Trees and Physics

[TheTreeSpyder]

Nice chart Bob; but i'd think we'd have to say certain rope constructions are more static or elastic?

i think just because we speak in a rule of thumb for every 1 foot of drop adding 1 unit of load force to the load force; we should not confuse that with "foot pounds" in a free fall. Even when we speak of all that force landing on end of a 1x1 cant vs. the same force/fall on the 1x8 side of the cant; in calculating a "ground psi" of the concussion on hard ground - at least formally.

But, we we lift the big rock with hoist, or carry it up so high; then i think we can talk in foot pounds; without time factor involved as pointed out.

Terminal velocity is were the air friction increase from the speed increase creates enough drag to not allow further acceleration; only constant falling rate. Though we won't see this; it is the bigger picture of the scenario; defining operatives more.

The total force in the rig; would be load x acceleration/deacceleration by the responding deformations (elastic and none). This is all really just leverage etc. Force x distance. Distance of lift, deformation, spread out of impact etc. Even the fall that is load x speed is the same argueably; in that the speed in itself is how much distance over how much time. So really, time is another distance factor itself(only working inversely here; whereby less is a higher multiplier); only set to a multiplier of 1; when we aren't measuring it IMLHO.

As Tom pointed out in the words of the late Pete Donzelli; there are so many factors we can't put hard numbers on it. But, we can sit here and theorize the patterns and variables to get a feel for it, and/or make sure we are tuning in to the correct feel as we work. Because mostly it is that feel and experience that will get you through the day. 2 men can appear to be doing the exact same thing; but one will rig better time, direction, prestretch(line tension and angle/direction being the ballast of load force to achieve float etc.) and impact etc. into the line subtlely; that will make all the differance. One will shockload the line, support and crew more; testing everything more; inviting Murphy's Law to step closer... On the flipside, one will know when to use the amplified force to advantage also!

Most just try to l-earn from their miss-takes; but if you study the successes just as hard, sifting the info from them; like that is the real paycheck for the day; that will 'fund' all your other days!

 

[clearance]

So, after all the semantics, theory and assorted b.s., you are back to trusting your lives to variables you can't control, am I wrong?

 

[TheTreeSpyder]

i think it is fairer to say that we try to minimize the load multipliers; until we hit the inverse of where we make them work for us; not against. As we at the same time maximize the force dividers; until we hit the curve where they work against and not for us. Using time, distance, angle and direction of force etc. to control forces to our success; like we were dancing wit'em of like driving a car.

And as i told Tom once; i don't understand why people can't control these things with hydraulics in a car; when we control these forces with nothing but the direction/angle and tension in a half inch of line! But, i guess you can't control the variable of the other driver totally; just do your best when it's your turn at bat. i've repounded in daily lessons of force, direction, friction reduction, shock absorption etc. many times driving home; by dropping the wall between these 2 volumes of information we take in. i guess it is all exactly the same; but different!

Even conversation can be viewed as the same dynamic in this framework i think; the real thing is to l-earn what you can as an investmeant for next time; and to be able to healthfully shake it all off as the dust from ye sandals if it brings you down/ hold on to it if it lifts ya higher; and go home at the end of the day and turn off the key(ki).

 

[deercatcher]

Most of us here offer our services for hire. We develop our own niches in the marketplace; and often a reputation can be built by the jobs we refuse. I have studied dynamics; and see a place for a guy like clearance that refuses to do any heavy rigging. But no one has mentioned the degradation of rope strength in tying a knot, which adds in another 50% reduction in rope strength. I admit to being surprized in this work, and surprises are bad. I eagerly awaited the third part of a technical paper written on tree rigging dynamics by Dr. Peter Donzelli, mentioned in this thread by Tom Dunlap. In the magazine, was Pete's obituary. Scared the h-ll out of me.

If you want to calculate wood rigging, remember first, the knot reduces about 50% with a bowline. If you rig a marl (half twist) between the bowline and the anchor, you reduce the rope bend to 90 degrees and keep more fiber bearing the load. Figure your block weight. Then multiply by drop distance for up to only 5 feet. Ad your block weight back in, and that is a safe impact calculation. Acceleration increases on an exponential curve too quickly to use this linear calculation past a drop of 5 feet. If you can layer your systems you can spread the load around some, but not as much as you might think. Swinging a block between two neighboring trees will apply total force to both trees! The two ropes will not(!) half the weight between them. I have butt hitched and used a large speed line at the same time to arrest the fall and stop the movement quickly.

