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Hellmut1956

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Design by Modeling
« on: March 14, 2015, 10:07:54 PM »

Hi friends


As commented in the thread of the report of my build from scratch of my sail boat model Carina, I would like to share with you my uphill fights to be able to use this methodology to design my sheet control system. I want to start presenting a block diagram of my sheet control system, then present the complexities inherent in it and presenting and explaining all the aspects of it and as a result based on the then shared perception of the challenges of the design of my sheet control system I would then introduce you to the methodology of the "Design by Modeling" and how this methodology combined with the mainly software tools available for it make it reasonable to expect to achieve a proper design of my sheet control system so that my over all 2 goals, the system works as designed and it achieves a high degree of energy efficiency.


The you will have the opportunity to share in my report how I am working to learn the abilities required and how I try to achieve my goals!


Lets start presenting the block diagram of my sheet control system implementation and use it to present the details of what each part is planned to be doing!





As it is my intention to have both the main and the foque sail to have a boom which rotates around a vertical axis, you can see in the block diagram that it has to identical threads, one on top planned for the main and an identical one on the bottom half of the block diagram fro the foque sail. So I will limit myself to present the upper half branch and you know that what is presented for the upper branch applies to the lower branch as well. Lets start with the left most block, "Interfaz receptora R/C". The skipper of this sail boat is at the pond with his R/C transmitter in his hands. I will start presenting it as being myself the skipper with my "robbe F14 Navy" transmitter in my hands and operating the split control stick, the left one, one half for the main sail, the other half for the foque sail:





You can also see the 8 rotary control elements that do belong to the Multiprop module that robbe offered for this R/C. It transmits using a single one of the 8 channels of the transmitter to encode 8 rotary control elements. By the way, it was my disappointment with this module that made me engage into doing my own electronics to overcome the evident poor design of this very expensive product from robbe! As you are all aware of, a classical R/C in the Megahertz band, here a 4o MHz system, transmits the position information of control elements on the transmitter of up to eight of those via encoding the position information in a PWM signal which is then available a the receiver sockets for those 8 channels once every 20 ms or 50 times per second. The encoding of the position information is done by defining the length of time where the PWM signal is at logical "1" and this length can be somewhere between 1 ms and 2 ms long.





This graph shows the example for the duty cycle being just 20% long, or being 60% long. The time between one rising edge and the next are those 20 ms. In a PWM signal as generated in the receiver the length of the duty cycle in a bit different. The length of time this line is in the upper state is 1ms in length in case the control stick and its trimmer are i.e. at the bottom edge and 2 ms when stick and trimmer are at the top edge position on the transmitter. The the length of time the signal has the "0" level, is at the bottom fills the time gap to complete the 20 ms cycle, so those signals are at "0" much longer then shown on this graph. Another aspect is, when you look at the PWM signals from all 8 channel is that the first channel signal goes to "1" at a beginning of a 20 ms cycle, the second channel only goes up 2 ms later that the first channel and so on until all 8 channels have been made available by the R/C receiver. So 8 times 2 ms = 16 ms and so approx. 4 ms pass until the first channel starts with its rising edge!


Well the robbe multiprop module sends the encoding for the first rotary control element, i.e. on channel 5, the second on the same channel 5 but 20 ms later and does this 8 times or 8 * 20 ms = 160 ms before he repeats the PWM signal for the first rotary control element! As those signal only repeat after 160 ms nothing connected to it, i.e. servos work awfully! The most disappointing fact was, that the multiprop module on the receiving end has 8 connectors like the receiver but still the behavior for each of the sockets signal was as described earlier, considering how simple it would be to have a circuitry in those models generate the signals every 20 ms, the length only being able to change after 160 ms and how expensive this module was, not acceptable!


So each of the 8 sockets in the receiver would supply the signal and a short cable would connect it to one of the general purpose I/O pins of the controller in the second block from the left in the above block diagram! The control would sense the rising edge as described before. With the rising edge of the first channel an internal counter would start. As soon as the falling edge of the signal is sensed the value of the counter would be assigned to a second variable, the counter would be resetted and so be ready for the second channel.  This way the length of the cycle would be sensed by the value of the counter on the falling edge, its length is digitized, means a digital value for the length of the signals duty cycle is known. So after the famous 8 * 20 ms = 160 ms all 8 channels are digitized. Depending how fast the counter is clocked the number of different possible signal length can be chosen.


This digitized duty cycle length is a value that reflects the position of the control stick on the transmitter and so it defines up to which angle the skipper wants to allow the sail boom to increase its angle to the hull center line! I call it the max_Position variable, as it defines up to which angle the skipper allows the sail to open!


The block named "Central" an LPCXpresso1769 board that just costs about 20.- USD plus shipping, has the function to monitor what the skipper wants by monitoring the PWM signals from the R/C receiver and has the function to control not just the sheet control system, but also other sub systems I do plan for my Carina! It communicates if a value changes, doing an "intelligent" judgement if it is a real change or just a jitter and only updates the other boards in the system when a real change happens!


Now lets go to the next block to the right of the "Central", the "Control Winche", also a LPCXpresso 1769 board, in this case in charge of the main sail sheet control! This controller board has a table in flash memory that reflects the following relationships:





This drawing needs some explanation as it is a key element of the logic that controls my sheet control system! The spanish words spelling is close enough I do believe to what would be the english spelling so it should be understandable for you! The upper green bar reflects the resolution the digitizing of the control stick position on the R/C transmitter! It is important to be aware of, that even the most sensitive R/C transmitter operator can only drive the position of the control stick for the sail position on the transmitter with a limited number of different positions. In this drawing I have assumed 64 different control stick positions on the transmitter between it being fully in the lower end and fully on the upper end of the possible control stick positions. 64 different position means 6 bit resolution as a result of 2^6 = 64. Now to include the finer control of the trimmer associated with each control stick moving directions, up&down or left&right 2 additional bits, for a total of 8 bits resolution would mean 2^8 = 256. As a variable in a register of the controller or in a memory location in flash memory is 32 bits wide, so if required the resolution can be chosen to be higher. The counter clock rate can be made as fast as the controller clock rate or between 70 Mhz to 120 MHt. The LPCXpresso boards use ARM Cortex M* controllers!


Between the 2 green bars the text written in red says angular resolution of mains boom!


Here comes to the explanation the function of the 2 blocks above the "Control Winche" block!





Here we have a picture showing an angular magnetic encoder. In green and red you see the magnet, whose poles are in the 2 hemispheres as shown on the picture. When the magnet rotates, its magnetic field rotates and the sensor below monitors this and get angular position changes of the magnet!





This simple drawing explains how the angular position of the boom of the main is monitored and sensed! the upper half of the drawing shows the boom of the main fixed connected to the vertically oriented axis, so that the axis rotates as the boom does. This vertical axis goes close to the deck surface and has the magnet shown in the previous picture mounted on its lower end such, that the magnet rotates fraction of a millimeter above the deck surface. The deck surface at tis point has an opening covered by a plastic foil to prevent hat water can come into the hull ar to the sensor place just below it. This openning is done in a way to ensure the magnetic field is not affected so that the magnetic angular encoder can detect the rotation of the magnetic field.


The sensor has an angular resolution of 14 bits for absolute angular encoding for a full 360° turn! 14 bits means 16 * 1024 = 16k position detected over a full 360° turn. Now, the boom can only rotate either 90° backboard or starboard, for the sheet control system it is not relevant to the length of the sheet made available to which side the boom rotates! This means that only 1/4 of the resolution related to those 90° are available! 1/4 of 16 * 1024 = 4 * 1024 = 4k different positions are sensed either starboard or backboard! This sensing is called absolute angular sensing and is available by querying the value of the register with the sensor IC by an external controller.


