# Torque, power, weight?

• Watuplol

#### Watuplol

TL;DR Summary
Trying to find out what it would take to pull out a tree
I was trying to do some research to find the difference in power of different vehicles. Mainly the difference between a Large hauling semi truck A battle tank and a bulldozer like a d11t. Let's say I hooked up a chain to the back of each of these vehicles and rapped it around a large 3 foot diameter tree which would have the best chance of rooting the tree. What is the difference in terms of torque between these three vehicles?

Also say if the vehicles had ultimate traction i.e the surface was made of gears and the wheels replace to interlock them what kind of power would be needed to pull down a large tree ? Trees are vertical and heavy yet have a root system what forces are at work here when the horizontal force is being applied what force is keeping the tree in place?

Last edited:

I was trying to do some research to find the difference in power of different vehicles. Mainly the difference between a Large hauling semi truck A battle tank and a bulldozer like a d11t. Let's say I hooked up a chain to the back of each of these vehicles and rapped it around a large 3 foot diameter tree which would have the best chance of rooting the tree. What is the difference in terms of torque between these three vehicles?
Probably the heaviest one.

Power is torque or force times speed, and since the equipment is barely moving when it yanks the tree out of the ground, it doesn't matter at all. Broader, it is often surprising how very little power the engines on heavy machinery generate, because they don't have to go very fast, they only have to apply a large force at very low speed.

Specific to a near zero-speed "tractor pull", the limiting factor is almost always friction with the ground (avoiding spinning the wheels or track), which is heavily dependent on the weight of the vehicle and also the surface and drive system (wheel or track).

Probably the heaviest one.

Power is torque or force times speed, and since the equipment is barely moving when it yanks the tree out of the ground, it doesn't matter at all. Broader, it is often surprising how very little power the engines on heavy machinery generate, because they don't have to go very fast, they only have to apply a large force at very low speed.

Specific to a near zero-speed "tractor pull", the limiting factor is almost always friction with the ground (avoiding spinning the wheels or track), which is heavily dependent on the weight of the vehicle and also the surface and drive system (wheel or track).
What if the ground for whatever reason was made of gears and so too were the wheels. What kind of power would it take to knock over a tree could a simple 9000 pound diesel truck do it if it had that kind of traction in this scenario ?

Specific to a near zero-speed "tractor pull", the limiting factor is almost always friction with the ground (avoiding spinning the wheels or track), which is heavily dependent on the weight of the vehicle and also the surface and drive system (wheel or track).
If you consider vehicles of identical mass, all would have the same frictional limit to horizontal force, based on their contact material and the coefficient of friction. So it is not friction that makes the difference.

Nor is it torque that makes the difference. It is horizontal shear failure in the soil below the wheel or track. A greater area of “low-pressure contact” can transmit more horizontal force through a larger area of soil before shear takes place and the soil flows.

If you let the truck tyres down to half pressure, you will have twice the contact area, and be able to apply twice the traction, as the limited horizontal soil shear is applied to twice the area.

For soils, the largest surface contact area will transmit the greatest horizontal force.

Watuplol
If you consider vehicles of identical mass, all would have the same frictional limit to horizontal force, based on their contact material and the coefficient of friction. So it is not friction that makes the difference.

Nor is it torque that makes the difference. It is horizontal shear failure in the soil below the wheel or track. A greater area of “low-pressure contact” can transmit more horizontal force through a larger area of soil before shear takes place and the soil flows.

If you let the truck tyres down to half pressure, you will have twice the contact area, and be able to apply twice the traction, as the limited horizontal soil shear is applied to twice the area.

For soils, the largest surface contact area will transmit the greatest horizontal force.
[/QUOTE]
Interesting, my next question would be what is the difference between pulling say A huge boulder vs a tree. I'm assuming the force being applied to the tree is frictional because of the roots but I could be wrong. And if you put say a large truck like a 9000 pound diesel truck on a track made of gears and changed out the tires with gears could that truck generate enough power given ultimate traction to pull down a large tree? Or if it couldn't does it fail somewhere along the drive train?

For trees, it all depends on the root structure and soil moisture.

A tree is often stuck to the ground by atmospheric pressure, until you break the roots or there is a drought. The roots hold a large area of damp soil, that forms a sucker to the water table which resists wind gusts. Other times, the tree roots wrap around the bedrock and roots must be cut, or the material lifted.

If the rock is on the surface, the tow vehicle will need to have a greater ground contact area than the rock before the rock can be dragged.

If the rock is in the ground it will be like a tree, stuck down by it's own weight, and atmospheric pressure. To move the rock you may need to open a hole or ramp next to it, then roll the rock into the hole and up the ramp.

