Tat, Thanks for the report! Always nice to hear from an appreciative engineer.

Thanks!

You're certainly welcome. I can almost picture students frowning in concentration.

Thanks Wry!

In my regular job, I'm an expert on roadside design. I occasionally get consulted on cases where cars go off the road and the distance they travel is affected by numerous factors, including the friction on the pavement and the friction on grass.

I wondered where you got your physical engineering knowledge from. it's great to see the mathematics evolved I think it help make my estimations more accurate.

Thanks Charles.

Thanks Alf.

Thanks RJ. Nice to hear from a fellow engineer.

Thanks, Mike. I hope you get a cool, overcast day with little wind.

Thanks Salame. I know it won't happen, but it would be nice to see your forests. Your forest climates are similar to our mixed forest climates here in upstate New York, but I'm sure the species are very different. Cheers!

Thanks Steve. I'm trying to look out for those who bought a chain saw with "How hard can it be?" on their mind.

Sorry you had to deal with that expense. Sounds like a damaged house would have been a lot worse.

@@terryhale9006 I didn't mind paying. You guys are worth the job well done. Hitting that house would have seen me with a one-way ticket to a distant land where no-one knows me.

Thanks Kyle. Stay safe!

Uh...Thanks Juston.

Seemed accurate.

If the video helped you make a good choice, I'm glad. (Plus, I am partial to white Oaks.)

Thanks Stephen.

Thanks Steve!

Wow! You're quick. Thanks for the nice feedback.

I was watching it as you uploaded it. ;) joking.

Thanks, Eric!

Made me laugh about the rope holding.

You got a degree in biology so you could gather wood 🪵?!?

Thanks, grb.

+Jim Fiorentino Thanks much Jim! Wouldn't have done the weighing and c.g. calcs, but I really tried to find some decent numbers on the internet and was surprised that they weren't available.

+Jim Fiorentino Plants grow in the direction that will allow them to capture the most light. If a tree is on the edge of a clearing, it will have canopy blocking light on the forest side and nothing blocking the light on the clearing side. It will thus grow/lean into the clearing to get more light. Humans then come along and build their homes in clearings. A tree growing in the middle of a thick forest will almost always grow straight. That's why plantation trees are planted with such close spacing - if you block the light to the sides, the tree has no option but to grow straight up if it wants sunlight.

The beauty of being out in the woods, though, is that you should seldom have need to make a tree fall opposite to its heartfelt desire.

don't forget Temp, and barometric pressure in that calculation...plus x-ray the tree for any insect damage or rot and bad growth rings and add that in....:)

I wish all math, chemistry, and physics classes were taught using pretty much nothing but practical problems.

This guy could be BS and would have no idea.Sounds convincing.

@@kleffner123456 just spend some time around tree cutting & you'd have clues

Thanks much, Mike! To further complicate matters, crack propagation gets really complicated by the highly anisotropic nature of the material.

If ya got it, flaunt it!

Thanks, Big Bird. If you say it was helpful, I'll hope your project(s) went well.

@@terryhale9006 it did! Took down a few leaners, two of which were made complicated by rot. But thanks to this video we employed the truck ropes and angles in such a way that they all worked perfectly! Now, making the cuts on the other hand... Folks in the videos make it look so easy, but getting the cuts just right definitely takes practice! One of them took way more wedging and hammering than it probably should have...

@@Gr8tBlueHeron Excellent! Just passed 70 and discovered my balance is fading. I'm starting to have trouble getting my cuts properly oriented. Getting old sucks.

@@terryhale9006 oh no! Well, at least you got the skills to pass on and can instruct an enthusiastic youngster in proper technique! And I sure appreciate your willingness to share your knowledge with us random strangers!

Thanks Teach! Keep up the hard work!

Man I wish I had you as a teacher in high school then.

Yes, but they make great KZfaq videos!

Thanks Jeremy. I occasionally like to credit personality and thought to other life forms.

Thanks again, D!

Thanks, Tim!

Correct.

+Daniel Murphy Thanks Dan. Must be the face in the window. I agree on the tree weight. Just wanted to work with a nice round number. You are right to get high with your pull lines. However, unless you can get farther away at the same time, most of the extra height will just be wasted as vertical pull. If you can fasten your pull line twice as high and be twice as far away, you will be pulling at the same angle and exerting twice the overturning moment. Viewed another way, if you have twice the height and distance, you will only have to exert half the force to generate the same overturning moment.

