Dear friends, I am a naval modelist and as i am retired due to health problems I use my project ob building a sail boat model as a red line to learn about the diverse technologies I am confronted on this path. So my goal is not that of finishing the project of my sail boat, but to learn ans study and practice the topics i am meeting on this path. here a pretty old foto I made of my model to gat a sense about how it will look like: Now the opening of the sail, means the rotation of the boom to which the sail is connected to on the bottom side, this boom is capable to rotate around the Z-Axis, the vertical axis. Now it is my goal to implement in my model the same kind of pulley as can be seen from a sail boat, the Endeavour, called J-Class from the beginning of last century. This boat had a hull length of about 35 to 40 yards! Now serious "experts" in building model sailboats wrote to me that due to the friction in the sheaves of the blocks in a model that is 1:20 times smaller, will not be operable. None of the methods existing this day allow to support a displacement of the sheet by 8400 mm in my model, this is the name for the rope that goes through the pulley and limits how much the sail can open, means rotating the boom about the vertical Z axis by increasing the angle between the boom and the hull center line! I have deviced a so called "sheet control system", pretty complex, here a block diagram I developed to be able to talk about my systems concept: I also have other objectives, like the one to get the most energy efficient implementation of the system. Now as you all are aware of it is best to start modelling a relatively simple part of my system. So I decided to model the pulley as seen on the photo from the original sailboat! So I did start by drawing the discs that make up the pulley on the photo! lets start from the bottom right: The sheet comes over the deck from the from part of the boat, where it goes under deck to the drum that is part of the winch. For this first part of the modeling effort I simply assume the winch will make sure sheet length is made available without a tension coming over the sheet is required. The sheet passes through the pulley on the deck and goes up to the first pulley connected to the boom of the sail. from here it goes to the block that contains 2 discs and from it to the rear disc connected to the boom and back to the second disc of the rear block on the deck. From their it gets to a second disc connected to the boom is invisible behind the one on the drawing and then back to another disc that is equally invisible and located on an opposite side of the deck. The the sheet goes back to the from of the boat and under deck, where it is fixed connected to the hulls hardware! So this end of the sheet is fixed! This drawing shows how the friction between a pulley and the rope depends on the tension to which the rope is exposed, here the tension is coming from the wind blowing into the sail and passing this pressure to the sheet over the 3 pulleys connected to the boom! But also on the size of the angle it is embracing the pulley. her the link to wikipedia regarding the Euler-Eytelwein equation! Now you have the background information for my request of help! I want to start modeling a single drum embraced by a rope and have the friction computed. The I want to represent the pulley on the photo and my drawing by using 7 instances of this first model. my objective is, in a first step, to be able to simulate the model to see by studying the plots how the friction is impacted over a range of pull forces applied to the rope. I want to see the same way how the parameters like "d" and "D" impact the resulting friction. To accomplish this I want to apply the methods coming from the complex dynamic systems by using a software tool called "Berkeley Madonna", so that at a later step i can translate this into the modeling environment "Modelica", of which their are a variety of free tools available under "OpenModelica.org", I am starting using a trial version of "Dymola" from Dassault. At the end I want to use "SystemModeler" from Wolfram Software together with Mathematica. As I plan to do this in an environment driven by Physics I will apply the Methodology of System Physics. system Physics, originally developed as a method for teaching physics in a modern way by research under the title "Karsruher Physics Course", Professor Werner Mauer from the University "ZAHW Winterthur" in Switzerland has started the last decades to evolve this into System Physics and uses it to teach in his Physics courses at the University he teaches. Werner Maurer somewhere defines System Physics as a methodology to address physics from the perspective of the modern complex dynamics system approach by using those tools to model the subject he teaches in his course and have his students apply the tools of the complex dynamic systems arena, like Berkeley Madonna for example, to model a work assignment. This way his students can verify what they are learning in the physics course by applying it to the modeling tool, simulate the model and verify that the results from the simulation correctly reflect what they have just learned. This way students not only learn how to apply mathematical formulas to solve assignments, but to verify that by the models they generate their understanding is really correct and how to apply it! The above flow chart, made using Berkeley Madonna shows the basic elements when applying modern methods from the science of complex dynamic systems. The basic structure consists of recipients and flows that add to the content of a recipient of that take substance from the recipient. You can see the full analogy the the fluids dynamics as mentioned in a thread here in the forum about 2 water tanks! SD stands for "system dynamics". So taking the analogy from the fluids