Use everyone's mind that is on the crew...
Expirament in a safe place sometime to familiarize yourself with technique.

Watch out for surprizes!

 

[BobEMoto]

Nice chart Bob; but i'd think we'd have to say certain rope constructions are more static or elastic?

Thanks. The type of rope is definitely variable. I used specs from a static kermantle rope. I think this has stretch factors that are typical, but its hard to find publishing specs on all types of ropes.

As for the second part, I may be incorrect, but I think that force = mass x velocity.

Force = mass x acceleration
but note that it is the acceleration of the stop.
The impact velocity sets the starting conditions (of the stop).


I think the biggest use for the table is not individual values, but to get an idea of when you're in the dieing range. I included 1000 pounds, but I wouldn't want to be anywhere close to dropping something that big.

 

[moray]

Not Quite Right

Ft lbs is an expression of WORK . No time involved period. Every object dropped or moving only falls or moves for so long (acted upon by outside forces ) Because TIME is now part of the equation this is a whole different ballgame . You move that bullet to the target by hand and you use exert less energy but take longer . Fire it from your rifle and you accomplish same amount of work but expend more energy .Work never changed , only amount of energy to accomplish it . This is a hard concept to grasp but thats how it is . Ask Sir Isaac Newton .

I've been away or I would have jumped into this thread sooner--I love this stuff! My first reaction is that no one is going to correctly calculate anything if they are confused about the quantities involved. If you are clear about the definitions, then the calculations for a particular problem are usually pretty straightforward, though I doubt anyone is going to actually do them at the job site except in very special circumstances.

We need to understand mass, force, energy, work, weight, time, power, velocity, and acceleration. With all due respect, the statement--"Work never changed , only amount of energy to accomplish it ."--is simply wrong. Work and energy are equivalent. What I think you are describing is the rate at which work is performed, (or energy expended), which is the definition of power.

I hope I am not insulting anyone by suggesting that a good way to get a solid grasp of this stuff is to study a good high school physics text. And even if one never actually calculates a rigging problem, it is very satisfying to understand this stuff.

Probably no one is going to follow my suggestion to brush up on their high school physics, and even those with an iron grip on the physics will rarely run through the calculations. Calculations or not, the strength of the wood at the rigging point can't be measured, and everything depends on that. So we fall back on seat-of-the-pants judgment, just like Clearance does every time he decides a tree is strong enough to support his weight.

We are probably naturally pretty talented at that. Our cousins, the great apes, do all sorts of fabulous dynamic moves in the trees, making great leaps across large gaps and safely landing in some surprisingly small wood. Even with all our math and physics, we are hopelessly inept compared to a gibbon.

 

[clearance]

Calculations or not, the strength of the wood at the rigging point can't be measured, and everything depends on that. So we fall back on seat-of-the-pants judgment, just like Clearance does every time he decides a tree is strong enough to support his weight.

Thank you.

 

[TheTreeSpyder]

Clearance's worries amuse me; not out of disrespect, but rather the flipside cuz i won't play around electricity. So, i guess we each have these great forces we think we can dance with intelligently; and just do the next most right thing to keep things on our side.

Here is the saved page from ol'ISA Tom spoke of. i did not have the foresight to also copy the pix before the forum took it's final crashing nosedive.

But, that is where i got my start on this: http://www.mytreelessons.com/Pages/Rope%20Angle%20Leverage%20Calculator.htm just reapplying the formula in the spreadsheet Dave pro-vided from the thread.

Which he then took an made a formulae for a DWT for lifting or lowering on spread supports like DeerCatcher speaks of. Notice it is the same, but adds another angle; that adjusts larger as the other does smaller!

i prefer to think of each leg of the speedline support as bearing half the load; but just at a leveraged angle; of how many degrees off inline with the flow of force(gravity)/vertical. So, directly overhead support is inline, no leveraged multiplier, so gives us a 2:1. As we spread the supports apart, there is still 2 supports bearing each half the load x the leveraged multiplier for degrees from vertical. Pulling from the end, we still have decreasing leverage over the bend until 120(where each leg is 30 degrees off of vertical) or 1/.5 is the multiplier for half the load or each leg of support line has a tension of the load... Flatter than that and you'd rather reverse your strategy and pull from the bend to have leverage over the end. This is the force for raising tension of line in sweating/swigging; that you then capture as a "purchase". And do it again.

