored by the sensor, being "X-1" and "X+1" the neighbouring positions as tracked by the microcontroller using the PWM signals fed to its peripheral function the quadrature encoder. By reading the value of the absolute angular position, 4 times the resolution, I can track "thresholds", here named "Umbral". When the boom passes one of this thresholds, the stepper motor moves to the next position so that i.e. the boom has enough sheet to continue to open, until it reaches the limit set by the control stick position at the R/C transmitter by the skipper.


I have received numerous high value and low value responses to my system. Some of them could be actually show stoppers. There is also a good chance that there are even more detail aspects I have not yet come to grasp.




In this technique I model the system presented in the graphic with all the block in it by using an appropriate software tool and the control theory that generalized consists of mapping the diverse elements of my system in a sheme as shown in the next graphic:




Looks awful complex and difficult, but conceptually it is not that difficult!


The diagram presents the different factors influencing a control loop over time, this is why the diverse influencing factors are references as a function i.e. r(t) with t in brackets indicating it varies over time. lets translate this to my sheet control system for a very simplified explanation! The Transducer monitors the drum position and the data from the angular sensor at the boom to give the information feedback.


"r(t)" could be i.e. the angular position as monitored by the sensor.. "e(t)" is the instruction or information update the LPCXpresso1769 gives the "stepRocker board" telling which position the stepper motor has to take! "u(t)" is the job of the stepRocker board to have the stepper motor turn as a consequence of the information received. "Plant" is the stepper motor with the drum and the sheet on it! Disturbance could i.e. be that a change in with direction, i.e. because the sailboat is turning, "y(t)" is the sheet length due to the command the stepRocker board as given the stepper motor. The LPCXpresso1769 takes this information and the reference value data and decides what has to be done, if anything has to be done to change the stepper motor position!


Well, if I do model my complete sheet control system this way i can i.e. identify if in my understanding are any show stoppers, i can have calculated the power consumption of the stepper motor and on, and on. So by simulating I can get a much more complete understanding of my sheet control system behaviour and improve it until it does what I want. I can verify if the warnings I received are justified and quantify their impact and I can play with the various parameters i.e. to prevent show stoppers and to achieve a minimum power consumption.


So far, I believe, with all the background information I have been giving you dear reader, you can understand my objectives and may be why this would help me tremendously to design my sheet5 control system much smarter and efficient than without it. So if this kind of analysis is fun to me, and it is, then i gain a lot by combing this design by modeling with the experiments. The probably most advanced tools for this job are either Matlab and Simulink, or Maple and MapleSim. This are very mature tools with huge libraries that can be used and extensive tutorial material.  The third tool is Mathematica and System Modeller. This tool is very advanced and powerful, but the System Modeller design and simulation tool is far behind the other ones as the extend and quality of the libraries available. The first 2 tools I can get access at no cost to by registering as student at the technical university in Munich, which is for free and I could use them while being a student. Mathematica has a special pricing for aficionados and so I would have access to the tool for an unlimited time! Mathematica form Wolfram is a very advanced and mature product and the System Modeller, while not being so extensively supported by libraries yet, allows to model relatively easy using a programing language called "Modelica".


But what is evident is, that since I was at the university 35 years ago my mathematical skills have eroded a lot and the mathematics required have also progressed dramatically over this time period.


The result is that I started to investigate the possibility to engage at the technical university and study the stuff required. Unfortunately in the last 3 years I have had 2 strokes, a few times my heart stopping to beat due to cardiac rhythm problems that have reduced my abilities to work and study under the pressure of a regular university learning schedule. But it soon became apparent, that without certain mathematical skills I would neither be able to grasp and work with the techniques teached at lectures in electronics and in physics. So I came to the conclusion that i would have to engage into a study of mathematics and so I informed myself about the lectures for a bachelor in mathematics.


You would not believe what extensive and fast growing offer can be found in the Internet. MIT in Boston offers top class courses, with videos of the lecture of the professor, of the instructor in the exercises, lecture notes, exercises and old exams for free. I would dare to say that it is better to study taking their self study courses offered for free at "OpenCourseware". You can stop a lecture video at any time, rewind and replay until you have a full understanding of what the prof is teaching, you can google or go to wikipedia to investigate about terms of scientists mentioned, you can even choose a professor that teaches a lecture the way that best fits your way of learning. In Germany the offering of such courses is also expanding at a high rate and with high quality!


So the result is, that now I am spending every free minute and any time my health allows to do so studying mathematics and always reflecting about the impact of what I am learning on my project of the sheet control system!

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  • 1 month later...

Last week we had a very important trade show here in Munich called "Electronica" which I did visit on Thursday. I used this opportunity to investigate how familiar companies present there were with the concept of "Design by Modelling" and found to my surprise that the knowledge between those present at the booths at the trade show and no idea of it. I then used the strategy to mention a commercial player in this area, mathworks and their products  Matlab and Simulink and so at least found a couple of persons that had heard about this product, but only as a tool to use their "Solvers", software tools that help to solve equations as part of the simulation and the mathematical description. Those individuals I did ask if they knew about the language "Modelica" and in this context about causal and acausal model elements. Surprisingly not a single one hat a clue abut it. The best question I was asked was about why design by modelling was different from using tools like Spice, an industry standard tool for modelling electronic components, specially under the perspective of analog behaviour. My response was, that design by modelling and a core tool in this context the language "Modelica" allowed to combine multiple domains into a simulation the way they were used to use Spice. To you my appreciated reader, with domains in this context we are talking about fields like electronics, mechanics, hydraulic and stuff like this that normally are perceived as different fields developed independently, but combined in embedded systems. Embedded systems in our hobby the naval modelism means embedding electronics in an application opposed to have an external computer involved.


I am writing you this, because it reflects that the use of system modelling is something new in the university environment and from where a new generation of engineers will start to have this move to a widespread use in the industry and that so our hobby is in touch and opens itself for the latest technologies!


But why is this of interest to us in our hobby, orr may be better asked, what benefit can this have for us as naval modellists? Well, as I have expressed in the past, naval modelling is a hobby that combines a rich portfolio of technologies, like working with wood, with metal, with plastics, which put us in touch with a rich portfolio of tools required for those materials like glueing, milling, lathing, laminating, 3D printing and many other craftsmanships. But since some time the some of us not only use electronics from vendors, but also see electronics a an open box to make wonders happen. Well, technically speaking, we are used to move in diverse domains and to see their behaviour in the physical reality of this world. The technology of system modelling in general and the language "Modelica", which can be downloaded for free from openmodelica.org alow to combine those diverse technologies, here named domains, into a single "modell" of a system that we might like to design as part of our projects in making a model.


Having written this generically to supply to you some background information I am working to use this system modelling technique to model my sheet control system, to analyze and verify its ability to do what I expect and to be able to optimize it for energy efficiency, something important when we keep in mind that our models all are battery driven.


Some of you may say, why should I bother about this, and right you are! Why should a fan of plastic models bother about carton models, why should a fan of regatta competition with sail boats bother about static models, and so on! My answer is that every aficionado of our hobby doesn't have to bother about techniques in our hobby if those do not contribute to his goals and objectives. But it is the wealth of our hobby that it spans a wide field of technologies and abilities and so it offers each of us a playground to pursue its own wishes. The use of electronics and now the use of system modelling shows and to my believe proves, that our hobby really is not something just for those of us that have collected a number of years in their lifespan, but that it really makes it possible to melt 21st century technology into our hobby.


So I want to end this contribution today by presenting what the concepts of causal and acausal systems mean!