Interesting is also the so called incremental angular decoding! This method does not report an absolute angular position, but reports if a rotation has taken place clock or counter clock wise!





This incremental encoding is reported by the use of 3 PWM signal, called "A", "B" and "I" as shown in the graphic. Depending from which PWM signal happens first, "A" or B", the information is supplied about the direction in this case the boom is rotating. The PWM-signal "I" is used to track when the rotating magnetic field has completed a full 360° turn. The "I" PWM signal happens only once per 360° turn. This kind of incremental encoding is named "quadrature encoding" and the controller on board of the LPCXpresso1769, the LPC1769 has a peripheral on board that decodes and evaluates those 3 PWM signals and is called quadrature encoder peripheral! Now the great thing about this incremental encoding is, that all I have to do is to connect those 3 PWM signal to the associated pins of the quadrature encoder on the LPC1769 controller and it takes care, independently form other jobs the controller might do of keeping track of the position of the boom by adding "1" or subtracting "1" from a variable that tracks the angular position! Here you might guess why I like to talk about "position" and not about "angle"! The sensor and the controllers software work on positions that have a numeric value that says how many positions the current position is from an initial value = 0! Here is the explanation why the magnet at the bottom end of the axis around which a boom rotates has to be able to be turned manually! When setting up the sail boat at the ponds site I will have to put the boom in what I see as the center position, have the sheet control system shorten the available sheet until a certain tension is on the sheet and turn the magnet until the "I" PWM signal shows the rising edge and I have to do it twice, once from each side. So the software can compute the middle position and so determine a center position to which the value "0" is assigned! When the software detects the rising edge of the "I" PWM signal it lights an LED so that I have a visual feedback that the magnet is in the desired position. It doesn't really matter how precise i do this as the resulting difference of the 90° angle of the boom would be slightly but irrelevant different! relevant is it just to have such a central positions best guess, as the resulting difference of the maximum angle permitted for the boom would be irrelevantly different by a small amount backboard or starboard! The problem with this quadrature encoding is its much lower resolution compared to the absolute angular position. The incremental angular resolution for a 360 full turn is 2048, so for the relevant just 90° 512 different angular positions can be reported by this method. But this apparent weakness is at the same time the means by which I can solve a problem I have found reflecting over my sheet control system while walking with my dog in the country side! i want to present you now with a problem I encountered just reflecting over my sheet control system and which made me refine the sheet control system by taking advantage of the different angular resolution given by the incremental angular resolution of just 2048 positions or 11 bits versus the absolute angular resolution of 14 bits, the difference being 3 bits or 8 positions!





Imagine that due to little wind or during a turn of the sail boat the boom is in an position between the hulls center line and the maximum permitted opening of the sail set by the skippers placement of the control stick on the transmitter! Here I mention something I will address more detailed later! lets assume the boom is in a position, as monitored by the incremental position monitoring and I will name it position "X", here drawn with green. Now lets assume the boom due to the forces effective on it by the wind blowing into the sail or by the inclinations of the hull due to the waves in the water. My sheet control system only makes available that amount of sheet length equivalent to the actual sail position as monitored by the quadrature encoding of the incremental sensing. That length of sheet available is different for the position "X", than it would be available for the position "X+1". This means the boom would never be able to move to the position "X+1" due to the limitation resulting from the available sheet length.For fixing this I took conceptually advantage of the absolute encoding position information! Here as the short green lines show, there are 9 positions from "X" to X+1", as the absolute angular position sensing has 3 more bits of resolution. I have used the spanish term "umbral" to name the "thresholds". Thresholds are absolute angular positions, one on each side of a incremental position like "X". Should the boom reach one of those thresholds the software in the system would change the current position data of the boom from "X" to "X+1" for example, making additional sheet length available and changing the threshold values be those belonging to the "X+1" position!


This detail looks trivial but as a consequence the sail would never open to reach the maximum value the skipper allowed. Some details remain regarding how to choose the values of those thresholds to reduce the number of times the stepper motor is activated to adapt the sheet length. Also no real knowledge is available as to understand the dynamic behaviour of this and its impact on energy consumption and as consequence of energy efficiency! Also a detail I had to investigate in the context of this refinement was if there could be a limitation due to the cycle times of the sensor and the processing of its data. as you might guess, what resolution makes sense of the incremental angular sensing and the width set by the values of the threshold are one example how the choice of parameters will have a huge impact on energy efficiency. Remember that a stepper motor with up to 8 NM torque has a huge power consumption and so its activation will cause a huge amount of power consumption what impacts the capacity requirements of the batteries placed in the sail boat. Similar issues are due to numerous parameters that are available to control the operation of the stepper motor by the Trinamic components used in the block that here is called "stepRocker" and where due to technical reasons a favour a board of which I got hold of a prototype called "motionCookie!.


To the right of the block of the stepRocker board is the stepper motor and next to it to the right the sheet for the drum that is turned by the stepper motor! It is important to understand the positions a stepper motor can take and what affects the available torque from the stepper motor to turn the sheet drum which takes the load resulting from the wind blowing into the sails!


A stepper motor of quality is called a hybrid stepper motor and those usually make 200 full steps per 360° full turn. The there is something I will explain in detail in the report step by step of building the Carina from scratch that is called microsteps. Microsteps are added partial steps that take place instead of a full step. I use the full 256 microsteps per full step available to me by the Trinamic. components. The consequence is that the stepper motor makes 200 * 256 = 51200 microsteps per full 360° turn. The drum I use has a circumference of 400 mm. So 21 full 360° turns result in a displacement of the sheet length of 8400 mm I am aiming for! 51,200 microsteps * 21 full turns = 1,075,200 microsteps over the full 8400 mm sheet length displacement or to use the term position: The stepper motor has more that 1 million positions to set the sheet length!





At the bottom green bar you can see the huge number of positions the stepper motor can take to take the most adequate one for the 512 possible incremental positions monitored for the angular position of the boom!


But it is not just this!Of course I do plan to have also an magnetic angular sensor placed in the case for the drum and a magnet rotating with the drum and here the incremental position will be reported by the 3 PWM signals to the ARM Cortex M0 on the stepRocker or the motionCookie board. just to make sure I have a closed loop control!


From the energy efficiency perspective the Trinamic components offer the possibility to control automatically the flow of current to the stepper motor load dependent! This has a huge impact on power consumption! While maneuvering and/or with slow winds the amount of torque required from the stepper motor to have the load generated from the wind taken by its torque the full torque of the stepper motor is not required and so a huge amount of energy can be saved! I also have, due to the technical development of the components driving stepper motors as made available by the Trinamic components started to question if a mechanical brake would make sense! For this it is important to understand that stepper motors potentially have the greatest amount of energy consumption while holding their position! if a sailboat is navigating keeping the sail position and have the wind blowing into the sails the stepper motor would be just holding its position! Would I use a mechanical brake that only releases the axis of the stepper motor rotor when 24 VDC are applied to the break, I could have the electronic disconnect the stepper motor or reduce to close to "0" the flow of current. But with all those control possibilities offered today and taking into account that while maneuvering and changing the sail position in great length of time the load by the sails is low but the breaks would demand their share of current, it is a question if the use of such a break is justifiable. I must confess, I do not know!


I hope that up to here you have understood the complexities and the impact of design decisions and parameter value selection on the ability of my sheet control system to actually work and to be energy efficient. it was getting aware more and more of this facts and details that I run into this design methodology and understood its great contributions to my project resulting from it.


