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Cosine, my friend

theTreeSpyder

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That was always going to be the tile of this for quite some time now.
Originally meaning cosine, as my friend; but then here now to friends in dual meaning as well.
I never get the sine cosine bits. Seems to be referenced without explanation.
from:
The Art and Science of Practical Rigging vs. TCIA Best Practices for Rigging in Arboriculture thread
i look at cosine as directness and sine as deflection >>any potential connected to scenario is 1 of the 2
A column with weight on top capitalizes on cosine in this model as the alignment of load to support
>>while at 90degrees from this line capitalize on sine across column like Samson or wrench across a linear column
>>column @pure vertical uses all length for reach, but can't use full length nor strength vertically @ lean
to this model a stone drop is cosine benchmark axis all rest of sine rings are measured from that benchmark etc.


Cosine is the simpler to start with; and has been my friend once got to know(and quit kicking my azz) as a decoder to events.
>>often taught as visible lengths/distance usually, but applies to force (as a distance reciprocal so one always implies the other)
Several ways of using the measuring stick tools of cos/sin to decode the changes all to same end, just how much work between..
Many find cosine as horizontal axis only from school, and can only see that way.
While builders etc. may only see it as gravity load bearing vertical aspect, as a Greek column of support.
Quite a chase trying to self teach.. Is best to be able to use cosine in any direction more fluently i think.
i walk it around a scenario like a measuring tape/stick, and claim one primary axis of scenario as the benchmark cosine.
>>to judge rest of scenario from this benchmark line of simplest 1D, for a scenario MUST have dimension(or no place to change to).
Cosine is a linear 1D so i align it to a similar 1D in scenario(force line or support against usually) for least calculations

Cosine can be seen as a remaining virtual column of support in a tree lean as support work achieved against weight and space(height)
>>the side force byproduct as the leverage making a triangle actual lean, and the vertical and horizontal EXPRRESSIONS of length and force in the actual lean as the total potential that can be expressed.
The main work i still seen as support CoG but can't do as well in strength nor height with present fixed assets:
We can capitalize on the leveraged byproduct of lean to fall tree in this chess game tho.
cosine-benchmark-as-gravity-forceline-view.png
Cosine is a graduated scale, but of unequal graduations per degree for a 1Dimensional axis benchmark line.
Easiest to L-earn as gravity load for our work i think, i look at it as a Greek column, co(lumn)sine i say(sine as the sin against laterally/crosswise) as memory aids
A slanted pillar can't hold as much weight as pure inline, and can read effect as cosine dropping as the precise scale of change to loss of efficient usage of strength and length potentials.
Cosine ranges as a multiplier from 0 to 1; i look at as 0-100% multiplier of efficiency of benchmark alignment.
Pure vertical is 100% strength and length potentials used, 30degrees deflection for support and is only now efficiently:
able to use 86.6% of full length (as a potential) for rise AND able to use 86.6% full strength(as a potential)for support.

A rigid device can internally resist on at least 1 cross axis, but rope/flexible devices cannot resist against on any cross axis.
>>so need an external imposer of side force or will self adjsut to none
>>the green rope below @250# is that, or another opposing support leg side force in opposite direction , pulley in center
.

BUT>>incurs a byproduct side load of 50%, a big jump from Zer0 vs. 13.4% drop in cosine each in 1/3 the travel
>>cos/sin give us these numbers,
>>but (in my imagery) the primal FFF caveman preprocessor brain assUmes different numbers to hand to brain mainframe(prev.discussion)..
>>does not expect the 250# side force below nor the slight loss in vertical drop at 1/3rd travel, must retrain/intercept that process and force new look.
.
This is as a system of balances, the above configurations MUST give these numbers; cos/sin is the key decoder to define change like it was a balance scale !
i used to look at cosine from the column of support perspective, as pictured Greeks did to hold up roof
>>but have 'evolved' to generally setting the initial force as cosine as flows to that column support,
>>to same numbers but think is more correct , at any angle, like used in electric/wind/water/light etc. waveforms as concept is consistent even to those depths
(from same numbers found decoded the stars movements) youtube.com/watch?v=rd4tY3brjT4 child's coin slam force transference:




These are all the same cos/sin to decode, the same rules just expressed in water, tree, rope, pulse wave examples of same things etc.
As are all displacements against physical space and against physical force, so must be able to define most pivotally as cos/sin.
>>as even the stars are commanded to do and so all below the Ancients found, we could never prove them wrong on that.
 
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cory

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Waaaay too deep for my walnut-sized brain, but I dig "In Rope We Trust" :dude:
 

Mellow

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I have no doubt that this is very interesting and informative but when I look at any of Kenny's posts, all I see is,

"Βλέπω το συνημίτονο ως ευθύτητα και το ημίτονο ως εκτροπή
Vlépo to synimítono os efthýtita kai to imítono os ektropí..."
 