Here a link to an introduction which I will try to explain less rigorous and hopefully easy to understand!


Imagine a simple circuit to feed a DC motor. On one side you have a power source, in our models i.e. a battery. This battery allows to apply a voltage to the DC motor and so a current flows through the DC motor making it turn. here we are combining an electrical domain, the electrical circuit connecting the DC motor to the battery and a physical domain, the DC motor creating a rotation movement and a torque that can i.e. move a bota by having a propeller turn. If we add into this picture the well known fact that a motor generates heat, we know if we apply a voltage to a DC motor that is above the specified value, too much current flows through the DC motor and it will get warm and eventually burn out. This would be another domain, the one of heat flow!


if we model such a system in a causal way, the traditional way, we have a sequence of events which start at the battery and its supply of voltage and current and the DC motor creating rotational movement and heat.


But what happens if now I do disconnect the battery from the circuit? well the motor sops rotating.  But what does it mean in I take my hand and fingers and rotate the shaft of the DC motor? Well, the motor becomes a generator that generates voltage. The flow of events turned a 180°! The input is a physical work, the one of rotating the shaft and the output is the generation of a voltage. If I do replace the battery by a small incandescent light bulb, the light  bulb will start to generate light.


If I have modelled the first system using the battery I cannot reuse this modelling solution for the second case. I have to start from scratch. Well, using the acausal modelling technique  the same model can be reused as it is.


Lets port this concepts to a sail boat. This sailboat is in a physical environment were the behaviour of the water by the waves and so on have an impact of the model behaviour. same is true for the wind, and so on. This physical domains influence my sheet control system by making i.e. the boom of my sail boat swing, oscillate, when no wind is blowing. When I look on the wind, it will generate a pressure on the sail surface which will issue a load on the sheet which in consequence has to overcome i.e. the friction within the tubes through which the sheet moves, it will generate a torque load on the drum of the sheet and the drum will pass this torque to the stepper motor. If I turn the sail boat the wind pressure might disappear as a load from the sheet but will make the boom turn. So just this example as a description of the many issues that impact my sheet system in very different ways. As my goal is to minimize the power consumption of my sheet control system and as my control circuit for the stepper motor offers diverse means to react and monitor the stepper motor behaviour and as a consequence the power consumption of it and as my goal is to achieve a maximum within reasonable limits of power efficiency, system modelling makes it possible to model my sheet control system. Using acausal schemes I can reuse the blocks I develop an adequate modelling of the system behaviour and have it evaluate the power consumption. More, supplying measurements results from physical models as i do while i experiment, my tutorial about stepper motors is an example of it, I can have "solvers", functionality in mathematica i.e. to propose an equation whose behaviour best approximates the results from measuring.


Now to the important fact why we have a hobby. We want fum! Now every one of us has its own way to get his or her fun out of our hobby. I get a lot of fun in understanding the behaviour of my sheet system and I learned for me, that diving into the details of the system behaviour, reflecting over the implications and thinking about ways to monitor it, about ways to take my advantages by using those insights gained by monitoring it, power efficiency being only one aspect of it and by learning new means to dive even deeper into the topics, is a lot of fun to me. I confess, that realizing how much my mathematics knowledge has eroded since my days at the university, how much mathematics would be required to deal with this in my pedantic and epic way, started building a barrier towards such an approach.


But as the amount of fun and the satisfaction of pursuing the objective grew, while the frustration about my limitations if not jumping into this equally grew, i started to study the possibility of learning the required techniques. So I started by contacting the technical university in Munich regarding the possibility to study electronics, as the framework through which I would learn control engineering. Yo should know, that universities in Germany are for free! Well, as a person then 57 years old the reaction at the university was very positive that I was willing to consider such a study and I got information about the courses that made up the bachelor degree, I got access to the intranet of the university to some of those courses and I found books for free in the Internet that i could use as reading while studying the lecture notes, the examples with the goals to write the exam under exam condition successfully.


The result of those first researches was, that mathematics as a prerequisite to be able to study those courses. Even more, i started to feel myself as an analpabet by not having the mathematical knowledge to grasp what was being said, written in the material I found. Was kind of like i was able to see and reflect about the pictures but unable to read. So facing this i found that 2 mathematical topics were unavoidable, "Linear Algebra" and "Analysis". my research now discovered, that in the Internet I could find for free videos from university professors giving lectures in such academic topics, that lecture notes, videos of exercises on examples related to those lectures and the exercises and exams could be found in the internet, as well as enough recommended reading materials as pdf archives, all for free. Even more, I was able to choose between the lectures from different professors, so that those that fitted best to my way of learning could be chosen. Even more. that lectures recorded in video could be stopped at any time and parts repeated until y completely grasp all implications of what was being presented or to stop and investigate about people and terms using google and wikipedia. As being retired due to health problems, as this is my hobby and not my profession, I am able to spend all the time left to me for those studies.


Well, i found a german professor teaching "Analysis" following the methodology used by Terence Tao, a mathematical genius teaching at the UCLA and who makes available his 2 books about "Analysis" at its personal webpage. His approach is to rigorously prove all starting from really the most basic, such allowing me to overcome the hurdle often found when dealing with mathematics, that mathematicians often consider a prove trivial ans I was unable to grasp it nevertheless. So in July this year I was invited to an "Infocafe" at the mathematical institute of the technical university in Munich and had the opportunity to chat there with a professor. Prof Brokade, He indicated to me that the rigorous approach pursued by Terence Tao had been replaced or expanded by an approach based on the study and understanding of mathematical structures. As you will and I did then, I had no clue about what he really meant, and so i went into investigating the topic at the same time while working on setting up my environment for the studies and developing an understanding from a wider perspective of the implications of my goal to use design by modelling to develop my sheet control system.


First, and this I believe is valuable information for those of you that still might have continued reading my text, I found that the "normal naval modelist" willing to use design by modelling technique in our hobby can be offered a short path as soon as I have advanced my studies by limiting his requirements to combine model elements, like lego parts, to describe his system. But being able to present such a short path, at least for me, it means to delve deeply into the subject.


As my sheet control system installed on a sailboat would be subject to the physical environment in which the sail boat moves and as the study for a mathematical bachelor demanded to include some courses from a none mathematical area, I studied the implication of making a bachelor in physics. I notice that i have missed to present why a mathematical bachelor study came to my radar screen after considering the study of electronic engineering! I said that the study of electronic engineering required at least Linear Algebra and Analysis. Well, why study those mathematical topics the limited way an engineer does, if i can acquire better knowledge by studying the same courses as part of a mathematical degree. The analysis course from Terence Tao was one with honours, so premium. So my initial intention was to study linear Algebra and Analysis at the mathematical institute and then cover this way those mathematical courses for the electronic degree.


The fact is that while studying the content for a bachelor in mathematics would benefit from applying those mathematical knowledges acquired there to describe and solve physical problems, something definitely not alien to my hobby in building a sailboat. Even more a profound understanding of physics and the application of  mathematical skills there would benefit my original goal of designing my sheet control system and also those knowledges would be accepted for the electronic engineering requirements for the bachelor there.


So I found OCW, OpenCourseWare, offered for free from the MIT in Boston, where the biggest offering of university courses for free in the internet  could be found. By the way, having always had an affinity to physics, I found tremendously interesting courses there, i.e. about Cosmology, that captured my interest and fascination! its worth to go there, and see what is being offered.