It will be more difficult to push over a tree if you park a vehicle on it's root area, since to roll the tree you must stretch the roots held down by the vehicle. It may be easier to pull the tree over, onto your head.

What if the ground for whatever reason was made of gears and so too were the wheels. What kind of power would it take to knock over a tree could a simple 9000 pound diesel truck do it if it had that kind of traction in this scenario ?
If friction were not an issue, it's whichever vehicle can deliver the most zero-speed force to the ground. Again, a vehicle optimized for high torque at low speed like a bulldozer would be better than a semi-trailer tractor.

Or if it couldn't does it fail somewhere along the drive train?
One characteristic of a gear drive train is face contact angle, typically between 12° and 25°. That pushes the two gears apart. Your gears will fail when it skips a gear tooth. Roller chain is less likely to skip a tooth than a pinion on a rack. That is because the chain wrap holds the chain onto the sprocket.

An alternative would be a winch or a chain block. To move a tree attach the winch point high on that tree, and low on a distant tree or vehicle. That will pull over the tree with the highest attachment point = longest lever arm.

For trees, it all depends on the root structure and soil moisture.

A tree is often stuck to the ground by atmospheric pressure, until you break the roots or there is a drought. The roots hold a large area of damp soil, that forms a sucker to the water table which resists wind gusts. Other times, the tree roots wrap around the bedrock and roots must be cut, or the material lifted.

If the rock is on the surface, the tow vehicle will need to have a greater ground contact area than the rock before the rock can be dragged.

If the rock is in the ground it will be like a tree, stuck down by it's own weight, and atmospheric pressure. To move the rock you may need to open a hole or ramp next to it, then roll the rock into the hole and up the ramp.

It will be more difficult to push over a tree if you park a vehicle on it's root area, since to roll the tree you must stretch the roots held down by the vehicle. It may be easier to pull the tree over, onto your head.

So its pressure that keeps the tree from moving not friction? I guess that makes sense since soil is damp. Is there a way to quantify this pressure in any meaningful way or the amount of Newtons it would take to root a tree?

Fundamentally as stated in post #2; Power is Torque multiplied by RPM. If your vehicle gearbox output shaft could get close to zero RPM, then you could get close to infinite torque, before the output shaft sheared, the soil sheared, or the frictional traction failed. Gear ratio is critical to getting high forces at lower speeds, while the ground traction limit is speed independent.

A semi-trailer prime mover gets it's traction from road friction. That traction is increased by the weight on the front half of the trailer it tows, as it uses a turntable (fifth wheel) to carry that load, which also reduces the tendency of the combination to jack-knife on the road. A truck with high pressure road tyres, and a road-speed gearbox, is quite unsuited to pulling or pushing trees. It is the wrong tool for the job. A fully loaded, rigid tip truck would be better, but is still unsuited to the job.

Trying to find out what it would take to pull out a tree
To pull out a tree, tension in the cable will tend to lift a tractor from the ground, reducing traction, while pulling the tree into the ground. The tree will also tend to fall in the direction of the tractor.

It is much easier to push over a tree. Use a bulldozer with a "tree push bar" attached high on the front blade. The bulldozer and push bar makes a steep diagonal prop. That pushes the bulldozer down into the ground increasing traction, while the point of contact with the tree gives it a long lever arm, and tends to lift the tree with it's roots, out of the ground.
A bulldozer has a very low speed gear and so can generate a very high force. Bulldozer tracks are roller chains running over a drive sprocket at the rear, so it will not skip a tooth.

Is there a way to quantify this pressure in any meaningful way or the amount of Newtons it would take to root a tree?
The instant force needed to lift a tree vertically out of the ground will be dependent on the area of the root patch multiplied by atmospheric pressure, plus the weight of the tree, plus the weight of soil attached to the root structure. Obviously cutting off the top of the tree will reduce the weight.

There is also a time function here. Air must flow into the area under the tree as the roots start to move and pull out of the soil. Digging holes between the roots (animals?) will allow air to enter faster, it will also cut some smaller roots and reduce the mass of attached soil.

Trees evolve by being selected to survive the local climate. A healthy tree will not be overturned by a wind gust because there is insufficient time for air to flow in under the roots. Trees are usually blown over during a drought, unless the tree has shed it's foliage and branches first.

Given a continuous lift over a long period of time the force needed is less, but there will be a lower limit set by the mass and the physical strength of the root contact with fixed rock.

The instant force needed to lift a tree vertically out of the ground will be dependent on the area of the root patch multiplied by atmospheric pressure, plus the weight of the tree, plus the weight of soil attached to the root structure. Obviously cutting off the top of the tree will reduce the weight.