First I got aware of the tools Matlab/Simulink and a bit later of Maple/MapleSim and even much later of the tool Dymola from Dassault Systems known for example by being one of the partners building the fighter aircraft "Alphajet". Later  found that this tools were prohibitively expensive for a none commercial user like me. But I also realized that for the methodology of the "Design by Modeling" the requirements for mathematical skills was very high and that even when at school I has excellent qualifications in mathematics and physics, in the past nearly 4 decades I have not used this knowledge my skills have eroded and that the mathematics had evolved a lot! I also noticed that the knowledge I would have to gather out of the field of electronics engineering and physics would demand to invest heavily in learning mathematics. I like to phase that I felt like a mathematical analphabet or a mathematical legasthenic person when looking into the topics I had to learn!


Now, as I had suffered damage in my grey cells during the events were my heart stopped beating, the result is that I lost a lot of my abilities to stay concentrated over prolonged period of time, as required to do the studies I have to do, it also came into my consciousness that putting the effort to study what I needed for applying the methodology of Design by Modelling this would be like a therapy for my health! Making my brain work as highly motivated I am due to the fact that it is for my Carina project and that as I dealt with those mathematical topics I was fascinated by them my brain might reorg my synapses and fix the damages I suffered from those times my heart stopped beating! So my hobby and the learning for the use of the methodology of the design by modelling is like taking a medicine. I am now about a bit more then a year into this efforts and while I am advancing much slower then I had hoped I notice I can stay concentrated again over longer and longer periods of time! Just think about how much time and concentration it takes for me to write this that hopefully is logically consistent.


Another side effect of those studies at home is that I can learn from home the courses that make up the bachelor of mathematics and should I ever complete those courses I could register at a university in Munich, which is for free as nearly all german universities and get my bachelor! German universities and specifically the MIT in Boston offer a huge array of real university courses, the lectures recorded on video, even the exercises, lectures notes and even books are mostly available for free. You can choose the lecture with the professor that most fits to your preferences! But also, when you register at a university and I could do this at no risk if I have learned enough to pass the courses of 2 semesters, is to get access to academical licenses for the tools I wanted to use!


But in this process I found out that Wolfram, the providers and developers of the famous tool "Mathematica" were now addressing the special areas that I did require for the methodology of the design by modeling, mainly the tool "SystemModeler" and that they had none commercial licenses that were tolerably expensive. So I looked into it and found the tool Modelica and the modeling scheme they use, mainly something called "a causal" components opposed to the causal objects used by Matlab/Simulink and found that also MapleSim had the ability to support components defined using the Modelica language! So at the recent trade show "Embedded World 2015" in Nürnberg, Germany I learned that Matlab was offering their tools now at a fraction of the cost Wolfram did I was excited and planned to purchase such a none commercial license. Here I got aware that Matlab/Simulink did not support Modelica and due to my investigations I decided still so to stay with Wolfram and their tool set of Mathematica and SystemModeler.


What I plan to write next in this thread is my progress in learning to model components using Modelica and to start doing what might be simplest and it is to model a pulley.





Look at this picture of the original sailboat Endeavour and how the sheet goes from the deck to the boom and how many pulleys are involved. Designing such a model using the language Modelica would be a great initial learning experience to learn the issues involved to design how the tension on the sheet, the angle at which it goes around the pulley and its effect on the friction. It also is linked close enough to our hobby and the topic of this forum, even when the means are virtual, mathematical and involve the science of physics! I had received warning that in a model the size of my Carina the friction of the sheet in the pulleys and the tube through which the sheet goes within the hull might render my sailboat inoperable! let me just tell you that my initial investigations have shown that the basic equation for the friction in the pulley dates back to the seventeens century. I have found thesis for master and PhD grades that deal with the topic. One i have gathered this information I will think about how to generate a first model of the pulley and then keep improving it until it is adequate for my needs!
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Best regards Hellmut

flashtwo

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Re: Design by Modeling
« Reply #1 on: March 15, 2015, 09:40:26 AM »

Hi Helmut,
Wow, that was a long read!

The first step in any engineering project is to define the problem and end objective, but not necessarily the solution.

The next is to consider the options – starting with the simplest and considering costs, timescales, maintainability, flexibility and nowadays being future-proof.

I agree with you the 160ms refresh rate is too slow and requires a method of “remembering” the PWM transmitted value.

The use of a microcontroller based system to “remember” the PWM value is very versatile – will you be using interrupts for handling the incoming  PWM pulses, or will the processor have a high enough processing rate to “pole” the required input?

If you don’t measure the PWMs precisely every time, then you will get “jitter”.

For stepper motor control “centring”, have you considered using a Hall type magnetic switch to “inform” the micro-controller that the boom is centred rather than you having to do it at the pond side? The controller would be centre checked every time the boom passed the centre.

The Hall switches could also be used at the boom mechanical limits to stop the stepper motor from over driving and causing damage.

It seems to me that your project is to learn about certain engineering methodologies and are using your model yacht as the test bed of those techniques – it is good to have a project where you can demonstrate your newly learnt skills in a practical way.

I enjoy developing microcontroller applications for controlling my steam boat – it adds that extra dimension to model boating …… and extra fun in a technical sense!

All the very best in your engineering project.

Ian.
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dreadnought72

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Re: Design by Modeling
« Reply #2 on: March 15, 2015, 10:52:39 AM »

Hi Helmut - thanks for the post. It's thought-provoking.

One thing that catches my eye: I love the boom-angle position sensor. There's a pile of gadgets that are now available which can be "read" by microprocessors, and I think your magnet solution is a great one.

However, is this not all the monitoring that you need? When sailing, if your transmitter stick only sends angle info for this sensor (for example "set boom to 45 degrees") you could write software to let out/take in the mainsheet until this angle is met. You wouldn't need to monitor the revs on the stepper motor, or deal with the hassles of the 3d geometry of whatever blocks and sheet run are involved. The stepper would simply run until the boom-angle sensor says "that's enough".

When sailing real boats, I don't care what the sheet is doing, or calculate the length of how it runs to the boom - I simply want the sail angle to be "right". Would this not be a better approach to what you're trying to achieve?

Andy
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Hellmut1956

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Re: Design by Modeling
« Reply #3 on: March 15, 2015, 07:09:41 PM »

Whoww! I am impressed by the quality of both responses. So I will try to respond as good as I can to reflect my appreciation for those 2 responses. At the same time i want to express clearly, that the issues related to my decision to engage into learning the skills required to use this methodology and my intention to share here my learning to achieve this skills as the topic of the thread are the result of decades dealing with technology and about a decade dealing with electronics as an additional technology that opens infinite doors to new possibilities in our hobby. I have found that electronics are intimidating to many and so they stay viewing what ever has to do with electronics as a number of black boxes that by magic to deliver certain functions.

About a bit more then one decade a friend of mine and myself came together in my workshop on an afternoon, just to see what it meant to decode the PWM signals from a R/C receiver. Believe me or not, it just took about 2 hours starting from an existing board with an Atmel mega8 controller ans a small display capable to display 24x2 alphanumeric digits to have the 8 channels digitized and the digitized values be displayed on the screen of this small display! So when you moved any control on the R/C transmitter you saw how the digitized value changed from a smallest number resulting i.e. by having the control stick on the transmitter pulled fully down, including the related trimmer, to the other extreme with the control stick pushed fully up, the same for the trimmer. In this first run we had the controller just watch the pins to which the 8 PWMs were connected to start a timer, then wait for the falling edge, stop the timer copy the value to the display, by far the slowest event, reset the counter and wait for the next rising edge.