Studying the course documentation about "Linear Algebra" there, I found that as a prerequisite for that course Calculus, for single and multiple variables, was listed. Well, I had learned those topics at school, but after some time i decided to take those 2 courses prior to studying Linear Algebra and Analysis, just to make sure that my studies started from a solid foundation. What is different from studying now at nearly 58 years of age compared to the past at school is, that here I focus pedantically and epically to grasp in depth every and each detail of the study, as not passing an examination is my goal, but to gain excellence is!


In this context I found a lecture of theoretical physics in mechanics, that addresses the topic not the traditional way, but using the most advanced mathematics, i.e. diverse kinds of topological manifolds to move to the classical newton based mechanics, dynamic of fluids, thermodynamics, electricity and magnetism, oscillations , special and general relativity, quantum mechanics by using the diverse kind of topological manifolds, claiming that this way a clearer and preciser expression of the Newton laws i.e. could be gained and that relativity and quantum physics would become evident and easier to understand. Now, topological manifolds are mathematical structures and so I learned that mathematical structures start by imposing more and more properties and mathematical objects. So I gained an understanding of the principle behind the approach Prof. Brokade had meant when he talked about the new and current way of mathematics was taking the approach via mathematical structures. I will not go into what topologies are and what manifolds are in this context, but just want to state that conceptually it is relatively simple. So for me I believe I have made up my mind to pursue a combined approach when learning mathematics and when applying this knowledge to physical systems as I do in my sheet control system. It is a combination of the rigorous approach and the categorization of the knowledge in terms of mathematical structures.


Sad is, that I am already nearly 58 years old, that I have suffered 2 strokes in the last 2 years, that I had cardiac rhythm problems due to medicamentation that had me getting a pacemaker implanted and suffered damage in my grey cells that limit the time i can spend concentrated doing something. i wish I were 20 years old and could pursue those studies with a whole life span in front of me! But it is said, that exercising the brain helps it to reorganize itself and fix existing damages! well should I continue bothering you with my epic writings you at least know that i am still alive!

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Fascinating reading for those with a tech bent, Hellmut.  I see tech being used more and more these days... PE is simple example.  What was once done by hand is now drawn by computers.  3D modeling is in it's infancy. 


I hope your health issues will let you continue to do what you love.

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Hi mtaylor. Thanks for your response! You are absolutely right, that the topics presented are very technical! I was surprised to find out during my visit to the trade show "electronica" in Munich, probably the biggest trade show for electronics worldwide, how little knowledge about this technology was in the minds of the really technical people I talked to during the show. Only very few knew details about simulation tools like those as Maple, Matlab or Mathematica in the context of simulation and none the difference to "standard tools" like Spice and similar. I was asked the smart question what was what this technique had to offer additionally to tools like "Spice" and in what way it goes beyond what Matlab, Maple or Mathematica have always offered. My response was, that as an extension to the functionality of tools like Maple, Matlab and Mathematica the simulation tools from those companies in combination with the functionality best described by referecing to the tools available under openmodelica.org and the description of models not only in "causal", but also in "acausal" objects made those tools powerful and heavily reusable and that while this led to speeding up the process of design it allowed for optimizations at a new level of detail in multidomain environments. Multidomain meaning in systems that combine not just electrical systems, but i.e. mechanical, rotational, and so on, just connected by "connectors", a key concept well introduced either in the documentation found at openmodelica.org or at Maple in the introduction to maplesim in their website.


I am aware, the more I dig into advanced and specialized topics, the less I will find reader willing to follow! But our hobby offers opportunities far beyond the usual scope and I am confident that future aficionados more familiar with those topics will one day embrace them. But it is also so, that digging into new areas requires much more extensive studies before elegant and easily applicable working schemes can be found and communicated. I hope that some of the contacts I am making on trade shows will lead to generate a community willing and able to pursue such goals. When starting to promote the use of electronics as a technology for our hobby I was lucky to find some supporters and I found that modelists in the plane building domain are more open to this new technologies, as the FPV, first person view, activities demonstrate. I know naval modelists tent to be more conservative and in avergae have a couple of additional years on their shoulder.


I have written about my health problems and their impact on this activities not to get compassion, but to present that the mental activity in such an area requiring extensive studies can combine a lot fun with the support of helping our brains to repair eventual damage by reorganizing itself. Working with the brain is like exercising physically, both develop the muscles involved. in case of the studies, our brains!

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  • 4 months later...

Hi friends, since my last post I have been having interesting developments, not at least also thanks to critical questions being asked or statements about either why I was not just building what I plan of the statement that what I was planing to build to control the sheet in my model sailboat Carina would not word due i.e. the friction in the pulley between the 7 sheaves which it contains and the rope of the sheet!


Sadly some even felt that they had to get angry about my stubbornness and may be seeing in my unwillingness to accept their expert opinion as not accepting their expertise! First, I believe we naval modelers are stubborn as otherwise we would not have the perseverance to work on a single project for such long time. Second it was my goal from day 1 to see the activities I engage in the context of building the model as the real objective. I have been engaged in learning a bit about using my lathe and my milling machine, I got into electronics i have been working on developing my workshop in parallel to the activities on my model. Now after nearly a decade working on the project it is not surprising that i am engaging into technical aspects pretty advanced!


On the other side as I do enter into projects of the most diverse kind I am by definition always an apprentice in what I am doing! I do write about what i am doing to share my experiences, to may be motivate one or the other to follow on some of the aspects of the project and by explaining and responding my understanding of the subjects improve! So, as there is no obligation to read any post and as I make clear how my projects relate to the topic in this forum, naval modeling, I hope it is fine for everybody that I do what I do!


Lets go into the activities and achievements since the last post and into what I am working right now in the context of this thread! may be some of the information has been written about already at another place of the thread, but I do so to put thinks in context!


Due to my objective to understand and hopefully verify my concept of a sheet control system able to change the length of the sheet by 8400 mm in a hull just 1650 mm. Over all that I have started to present above an in depth understanding of the impact of any parameter existing in the way the concept is implemented. There are the following goals:


1. Achieving the most energy efficient implementation possible.


Remember this model is sourced by batteries and the 2 large stepper motors can consume a lot of energy! So an energy efficient implementation makes it possible to use a much smaller battery capacity. The 12 LiFePO4 cells, each with 16Ah capacity was the biggest capacity available at the time I made the decision to ensure the model would not have to be recharged during a single day at the pond site!


2. Verifying that my concept of a sheet control system achieves not only the desired functional operation, but also to be reliable.


3. To identify what wind speed minimum was required to generate the pull force on the sheet to open the sail, something experts consider a fatal problem of my concept to implement the pulley as used in the original sailboat Endeavour:




4. Find which physical dimensions and position of the 6 blocks and 7 sheaves result in a good visual implementation as the one on the original sailboat and what the many parameters affect the wind speed required to open the sail against the friction in the pulley!


So with such objectives as I wrote I learned about the methodology of the "Design by Modeling" and as a result I am convinced that this methodology makes it possible to have the greatest chance to achieve my objectives!


When I learned about the existence of this methodology I learned this in the context of using either "Matlab/Simulink" with several toolboxes from MathWorks or Maple/Maplesim from Maplesoft. Both sources had one big problem for me. They had no licenses offered for home users and so the cost of the license was prohibitively expensive! Now I am such a fool, but I only use legal software, so cracked version were a no way! But I learned that for students the access to special student or academic versions was possible, but only usable while registered at a university!


Now the other aspect I found out soon was, that for what ever tool I was going to decide myself to go with my nearly 4 decades old mathematical skills had eroded and that the development of the PC and its performance had between other reasons led to an impressive development in the field of mathematics. Even more, no university course relevant to my interests was possible to be studied without getting deep into mathematics!