 

[moray]

i prefer to think of each leg of the speedline support as bearing half the load; but just at a leveraged angle; of how many degrees off inline with the flow of force(gravity)/vertical. So, directly overhead support is inline, no leveraged multiplier, so gives us a 2:1. As we spread the supports apart, there is still 2 supports bearing each half the load x the leveraged multiplier for degrees from vertical.

Correct, as usual.

For those who know their math, the technical language of vectors and trigonometry is a bit easier to understand than SpyderSpeak.

But there is a shortcut to getting the numbers right that doesn't require any talk of leverage or degrees, and doesn't require any math beyond the ability to use a ruler. You simply draw the problem to scale (see one of Spyder's links, above, for a diagram). From the load, draw a horizontal line to the right-hand vertical support, and a similar line to the left-hand support. You now have two triangles. The lengths of the lines are proportional to the loads (ignore the imaginary horizontal lines). The longest lines are the two legs of the rope and represent tension. The shorter vertical lines at the supports represent the downward force from the load in the center. This simple method works when the load is halfway between the two supports. With minor adjustment, it will work for any configuration of load and supports.

 

[safeT1st]

[
We need to understand mass, force, energy, work, weight, time, power, velocity, and acceleration. With all due respect, the statement--"Work never changed , only amount of energy to accomplish it ."--is simply wrong. Work and energy are equivalent. What I think you are describing is the rate at which work is performed, (or energy expended), which is the definition of power.

Well said Moray . Indeed I was trying to convey that without considering time,only work can be determined .I mistakenly infered that energy mirrors power which you have corrected me on . Reason being is that the most common unit for both energy and power is the horsepower which is calculated using time . I too enjoy these topics despite what others might think of them . I refer to my old texts constantly and find it re-sets the information in my head . Remember learning this stuff for the first time and thinking "when will I ever use this stuff " ? Every step we take each day is actually a calculated risk and we are always playing the odds . If nothing else, I think having a better handle on the forces at work around us gives us a better chance to beat the dealer in life ,or hold him at bay .

 

[ddhlakebound]

So we've arrived at:

It's nearly impossible to accurately calculate the forces involved in a dynamic rigging scenario.

Even if we could calculate the forces accurately, we still don't have any idea how much stress the rig point will support before failure.

If the terminology isn't used properly, it affects the acceleration of gravity.







Sorry for the sarcasm, I'm somewhat joking, I do understand that the proper use of the terminology in critical to understanding and applying the math. And I'm working on understanding and using it correctly.

I understand (somewhat) the difficulty in accessing the effect of all the variables involved, (part of the reason we use a 10:1 saftey factor), but I'm unwilling to accept that we can't regularly arrive at a (close to) accurate figure for our loads.

It may take a long time to reach the level of understanding I'd like to be at, but......watcha gonna do?

Will it be worth it? To be able to put a numerical figure on the load I'll apply to my rigging set? Maybe not, but more information has got to be better than less. But I guess even with the math, it all boils down to judgement.

Could someone please explain F=MxA? I'm having a hard time grasping how Acceleration matters instead of Velocity. When we drop that block or log into the rigging, the acceleration in freefall will be constant (32 ft/sec2), and from this we should be able to calculate the velocity at impact. How is it that acceleration matters instead of velocity?

 

[safeT1st]