Pelorus

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A background in advanced pathophysiology and Boolean algebra would certainly be helpful.
 

theTreeSpyder

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If lean 100" pipe @ 30degrees deflected from straight against a tall building, how high will the pipe reach upward?
How efficiently (cosine) does it use it's potential (length) to displace against space(height)?
How well does it line up on this single target(up) with all that it has(potential)?
>>Is the same math that is used to decode all of this in ALL physical distance( and thus force) instances.
(Because only force can overtake distance as they trade for each other so are entwined as reciprocals)
cosine-as-vertical-column-1of2.png
My clock calculation in head would say 86" at a glance constantly read in everyday life w/o looking anything up, just a decoder.
>>everything daily self confirming everything else around me, once have decoder ring(clock) to talk to cosine, my friend.
cosine-as-vertical-column-2of2.png
And tough as it may seem, the decoded numbers make it all make sense logically just like the needle on a balance that they in fact are.
This is how they put man on moon and bring'em back whole, with just how much fuel starting when in what cycle to not crash into anything and sling shot around on moon's pull to throw back to where, when by calcs on a slide rule!
This stuff kinda works..they could only even think to do that because even the heavenly bodies had to obey the same laws.
 
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theTreeSpyder

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This decoding gives a full open world view of the happening, rather than usual peek thru crack under the door to read world thru..
Otherwise can be as a language in a foreign country, guessing what is said from a few hand motions hope reading right; unsure of next move in these strange rules of this 'society' that all rest of world moves so Naturally with around us as a flowing logic.
.
Most all things fail from the side force overload from sin(e) much more than aligned loss of cosine/efficiency inline part of support against load.
These fails show across and express as a buckling, shearing etc. from overrun of across/not inline forces
>>not expressed as inline crush w/o side blow out etc. type fail etc.
This is how stuff is commanded to work, up until it doesn't, and how to read, tune and manage it; w/o getting killed by it.
>>also how to even use byproduct as a power utility to assist rather than just tax efforts; turn things around in the chess game.
.
Against a target distance we can show these things more visually as examples to all else;
but as work we can tune to feel them as do and burnt into memories and even scars of past to sort.
The numbers truly, truly faithfully decode and explain what saw and felt in present or excavated past memories..as well how to plot and command in future.
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
is all that it is; done thru /read thru this language to command, or even see what are inadvertently commanding, or sift out why something really works so can use it else where etc. Once catch enough glimpses in shituations etc. ; more easily can sift the same silhouette from several instances commanding stuff in each expression as same; for 1 lesson not 5 to command same amount, and expands to more as in fact commands all.
.
Once understand the language, decode it to your own internal Native; 'easily' understand the 'expressions' of the rest of the society 'hustling and bustling' around you in physical distance and physical force enough to miss getting hit by a bus.
The biggest G'D bus ya ever seen; leading w/drooling grin to make another juicy dark reddish grease spot pancake outta someone
....even has scorecard on the back as it goes by; still hungry as a shark while you now just watch scene(not be part of scene) w/locals.
(brotherly rant over)



This pic starts with counter-intuitive warning of borderline limits of no support @90degrees/180 spread of Zer0 cosine .
Shows at end standard safety thumbrule of no wider than 60degrees deflection/120spread as now in red zone of last 3rd of of deflections from load
Then support singly efficiently cos100%, and shared support cos100% efficiency thru pulley with straight support legs aligned against work;
and then shared supports used less efficiently, needing more tension for same work at angle not aligned fully to work.
Work done is as any other expenditures;
>>cost$ more if assets lent inefficiently, as now carry byproducts of tax etc. for same raw 'purchase' of work done in trade.

flexible-support-rope-cosine-as-gravity-force-line-examples.png
120 degree spread (thumb to baby finger spread angle as checkmark)thru a pulley weight in center,
where each leg of rope support deflects 60degrees from the center load line;
is usually safety limit on spread apart, as at that point the rope tension = load as a benchmark w/o math
The efficiency of both support legs is 50% each, so together the 2 x 50% = capacity of single leg of line.
.
DANGER: the cosine falls very rapidly in the final 3rd range of deflection after efficiency of .5cos @60degrees ea.leg/120 total spread before blows out....
>>just 15degrees later @75 degrees on each of shared support legs/150 degrees total spread the cosine drops to .2588
>>look for rope tension to be ~2xLoad and doing nothing but getting frightfully worse fast if continue wider deflections/spread of supports past 120degrees...
>>and rapidly expands to theoretically infinite 15degrees later @90degrees ea.leg deflection of trying to carry load w/0cos as no support
>>upwards towards this is how stuff breaks, recoils, maims, kills etc. like rope center break and recoil back like breech end of rocket launcher..game over if on the power axis.
 

treebilly

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I use a few of the words mentioned but can’t follow what Kenny is putting down. Obviously I’ve forgotten a lot of advanced math courses I took over two decades ago
 

Jomo

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Sounds like a fancy way of sayin a 90 degree bend in arope has mare of it!s rated tensile strength than beyond 90 degrees of deflection.

The exact reason Inutilze Double Cloves locked off with a TimberHitch, on serious big wood when catching it.

Jomo
 
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