Now, as I have suffered 2 strokes, multiple times I heart stopped beating due to problems with my medicamentation that resulted in cardiac rhythm problems I got a pacemaker and as a consequence of it a heavy thrombosis in my right shoulder. But worse was that those times my heart stopped beating some of my grey cells had suffered due to luck of oxygen, what results in a degradation of my concentration endurance! The nice side effects of this were one one side that I got very aware of that my lifespan is limited and that as a consequence I might never finish my projects, the other side is that by doing the research work, the studies I have to do in the context of my design by modeling project those activities are actually a therapy to help my brain to reorganize and fix what got damaged! I am writing this not searching for compassion, but to give you some background of myself and this project!


Now as a consequence of the prohibitive cost of the software tools from the 2 companies mentioned above I started to look in the offering from Wolfram, Mathematica and SystemModeler. Let me just summarize by telling you that during my visit to the Embedded World 2015 trade show in Nürnberg I learned that MathWorks actually now has an inexpensive license in its offering, even cheaper than the home license offered by Wolfram! Still so I have decided to go with the offering from Wolfram.


To explain why i want to start showing the environments in which the design by modeling work takes place:


post-556-0-72022600-1428425620.jpg           post-556-0-02311900-1428425042.jpg


This to images are meant to represent the 2 complementary environments. The PC on the left is the virtual environment in which design, modeling, simulation and verification takes place.


On the right the PCB i use to control a stepper motor is representation of the physical real electronics which execute software and in this combination represent what one day will be build into the sailboat model. To just give you a glance of the complexity next a diagram I made to explain the constitutive elements planned to be used to implement my sheet control system:




I will not get into details right now as a lot has been already been done earlier in this thread. But this diagram, were the PCB shown above is just one of two "stepRocker" PCB used in the system to control the 2 stepper motors, one for the main sail, the other one for the Foque sail!


Let me indicate that modeling something is fine, but that the quality of the simulation results using such model has to match what is measured physically in the real embedded world! This step is named verification and it demands to define experiments to verify the different parts of the model being developed!


As of about a month or 2 ago I felt that my studies to refresh my mathematical skills, while far behind what I had hoped to accomplish after one year of studies and the purchase of the tools required I feld I could start modeling and did choose a subsystem that while being comparatively simple it addressed the important question about what a wind speed would generate the pulling force in the rope enough to equal the friction!


The reasons were that I felt enough development in my mathematical skills not to be intimidated by the mathematical notation so that I could grasp the properties of equations enough to identify what those equations meant for my objective of modeling. But also because I finally had identified 3 pillars based upon which I could pursue my objective of modeling:


The 3 pillars:


1. Methodology developed at the MIT in Boston starting 1956 in the field of the science of complex dynamic systems.


2. The modeling language Modelica, an object-oriented equation based modeling language and simulation environment which is being supported by SystemModeler from Wolfram.


3. System Physics: An innovative perspective on physics that applies the methodology coming from the science of complex dynamic systems and allows the modeling of the physical concepts in Modelica.


Finally Wolfram offering both the software Mathematica, probably one of the most powerful and universal mathematics tools in the market in combination with SystemModeler and the modeling language Modelica offered a powerful but affordable environment to model in the first part the pulley.


But also the software Mathematica has been made available for free with the RaspBerry Pi running on it. This way the software Mathematica delivers multiple services key for the virtual environment, i.e. setting the parameters in a model according to mathematica equations so that multiple runs of the simulation could be done with the parameters under the control of the Mathematica functionality. But also in combination with the RaspBerry Pi i could start learning and experimenting how to best combine the virtual environment running on my PC with the physical environment and so learn what experiments run on the physical embedded hardware could be verified with the simulations running on the PC in the virtual environment.




But additionally for the SystemModeler there do exist the means and the tutorials to interact between the modeling and simulation environment from Wolfram with an ARM Cortex M4 board, the Teensy 3.1 with a supported protocol called Firmata:







Fortunately I am about to have my electronic lab ready for the purpose of studying the interaction of the 2 boards with the respective Wolfram software. Goal is to enable the boards planned for my sheet control system to be able to interact with the Wolfram software at least at the same extend as the 2 boards can actually do!


Well, enough for this post, as i am noticing that I am starting to get tired!

Edited by Hellmut1956
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@druxey: You are qualified! When I admire the craftsmanship work in other fields of our hobby, then what I am doing is not more then just apprenticeship. What I am frequently encountering is that be it electronics, or be it like in this case a combination of electronics and virtual technologies, the inexperienced naval modelist is being intimidated by the subject! If you the naval modelist builds radio controlled models, electronics has plenty to offer. A decade ago a friend and myself decided to publish a tutorial to build an experimental board just to learn hands on that 90% of the application of self build electronics can be achieved by learning some simple steps and so get a set of "lego" stones, which combined allow to build stuff that can enhance radio control models.


As to the technique of design by modeling! I am close to a decade and a half active in my hobby sine it became evident I would not be hired anymore. If after such a long time dealing with our hobby with the goals I have presented I would still be dealing with trivials, then my focus would not be in advancing in my fields of interest. by the way, always moving into new fields by definition I am always an apprentice and as such prone to mistakes!


You my dear druxey are more then just welcome to ask any question that you might have. You would be doing me a great favour, as answering questions has to my experience a huge impact on my own learning curve!

Edited by Hellmut1956
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Hi to those that still read the thread! i want to go into the details of presenting the 3 pillars upon which I base my efforts to model the pulley that is part of the sheet control system as shown in my picture from the original Endeavour and which was the first picture presented on my post dated April 7th. I have decided to keep it as simple as I can. This means that it is very probable that I will miss some aspects which make it either impossible or difficult to follow. I will do my best to prevent this, but I want to let you know that I have interesting links to more solid data.


1. Complex dynamic systems:


This science was initially developed by the "Sloan Institute" at the MIT in Boston starting 1956 in the financial domain. I want to give you the link to this page, where I would say the information presented is what I would consider the fundamental.




Right, that this picture is intimidating and pretty sure not understandable by a normal reader. But you would agree with me, that what the author is trying to model is a really complex system which requires a method to grasp all the interdependencies in an incremental way to be able to really have the model reflect this complex system!


When you look back onto what I have presented over the comparatively simply aspect of the control of the sheet when the sail wants to open more and my sheet control system has to manage to deliver the sheet length required for the boom of the sail to do so, you would agree that what I presented there in my first post in this thread is a complex system and that it has many aspects influencing and interacting. 


What soon became evident to me was that I need to have a method applied to no just consider those relations I had identified by reflecting over the subject, but a method that would make it possible to model that system and in this way capture all aspects that will end up being relevant. I have assumed I had not grasped all!




To present what is the essence of what complex system dynamics has to offer to me to model my sheet control system and in the first step to model the pulley, I believe can be achieved by taking my current status of the flow chart I am developing to model my sheet control system in the same way this overly complex flow chart above does. I do use a tool that is available for free in a demo version that has just the limitation not to allow to save the work, "Berkeley Madonna". I have purchased a license of this tool. I believe the beauty of the graphics in its flow chart is supporting to grasp the content of a flow chart and besides this, my source for learning the other 2 pillars upon which i base my modeling effort uses this tool in its videos in Youtube!


The flow chart contains 3 building blocks, of which 2 are already available in my most simple initial flow chart. The recipient and the flows! The recipient is there to catch magnitudes that are accountable, means where you can add and subtract what inflows contribute and what outflows take from it. So when you look in the over complex mature flow chart shown initially, you can see those recipients as square boxes and the flows as arrows consisting of 2 parallel lines. The 3rd. element are those circles or globes. 