: )

It provides properties for each direction.

@@terryhale9006 OK. That would be a great book to have.

@@shopnwoods9901 Mine is pretty old, but I doubt the numbers have changed. You could probably get a decent secondhand book on Amazon for a fairly low price.

@@terryhale9006 I'll take a look around. Thanks

I've never done it myself, but it is fairly common European practice with large trees. A key detail is to use a fairly thick steel plate above, and often below, the jack to distribute its force over a larger area to avoid punching into the wood. The usual process is to cut the notch, then cut a pocket into the side of the tree opposite from where you want it to fall, insert the jack and plate(s), then pump the jack, followed by finishing the rest of the back cut.and additional jacking as needed.

​@@terryhale9006 Great! I'll give it a try then, once I get my hands on a piece of thick plate. I want to fell some spruce trees, in an area that I cant reach with my 2WD tractor with winch.

Footing on a hillside can be really treacherous, especially with lots of fallen leaves on the ground. You didn't mention whether there were any constraints on the direction you could fell the tree. In a wooded area on a slope, most branches will grow towards light, which means up and away from the slope. If that direction works, an escape route along contour is best. Whatever direction you are felling the tree in, if the escape route is tricky, you want to be away from the tree when it begins to fall. A good way to do this is to get a rope up into your tree and run it to the base of another tree which is in the general direction you want the tree to go. Fasten a pulley to the base of this second tree and run your rope through it. Then run your rope back towards the tree you are cutting, but off to the side to your safe retreat area. Cut your notch and part of your back cut. Stop and give a pull on your rope. Do a bit more cutting, then try to pull it down again. Eventually, you will reach a point where the hinge is strong enough to keep the tree from falling, but not strong enough to resist your pull. At that time, you will be in your safe place and the tree will fall. Make sure not to leave the rope in tension when making your cuts.

Thanks.

You are more or less headed in the correct direction. The formula is Section Modulus (S) = b times (h squared) / 6 , where b is the 11.5", and h is the 1.5". This gives 11.5 x 2.25 / 6 = 4.3125. The Timber Construction Handbook may be making deductions for the rounded-off corners of most real-world 2x4 lumber to arrive at the slightly lower 4.219. Trying to describe the derivation of b x h x h/6 is pretty tough without being able to use a diagram. Given that difficulty, I'll only give it one shot. Imagine a board 1.5 inches thick that is being bent to the point it will rupture. Ignoring the anisotropic behavior of wood and its non-linear stress-strain curve, we can assume that, at the moment of rupture, one surface is at the maximum tensile stress while the other is at the maximum compressive stress. Further assume that those maximum strengths are equal and that the stress varies linearly between the two surfaces. (We're already well away from reality. but you sometimes have to make simplifying assumptions to be able to do reasonable calculations.) That would mean that the stress would be zero at the neutral axis (dead middle) of the board thickness. On either side of the neutral axis, the stress would increase linearly from zero to the maximum. Each of these stressed areas would extend out from zero at the neutral axis to half of the thickness of the board, or h/2, where the stress would be the maximum. Let's call that maximum stress Fy for the stress at yield of the board. Looking at one of these stressed areas, it is in the form of a triangle where one side is h/2 and the other is Fy. The formula for the area of a triangle is 1/2 the length of one side time the length of the other side, giving an area of Fy x h /4. On average, this area of stress (tension or compression, depending on which side of the neutral axis) will be acting at 2/3 of the distance between the apex of the triangle and the outside surface of the board. The stress will be acting at 2/3 x h/2 or h/3. The moment that each stressed area will be providing to resist the bending of the boars will be the moment arm (h/3) times the sum of the stress (Fy x h/4). Multiplying, that gives us Fy x h x h /12. However, there are TWO stressed areas, one in tension and one in compression. Adding the two moment contributions, we have Fy x h x h /6. So far we have only been considering the section of the board. Toe capture its real moment resistance, we have to also consider the board's width, b, which is equal to 11.5" in our example. When we multiple that in, we get Fy x b x h x h/ 6. That is the classic solution for the maximum moment capacity of a rectangular solid. It consists of two parts, the maximum stress of the material, Fy, and the Section Mdoulus, b times (h squared) / 6. Engineering text books have accumulated the derived section moduli for many different sizes and shapes of possible beam cross sections. While most engineering graduates have gone through some of the basic derivations, I'm pretty sure most who are in practice simply use the manuals and have probably not done a derivation since college. If you like frustration, you can try to draw out the diagrams to make the above derivation make sense.