This friend of mine drove back home and that same evening he send me an email informing me that he has changed the code to use interrupts.

He then developed a tutorial where people wishing to learn could build from scratch the device to store the program in the flash memory of the controller and then build a so called experimental board using a PCB with through holes in small steps to learn to apply what was in a schematic of a circuit and implement it in hardware using short cables soldered as the schematic said.same along that pass they learned how to write and burn those programs into the flash memory and have a LED blink. This blinking of an LED is in so called embedded applications what in programming software is called the "Hello World" program! Due to the process of implementing small parts of the circuit on the PCB with verification that the hardware implementation was properly done and then experience that "your own circuit" does what it is supposed to do motivates you and teaches you the important lessons of reading the schematic of a circuit, build the hardware following that schematic, verify the hardware to find eventual errors in soldering or implementing of the hardware. This process is called debugging and uses a multimeter mainly to measure the resistance of a line. It also teaches you to verify upfront that the power supply only shows up at the pins it should and so to be certain you will not kill your controller when plugged into the socket!





You don not learn this and loose the black box attitude towards schematics and hardware if you have not gone through such an exercise! Once you have completed the experimental board and verified the software components you have a set of "legolike" building blocks, which properly combined enable yo to build all you dream of, being able to have a first judgement of what can be easily accomplished and what not. Then and only then, it makes sense to go and use Arduinos or similar boards in the market, because with the knowledge acquired you have the skillset to deal with those boards, now not as black boxes anymore!


Well, similar it is with the methodology of the design by modeling! As I am new in this field and I try to study and understand thinks to the extreme detail, I start looking into many fields to loose the intimidation of the new area. First thing that became obvious to me when starting to look into the tools and the university courses that offer knowledge I believe might be valuable was, that without a certain level of ability to deal wit the mathematics that pop up everywhere in the topics to which this methodology brought me in touch with, I would be a mathematical analpabet or at least a mathematica legasthenic person. I felt like a person without the ability to read trying to understand stuff in books or magazines and all he can do is grasp general concepts by studying the pictures. So here as I tried to refresh my mathematica knowledge from high school and university and having a first look into 2 of the mathematical courses that I had to learn, "Linear Algebra" and "Analysis", those courses from the MIT OpenCourseware are all for free, I decided to go the path of not tolerating luck of knowledge. So those courses refer to 2 other courses as prerequisites, "Calculus Single Variable" and "Calculus Multivariable". Prof Gilbert Strang who gives the lectures for Linear Algebra in a way I found to be a good fit, also has written the Book for the 2 Calculus Courses that is available as pdf file in the Internet. I found that the Calculus courses were the ideal tool to refresh my mathematical skills and working through the intense and extended set of exercises additionally to the lectures recorded as a video, same by the way for the "Recitation Classes" were assistant to the professor guide you in videos through some of the exercises are a wonderful 24/7. Available lectures that can be repeated unlimited times until you grasp completely what is being presented or investigate in the internet background information about people, terms and concepts using wikipedia and google make learning much better and less stressful than going in person to a lecture and all this for free! By know I am still behind the goals I had set for myself, my health is the limiting factor as well as the concentration problems due to my damage in the brain resulting from when my heart stopped beating. But believe me or not, its fun learning. But now I feel confident enough to embrace, parallel to the studies the charter of dealing with learning the use of the tools "Mathematica", "SystemModeler" and the "Wolfram Language" and by having purchased the RaspBerry Pi b+ board that runs a free version of "Mathematica" and of the "Wolfram Language" I can study and learn how to have Mathematica and/or SystemModeler communicate from the PC on which they run with the RaspBerry Pi B+ board. Additionally I have purchased the Teensy 3.1 board which has the "Firmata" protocol available for it and which enables SystemModeler to communicate and use the Teensy 3.1 board. Here some pictures:








This 2 pictures show the Teensy 3.1 board and shows the functionality available. I will use this with the SystemModeler to try out examples of how SystemModeler running on my PC communicates and uses the different functionalities available on the Teensy 3.1 board. My goal is to understand in detail how the "Firmata" protocol is used from SystemModeler running on the PC to the Teensy 3.1 running the same protocol "firmata". Then I want to learn how to overcome the limitations of the "Firmata" protocol and change it on both sides to overcome those limitations. Finally I want to make the "Firmata" protocol available on my LPCXpresso 1769s so that SystemModeler can communicate the same way with my LPCXpresso boards!





For the RaspBerry Pi B+ Wolfram makes "Mathematica" and the "Wolfram Language" available for free. So analogous to what the Teensy 3.1 board is for learning how the software SystemModeler" running on the PC can communicate and operate the Teensy 3.1 board using the "Firmata" protocol, I want to learn from the RaspBerry Pi B+ board how Mathematica and Wolfram Language can communicate and operate the RaspBerry Pi B+ board. by the way also a nice platform to learn finally about Linux!


Here I am moving a bit ahead but as flashtwo correctly stated in his message, it is good engineering practice is to define the problem and the objectives! my problem and challenge is to know how to achieve my objective. My objective is using Mathematica and SystemModeler using the Modelica language to model the components of my sheet control system with my LPCXpresso boards to model my sheet control concept, identify and study potential areas of problems and to have as a final result of the design and modeling phase a concept that has proven to be of enough quality so that the real hardware an the model achieve the same results, a working energy efficient sheet control system that is as optimized as possible.
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Re: Design by Modeling
« Reply #4 on: March 15, 2015, 09:03:55 PM »

So, now I want to respond in detail to the two replies received! First, whoww really good replies! let me state that even while I was trying to keep the contribution short, the result is as usual an epic reply! But still so the replies received document the need to explain some of the reasons to make it possible to understand the topics! So in the last reply I did try a bit to explain why my decision to embarque into the challenge of applying the methodology of the design by modeling was the result of potential problems that I had received advices of from members of different forums. They basically stated that while the sheet system used in the Endeavour was a necessity because of the size of its sails:As you can see in the picture the huge size of the main sail made the requirement to enable human beings to cope with it a pulley system had to be used to reduce the tension on the sheet due to the wing pressing the main sail manageable by human beings. The winches were below the deck and did require a whole team to operate it and the Endeavour had 2 winches below the deck to enable doubling the human force. Now in a model the friction caused by the blocks in the pulley might prevent the main sale from opening rendering the whole sailboat inoperable. The sheet going under deck through tubes would generate static electricity which would add to the forces opposing the move of the sheet and as a consequence the possibility to operate the sailboat. Also as I mentioned earlier the torque required to operate the main sale and to be supplied by a winch in a model represents a problem slightly made easier to handle thanks to the pulley system. Also the ability to reliably operate a sheet displacement length of up to 8400 mm in a sailboat model of the size of mine could hardly be handled by any existing commercial sourced winch. Well, there are some systems out there that might be able to handle this:Klaus Prystaz presented his magic box shown in the next to pictures that basically uses 2 drums of different diameters to achieve longer sheet displacements:



Other system work with drums of conic shape to achieve longer sheet displacement. All of this techniques suffer from a common weaknesses. As the principle of lever says, the larger you make the diameter of a drum the stronger the resulting torque from the load is:

Torque = Radius * Force

Being Radius the radius of the drum and force being the tension transmitted to the drum via the load of the sail. So if the radius of a drum is doubled the same force will create a torque load on the winch motor of twice the size! So any solution to increase the sheet displacement length based on a larger drum immediately increases the torque load on the motor! This is why I choose to use in my sheet control system a stepper motor! The larger the drum diameter, the larger the circumference of the drum where the sheet is placed or taken from. So for the same amount of displacement of the sheet per time unit less rotation speed is demanded from the stepper motor, and the slower it turns the higher the torque is has available gets. So the effect of the principle of lever and the torque available from the stepper motor do compensate to an yet unknown amount. A sheet drum with 400 mm circumference was the biggest diameter that would fit in the hull of the Carina and as a consequence i could have the stepper motor operate as slow as possible.