In the recipient you have equations that contain parameters that describe mathematically how the magnitude changes do take place. The globes to visually show in the flow chart from which are part of the system those parameters are coming from and contain the formulas to compute the values of the parameters in those equations in the recipients. The flow chart tool shows question marks when parameters are still undefinable by the available relations reflected by the globes and their associated ingle line arrows. As a consequence the flow chart makes the complex task manageable by allowing to depict dependencies and by supporting to have those dependencies and the related equations consistent and complete.


In my own simple initial chart I am expressing a single sheaves of the 7 in the pulley shown in the picture from the Endeavour which are in a total of 6 blocks. So once I have completed the model of a single sheaves to reflect how the friction in a single sheaves relates to the tension of the sheet, of the angle it is embracing the sheaves and some other aspects, I can then use 7 instances of the model of this single sheaves to model the pulley as a whole!


I hope this helps you to explain why the complex dynamic systems science contributes an important element to my objectives.


2. Second Pillar, the equation based object-oriented modeling language and simulation environment given by "Modelica".


The modelling language Modelica basically uses the methodology developed and constantly being improved by the science of complex system dynamics of the recipients and the flows. This is tremendously important and is probably one of the reasons why Modelica is used extensively in the industry of auto makers and plane makers, probably the most important software player for such tools being "Dymola" from "Dassault"!




This is the graphical representation of what in Modelica terms is being called the model of a component. As it can be seen on the graphics, you have the symbol of a spring, you have 2 connectors and you have a large grey arrow that reflects a direction that in this context has no ther meaning than to define what is a "positive" direction, so parameters effective in this direction have "+" sign, and what is the opposite direction and has a "-" sign. What it does not impose is the direction of what are "inputs" and what are "outputs". 


This is one of the tremendous impacts of the fact that Modelica can use what is caused "acausal" models, opposed to what "Matlab" only supports and it is "causal" objects! Now I can imagine that this terms used in the previous sentence can be and probably is intimidating at the first glance. But I assure you it is simple and clear.  Her just the textual version of the spring model:




As you can see, under the title "equation" all that sows up is the normal spring equation. The red colored text gives a reference that the objects used in the model do inherit properties by showing the class hierarchy of the used components in the circuit, here the simple case of a spring.


The challenge that makes this kind of modeling language possible is that the software by its own has to generate the equations to calculate the unknowns. Tools like mathematica from Wolfram reflect the tremendous advances that have taken place in developing mathematical "solvers". This actually makes it possible to have the software tools apply themselves the mathematics required to solve mathematical problems, here calculating the unknowns depending of the "direction" which the model is used. It is a bit like when I was in high school and the electronic calculators did enter school. Did we get points in the past by calculating the solution, now with electronic calculators the points were only given by expressing and defining the equations into which the numbers were entered and calculated using the electronic calculator! same is possible now! The tool, the Modelica development environment, applies the mathematics to the equation to solve the job by applying mathematics! So the challenge for a naval modeler could be seen not in developing the skills to apply mathematics, but to apply his or her understanding to formulate the equations and understand how to formulate mathematically the relations between the elements of a system! The simulation environment of Modelica then applies the mathematics.


Causal objects are causal in the sense that inputs are clearly defined as causes that happen, that then are processed according to some rules and as a consequence generate "outputs"! Simple familiar cause and result, a concept we are all familiar with!


So acausal components state in their name that this fixed direction from an input being processed to generate an output  based on those inputs does not apply the same way!


Acausal components have, as shown in the graphics of a simple model of a spring, and equation in the model and that equations are being supplied with the required parameters from the "connectors". The consequence is, that the same unmodified acausal model can be used when inputs are those entering the model from the left and generate the outputs that are displayed on the right, as any causal object does. But that same unmodified component can receive inputs from the right side and generate outputs on the left side. Lets take a very simple example we naval modelists are all familiar with:


Lets take the simple model of a DC motor:




This simple graphics shows how a model of a system looks like, to which you apply a voltage. The resistor and the inductance shown in the graphics are used to model the electrical behaviour of the DC motor resulting on the right side in a rotational speed of the rotor in the DC motor and a torque available.




Here the relatively complex modeling of the above circuit using Matlab, respectively generating a causal model.


Now if I take the original Modelica modeling of a DC Motor and instead of applying a voltage, I do put a scope that shows the tension over those same poles. If I now apply a torque to the same model above, that the scope will show the voltage generator by the DC motor now operating as a generator. As you can well imagine if you would have to model this were the DC Motor becomes a generator would require a complete redesign from scratch using causal objet methodology. Murphy was active, I could not find the graphic showing the inverse use!


What Modelica environment does depending on how models are connected using the "connector elements" called "flange" in the symbol for a spring above, is to generate equations to have the same number of equations as there are unknowns! I. e. it applies what is known analogously in analog electronics, the "Kirchhoff Laws"!




This is called the voltage law from Kirchhoff and it states the obvious, that in any circuit the sum of the tensions = 0. This analogy in complex dynamic circuits diagrams and in Modelica represent the content of the recipients.  




This is the current law. it states equally obvious, that the sum of the currents at any node = 0. using such principles, on which I will elaborate in the next pillar description about System Physics are examples about how the Modelica simulation environment generates equations so to be able to solve the equation within, transformed to the actual direction of input to output, to compute the unknowns!


3. Pillar, System Physics:


System Physics is a new method to view physics and that takes advantage of the methodologies of the other 2 pillars I have presented so far. I will introduce you to it in my next post. It will show how all 3 pillars together make a modeling possible and not intimidating, if you are introduced to the simplified perspective that I am working to develop and simply start to use the powerful software tools available, a lot of them for free.

Edited by Hellmut1956
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  • 2 weeks later...

Hi druxey, not every one is so knowledgeable as you are. but may be you can then help me with my road blocker! According to system physics, a way to deal with physics based on the methodology of the method originated with complex dynamic systems, mechanics are described around "Momentum" being the content of a recipient, and momentum flow, force, being what is following into and out of the recipient. I am stuck as I do not find how to model an individual sheave embraced by a rope with a certain angle. i do have the Euler-Eytelwein-Formula in mind to be used as equation in the recipient.


If you look that "draft" of a flow chart describing a single sheave I have made using Berkeley Madonna, I do not know how to reflect the "Momentum" within the recipient that represents the sheave! The forces are pretty clear, so the pull tension applied to the rope would be varied in a simulation from a value of "0" to some higher value. Based on this the Euler-Eytelwein-Formula would give me the friction that works against the pull tension. So at some point there will be an equilibrium condition between the pull force on the rope and the friction and as a result the third arrow would have a value of "0".


But what is the mass in the equations for momentum and the pulling force according to the system physics?


I have been collecting material to study this aspects of system physics. As soon as I am enough through to either know the response,  in which case I will publish it, or know that I am not able to find a response, then I will contact Professor Maurer and publish his feedback! If you are able to help me I would be very thankful, as I am keen to do my first simulation just around the behaviour with a single sheave!

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I'm not that familiar with the physics involved, Hellmut, but the frictional forces in a sheave will surely vary. The factors to be considered are:


1) friction between the sheave and its pin

2) the angle at which the line enters and leaves the sheave (i.e. how much contact surface there is between them)

3) the diameter of the line and the groove in the sheave (surface area of contact)

4) the coefficient of friction between the two elements

5) diameter of the sheave


There maybe other factors that I've overlooked. Of course, multiple sheaves will complicate things even more.... Perhaps this can all be reduced to a vector diagram.


Mit grusse

Edited by druxey
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  • 2 weeks later...