There is also a time function here. Air must flow into the area under the tree as the roots start to move and pull out of the soil. Digging holes between the roots (animals?) will allow air to enter faster, it will also cut some smaller roots and reduce the mass of attached soil.

Trees evolve by being selected to survive the local climate. A healthy tree will not be overturned by a wind gust because there is insufficient time for air to flow in under the roots. Trees are usually blown over during a drought, unless the tree has shed it's foliage and branches first.

Given a continuous lift over a long period of time the force needed is less, but there will be a lower limit set by the mass and the physical strength of the root contact with fixed rock.
Very interesting. Do you believe a large rocket like the saturn v has sufficient thrust to uproot a large 1000 ton sequoia tree?

Watuplol said:
Do you believe a large rocket like the saturn v has sufficient thrust to uproot a large 1000 ton sequoia tree?
What sort of evil mind could contemplate such a multiple environmental tragedy, to turn so much fossil fuel into CO2 and to destroy a massive tree.

The Saturn V weighs in at over 2000 tonne. I guess it would blast the soil free of the Sequoia roots and take the smouldering remains up several thousand feet. It will probably depend on how you attach the rocket to the tree.

What sort of evil mind could contemplate such a multiple environmental tragedy, to turn so much fossil fuel into CO2 and to destroy a massive tree.

The Saturn V weighs in at over 2000 tonne. I guess it would blast the soil free of the Sequoia roots and take the smouldering remains up several thousand feet. It will probably depend on how you attach the rocket to the tree.
Let's be very hypothetical and say a chain is attached to the rocket in a way that isn't going to destroy it. But let's say we have a very large chain wrapped liberally around said 1000 ton tree and off some ways is the Rocketship with chain attached so it won't blast off soil. I guess what I'm trying to get out of this is what is the unit range of pressure keeping the tree in or how much force necessary OR would the tensile strength of the tree not allow for such an event to occur?

It sounds like you're working on a SF story or a bar bet. Is that correct?

It sounds like you're working on a SF story or a bar bet. Is that correct?
I have adhd and a little ocd that comes with it when I get a idea in my head no matter how trivial I'll try to bring it to its most detailed conclusion.

OK. First of all, the force obviously depends on the tree size, species, and the type of ground or rock it grows in. Second, I know of no reference to look up table of tree uprooting forces, so I don't think your question can be answered with confidence.

Power is Torque multiplied by RPM. If your vehicle gearbox output shaft could get close to zero RPM, then you could get close to infinite torque, before the output shaft sheared, the soil sheared, or the frictional traction failed. Gear ratio is critical to getting high forces at lower speeds, while the ground traction limit is speed independent.
You will never get a 'close to infinite torque'. Any powertrain gives a specific maximum torque at a given RPM. If the RPM is zero, the torque is still well defined. But the power is zero because the RPM is zero.

Theoretically, an engine of any size can deliver any desired force at rest, given the proper gear ratio and wheel radius. And, when at rest, it will be the maximum force you can get. In practice it will be limited by material strength or efficiency losses.

Taking the tree down will require a certain pulling force. If the vehicle is using to ground to brace itself, then the ground must be able to hold that force. Else, the vehicle will not be able to create the pulling force on the tree either. If friction is involved for the vehicle traction force, then the maximum force the ground can produce will increase with the vehicle mass.

But assuming there are no limits on the force from the ground, then the mass, power and engine torque don't matter. Only the force coming from the powertrain do. (You will most likely have some minimum size restrictions for strength reasons, to be able to produce that force, though.)

I have adhd and a little ocd that comes with it when I get a idea in my head no matter how trivial I'll try to bring it to its most detailed conclusion.
You would make an excellent specialist engineer, if you could develop a little discipline.

Break the problem down. Ignore the Saturn V specs for the moment.
Develop a model of a tree. Define parameters that can be measured for the following.
1. Mass of roots below ground, Mr. kg.
2. Mass of trunk and branches; Mw. kg.
3. Mass of foliage and twig; Mf. kg.
4. Mass of soil attached to roots; Ms. kg.
5. Effective area of root patch; Ar. M².
6. Root to geology attachment strength; Pg. N/m².
7. Atmospheric pressure; Pa.
Now you can work out the vertical force needed to uproot a plant, bush or tree.
Look at the difference between with or without atmospheric pressure, equivalent to a fast or a slow application of vertical force.

Can you apply the same process to concrete footings on fence posts ?
How will you calculate wind pressure and forces on a tree ?

Taking the tree down will require a certain pulling force.
It is much easier to push over a tree.
As I explained in post #10.

One could Google the tensile strength of wood (e.g. white pine at 2.10 MPa) and get an upper bound on the force required to tear the thing apart with pure vertical brute Saturn rocket strength.