Here you can see one of the 2 stepper motors that will be working in my Carina with a yet unfinished version of the drum:



Here the view from another side of the same pair of drum and stepper motor. next a picture of just the drum, not yet finished as I wrote:



Finally a link to a video I recorded while trying to find out under the choice of the most adequate set of parameters available for the "stepRocker" stepper motor control board from Trinamic. I did not know how to embed the video:

http://flic.kr/p/eV2qP8

If you keep in mind that the drum having a circumference of 400 mm, only 21 full turns are required to achieve the length change of the sheet of 8400 mm. Seeing how fast the stepper motor can rotate at no load and just 25 VDC tension of the power applied, in my Carina the 12 LiFePO4 battery cells fully loaded will provide close to 40 VDC or nearly twice the torque. This huge speed raises the question about another problem that needs to be resolved. If i would accelerate the stepper motor shortening the available sheet length at a very high speed starting i.e. from velocity "0" as shown in this video for example this would destroy all the sheet control system part consisting of pulleys, blocks and the sheet itself. So here the trinamic components offer good capabilities that I will present in detail when getting to it in my report from scratch of the Carina. So as you can see plenty of question come to the surface as I get into more detail of my sheet control system. here the methodology will be of high value!Next I would like to comment on the remark about the jitter while digitizing the PWM. I fear my dear friend flashtwo that you are either wrong or not precise enough! measuring the length of the duty cycle of a PWM signal due to many reasons will result in slight changes of the measured length and this has diverse reasons:One is that the changes of the length information are called "jitter" when referring to the tendency of signals to vary around a certain value. What is usually done is to either compute an average over a number of events so i.e. measure the length of the duty cycle of the PWM of a certain channel. You get a value. repeat this the next cycle 20 ms later, add the 2 values and divide by 2, measure the length of the 3rd value add it to the previous sum and divide by 3 and so on until you have the number of data items over which you want to average. lets assume you take 5 such values. When the 6th value is measured, you erase the first and so you again compute the average of the last 5 values on so on!Another technique works on the bit level. lets assume you measure the length of the duty cycle using a counter that is counted at a pretty high rate. When you get the result from counting the length of the duty cycle yo simply shift the bits of the value encoded in a 32 bit integer in my ARM Cortex M3, the LPC1769 and shift the data to the left by 2 or more bits. Every bit that you shift to the left is a division by 2 After a certain number of such shifts the remaining value does not present a jitter. Jitters can happen and do happen due to may causes, to present and explain them would be too long for this thread. But basically a principle in physics is that no value is worth anything if the tolerance of the measurement is not mentioned. its a principle in experimental physics taught, that any value measured has a limit a to how precise it is!The next topic flashtwo brought up is the issue of centering the boom. I am sure you are aware of, that the center boom position has certain characteristics and certain uncertainties. I want to name two characteristics. One is that due to the fact that between the boom and the deck surface there is a certain vertical distance and second that the boom center position is characterized by being that location of the boom where the sheet is to be as short as it can get. a resulting uncertainty results from the fact that the sheets are flexible cords so that at any position in the area of 5° to 7° degrees around the real center position of the boom just by the "shortest sheet length the boom center position is uncertain! Now, if I ignore this uncertainty and lets assume I wrongly define as the center position of the boom one where the boom is 7° to backbord side from the hull center line. Than any position detected by the angular sensor wii indicate 7° less that what the actual position to the backboard side should be and opposite any position detected to the starboard side would be wrong as it would be 7° larger then what it actually is. Remember that when the boom is in the real center position I want the variable tracing the incremental angular position of the boom to have the value "0", same by the way the internal absolute position available in register within the sensor should also have the value "0". Now further consider that when the magnetic angular sensor detects the center position I want it to show the rising edge of its "I" PWM and I use this data to light an LED to give me a visual feedback. Now, when I setup the magnet in my workshop to make the sensor show the rising edge of the "I" PWM when the boom is in its center position. Now I go to the pond site and do setup my sailboat by inserting the mast with the sail into the hull is it not highly probable that the position of the axis related to the boom position might have changed due to inaccuracies? Might it not be probable that the stepper motor and the drum have turned somehow and that they are not really in the "0" position when setting up the sailboat at the ponds site? By defining a procedure upfront and designing it from day 1 into my sheet control system concept the process is already available!

Next is the suggestion to think about using hall sensors to limit the movement of the stepper motor to prevent damages! Well, the magnetic angular sensor i get for free as a sample, its precision is over 1 million positions over the 21 full turns Feeding the ABI PWMS from the sensor in the already available quadrature encoder peripheral on the stepRocker controller, a samsung ARM Cortex M0 i do get 2048 positions sensed by the sensor during each of the 21 full 360° turn of the stepper motor and so i have a closed loop control scheme. But even additional to that, the controller of the stepper motor can sense the load of the stepper motor, here I want to refer to a video from trinamic, i have the written permit from the marketing director to use their material fro purposes like this:

https://youtu.be/7eCLV7pALig


On the video from Trinamic you can see how the function "stallGuard allows the stepper motor / stepper controller system to react automatically in hardware when obstacles prevent a movement of a stepper motor reach the point it is supposed to reach! Taking into account that the stepper motor will have between 3 Nm and 8 Nm torque this stallGuard function is essential! You will be able to see many of those fantastic features available by use of the Trinamic controllers by going to Youtube and search for "Trinamic"!
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Re: Design by Modeling
« Reply #5 on: March 16, 2015, 09:09:35 AM »

Hi Helmut,

My thoughts regarding the PWM "jitter" were about the controller's type of operating system - does it respond in real time to external events (like the rising and falling edges of the PWM signal) with the use of interrupts, or, does it have to poll the inputs to detect change of signal.

Reading the Teensy description ( http://www.pjrc.com/teensy/interrupts.html ) , I see that it has interrupts that will respond to external events and will enable jitter free (in a practical sense) measurement of the PWM signal without the need for averaging.

I do like the Austriamicrosystems angular encoder with its choice of PWM output or I2C or SPI interfaces - though I couldn't find any information on it's speed of response.

How will your design handle the situation where the boom flaps suddenly from side to side due to a head wind? Will the stepper motor respond immediately to the incorrect boom angular data or will it have some intelligence to know what the situation is and not respond? Perhaps Andy has a view on this.

Will you be using existing library code or will you be writing all your own code?

It would be helpful if you could arrange your replies in smaller, sub-topic paragraphs (with line gaps), since it would make it easier to read - I do loose the line moving from right to left.

all the best

Ian

 
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Re: Design by Modeling
« Reply #6 on: March 16, 2015, 10:34:01 AM »

ian, I will try!


As an operating system I do plan to use FreeRTOS in combination with the CMSIS library:





So FreeRTOS fits as a Real Time Kernel. I have purchased the PDF file of the book were FreeRTOS is shown working on the LPCXpresso1769, see here.
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Re: Design by Modeling
« Reply #7 on: March 16, 2015, 10:58:00 AM »

Here the link to the datasheet of the AS5047D in PDF format. If you go to page 8 on the top table you find the rate for reporting the angle information every 275 ns max. via SPI. Also important is to read regarding their new feature called "Dynamic Angle Error Correction"! Basically what this feature does is that at a given rotational speed is computes the latency from sensing the angular position to the point in time it reports it so that the angular value reported is computed to be the one when its value is reported! At 1700 rpm for example it is 0.02° and this correction applies to the SPI, ABI and UVW reporting mechanism.