Dear friends and specially those so brave to still read what I write, hallo!

In the last months I have received partly very emotional and in times personally aggressive replies to my report on this subject! Such reaction s are expression of underlying reasons that induce people to respond! On one side, and fully understandable, the subject of this subproject of my building from scratch the sailboat model I named Carina, is pretty distant from what naval modelist usually present!

On the other side I have gotten such reactions from 2 different communities. One are the naval modelists, and this in all languages I deal with, spanish, english and german, so it is pretty much across cultural borders, the other source is from forum members dealing with physics!

The naval modelist and real sailboat skippers argue along the lines that implementing a pulley with seven sheaves as it was used on the original sailboat Endeavour does not work on a model with a scale of 1:20! The basic argument here is, after accepting the fact that my systems concepts has no problems to deal with changing the length of the sheet by up to 8400 mm, that the friction in the sheaves makes the sailboat inoperable due to the friction between the rope and the sheaves in the pulley!

The community dealing with physics argues about totally opposing lines of arguments. They say there is only the friction between the sheave and the axis and that by using ball bearing as I plan to do this friction is neglectable!

So you can see that depending from the background the experts are coming you get to completely different results about the issue of the friction! I want, nevertheless add, that a real sailboat skipper that has a small pulley on his sailboat wrote that effectively the friction represents a major factor when operating his real sailboat. What he wrote is that the friction between the rope and the lateral walls of the blocks has a major effect!

So advancing my studies on "System Physics", the way I want to apply the impact of physical effects in my model and the preliminary results from my investigations on the subject of friction in the sheaves of a pulley. I have felt able to give a call to the physics institute of the highly respected Munich university, Ludwig Maximilian Universität, short LMU. There I was lucky enough to get hold by phone of a scientist willing to respond to my questions.

I presented to him the fact that I was planing to study Physics for the Bachelor degree, but that as a person with serious health problems I had to teach the subjects upfront myself, something as will never ever get a job in the industry, gave me the time to do so! I presented to him the two view points I have met and just presented to you, I told him about the limitations of the Euler-Eytelwein-Formula that just represents a formula, not with an "=" sign, but with an unequal symbol =<, that basically says that the real friction impact could be up to the value computed when replacing the unequal sign by an equal sign. I also told him that I had found out so far that even for the classical mechanics in Physics you met very different ways to deal with the same aspects of physics in mechanics giving as an example the classical physics way as reflected i.e. in the Euler-Eytelwein-Formula, but also the views and methods applied by System Physics and by topological manifolds! It became apparent by his reaction that he was willing to take my question seriously and he laughed when I talk about those different ways to deal with mechanics.

His explanation about the reactions from the physics community towards the friction in the pulley was due to the fact that many physics view the physical issue from an idealized perspective and that in this view it was correct to say that only the friction of the bearing of the sheaves was present. But that in real world due to diverse reasons even without the rope slipping around a sheave there was a friction component that could be relevant and that the inequality symbol used in the Euler-Eytelwein-Formula was due to those aspects that impacted the exact amount.

I informed him further That I had started to study a Master-Thesis hat dealt with the friction between cylindrical bodies and a rope and that did analyze the friction is sailor nodes using the mathematical method of finite elements. For your information dear readers without the intention to lecture those of you that do well know the issue, the finite element mathematical method is a method that computes problems by splitting an object into infinitesimal fractions and integrating the results to get the grand total. So it is what is called a numerical or discrete mathematical method that approximates its results depending onto in to how many sections it splits an object.

Simply stating it, it uses the mathematical power of computers to compute a subject split into many, many pieces and adds them to get the final result.

Well, this is one of the reasons why i decided to use tools that combine modeling and simulation with strong mathematical capabilities and due to many reasons I believe I have already tried to explain I decided to use the software from Wolfram Software, Mathematica and SystemModeler. So I can start modeling my sheaves and the pulley with seven of those using the modeling and simulation capabilities of Modelica, an essential element of SystemModeler and to use Mathematica to compute, i.e. by the finite element method as applied to the friction between a rope and a cylindrical body, here the sheaves in my pulley, as described in the Master-Thesis I downloaded a copy from.

But any modeling and consecutive simulation results depends in a very essential way from the quality of the models used! And exactly here comes into play what i have presented earlier in this thread, the "Hardware-in-the-Loop", short HiL, and "Software-in-the-Loop", short SiL, for which the Teensy 3.1 and the RaspBerry Pi B+ boards have been purchased. I will have to define experiments were I can compare the data resulting from measuring in the experiments and the data generated through simulations using those models! mathematica offers so called "solvers" that can generate equations that follow the experimental data at the minimum error defined and so adapting the models to the real world data.

May be, if I do not die earlier due to my health problems this thread and other similar ones in the different forums that I use to get support and feedbacks, I will be able to present the facts resulting from modeling the pulley. I am completely aware and I do accept the following possible results:

1. The experts from the physics forums are right and friction using ball bearing in the sheaves is irrelevant for the operation of my sheet control system in my model scaled 1:20 to the original Endeavour!

2. The experts from the naval communities are right and the pulley is not able to produce results that do not render my sailboat model inoperable due to the friction in the pulley!

3. Any results between those two contradicting positions, or may be even a completely different and unexpected result.

But what will definitely be a result if I succeed to accomplish the modeling and simulation of the pulley in my sheet control system, is that i will know and understand the relevant and irrelevant parameters and their impacts! With the following graphic, simple and full of errors, but still the best I have, I will try to present what really understanding the friction in the pulley and the impact of the design parameters have.




If you look on this drawing and if you keep in mind that the angle with which the rope embraces a sheave has a major impact on the friction to the movement of the rope around each of the individual 7 sheaves of the pulley, you will see that where you place those blocks containing the sheaves has an important impact on the angle with which the rope embraces a sheave! If the distance horizontally between the sheaves increases, the angle will get smaller. by smartly selecting the diameters of the sheaves this can additionally be influenced.

Now you have to be aware of, that the "Momentum" used in System Physics to represent mechanical systems and the pulley is such a mechanical system, requires to analyze and consider independently the momentum in the 3 directions of space, Px, Py and Pz, it becomes apparent that the proper choice of the cartesian coordinate system is relevant.

The X-axis of a cartesian coordinate  system would be along the center line of the hull, the Y-axis would be parallel to the water surface, horizontal and perpendicular to the center line of the hull and the Z-axis would be vertical. As usual the problems arise when you start to deal with details! Would the position (0, 0, 0) of this cartesian coordinate system be at the floating line level of the hull, means placed at the height of the water surface, would it be better placed at the rotational axis height around which the hull rotates when due to wind pressure in the sail i.e. gets inclined, or would it be better placed at the height of the boom? This is just reflection about where to place the origin of the cartesian coordinate system along the vertical axis!

The orientation of the Y-axis is probably less difficult to decide? It should be parallel to the water surface! But where along the X-axis and the Z-axis? Along the Z-axis i have already presented the issues above. Should it be placed where the hull rotates when turning around it, or should it be placed where the rotation axis of the boom of the sail is?

But with the Z-axis it is a bit more complicated. The questions as to where it has to be placed along the X-axis raises the same question as to where is the rotation axis when the hull turns left or right? Should the orientation of the mast be the direction, so that any rotation of the boom keeps the Z-axis value of the boom along the length of the boom the same, and so on!

The issue to be considered from the mathematical complexities resulting from a bad choice of the reference coordinate system. if an axis of the coordinate system at the same time is the axis around which rotational movements take place, computation is simple, if not, then it is more complex. But besides the complexity of the computations of equal importance is to keep it adequate so that the interpretation of simulation results is kept as simple as possible!

