Just to let you know that I am still working on this project! Right now I am trying to grasp how to express what i want, modeling the pulley and identifying at which force of pull on the sheet the friction in the pulley is equaled, to the ways this has to be done in System Physics! Basically the challenge is to be able to assign the physical magnitudes to the System Physics environment, so to speak!
In System Physics mechanical systems are expressed in terms of “Momentum” for which the letter"p is used. The equation for momentum I believe makes clear the challenge!
p = m * v where:
p: is the momentum
m: is the mass and
v: is the velocity!
The first hurdle I had to phase was that my thinking was focused on finding the equilibrium, where the friction force and the pulling force are equal. Any pulling force greater would have the sheet being pulled out by the sail! Equilibrium also means that the pulley at this condition would have the rope not moving and as a consequence the velocity “v” would equal “0”. Inserting a speed of “0” in the above equation would render the equation useless, as the mass could have any magnitude, multiplied with “0” gives “0”!
So my next step was to use the fluids model popular in System Physics as a means to express physical systems.
This image shows what is the basic point of view of System Physics. You have 2 elements and equations describing their relations. Recipients that contain a magnitude dealt with and fows into an from that recipient that impact its content! So if I translate my pulley in general and an individual sheave of that pulley, the force pulling the rope, in my project the wind pushing the sail to have it open and so demanding more rope length. This represents a flow into the recipient adding momentum to it.
The friction force opposing this pull has the opposite direction and so it will be decreasing the “momentum” content of the recipient. In System Physics this flow is a force!
You can see, that the altitude of the “content” of momentum in the recipient is defined by the “velocity” and the surface of the cylinder area is the mass! So multiplying the area equals the mass with the velocity gives you the momentum content. I am assuming this recipient are the individual sheaves of my pulley, each sheaves its own recipient!
What I have been starting to grasp by not just viewing the equilibrium with the problems presented above is the meaning of the environment, here called “earth”! To visually explain this the image of an inelastic collision is helpful!
Without going into the details of the content of the graphic i want to highlight what I consider key! As you can see you can have “positive” velocity" and “negative velocity”, which does not say more that the direction of movement is in opposite directions. So when a certain direction of the movement is considered to be positive, the height of momentum content is above the “earth” level shown by the orange colored environment. Is the direction of movement the filling level of our cylinder is below the “earth level”!
So the equilibrium status just reflects the special case when the content of the cylinder is at the same level as the environment named earth!
What I still have to really grasp and understand its impact are the 3 different topics contained in the graphs!
The first is rendered in green and reflects the dynamical energy, called kinetic energy. The counterpart to it is the potential energy and so the second topic. Everyone knows from school, that an object held at a certain level above ground has assigned a potential energy. If the object does not move there its kinetic energy is 0. When we let the object fall, it drops to the floor, at the moment of impact on the ground the potential energy has been converted to kinetic energy.
The third element is how the “forces”, pulling of the rope by the sail when the sail opens, or in opposite direction pulling of the rope by the winch!
By the way, another aspect is what is called “process energy”. So when an object is accelerated energy has to be pumped into the system. When an object movement is stopped by friction the momentum is returned to the environment. The difference in potential energy at the start and at the end sets how much energy in being released. To use another example.
If water drops from a higher level to a lower level the difference of the level represent the potential of energy that can be gained. This is used when electricity is generated at a dam!
Lets show the relevance to one of the objectives I want t get from modeling my sheet control system. It is to find an energy efficient operation for it! As the energy for the sheet control system in my sailboat model comes from batteries in the model it has to be my goal to achieve best efficiency possible as energy is a scarce resource! You can see that this is also being addressable in my model and so a goal to be pursued!
The equation I want to apply to reflect the physical effects in the pulley is the Euler-Eytelwein-Formula!
You will not believe how controversial my project is perceived in the communities in physics forums! First is a luck of understanding why I want to apply System Physics. But not least controversial are the responses regarding an important aspect I want to study with this model and it is the aspect of friction in general!
Experts in model sailboats indicated to me that it is impossible to operate in a sailboat model like mine, 1:20 scale of the original, a pulley like the one shown and used on the original Endeavour! The reason being that the friction in the pulley is so prohibitively high, that the wind will be unable to open the sail by pulling rope against the friction in the pulley! I have received this warning from more then one expert in all 3 languages in which I publish my projects, english, german and spanish! Those warnings were followed by a personal feeling of offence by my decision to still so pursue my objective, even now by first modeling it!
Real skippers from real sailboats have confirmed that the friction can represent a problem when in a model of the scale I do pursue!
In the physics forums I have had equally emotional feedbacks telling me from the second law of Newton is not applicable, over that the only relevant friction in the sheaves of a pulley is the one between the disc of the sheave and the axis around which it turns! Others have written, that the Euler-Eytelwein-Formula only expressed a thinkable maximum friction value!
This partly high emotional colored feedbacks have strengthened my intention to model the pulley and see how the results compare to physical experiments! My studies will show! Hopefully!
But exactly when starting to think about applying the Euler-Eytelwein-Formula in a model of the pulley in my sheet control system I get into the problem of what the value for “mass” has to be! is it the mass of the sheaves? Is it the mass of the rope? What is the area size reflecting the mass in a graphical representation as in the graphs presented above?
I know and I am aware of, that I am by no means efficient in my studies, that I am combining lots of fields of knowledge were my own knowledge is very rudimentarily and were I have yet no real understanding what makes sense to be combined! So I am in a working mode where I do work on advancing my knowledge in many fields in parallel and reflecting in the light of those fields on my agenda! But hey friends, until god or the devil call me to their presence as a jobless sick person I spend my time on this studies. In some of the fields I have been dealing with I have also been able to generate the interest of industrial people that are hiring consulting services from me! So I am probably not totally crazy!