The AS5047D allows to switch OFF the UVW output interface to display the absolute angle as PWM-encoded signal on the pin W. This will be the method I will use for my system as it does not require to read the absolute value from a register via SPI for example. This way i can switch between ABI PWM for the incremental position tracking and the other use of the W pin for sensing when a threshold is met.


On page 22 of the datasheet the rate can be computed based on what is shown there. But I remember reading that when the rpm is too high to deliver ABI PWM based on sensed data the AS5047D does generate ABI PWM signal based on the past rate!
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Re: Design by Modeling
« Reply #8 on: March 16, 2015, 11:30:55 AM »

How will your design handle the situation where the boom flaps suddenly from side to side due to a head wind? Will the stepper motor respond immediately to the incorrect boom angular data or will it have some intelligence to know what the situation is and not respond?

This is exactly the case were the speed with which the stepper motor can correct the available sheet length comes into play! As a first approach, and watching the video of my experiment to determine how fast the stepper motor can turn, linked supplied above, the stepper motor is fast enough, as is the magnetic sensor to follow the boom under the conditions you describe! But what is linked and to be considered under those circumstances is what does mean in terms of mechanical stress to the lines and the blocks! Imagine you would pull violent on the lines. This is equivalent to a sudden very fast acceleration of the stepper motor turning the drum, which it can do! This would kill mechanically the blocks! But what is clear in such an operating case is, that the lines will have only a very low load, as the sail is not withstanding wind pressure during this event. Look at this video showing the effect of a function called "S-Ramp.

The traditional speed profile of a stepper motor moving from one position to another one looks trapezoidal as this picture shows. To the left and right the defined value for acceleration or deceleration handled by the appropriate parameter setting defines how steep those lines are. The maximum speed defines how high the horizontal line is. The microcontroller on board together with the Trinamic components computes how this profile is set so that the stepper motor stops at the target position. This software is available as source code for free from Trinamic and it is written for an ARM Cortex M0 controller from Samsung using the CMSIS library. So the porting of it to another controller based on an ARM Cortex M* license from ARM from any provider is relatively simple. by the way I will do the programming starting from that software available for free. and the library implementation of NXP of the CMSIS from NXP.

S-ramp is a function implemented in the software running on the ARM Cortex M0 of the stepRocker board for example that generates a much gentler speed profile:Now the video in the link I place here shows based a a glas filled half with water the effect of both types of speed profiles. I do strongly believe this to be the method I will have to use!


https://youtu.be/PGYBqAphBHw

Now if you look in detail into the information I presented about the use of thresholds you will see, as I did, that any movement of the boom, even the one you are writing about here is unfortunately not a move between to positions distant from each other so that the functionality of those two kinds of speed profiles could be used. Its more a case of tracking the position incrementally and absolute as showing in my description of the thresholds. This means that I have to use my intelligence to think about its consequences for my software and the mechanical stress on the lines and blocks! Another reason of why modeling and simulating my sheet control system via the methodology of the design by modeling is the tool to study this upfront! It is my feeling so to speak, that even in the case you described and I stated at the beginning of this reply, the booms movement is relatively slow to what both the stepper motor and the sensor can handle and so I believe the scheme presented in the description of the threshold technique can be applied with the controller offering enough speed and processing power to do its job while the event takes place and so it can follow the movement of the boom. Nevertheless, and here I am just guessing and so presenting the case study I will make on the model once available is, I do assume that the lines, due to the way they are and is shown in the picture from the original Endeavour will force the boom to overcome a certain inertia due to the forces opposing a change generated by the friction in the system. I want to remind you that there have been voices from other forums that said that those inertia forces might render the complete sheet control system inoperable! as you can see, there are many reasons to use and justify the effort to make the modelling of the sheet control system. It is really so, that as you penetrate the intrinsics of the system and learn more and more of the details a full world of fascinating issues pops to the surface. Questions and issues which in themselves represent an attractive topic to deal with!

I hope this splitting is making the reading easier. I have to tell you that I suffer from changes in the font size being inserted into the reply whenever I do insert a graphic or a link and that images and links suddenly get out of layout and I then try to fix it manually!
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Re: Design by Modeling
« Reply #9 on: April 22, 2015, 12:32:40 PM »

A lot has happened since my last post! Lets try to update this thread!


I have finally identified 3 pillars on which I will try to build my model. They represent the application of a methodology based on a didactic method developed by the University of Karlsruhe and is called the "Karlsruher Physics Course" for which I have added the link for those interested to know more about! As the name indicates it has as its objective to develop a method to teach physics reflecting the modern physics findings.Basically it addresses the topics in physics based on a view that is in line with the way quantum mechanics works. The result is that not just the classical fields of physics follow the same principles, but also modern physics like quantum physics and relativity physics. is t not fascinating that most advanced didactics can be applied to naval modelism?


But before getting into it I want to address a concern expressed by some forum members of another forum! The impression there was that I did consider myself superior to "normal forum members", or to say it in another way, I did consider them inferior! Linked to this criticism came a remark that all I was doing was copying the content of technical pages regarding the topics I am dealing with!


I responded that I felt sad about that impression, I asked to be informed about what was the reason for this opinion and I tried to present why I proceed as I do. I pointed out, that in the forum there were plenty of examples of masterpieces that reflected the excellence of the naval modelists that did them! On the other side I was dealing with topics new to me and as a consequence of it I am just an apprentice and would probably remain being it.


I want to emphasize that I do what I do because it represents a way for me to get what I believe is a deeper understanding of details of my concept of a sheet control system and that already on this early stage I have got the awareness of many parameters that have an influence on the friction between the sheet and the discs in the blocks. For me, and I can only reemphasize it, for me this represents a high degree of satisfaction I am gaining from my dedication to our mutual hobby. Nothing is more remote to my intentions than to consider myself superior to others or to consider others of less value and inferior to me! It is even more so that learning and studying all the topics related to this part of the project of my building from scratch of a sailboat enforces a feeling of humility being made aware how little I know and how what i am learning are really not more than the basics in their relative fields. It is even so that I have described myself as being a mathematical analfabet, because I might grasp concepts while reading materials, but the luck of maturity in mathematics limits my possibilities to really grasp the implications of what I read! Having tried to address a topic I sadly am encountering when reporting about this part of my projects I want to express my awareness of this and emphasize as honest as I can that I consider myself an apprentice between so many real experts in topics related to our hobby.


1. Pillar:


The science of complex dynamic systems being developed by the Sloan Institute of the MIT in the fifties of the last century. It is a means to express the many relations that are effective in complex dynamic systems by using recipients that contain accountable magnitudes and a content that is impacted by inflows and outflows. The Sloan Institute is related to the study of financial systems and so a bank account is a good way to represent a recipient, the monthly salary payment as an inflow and the expenses as an outflow.





i love to take this graphic as an example to demonstrate a complex dynamic system. The rectangular boxes are the recipients, the double lined arrows represent the flow, the symbol at the center of those arrows does represent a valve that controls the behaviour of the flow. The curved arrows express the relations that influence those flows and as a consequence the content o the recipients.


2. Pillar:


Modeling and Simulation language and environment Modelica. This language actually reflects by the way it works that method from pillar 1 by having equations contained in the recipients, here called models and relations defined in the connectors used to link models together to form a more complex system. A way Modelica is sometimes described is: Modelica is an object oriented language equation based.


3. Pillar:


System Physics: A professor Werner Maurer from the swize university ZAHW Winterthur has taken in nearly 2 decades the didactic concept from the Karlsruher Physics Course, short KPK, to teach physics to his engineering students.