So to summarize the issues around the selection of the proper cartesian coordinate system, ignoring that there are also other coordinate systems. Any object could move in 6 ways, called the number of degrees of freedom of the movements!

An object can move along any and all of the 3 coordinate axis , the first 3 degrees of freedom of movement, each resulting in its own formula to describe the movement of an object along those axis, a total of 3 of what are called translational movements and as a result translational mechanics.

But the same object can also rotate around each of this 3 axis, those are 3 additional degrees of freedom of movement an object has and as a result you can have 3 more formulas or equations that describe the objects rotational movement and as a result we talk about rotational mechanics.

The method I plan to use is to have a reference cartesian coordinate system which has its origin at that location in 3D space where the 3 axis around which the sailboat hull can rotate. Additionally I will use auxiliary coordinate systems that are placed in such a way that the mathematical description is kept as simple as possible. So as a result there will be equations that describe how to convert coordinate values from an auxiliary coordinate system to any of the auxiliary ones used This conversion equations between different cartesian coordinate systems are relatively simple, but the key is that the computations taken place in the adequate auxiliary coordinate systems will keep the mathematics as simple as possible and make it much easier to understand the results within those auxiliary coordinate systems. lets take an example of one auxiliary coordinate system assuming the "reference cartesian coordinate system" to be as explained at the beginning of this paragraph!

In one such auxiliary coordinate system the X-axis would follow the direction of the boom and the Z-axis the mast! So in the plane defined by those 2 axis is where the sail is located, what ever position the sail and its boom might have in relationship to the hull. So if the sailboat leans to one side by 30°, this would have no effect on the auxiliary cartesian coordinate system. The same applies to the X-axis when the boom rotates. Lets assume the boom rotates to the center line of the hull by 45°. The Y-axis of the auxiliary cartesian coordinate system, being oriented vertically to the plane defined by the X-axis and the Z-axis of the auxiliary coordinate system would follow the rotation of the other 2 axis.

So to convert a coordinate value described by the auxiliary cartesian coordinate system to the reference value we would combine by applying the 6 degrees of freedom equations that describe the movements of the auxiliary cartesian coordinate system and so get the values in the reference coordinate siýstem!

So what i just described and has to be applied to the 3 momentum equations for translational mechanical movement and to the 3 rotational momentum equations. Now you can see that just by describing the 6 degrees of freedom of an object and having as a result 6 equations is what the Modelica simulation environment has to do with the equations included in a model! So the modelica environment takes advantage of this "knowledge" to generate automatically and invisible to the user i.e. what I just presented to do the computations required to simulate a system using the models that describe this system!

Here is where the object oriented implementation of the language Modelica comes into play! When I define a proprietary model of a system or any part of it I start from using object classes given in the "standard object library" of Modelica. So mechanical objects in this library, be they translational or be they rotational have in their classes already included the properties that such mechanical translational or rotational objects have and those are inherited in the new classes that I define using objects from the standard library!

So key for any beginner and apprentice like I am is to grasp this concepts and learn to properly apply them when designing our own objects and to use this knowledge when interpreting the results of simulations! Finally I have been told that this weekend i will receive a copy of the brand new version of the Modelica master book, so that I can learn and study it! Let me reemphasize this! I am new into this, I am a beginner and I am an apprentice. So making the assumption I am lecturing you is far away from being so! All I am doing is to share with you, the same way we do it when writing a report from scratch, the up and downs when dealing with the challenges I encounter and as an optimist I am, to may be find some valuable advice from you my dear few readers left! But let me also emphasize it! Even those that get emotional and sometimes offensive as a reaction to my reports. The fact that I have been confronted with such behaviour and attacks from the naval modelist community and from the physics community has been of incredible value to me! The fact that those 2 communities have opposing and conflicting opinions about the friction in a pulley as I am planing to implement in my sailboat model at a 1:20 scale, is in its own right a valuable piece of data for me!

Believe me. Just getting to the point were I felt capable to contact a physics scientist at the physics institute at the LMU and ask the question has taken a large effort from my side! To ask the question properly i did face 3 challenges, at least!

1. Understand and put in context the statements received from experts in the naval modeling community.
2. Understand and put in context the statements received from experts in the community pf the physics.
3. To be able to formulate my question such that my counter part at the LMU took my question seriously!
4. To be able to put the former 3 sources in relationship to refine the objectives of my design by modeling.

I am certain and not yet even close to be able to grasp the problems I will encounter when dealing with the mathematics in this context! And so I am not even able to say what questions I might have that I will present in the mathematical communities in the proper forums. I know, that the very little I have been improving my studies just to get back and up to speed with the mathematics I once knew when I joint the university and I was an excellent student at school kind of just enabled me to have a framework of understanding of what those mathematical courses that form part of the bachelor of mathematics and of physics are all about. They really are not more than just the basics skills required to get away from beeing a mathematical analphabet. As a result I have an idea about the mathematical methods available and I have the means to know where to look in to acquire the knowledge in the different fields of mathematics as the need pops up! I hope that learning to use the software tool Mathematica will help me to overcome my lack of experience in applying mathematics by understanding enough of the mathematical methods and of the use of the software Mathematica to "use" the mathematics for my goals. I am very explicit! I am in doubt if I ever will have the courage to say about myself to be a mathematician, but I do have the hope to be enabled to apply mathematics as required for reaching my objectives!

As we are in a naval modeling website i would like to add 2 pictures from the self made sheaves that I plan to use in the blocks that will make up the pulley in my sailboat:






This sheaves I did make using my lathe in aluminium and I have inserted a ball bearing and allow for an axis with 2.5 mm diameter and have an external diameter of 20 mm and an internal diameter for the rope of 12 mm. The height of 4 mm of the shoulders I hope will allow me to prevent the 0.9 mm diameter Aramid rope to get in touch with the wooden case of the block in which the sheave will be installed!

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I understand part of your dissertation, at least! The fact that you are examining a dynamic system, where the relative positions of the sheaves keep changing, means you are chasing a chimera that is shape-shifting. Thank goodness for computer analysis!


I'd be concerned about the sheave groove depth increasing friction. A shallower groove with a wider rim on each side will keep the line clear of the block sides. What do you think?


You mention health issues, Hellmut. I hope that these can be resolved or, if not, ameliorated.


Mit grusse

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I'd be concerned about the sheave groove depth increasing friction. A shallower groove with a wider rim on each side will keep the line clear of the block sides. What do you think?



As I recall from my racing days with pulleys and belts (same principle), the deeper the groove, the higher the friction. Much depends on if the sides of the sheave rub/touch the (in this case) rope. Wider sides would be preferable to a shallow groove.  We'd want the rope to be as loose in the groove as possible with minimum touching friction on the sides.   I've seen a chart somewhere but it was for pullys and v-belts and minimizing horsepower losses depending on rpm, etc. so I'll have to do some digging.

Edited by mtaylor
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The sheave shown in the 2 images is many, many years old and I did make it using my own lathe. So any changes required or any new design for sheaves will not be a problem! @mtaylor, any data would be very much appreciated!


I will look into the lateral friction issue, as I have been told that also friction between rope and the lateral walls of the blocks is also something I have to take into account! To look closer to the original the lateral walls of the blocks have to have at least at the surface a wooden lateral wall.


@druxey: just imagine the pulley with the boom in an angular position close to 90°! Here not just the friction between the rope and the lateral walls, be it of the sheaves or be it of the blocks, but also with the water. But good think about this pulley touching the water is that that helps the sail to open! In the opposite direction when the winch is pulling I do use a 3 Nm torque stepper motor and can change it to a 8 Nm one, so pulling force from the winch should not be an issue!