@@terryhale9006 Thanks for that, all makes sense given the assumptions/simplifications of the model. As you say, reality is a whole different beast, but a simple model is always a nice tool for helping one wrap their head around the magnitude of scalar or vector quantities that they are going to be doing battle with. Really appreciate the amount of time you have taken to provide that answer, and to have answered so promptly!

@@TheMadMagician87 Thanks and welcome, MM.

@@terryhale9006 For anyone else that's interested, Terry has another excellent video that looks at the details of the hinge: kzfaq.info/get/bejne/nNaRftKdqr3cd2g.html

I'd say they never do. With the uncertainties involved, it is just easier to take a guess at what's needed and provide much more than what is needed. Bad things happen when the guess is way off and only what was assumed sufficient was provided. Non-professionals often don't have the experience to make either judgment and then have events that may end up on KZfaq in an unflattering context.

I won't claim to have enough experience to be able to give a good answer. For the part that goes through the bark, the actual spur, you want a length that is appropriate for the trees you will be climbing. For most trees with average bark thickness, you want a normal length spur. There are some trees that have very thick bark, two or more inches thick. If you will be climbing those, you want long spurs to get deep into or through the bark. Since bark is a lot weaker than wood, you don't want a short spur that is just an inch into some weak, platy bark. For what fastens around your calf, you want something that is easy to put on. Mine are older and not easy to put on. Some sets are designed to be light weight, but are more expensive because of that. As you are usually standing on top of that weight, I have not considered it an issue. My simple advice would be to make sure the bit is the right length for what you need and then get a design that looks like it will be easy to put on.

Caught me. I started cutting trees and removing stumps when I was 8, but chose Civil Engineering and computer programming over Forestry.

What kind of and language(s) computer programming, sir?

Let me guess which languages.... Assembler, Fortran, and maybe C. am i close?

... and possibly BASIC or RPG depending how long ago he took up computer programming!

I started using APL in 1970, then Fortran, BASIC, Visual Basic, VBA (in Access, lots of those), and a couple of JavaScript apps. Now, I'm mostly using ApEx and PL/SQL. All are exercises in patience.

Good catch! Darn typos.

Nat, You are correct that there are big differences in a beam's capacity, depending on whether it is being bent about the weak or strong axis. With a felling hinge, we are bending about the weak axis, The formula for Section Modulus is (BxHxH) / 6. For weak axis bending of a nominal 2x12, B=11.25" and H=1.5". Running the numbers, the weak axis section modulus is 4.219 cubic inches. If we are interested in bending about the strong axis, we would reverse the B and H measurements and get a Section Modulus of 31.64 cubic inches. This shows that our assumed hinge has 7.5 times the capacity to resist side lean that it has to resist falling.

Cory, I have no experience with chain falls. I don't see a good reason why they couldn't be used for this work. Just want to keep them out of the dirt, Terry

Please. It's a six-man operation. Three to operate the three directions and three men to hold their six beers.

Questions that have plagued Accident Reconstructionists for decades.

I will keep working on it Terry, but seriously that was some fine maths my friend. Excellent vid. Chhers

Skip the math; enjoy the cutting.

It's tough to get my wife to condone a tree murder.

+Matt Comchoc I still have that notebook someplace. I'll see if I can find it.

I've been lucky, too!

I considered that one example of "an interesting trip". ; )

Probably that nasty "Use it or lose" thing. I remember that I took two years of French, but that's about all I remember from the experience.

And it wasn't even past midnight. I'm crushed!

kzfaq.info/get/bejne/isCKeb2JuamolI0.html is the closest I can get you on that.

+Ray Duerksen Correct.

+Terry Hale Are you sure this is correct? I do not see how weight would be transferred to the rear axle in the front-pulling case. The weight "lost" by the front axle would be picked up by the tension in the rope, not the rear axle.

The rear wheels do the pulling. They are limited in how much force they can apply horizontally by how much force is applied to them vertically. Therefore, as one factor, not having the rope's pull lifting on the back end will mean they can be more effective. As the second factor, the rear tires have no idea what is holding up the front end. However, they can tell WHERE the front end is being held up. Looking at extremes, if the front tires were directly under the truck's center of gravity, those front tires would be taking all of the load and the rear tires would have no load on them. At the other extreme, if the front tires were attached way ahead of the truck by some long, lightweight frame (think drag racer) nearly all of the weight of the truck would be on the back tires and the force they could apply would be maximized. When you pull with the front of the truck, the rope's force is being applied several feet ahead of the front tires, so some of the truck's weight gets transferred to the back tires. Considering that the engine is a significant part of the weight, the amount of weight transferred to the back is not trivial.