So watching this flow chart generated using a dedicated software tool called Berkeley Madonna he shows it here applied to mechanics as part of his teaching in physics. The similarity between the complex dynamic systems and this chart is recognizable. I have searched and found books in which system Physics is taught and I am right now starting to study those to grasp the way the dependencies in the chart are and to apply it to my modeling effort of the pulley as shown in the photo from the original Endeavour that I want to use in my model. I used to be pretty firm in physics and mathematics, but as i wrote, in nearly 4 decades a lot of my knowledge has eroded. But added to this comes that I need to learn to "view" physics in general and mechanics in special the way system physics does.





This slide of Werner Maurers teaching visually presents the flow taking place while 2 individuals pull a rope, being so far the closest I have found to the situation in my pulley. Werne Maurer emphasizes in his speeches recorded on videos and available unfortunately mainly in german language an aspect of system physics that represents one strong argument for the methodology he applies to teaching physics. While it is possible without a real complete understanding of the physical concepts to select adequate equations, enter the parameters that map an actual problem dealt with in an assignment of his students to get a proper result, system physics demands to translate the understanding of the physical concept in a model that reflects the problem to deal with in an assignment. Well, exactly here is where I am still running into a a block!


The recipients in system physics csan contain one of 7 possible quantities depending of the field of physics I am dealing with:





This table shows the 7 magnitude or "substances" that are accountable the way I wrote about recipients when presenting the first pillar. Well for my pulley what applies to my understanding is the fifth row in the table, the recipient has to contain "Momentum" "P" and Px being the single dimension related to the direction of the rope! The equation for momentum makes clear what my problem is:


P = m * v


being
P the momentum
m the mass and
v the velocity.


What I am looking for is the equilibrium condition, where the Pull force from the sail passed to the rope equals the friction in the block! Equilibrium means the velocity is equal to "0". I f the velocity is "0" the content of the recipient will always be empty or "0", independently what the mass is. So the equation is kind of meaningless!


The second problem I am facing is what value does the "mass" have!


The third problem is related to a principle related to the magnitude in the recipients. A recipient has always be related to a volume in space, and be the product of a crosscut surface and the altitude of the level of "substance it contains!





As the same mathematical equations apply to all the fields in physics, the fluid image as shown in this graph is used to represent the problem graphically! In this graphic a translational mechanical situation is presented as it applies to the problem I am dealing with in my pulley! Red colored is the recipient containing momentum as the equation shows! It further presents that the mass is the cross cut surface of this recipient and that the velocity above earth level is the filling level of the recipient. System physics relates all substances, magnitudes to a potential, as the table above also shows. In translational mechanics the infinite source of momentum is earth. So the analyzed body so to speak has to be seen in its environment that reflect the potential.


The momentum flow that flows into and out of the recipient is actually a force and those flows always have a property of crosscut area that related to time reflects the amount of inflow or outflow to and from a recipient. Here we see the second newton axiom that F = m * a! P = m * v is the momentum, the derivative of the momentum over time is the derivation over time of the velocity and this is the acceleration "a". By the way when I found out this I was excited! This allows me to calculate the stress on the blocks when the stepper motor I use as a winch does accelerate. We all know from experience if this acceleration is to high it can kill the block! Another important information for my objectives is contained as well in the flow chart, within the green rectangular box and here in green too. It is the computation of the energy involved. remember that to find the most energy efficient solution possible to maximize the operation time while being fed by my battery pack is also one of my objectives!





So my first step to try to learn how to apply it to my pulley was to generate a flow chart using my purchased license of Berkeley Madonna to show the individual sheave of a block and the inflows and outflows being related to the rope embracing this sheave. So applying the image of the two person pulling on a rope i defined the directions of the arrows. Well, it is so that the sign of what direction is positive and what direction is negative depends from the orientation of the reference cartesian coordinate system and its placement in relation to my sailboat. I am assuming right now that the origin of my reference cartesian coordinate system will be somewhere along the vertical axis around which the boom of the sail rotates, means close to the position of the mast. The "X" axis therefor would be meaningful to go from that vertically defined position backwards, as this is the direction the boom has parting from its rotational angle! The "Y" axis would be parallel to the water surface. So the "X" and "Y" coordinate axis would describe a place parallel to the water surface. This is meaningful as so I could apply any tilt of the sailboat as a rotation around one of the axis of my reference cartesian coordinate system. What I am not yet certain of is the placement of the origin along the vertical axis "Z". Meaningful is a position along the vertical direction that reflects the rotation axis around the "Y" axis. This is because if the wind blowing into the sail tilts the sailboat  the axis around which it tilts would be the best choice. But where is this point along the vertical axis actually? my intention is to start by just assuming it is at the position along the Z-axis, where the rotation axis of the hull around the "X" axis is. my first guess is that this is at the depth at which the center of gravity of the hull is. But I will start assuming it is a the flotation level!


The next I draw was the pulley as a whole as shown in the photo from the original Endeavour:





Here the recipients would be an instance of the model of the individual sheave and the arrows would indicate the rope between those sheaves. As an equation I am planing to use the Euler-Eytelwein-Formula presented earlier and it would use the graph of the sheave embraced by a rope with the angle "Beta"


Drawing this flow chart already made me aware of the complexity of how the pull forces generated by the wind, dependent from the speed of the wind and the relative angle in which it flows into and around the sail are passed to the rope that goes through the pulley!









Lets assume, as I do right now, that the force of the wind into and around the sail can be seen to be as a single force vector applied to the center of gravity of the sail.





Then my question is how is this force being distribute to the points where the pulley is attached to the boom?





This is very important to know, because as we saw earlier when presenting the Euler-Eytelwein-Formula and the graph of the rope embracing a sheave, the friction force depends on F[/size]N and so on the magnitude of the force that is applied to the rope! If you look in detail of the graphs I presented in relationship to the Euler-Eytelwein-Formula and the graph of a sheave not only can the friction be influenced by the size of the diameter of each individual sheave, but also by the size of the embracing angle the rope has around such an instance of a sheave and this is impacted by where on the boom and the deck the individual blocks containing those sheaves are placed. And obviously by how the force being seen as centered in the center of gravity of the sail is being distributed to the blocks!So far, even if I am not able yet to properly understand the application of the system physics methodology to my pulley and its sheaves, I have gathered a lot of knowledge about why certain parameters influence the friction is the pulley. Remember, the warnings I have received from quiet a few real experts in sailboats about the friction in my model build at a scale of 1:20 to the original Endeavour. they claimed that this friction would render my sailboat with such a pulley inoperable. Y will be able to identify at which force generated from the wind in the sail the pull force generated by the sail on the rope would equal the friction forces in all sheaves of the pulley!This is not a trivial issue of just adding the friction forces! The frictiOn forces depend directly from the pull force in the rope embracing the individual sheave! To say it simple. If the pulling force by the sail on the rope through the pulley increases, the friction forces generated in the 7 sheaves also increases! So it will be very interesting to find out how the equilibrium between the pulling on the rope from the sail behaves in a chart against the friction in the sheaves. And also it will be interesting to find out how playing with the other parameters presented here will affect this.I have also started to reflect about possible ways my system could assist the sail to overcome the friction in the 7 sheaves of the pulley. The result so far is, that this will depend very much about the property the curve of the equilibrium of forces between pull and friction has.Probably this is boring to many readers, if any one reads this thread, but for me this is fascinating!
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Re: Design by Modeling
« Reply #10 on: May 12, 2015, 03:36:27 PM »


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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Hellmut1956