Study this

I will quote from a text of mine to minimize confusion :Newton's second law states that the acceleration produced in a mass by the addition of a given force is directly proportional to the force and inversely proportional to the mass . When all forces acting on the body are in balance the object remains at a constant velocity. However, if one force exceeds the other, the velocity of the object changes. Newetons second law is expressed by the formula:
Force=Mass x Acceleration . Speed and velocity : speed and velocity are often used interchangeably but are actually quite different . Speed is simply a rate of motion or the distance an object travels in a given time : mph, feet per second , knots ,kilometers per hr etc. Speed DOES NOT take into consideration any direction. For instance I can walk around the block ( 4 different directions ) and still apply a final figure of speed to my walk:say 3 mph. Velocity on the other hand is the rate of motion in a given direction and is expressed in terms like 500 ft per minute downward or 300 knots eastward.An increase in the rate of motion is called acceleration and a decrease is deceleration,both measured in terms like feet per second per second or metres per second per second. Now my velocity's on that walk around the block will be expressed in 4 seperate figures: 2.5 mph east,1 mph north 4mph west and 4.5 mph south . Do you see the difference ? Now you simply have to accept that to calculate force you use acceleration rather than velocity Going back to Newtons law , the only time the forces are in balance and velocity is constant is terminal velocity. I don't recall but it's about 120 mph ? We will not see this in every day rigging so as a result we are always dealing with acceleration . Again , it's hard to explain and sometimes you just have to say "alright,I dont really get it but I will accept it "

 

[dc59222]

We must remember two things when we talk about objects falling. One is that terminal velocity is determined by three different factors. The first is the density of air the object is falling through, the second is the amount of drag imparted upon the object by the air through which it is falling (i.e. the size and shape of the object that is falling dictates how fast it can fall through a given density of air), and the third is the weight of the object. For example, the terminal velocity for the average human is about 120 mph at sea level. Terminal velocity for a penny is about 60 mph at sea level. the further away from sea level you rise the higher the terminal velocity becomes for either object due to the decrease in the density of air. Second, we must remember that Newton's second law applies only to objects in a vacuum (i.e. a space with no air and subsoquently no drag). According to Newton two objects of different weights and sizes dropped from the same height will fall at the same height, but that only works in a vacuum because the differences in size are negated by the lack of drag. For an extreme example, if you drop a baseball and a sheet of paper off of the same building undoubtedly the baseball will hit the ground first. Conversely, do the same experiment in a vacuum and both will hit the ground at the same time. Sorry for the high school physics lesson, but there were some over generalizations being made.
Back to the topic at hand, I subscribe to the philosophy of "use strong rope, place your block in the strongest place available, and cut small pieces." This way may take longer, but there is absolutely no reason to toy with the envelope in this business when lives are on the line.... especially when it is your own. The bottom line is that there are so many variables in tree rigging that no matter what mathmatical formula you use, you never get any closer than an "educated guess" as to how much weight is safe to rig out of any given tree. My motto is make an educated guess and cut smaller just to be safe. Maybe that is stupid, but I am not aware or any climber who has been killed because a tree failed from a load that was too light.

 

[TheTreeSpyder]

i maid this lil'widget a while back. You can adjust the force at the pulley by typing. Also, you can adjust the ends or bend (pulley) position by dragging either end or pulley; to ultimately adjust the angle (multiplier of the minimal/nominal/ inline force) with mouse drags. Then read out the nominal force per leg (half the load); angle of each leg from inline, sine of that angle and the tension force in the system from this leveraging as outputs.

i'm kinda rough cutting it; but i'm taking half the load X leveraged multiplier; leveraged multiplier being 1 divided by the sine of each leg from inline. Stay on the pulley or center of the end; so you don't slip off; and move slower than the 12/second frame rate and it works best on the drags.

http://www.mytreelessons.com/Flash/knots/lineBend.swf

i purposefully did this pulling across with produced rather than gravitational force; to show it is the direction of the load force in comparison to the opposing direction of the support force that gives the multiplier for the nominal (load\supports as minimal loading). we just usually see that as vertical force on a speedline; but that is just because gravity makes the load force up and down against the nearer horizontal supports (giving leveraged angle multiplier to the equal and opposites). Direction is very important to the relationship/marriage of the equal and opposites; another multiplier like time and distance; sometimes just set as a multiplier to 1 when inline or not treating/looking at it; but all ways there!

Notice if this was a rig catching force; the catching of the load would be while ropes where in the most leveraged angle multiplier of that force; then less of an angle as it lowered. The catch is also the speed/impact moment; and the point when there is less elastic rope length in the system to take all this sudden dynamics; especially if redirect to a control leg is frictional/not a pulley. This is especially where running load a bit can ease forces; as long as you were snubbing force out, not building it with the added distance of fall.

Great Discussion!