in the 2 tanks thread in this form, water is flowing from tank 1 to tank 2, here Vol 1 and Vol 2, marked with a red box. To explain the "law of resistance" and "law of capacitance" I like to use a table that shows for the different kind of areas in physics what those term mean. I get this from material in english language available at this site: Here you can see what magnitudes, titled "Quantity" in the table reflect the different areas of physics as teached in a bachelor course of physics, the related symbol and the units. The Potential reflects the nature of the second element. So i.e. mass in combination with the earth gravity field leads to the weight or potential energy. Mass in combination with velocity leads to Momentum. Equivalently for each of the seven kind of quantities there is an associated potential. Just as a side comment. The same equations, relations are found in the different areas of physics, uncovering by this perspective a common property across apparently completely different fields in physics! Lets take what in system Physics applies to Mechanics, the Momentum "p"! The equation for the Momentum P = Mass * Velocity = m * v. i do not have neither the ability as I am just learning it myself, nor can this be the topic of this post and threat to teach System Physics methodology and concepts. I just want to brief you and give you access to more resources on the subject to be able to have a chance for support! Basically I can say the in mechanics the content of the recipient is "Momentum" as defined by the above formula and the flow in and out is "momentum-flow-strength". This happens to be force F. I do refer to the material available at the site my link to the Karlsruher Physics Course, where this is explained in a lengthy way in english! The final concept related to system physics is the energy part of it. Professor Werner Maurer also calls it "process energy" and uses a waterfall as an example for it! The water falling from its starting point further up has a higher potential energy than the water after it has passed the water fall, where the amount of potential energy is lower. The difference between the 2 is the process energy gained from the water falling. We use this process energy in hydrodynamic plants that generate electrical energy by converting the process energy available as kinetic energy to rotate turbines to generate electricity! Now I want to present you with my first trial to model a pulley llnked to the image of the pulley and the forces on it! All I did in this image was to draw for every disc in the pulley a recipient and for the rope through that pulley arrows reflecting the rope! As you can see by the question marks on the violet colored globes, those are still empty. In here I will have to place the equations. What is till missing completely are those brownish globes and the curved lines that you can see on the flow chart above. Those brownish globes are used to contain the formula that reflects the relation and the source from which a parameter of the equations in the violet globe on the flow arrows gets its value from! So this way, until not all the question marks on the violet globes disappear, there are still undefined parameters in the equations they contain. This I consider a wonderful way to handle a complex system design! The graphics feedback in the flow chart not only makes it easy to keep adding dependencies, but it also helps to keep track of eventually uncomplete definitions of parameters in equations! Now I have said that each recipient in this flow chart represents one of the 7 drums of the pulley and each of this recipients stands for the model of each individual drum! This flow chart is my first trial to generate a model of an individual drum by reflecting the red colored forces on the graphic of a pulley i have made available above and on which the Euler-Eytelwein equations are based. Now finally my problem and question: If the Pulley recipient in the last image represents a physical disc, then its content is "Momentum". The flows into that recipent is the pull tension coming from the sail over the sheet, a force: Fine. The other arrow pointing into the recipient is the friction, I guess and whose direction is opposite to the pull force from the sail! What I am searching for is the balance, were the force coming into the recipient from the pull of the sail is equal to the friction. or better expressed the sum of this 2 forces equals "0". If a pulling force on the sheet is the result from wind blowing into the sail, then this equality would reflect the wind speed at which the force the sail pulling the sheet equals the friction in the pulley. any wind faster then this one would be able to overcome the friction is the pulley! But at this condition the "velocity" = "0" and as a consequence the content of momentum in the recipient equal "0". So the balance only happens, when the momentum content of the recipient is empty! But what value has to be taken for the mass? The rope is considered to be free of mass! May be this "fluid image" often used in system physics as a visual mean to reflect physical situation, as the same principle apply to any of the 7 quantities listed above! The image shows in detail a recipient and uses it, as I do need to do it, to represent a mechanical system! The mass represent the cross cut area of the recipient, the velocity the filling level are fluid level in the recipient. You can also see that in system physics, here translational mechanics the reference Momentum is given by earth! In my thinking right now when my pulley is in balance the recipient filling level is equal to the surrounding earth level! Still so, what would be the mass in my case? I hope here in the forum is anybody that can help me! I am trying to get hold of a school book about systems physics, as I obviously am missing something!