Slice by Slice;

as i drive car immediate pure inline, flat forward direction is my cosine of 1 dimensional focus(no side nothing);

i can feel the sine/numbers of a curve or hill that is off the MINIMAL distance/base/nominal (for work) pure flat linear UNIQUE 1 dimensional path.

If know the associated numbers, can feel the numbers to 'see' even more sense to them more innately i think.

See this in everyday things becomes so common is not exercise, easier to see in work things.

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Clock Allegory, have shown, is my always handy 'decoder ring' of angles and associated cos/sin/tan that tell story eye to simple to see.

Surprise sideward force on small curve, is the amazing, maximum sine changes in that end of the powerband just off pure alignment/straight that eye only sees thru decoding chart.

While same soft angles of deflection not giving much softer RR track crossing (until greater angle to be effective at dropping cosine faster) is how conversely the cosine barely moves at same range as sine so intense, as are antagonistic reciprocals, that eye doesn't catch.

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For 6degrees deflection from pure inline (1 minute on clock) returns 10% side force on the turn a surprising amplitude of force that is immediate so carries impact wallop too,

but going across speed bump or RR tracks, same 6 degrees only reduces the confrontation to the RR tracks 1% as drop in cosine/unnoticeable.

This makes the counter-intuitives seem even farther away, like as inconsistent; until can decode and sort to proper piles.

Increase angle hit tracks to 30degrees deflection, drops cosine by 14% as also giving longer speed reduction time to compound in on reduction multipliers chain, were can appreciate some of the effort, less confronting, more along tracks direction.

(i do prefer aiming at angle, but actual crossing wheels square with car frame).

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On non radial rope elements; can model force path(as all above) slice as cosine down center of rope of simplest needed (anti)Load force, reducing influences as sine across that cosine as benchmark line in scenario.

Radial elements more to overall scenario force path model i think(than segmented as above) for benchmark cosine, from the input Load direction(until over-ruled to new cosine reference from there from shear across cross axis).

Showing dynamically setting benchmark line of cosine to the scenario, rather than statically a preset frame guide of cosine, that set scenario inside of to weigh and measure scenario as classically taught i guess.

For cosine/sine are just graduated rulers with associated values; that like a measuring tape can take and walk around problem points if want more so to me.

Each way of use, just measuring the same facets/relationships from a different benchmark; sometimes to show different insights , or same insights better at that 'angle' of view. So each paradigm very illustrative, but not exhaustive model alone to me.

Model: "Wages of Sin(e)" as a side tax shearing across your work as Samson to pillar:

In ropes lessor sine across causing seating to host is automatic, implicit in the Load x Angle as Load cause/cos, sine is incurred as host interrupts that direct flow.

Radial host interrupt/redirect of cosine flow to Load, is most organic/gradual/Natural interruption.

>>That Linear face host can't offer, for can only give harsher impact of change/interruption.

Seating to host gives utilities of : potential frictions, nips and grips controlling the Load held by cosine thru core of rope(slice by slice model).

Co$t of Conversion at change of direction is when the greater cosine(to lessor sine)joins in as a controller of the Load.

>>on a Linear faced host this would be at a spot on a corner

>>but on a rope arc, especially 180, the conversion co$t is over a more usable RANGE not a point of the deformity causing conversion/direction change.,

>>therefore also the returns traded(for co$ts) of controls from seating to host(friction, nip, grip potentials).

>>arc also increases the sine value and uses both cosine and sine together for control

>>where previously only used sine at a lessor value, to power controls over Load (thru seating to host )of :friction, nip and even grip in self opposing multiples

>>in 180 arc from Linear source/initial input force type, find seating to host as most compound for strongest compound controls of compound friction and compound nip possible w/some nominal, sine(that is increased in arc) powered only grip potentials.

>>compound grip achieved as go again to opposing multiples; this time of 180's for 1D grip w/2opposing 180s potential and if more 180s 2D framework of grip potential.

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Another place can feel the sin(e) shearing across efforts is vertical Prusiking or camming etc. leg compression lifts.

Benchmark cosine as inline target, aligned to gravity line, every single drop of your center of gravity not inline with cosine is less efficiency;

AND carrying force of sine thru bod as a device too, to a new and crossing direction.

If input pull tension from cam handle overhead, sine more cradles and grooms you to more efficient inline as tension pulls to centerline.

But if input is from more powerful leg, the sine is fought more from pushing you more out of line to less efficient as part of the work.

>>for compression pushes E&Os apart more

The more you give in to that side/sine push across to more deflection from centerline

>>the more effort it cost$, in 2 different ways, each to a different direction(cos and sin across) as it tries to beat you in the open weather.

The harder you piston hit with leg(s)upward; the more upward return and also this crosswise, trying to break you as a force vessel (d)effect in return also in this dbl.edged sword.

The thinness of own powerband at that point/range between twilight of can and can't;

is to the good side; the most sensitive to change range; so yielding most body sense.

Sometimes put self(or scenario) to point between can and cant /almost upside down of what can do; to sift by this measure purposefully in many things, for the magnified/more sensitive view.

Other times, only way to find there is a line, or where it drops off like a cliff, is to step over it/or close to feign to.

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Driving, rope, water hose etc. can be shown as slices of focused direction as core linear of focus; directly to cause/cos(minimal path) and the co$t of sin(e) shearing across; to contain all connected parts.

Different insights to each can be found from another, if know what parts of the separate knowledge banks link as one.

Including feeling with body the forces in driving, for a more body sense/knowing, gut level familiarity once experience realized and sorted to correct piles.

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