Linear Force as a Dimension Model

[TheTreeSpyder]

HNY to all !

All the examples shown in drawings and real life are this same principle of when within the same system: If in the same UNIQUE Dimension or not; to cover all possibilities. Mostly, each is a mix of the 2 extremes of purely in the SAME UNIQUE Dimension, or purely NOT (as parent extremes). cos:sin ratio shows how much length, force is expressed in Same Dimension vs not. The chart of ALIGNED and NON-ALIGNED shows this goes beyond cos:sin definitions.

Really all this is as 'simple' and (yet) complete as a Zen riddle..
pic: same chart as above post#18
Either something of the same system/space is :
•in the same unique benchmark dimension(cos force and of cos patterns in left column of above chart)
or
•it is not(sin force and of sin patterns in right column of above chart)
To Be or NOT To Be is the question( yin/yang) and then the sum total of both's expressions in a system!

For rigids/non flexibles another slice of the that same previous chart focuses another category of forces in:
•the unique aligned dimension of force in the system/space(left side effects of chart at cos value)
or
•the not aligned parts(right side of chart effects at sin value)
(from: same chart referenced as from above post#18)


Again the cos/aligned dimension carries 1 force and force pattern;
while the sin /not aligned Dimension carries the other force(s) and pattern.
Failure happens when either Dimension forces are greater than that dimension's support capacity(usually from cross dimension effects). The crossing dimension forces can not be carried by the inline capacity NOR pattern(and vice versa). This makes all the difference..

Notice in the simple models we have only 3 types of how linear input forces can be expressed:
•tension only (so is of the aligned Dimension in the system)
•compression only (so is of the aligned Dimension in the system)
•both at once (so is of the crossing Dimension in the system)
So even these force patterns are per Dimension, like cos:sin ratio; and the leveraged length clip of chart shown above. Everything is about if in the same Unique Dimension of the system or not (and how much so of each for cos:sin) as key factors. This defines how knots, rigging, hinging, leveraging, reaching etc. etc. plays out.

Relating to things by Dimension , it’s attributes including cos:sin value pair of how much of Same vs. Not Dimensions; has made me a better rigger, driver, knottier, worker etc. as i do things more purposefully to these powers, L-earn from that, and can see reflections of the same common principle into the other skills. For they are all facets/examples of this same lesson to me. So the knowledge, familiarity in one can be reflected into others; as they each re-affirm as echo each other’s same root functions in this model. To the point of seeing how could it be any different in rope, when even stars and microbes follow this pattern.

 

[TheTreeSpyder]

Once again to divide the examination between 2 opposing parts of to the unique Same Dimension of the force flow (as benchmark Dimension) in the system vs. not(everything else) to the sum total of the all; i show this part too from same chart referenced as from above post#18. As it's own stand alone aspect of the orchestration of the scenario; and as further proof that this is the way to look at things, including the cos:sin value pair usage.

This one applies to all things too; including even backing a trailer..
The model i find for direction of Dimensional forces (that cos:sin shows how much of the total to the Same Dimension vs. Crossing Dimension) is like an elastic reference. Where as the E&O(Equal & Opposite)forces serve toward's the center of an device in the Force's Same Dimension, the reaction is for Cross Dimension forces to serve away from center. And vice-versa.

So pulling a trailer forward forces in Same Dimension pull away from center (cos xForce): so the E&O side force conjured in Crossing Dimension serves towards center(sin xForce). Like if going to be tall/long must be skinny kind of effect.
vs.
When pushing a trailer backwards the Same Dimension forces push towards center (cos xForce); the E&O side force conjured in Crossing Dimension serves away from center(sin xForce). In other words it wants to go to the side towards jackknifing when backing because of the sin xForce urging it so. Same value pulling forward serves towards centerline not away so easier to pull. So elastic model referred to if compress, force urges must swell from center on cross axis, where if stretched goes skinny on cross axis. Each time cross Dimension force Direction is opposite Direction of original Direction like can model with putty, the volume has to go somewhere..

The sin xForce at 30° is 50% xForce; after that more of the force (and distance) input by the vehicle is serving towards jackknife. So if 12 and 6 on the clock shows the Aligned Dimension, once backing trailer want to for sure keep straight as can and definitely between 5 and 7 o'clock, cuz the math says so. After that more of trailer going out of line than inline.. You can feel this, especially when can define it and watch it play out, then applies to EVERYTHING !


From the original table (from above post#18). i show this like this:


All the rigging, hinging, pulling, backing etc. etc. works by these Dimensional values of if something is in the Force Dimension vs. Crossing Dimension or not. And if not purely in either, then a mix of both to these patterns in the table, and values of cos:sin. i have an EASY mnemonic of cos:sin value pair rounded to the 'minutes' on the 360°clock; that is always with me to be my 'decoder ring' to constantly examine and re-affirm back these principles.

In the 'magic' of our rigging and hinging scenarios; this is the hand of the magician to watch to see the secrets as if 'behind the curtain'. Many other things can be the other distracting hand, perhaps say on the visible side of the curtain..

i like stuff especially where not only can numerically define, but then also be in touch with the feel/have a feel for these things that the math defines so can even tune in better as also re-affirms the math. Or rather they re-affirm each other. Hear with the trailer struggle, and another is a child's swing. Straight hang without side force in swing is cos benchmark position of 100%cos(and of max vert reach)as the definitive organic balanced, static position. Statically 90° horizontal to support bar would be 0%cos thus 100%sin(of max horiz reach). BUT dynamically/in motion the limit of the swing (and of horiz reach)arc is 0% cos at the breathless stall (that can feel)before return. 100% is still straight down and is full speed felt(and furthest vert Dimension reach). This cos:sin stuff of Dimensional influence amount goes this far here, the same rate for static vs dynamic changes, even tho different ranges ... The changes in speed on swing between breathless stall of 0 at sides and full 100% speed at bottom once defined can define speed at any point in swing by cosine% of the range of motion!!! Every thing follows this same scale of change from null to full, as feel in child's swing!!!