 

[moray]

[

Well said Moray . I too enjoy these topics despite what others might think of them . I refer to my old texts constantly and find it re-sets the information in my head . Remember learning this stuff for the first time and thinking "when will I ever use this stuff " ? Every step we take each day is actually a calculated risk and we are always playing the odds . If nothing else, I think having a better handle on the forces at work around us gives us a better chance to beat the dealer in life ,or hold him at bay .

Very well said, yourself! You have nailed what I consider the heart of the matter: that the real benefit of a working competence at math and science is that it deepens your judgment and appreciation of things, not that it allows you to calculate complicated formulas. If only it were taught that way in school! A few nerdy types like myself like to do the calculations as well, but as you suggest, it is not really about numbers and calculations. It adds a whole dimension to things, like adding color to a black-and-white world. This may sound a little over the top, but having known a few people really well who had no numerical sense at all, I don't think so.

I remember that Harrison Ford movie where he is making a mid-air transfer from one plane to another, and ends up at the end of a rope trailing from the cargo plane. The rope is nearly horizontal with a slope of maybe 1:20. The non-mathematical among us would probably see nothing wrong with this picture, but I instantly knew it was absurd because he would be supporting something like 20 times his weight. Even if his wrists had been shackled to the rope, the force would have pulled his shoulders from their sockets.

It doesn't just happen in movies. I saw a video a few years back of a dramatic and tragic stunt, again involving a rope and some people with no mathematical sense. Six or seven people were planning to do a long swinging jump from a high bridge over water. The rope was maybe 150 feet long, and the jumpers were standing on the bridge deck, clipped in together at one end of the rope. The other end was anchored to the bridge deck 150 feet away. The jumpers climb over the rail and start a countdown.

Since the rope is horizontal, the jump is going to be a huge swing, not a bungie jump. One, two, three...they all jump together. Everything is going according to plan until they reach the bottom, at which point the rope breaks. They hit the water going about 90 mph, which results in at least one death and several grievous injuries, if I remember right. Apparently they didn't reckon on centrifugal force dramatically increasing the load on the rope.

 

[moray]

The bottom line is that there are so many variables in tree rigging that no matter what mathmatical formula you use, you never get any closer than an "educated guess" as to how much weight is safe to rig out of any given tree. My motto is make an educated guess and cut smaller just to be safe.

Right on. But the "educated" guess is way better than an uneducated one, so having a good grasp of the math and physics, even without outright calculations, is all to the good.

It may take a long time to reach the level of understanding I'd like to be at, but......watcha gonna do?

Could someone please explain F=MxA? I'm having a hard time grasping how Acceleration matters instead of Velocity. When we drop that block or log into the rigging, the acceleration in freefall will be constant (32 ft/sec2), and from this we should be able to calculate the velocity at impact. How is it that acceleration matters instead of velocity?

I admire your desire to better learn this stuff. Bravo!

To answer your questions, I would first note you are on the right track to think velocity matters (it does), but by itself it tells you nothing about the force your rope is going to experience. The complete picture of what happens when you drop a load on a rope involves the velocity when the rope goes taut, the length of the rope supporting the load, the stretchiness of the rope, the mass of the falling piece. In a complicated scenario, other factors like pulley friction, swing angle, rope runout through a friction device like a Porty, etc., might be involved. These don't make the problem hopelessly complicated at all; they just mean your final estimate is going to be a bit rougher than in a simpler case.

Let me just deal with one thing here: F = M x A. (Incidentally, this is not very useful in thinking about this problem. What you really want to know is how much is my rope going to stretch, because that directly tells you the force it is experiencing.) If you were an astronaut in orbit, where things are weightless, and you were asked to take an ordinary baseball and throw it at a target, you might think, because the ball is weightless, this would require no effort. But it requires the same effort (force) that it does on earth. Changing the state of motion of an object is acceleration. Catching or throwing a baseball are examples. To do this requires force, as your own experience shows. Catching or throwing a basketball takes more force, because the mass of the basketball is greater.

When your rope catches a falling load, it continues to stretch until the load is stopped. At that point, because the rope is like a spring, it is applying the maximum force to the dropped load and it is experiencing the maximum tension. The tension in the rope varies from zero when the rope first goes taut to this maximum value when the load has stopped. In theory, the tension in the rope should be proportional to the stretch at each point in this process. This linear relationship makes it easy to calculate how much the rope will have to stretch to absorb all the energy of the falling load. But as you will have noticed, we aren't really using F = M x A at all.