Just a small remark on my health issues! 3 years ago I had my first stroke and it was located in the brainstem where besides the function of swallowing is located, but also the respiration center. For the first week I had to be fed and received to drink and medicine through a tube, no fun! But if the respiration center would have been affected, well I would be either in hell or heaven!


Then I had strong problems with my medication so that I got cardiac rhythm problems that let my heart stop beating a couple of times, the first time unfortunately so long that some grey cells were damaged resulting in a problem of reduced concentration capabilities.. So I got a pacemaker, medication was improved and then I got a thrombosis were the cables from the pacemaker entered the vein and so i got medicine to fight the thrombosis! nobody knows what thinks are good for, because i suffered a second stroke while taking those medicines. The consequence was that while it is surprising I suffered a stroke while taking the medicine to fight the thrombosis this had the effect that the stroke was light and just of short endurance. Then they discovered, I am participating on a long term study made on stroke patients a bigger stuff close to my brain and it had to be removed. Fortunately harmless! 


So my therapy to fight the damage in my grey cells are the studies I am presenting here. No better therapy to have the brain reorganize itself to fix the damage then exercising the muscle between the 2 ears!  :). This combined with the fascination of dealing with our wonderful hobby is the source for positive thinking which i have been told also helps!


I am not describing my health problems to get compassion, but to show to others that might have the same or other serious health problems that it is never too late and that the forces brought to life by the fun we have for our hobby is a source that helps to face the challenges! But one side effect of this health problems that I have had no event in the last year, is that I am aware of that our lifespan is limited and that I might have not too much time left! So when I took the decision to continue with these activities that possibility that I might not see and reach the result, the time and the activities spend with it are a good choice within the options I have. Luckily I have a wonderful and brave wife and 3 wonderful kids, so that all sides of my life are great. 

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Thanks for your explanation and positive attitude in overcoming health problems. Hopefully the discussion here will continue to exercise your mind!


Certainly adding water to an already complex problem makes things even more interesting. It will be interesting to read your conclusions, Hellmut.


Mit grusse

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Most of your math is way over my head.  The fact you can present it and discuss says a lot about your mental acuity and more about your attitude. 


I'm searching but not finding it.  I thought it was in a box of some documents.  I'll have to start online.   While it was more for high speed, high horsepower applications, I think it would apply here as a sheave is a sheave and it doesn't matter if it's a belt or rope, the forces are still present.

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Thanks for both of your replies! @mtaylor: I am dealing with defeating the erosion of my math knowledge over the last 4 decades since about a year. I had to start working on it as it became apparent to me that without a certain level of mathematical skills it would be impossible to accomplish my goals!


But what is key to say is that there are wonderful resources available online and for free to work on the mathematics and if you keep in mind and pursue the intention to apply it to naval modeling issues they are neither boring, or tough or dry to deal with, but a key to get access to a whole world of new possibilities. Here the link to a course offered for free from the MIT in Boston by its "OpenCourseWare" program. The book can be downloaded for free and legal as a pdf archive at the homepage of professor Gilbert Strang! Once you overcome a certain degree of intimidation, is really just in the mind and not real, you start to realize that this whole course of calculus for single variable equations is just the presentation of diverse techniques used to solve the creation of derivatives and integrations! I have had access to a book about analysis and one of linear algebra for dummies from our local library and there were tables that put all those schemes in tables. But what helps a lot more is when solving in parallel the work assignments from the course and the book by learning how to apply the software "Mathematica" from Wolfram Software! A Home edition license is really not too expensive. The key benefit of doing this is, that as we plan to use the mathematics for our naval modeling hobby and not to become mathematicians, through the course you learn to interpret the results from mathematical solutions, but have the software tool Mathematica do apply the mathematics required!

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  • 2 years later...

Sorry for not having updated my threads in this forum. Just last week I had me third stroke, fortunately it did not cause any permanent problems besides blocking a second arteria that feeds my brain. Both arterias fortunately hat second ones that could take over the job of feeding the cells in my brain! Pictures taken from my brain have shown that my intense efforts to continue my studies and learning have created and strengthened alternative routes to feed my brain. The stuff I am studying, the experiments I start to do once I have solved the vulnerability issues that rendered my PC inoperable, Windows 7 Ultimate 64 bits with all protection software in place and all updated on a daily basis if required, Allow me to take the short path. Learning, studying and implementing the technologies that are rapidly being developed requires to develop my own scheme to merge them into creating a safe environment for my lab and for the future use of my electronics in the model of the sailboat Carina on the lakes!





The picture shows the structure of the electronics in my workshop! It shows me sitting on my PC and being in touch with the Internet via the Modem. By the same means I do access RaspBerry Pi boards which the control the dedicated boards, being the either Arduino kind, supplier specific boards that cannot run Linux like the LPCXpresso ones and/or dedicated control boards for controlling stepper motors or magnetic angle sensors.


With devices connected with the Internet are growing in numbers due to what is called IoT, IIoT or Industry 4.0 and the ever stronger hacker activities in the Internet, technologies to reduce the vulnerability of devices connected to the Internet are explosively being developed. Understanding those technologies enough to develop a picture about how to use the to the benefit of securing not just my workshop, but also the electronics in my modelboat is a pretty challenging job, as this is currently taking place in the involved industry! I will go into more detail once I feel better!

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I'm sorry to read of your health issues, Hellmut. I hope that the medical community can stabilize things and that you will continue to recover without further cerebro-vascular problems. Best wishes as you recuperate.

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Thx druxley. Unfortunately I will never regain my full health, I have good days and good parts of a day and less good ones. Positive actitud helps my body to recover, fascination and curiosity for what I am learning keeps my endurance to pursue my goals and my mood high. Every day I have is a present and every day or part of the day that I cannot learn and cannot continue working on my workshop is a waste of the precious time I have left. I do not feel fear for dying. Dying is a part of life and the health problems I am enduring teaches you to really take death as a part of life. Worrying about it or complaining about not having to expect too much life time ahead of me is working for illnesses in my body and this would leave less days I can continue! I am very luck that presumably I will die by the consequences of my circulatory problems and not because of cancer! When I had those incidences where my heart stopped beating, reason why I got a pacemaker, have shown me what to expect when GOD calls me to him! Feeling bad, a bit of nausea y and bit of fear come prior to lose my consciousness. I did wake up in the past, but there will be a time I won't!


A good friend of mine, US citizen, never smoked, never drank alcohol, had no problems with overweight and was a DAN 5 of japanese Karate. Now he got cancer in his mouth and is rapidly decaying. He was recognized that this health problems was a late consequence of his time in Vietnam during the war! So at least he has now financial problems! We used to share the hobby of flying single engine airplanes while he lived in San Jose, CA, where he had a share of a Bonanza airplane. Compared to him, I do have overweight, I do have high blood pressure, I do have Diabetes type 2 and so on and will probably die 10 years earlier then he probably will.  


But I still have a hope that reading this contribution here in 10 years will have proven that I was to realistic this days! I wish this will happen not to leave my wonderful wife alone and never going to get to know my future grandchildren. I share this destiny with 3 generation of males from the ancestros of my father and my mother who all died due to circulatory problems!


But hey, there's this new generation of controllers about to get public, i.e. "i.MX8" from NXP, that ensure that the revolutionary development of science and technology that we are experiencing right now will continue to keep my wish and energy to learn high and my creativity to think about applying this to our mutual hobby of naval modeling. 

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