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Re: Design by Modeling
« Reply #11 on: July 11, 2015, 01:31:53 PM »

i have been unable to move forward as I had some serious problems with my health, impacting my ability to study as it is required. So right now I try to get up to speed again by working on improving my workbenches!
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Hellmut1956

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Re: Design by Modeling
« Reply #12 on: May 21, 2017, 09:58:20 PM »

Funny to read my latest contribution in this thread, 2 years later! Just had my third stroke, the last 2 where what doctors called TIA, which is just a temporary blockade. Now I have 2 arterias into my brain blocked, which fortunately have other arterias being able to take their job! I guess that for a fourth this would not be able.
Still today I am advancing on all the frontiers that have to do with my model sailboat, the "Carina", for which I have a thread published here. In parallel I am also advancing with the work I have with my workshop. I tell my wife and my kids, when they tell me not to face what I consider a fact that I am getting close to get the definite answer to humanity's biggest question: What comes after you die, that I am aware of the fact that all the stuff that cannot be easily sold will go to the garbage, my workshop will be dismantled!
But the fact that I go on my work to improve my workshop, the fact that I go on with my research and studies in the areas of electronics, physics and mathematics, the fact that I just recently upgraded the licenses for my software for programming for a full year, that what I do does fascinate me, that I use this tasks to push me to overcome limitations due to health problems and that after a day I feel I have accomplished something I feel satisfaction!
Right now , just slowed down to to my problems I am getting close to the point where I can reinitiate my experiments which have the goal to enable me to use HiL and SiL to see if the models I am developing using the modelling language Modelica actually reflect the behaviour of real life hardware and software. A simulation is only as good as the quality and accuracy of the models used are!
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Re: Design by Modeling
« Reply #13 on: May 21, 2017, 11:19:43 PM »

Helmut...as all things with modelling, sometimes time is needed as there is no race.

You have taken on a most specific line or field in our hobby and it may not be relative to some readers, however there are members with an interest in research :-))

I was interested in your work from 2015 with...'that dealt with the friction between cylindrical bodies'

Carry on at your own pace and continue to post your results

Derek
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Hellmut1956

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Re: Design by Modeling
« Reply #14 on: June 03, 2017, 12:36:16 PM »

Thanks for the response! You are right that our activities related to the hobby are in no race condition! What happens in my case is that there are so many thinks I want to investigate, that I do pursue with passion. On the other side my health problems are the prove that my time left for this activities has a high probability to be too limited. But even more important to address my first 2 goals listed, specially the limited time left one, benefits from my passion and to name it this way "race". I just had the final health check from the 60 months study I have participated in the last 5 years. The pictures taken from my brain show that my intense efforts to overcome the limitations which specially came from my heart stopping to beat a couple of times which led to get a pacemaker. Sections responsible for concentration and stress-ability for doing my studies show that the brain has created new blood veins to feed the cells that suffered the most from luck of oxygen. My capabilities for memory work are above average for my age. Unfortunately the 3. stroke suffered just a week after that checkup show that my defenses against brain damages, the arteries feeding the brain have lost a second arteria.
So I like to believe that the push I have for advancing my hobby do have healthy side effects additionally to keep me in a positive mood.


Due to the above I have changed my focus to advance the work on my workshop, I do report it elsewhere in this Forum.  I did run into problems due to from attacks from the Internet during the first phase of learning how to feed back data from real experiments to be available to make sure the models I do develop actually reflect with adequate accuracy the data generated by doing simulations using the models I will develop. My PC was rendered inoperable by having the attacker generated so many processes that made it impossible to be able to use my PC. Updating it from Windows 7 Ultimate 64 bits to Windows 10 Pro resolved those problems. Since then I am , within the limitations due to my health problems, studying the topics that will prevent or at least make it much harder for potential attackers to do harm to my PC. It happens to be that the development of software and hardware related technologies to protect devices connected to the Internet is developing at tremendous speed. As electronics that could be used in naval modeling fits into the category of IoT, Internet of Things, revolutionary advances are taking place in this field.


One interesting aspect is that new communication technologies and new very affordable rates are coming in place that really allow revolutionary solutions that can benefit naval modelling. I want to give as an example, that my provider allows to "buy" 100 MByte of data volume for just 1 Euro per month and to book additional volumes just for a single day. This means that all the data transport services that have been rolled out for smartphones are available for us in naval modelling at very low rates. I do remember when the 2.4 GHz communication became available, ZigBee Pro modules where an inexpensive mean to implement new powerful solutions for naval modeling. Suddenly the "old concept" of having just a receiver in a naval model and the R/C transmitter in the hands of the user did give place to the "then new concept" of having both the "Transmitter" in the users hand and the receiver in the model became transmitters and receivers allowing to have the ability of the model to transmit data to the "R/C Transmitter" and the R/C transmitter to receive data from the model at the same data rate. The effect of this new technology was on one side that availability of Chinese R/C systems at very low cost and for the suppliers of traditional R/C systems to develop premium systems that did benefit a bit well below the capabilities of the 2.4 GHz. They kept talking about channels, a concept that is alien to the 2.4 GHz technology, a serial bi-directional data stream, just to keep clients willing to pay premium prices for their "computer-Transmitters"!


Now, you can have the capabilities of a smartphone or tablet PC to be available for R/C operation of naval models. This means not just the data transmition, but also that of human interface called GUI! Drones that have become so popular and that really do benefit from the technologies related to smartphones and tablets, also are innovative in taking advantage of technologies that benefit from the new abilities of wireless communication and Internet connectivity. Autonomous cars and autonomous drones use technologies that are now also available for our hobby, naval modelling. The revolutionary development of multiple technologies in this area, funded by the huge demands from the automotive marketplace, have promoted to make all of this available in what are called embedded technologies! The most advanced device that reflects and implements technologies starting with the intellectual properties of latest ARM processing cores, specifically ARM Cortex M23 and 33 and the concepts around "TrustedZones", via technologies around the operating systems, hypervisors, virtualization and containerization to technologoes that deal with sensors and actuators. This terms mean functionality able to sense the physical world to devices that perform or control actions., is the NXP i.MX8 microcontroller. Here the link to the page at NXP that documents the "i.MX8 Multisensory Enablement Kit" and the picture of that kit:





This kit shows and makes available the multitude of functionalities implemented in the i.MX8. I just want to point out the multitude of cameras it supports. Being this kit to enable early adopters of the new family architecture member from NXP makes it easy for engineers to do their development work. The previous generation of that family of devices from NXP is the i.MX7. You can get a board from that family of devices for just below 40 USD's! Here the link for the webpage of the provider about such a board! I am on their distribution list to be informed as soon as they have a i.MX8 based board!


So it is my believe, as soon as a new generation of naval modelists appear that are willing to see in applying the maturing technologies in naval modeling their objective, naval modeling will be enriched by 2 mayor branches. One is the traditional view of achieving the personal objectives by learning and applying manual technologies and a second branch that sees its objective in applying the technologies then familiar to them that have to do with electronics, informatics and telecommunication. From my own perspective, dealing and loving both branches and not having yet processes that facilitate the application of technologies in naval modeling, the scope is overwhelming. But just as in the past before radio controls became mainstream, there was no use of electronics in naval modeling, the availability of radio controls revolutionized naval modelling. I do believe suppliers, searching for a new business model that integrates the new technologies into their products, will find "easy ways" to enable naval modellists to take advantage. But it will be a challenge. We are already seeing right now that the average age of naval modelists is probably above 50 years and that the numbers of people dedicated to naval modelists is in such a decrease that mainly sources in the Internet and production in China have a chance to survive!


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