 

[TheTreeSpyder]

i think a lot of good info and feel has/is being given for the subject.

Any sitting back a lil'lost or whatever and wondering why worry about all this etc.; should hang in there along with everyone else.

Because, as we've said these are just guesstimations; in other words proper assessmeant and feel, building on experience is the way one progresses hear. And this information is how you digest your experiences to understand and compare what forces went right or wrong, not quite as expected etc. to get the most out of the experiences; wringing them dry! These things also suggest how and why to minimize what forces present that stand against ye and maximize what forces are working for ya. They also show in time; when just a little correction makes a lot of difference-or not worth the time/fight to correct, and working from the weakest link to upgrade the whole system immediately etc.

We build mostly machines that work by friction and tension; McGuyvering along with the simplest of tools in remote places; no 2 exactly alike. The more you know about the distilled out bare operating properties of each item and their linked/paired relationship to each other; the more things you can pull off safely IMLHO.

But, mostly i think; Sir Francis Bacon said it best in my sig....

 

[BobL]

Greetings all, ddhlakebound suggested I take a look at this thread because I am a physicist to see if I could contribute.

I should perhaps preface any remarks with the fact that I am a home miller (076AV with 52" mill) and know very little about the practicalities of bringing down heavy lumps of wood from a tree. My only direct experience in this regard was some 20 years ago when I was in a hurry and tied up a 20 ft long x 8" branch with a piece of old rope before cutting the branch with a bow saw. What I didn't take into account was the levering action of the length of the branch so the rope snapped and the branch fell - only about 3 ft, flat onto the neighbors wooden shed. The shed made a couple snapping sounds and wobbled a bit but stayed upright. I managed to get the branch off the shed without any further damage. A year or so later we had a big storm and the shed collapsed!

OK - that aside, I can still help with concepts and formulas. To really understand these problems with, diagrams would be useful - you would all get marks docked if you were in my Physics 101 class. Moray's post on scale drawings is a good one but would really benefit from a diagram or two.

Bobemoto, I'm not quite agreeing with the results on your table .
Lets start by seeing if my diagram represents what you are calculating.
For a 100 lb lump (or for that matter any lump) falling freely from rest over any distance S will reach a velocity of SQRT(2 x g x S).
g = 32.2 ft/s/s/ for most placed on the earth.

When S = 12 ft , v = SQRT(2 x 32.2 x S) = 27.8 ft/second

To decelerate this to zero velocity over distance d =1.27 ft requires a deceleration of v^2/(2d) = 28^2/(2x1.27) = 309 ft/s/s

Now here is where you use F = m x a.

The force F, generated on the rope during the deceleration = mass x deceleration = 100 x 309 = 30900 lbs ft/s/s which is you divide by g = 32.2 ft/s/s you get a weight equivalent of 959 lbs PLUS the actual 100lb mass of the lump = a total of 1059 lbs (Bobemoto gets 1043 lbs) Bobemoto , are you taking rope/pulley friction - ie non free falling, into account?

I hope this helps. BTW there is some very good physics software out there that simulates these situations including angles and rope elasticity very well, see something like http://www.knowplay.com/science/interactive-physics.html

Like others have said, none of this will predict super accurately what happens in reality but you will gain some idea of what to expect. I believe a good experiment under controlled conditions will also give you other ideas and help build your experience.

Happy to try to answer other questions

Cheers

 

[BobEMoto]

Nice picture.

Bobemoto, I'm not quite agreeing with the results on your table .

I think the difference can be explained by the precision used in some of the fundamental constants. I used:
3.28083989501312 feet/meter
0.45359237 kg/pound
9.80665 m/s^2, but gravity really varies from 9.789 to 9.832.

 

[BobL]

Nice picture.


I think the difference can be explained by the precision used in some of the fundamental constants. I used:
3.28083989501312 feet/meter
0.45359237 kg/pound
9.80665 m/s^2, but gravity really varies from 9.789 to 9.832.

Wow - you did it in SI units and the converted! I went to all the trouble of doing it in ft/lb/s from scratch. I haven't done that since high school in teh 60's.

Anyway - glad you liked the diagram.
Cheers