In my haste I assumed that the tension force was applied at the front axle. A simple moment balance confirms what has been said when the tension force is not applied exactly at the front axle. Thanks for your time!

You're certainly welcome. An understandable oversight.

+James Jahoda They actually do have those! I've seen videos of them munching into a conifer and then chasing the trunk all the way to the ground. It seemed like it took about 20 seconds to destroy a 70 foot pine tree. It left one big scattered mess, however.

Thanks for the reply. I have a friend with a grinder on a skid steer. Hard to imagine it on a boom. I sent your Back leaners -part 1 to a young cousin in college. I think he will be beside himself with joy with the math. Nice going.

"Young...in college". That makes you old like me.

Heck yeah. Still getting it done. Good luck with everything. Thanks for the great work. I imagine you spent a lot of time working on this. It's so dry, informative and hilarious. You are appreciated. I'm scanning youtube for safety refreshers. I'll be cutting up a fallen tree on my friends farm tomorrow.

P.S. College cousin says COOL!

Trying to. I also need to spend more time getting into good positions to facilitate the use of two hands.

Practice moving around & positioning while leaving the saw on the ground. With your attention to detail, (over time), it will become easier and more intuitive.

Sounds reasonable. I'll give it a few climbs.

The older I get, the more that sounds like a good idea.

he hee i know a limb came back on and fell out of the tree. It was fun tho The grass was thick. wanted to do it again

Engineering stuff. If you're not an engineer, a fair bit of that SHOULD be unfamiliar.

Jus, It sounds like you're thinking of nearly all the steps you'd need to improve your chances of success. The degree of lean in each direction would be critical concerns. If you've got a lot of back lean, even if you succeeded in pulling hard enough to overcome it, your hinge might snap and your tree might decorate your neighbor's garage. You might be able to add an anchor rope perpendicular to your primary pull to prevent the tree from falling sideways. However, this might be the perfect case to suck it up and pay an INSURED pro.

Thanks man. Yeah, I'm at the head of a cul de sac, and it's next to my driveway on the right as I look out, near the street (in fact, my mailbox is attached to it). It leans with the center of the trunk at the top about 4 feet left and 1.5 feet behind the center of the trunk at ground level, so that it wants to fall across my driveway and the top of it end up somewhere around my neighbor's garage door. After seeing your excellent and enlightening information on the forces involved, now I don't have to guess at something for which I have absolutely no feel or experience. It sounds like I'd need a full cement truck pulling on it straight down the cul de sac to overcome the direction it wants to fall, even if I could find a strong enough and long enough chain, and pay a younger more limber person to scramble up there and attach it (and trust their attaching skills). And even assuming I could get all that right, my hinge would likely snap and I'd have the bottom skipping off the back of the stump and creating an entirely uncontrolled fall. It's probably gonna require a removal service with some climbing and chunking, and not drop it all in one go, like I was fantasizing doing myself. So my only remaining question is, where do I send you the money I was gonna have to pay the neighbor for his garage? :)

HA HA HA!

Alas! I fall well short on both.

True. The series is intended for those who do not have a lot of experience and would like a detailed explanation of what they may have problems with when approaching what may be a risky situation.

Almost always an effective strategy. The video is intended to be a "heads up" for homeowners who might be tempted to use a lesser rope and to rely on some less-than-overwhelming means of pulling on the tree.

I have a landscaping business in central New York and we like to do trees. Been doin it for years we climb and lower trees and pull leaners also. If we can’t use the machines or pickup to yank a big one, we use 45* angle and drive a pin into the ground, useing as a minimum about 2/3 the height of the tree for the distance from stump. Attach a pulley to the pin and then use the pickups. I been doin this a long time but terry is still the man. Love your vids terry

Another in a long line of great mathematicians who decided they'd rather do something fun with their lives.

Point well taken. I will try to be more sensitive in the future.

Well alright then. Just remember to check your animal privilege...and keep up the excellent videos; they're entertaining and educational, and may even save a life or two.

That is my hope.