Which mallet and why

[Warren Mickley]

It doesn't take much experience to figure out how important a heavy mallet is to making mortises and such. I feel sorry for Sellers and his ilk who try to make mortises with dinky mallets.

[steven c newman]

Also....depends on the wood being chopped, doesn't it......from Pine, to Poplar, to Ash, to Oak...to Sycamore (BTDT) to Walnut....

I do watch a video now and then...Traditional Chinese Working Forums ( David Weaver LIKED the show) that only used a "No. 2 Carpenter's Hatchet" He used the non-sharped part of the hatchet to drive his chisels....and could chop a through mortise in about the time it took to type this.....and without the "Usual" Anti-Sellers" digs some are wont to type in this site.

A Chopping Day, 5 done .JPG
YMMV, of course....

[Rafael Herrera]

I'm not sure what you're trying to show. There was some simplification w my description, but the purpose was to give a sense of what is going on.

The kinetic energy of the mallet and its momentum are related, E=1/2 p^2 / m, where p is momentum, m is mass. They're not distinct, independent properties in the description of what is happening. More of one means more of the other, how they transform into heat, work, or whatever it is, will happen whether you use energy or momentum to quantify the mallet action.

The bottom line is a light mallet needs a fast swing to accomplish what a heavy mallet will do swung slower.

[Michael Bulatowicz]

Momentum and kinetic energy are, as you say, related—but they’re not interchangeable. As you state, p^2 = 2 m E. It’s the (square root of the) product of mass and kinetic energy that provides the impetus to cut the wood fibers, not the energy alone. In your simplified example of two mallets with 1 versus 2 units of mass, the lighter mallet will need to be swung twice as fast as the heavier one, not 40% faster. The difference is larger than you indicated, hence the commentary about the energy perspective being misleading.

[Rafael Herrera]

The losses to the other factors you mentioned may be major or may be negligible in our situation, I don't know if they matter much.

The conservation of momentum principle is simpler to apply when you have two objects colliding, like two billiard balls. However, in our case you have both objects moving and then stopping. I don't think it's any simpler to describe what's happening using momentum.

If you have a better explanation that can quantify what's going on, I'd be interested in seeing it.

For practical purposes, the consensus still is that, for a given job, a heavier mallet (within reason) is better than a lighter one.

--

As an aside, once I took a carving lesson. I took my lignum vitae mallet. I soon switched to a lighter mallet, it was too heavy. One needs to determine what's best suited for the job.

[Michael Bulatowicz]

The losses to the other factors you mentioned may be major or may be negligible in our situation, I don't know if they matter much.

The conservation of momentum principle is simpler to apply when you have two objects colliding, like two billiard balls. However, in our case you have both objects moving and then stopping. I don't think it's any simpler to describe what's happening using momentum.

If you have a better explanation that can quantify what's going on, I'd be interested in seeing it.

For practical purposes, the consensus still is that, for a given job, a heavier mallet (within reason) is better than a lighter one.

--

As an aside, once I took a carving lesson. I took my lignum vitae mallet. I soon switched to a lighter mallet, it was too heavy. One needs to determine what's best suited for the job.

I never claimed simplicity: only accuracy. The difference between 2 and its square root is non negligible.

It’s easy to observe the effects of the losses; quantifying accurately would be more challenging. Take two mallets with significantly different weights; the greater the difference, the better. Weigh them. Let’s say they’re X and Y units of weight, respectively. Drive the same chisel using each, letting the lighter one simply fall from Y units of height and the heavier one fall from X units of height. If the ratio of weight is 1:3, the ratio of height should be 3:1, and so on. The energy will be the same, but the momentum will be higher for the larger mallet. Look at the depth of penetration. This will immediately show whether equal energy drives the chisel to equal depth. You can do the same experiment with nails and hammers rather than chisels and mallets, and so on.

You keep repeating your point about choosing the right mallet for the application. Nowhere did I disagree with that point, nor do I disagree with it in any way. I always choose a mallet based on what I am doing. The only disagreement is the degree to which the mallet weight makes a difference.

[Justin Allen]

The losses to the other factors you mentioned may be major or may be negligible in our situation, I don't know if they matter much.

The conservation of momentum principle is simpler to apply when you have two objects colliding, like two billiard balls. However, in our case you have both objects moving and then stopping. I don't think it's any simpler to describe what's happening using momentum.

If you have a better explanation that can quantify what's going on, I'd be interested in seeing it.

For practical purposes, the consensus still is that, for a given job, a heavier mallet (within reason) is better than a lighter one.

--

As an aside, once I took a carving lesson. I took my lignum vitae mallet. I soon switched to a lighter mallet, it was too heavy. One needs to determine what's best suited for the job.

The KE losses can be quite significant. Just as an example, take the scenario where the cutting depth is 0. With no work output done by the chisel, 100% of the KE in the chisel has now been lost to these factors.

[Richard Hutchings]

Slightly off topic but since we are talking mallets, does it matter which way the grain is facing on turned mallets? It seems to matter with baseball bats.

[Tom Bender]

Let's head back to the shop for another experiment. For a given amount of fibers cut, the heavy mallet is causing more collateral damage, split workpiece, slipping clamping, crushed fibers ahead of the cut etc. Why is that?

The heavy mallet delivers more momentum. The lighter and faster blow delivers more energy.

[Justin Allen]

Slightly off topic but since we are talking mallets, does it matter which way the grain is facing on turned mallets? It seems to matter with baseball bats.

Yes. The impulse characteristics will change with the compressibility of the fibers in the wood mallet. You may transfer the same momentum, but aligning the fibers in their "stiffer" direction will exert a higher force over a shorter time (versus a lower force over a longer time). This force delta could be the difference between severing the fibers in the cut or just compressing them.

[Rafael Herrera]

The KE losses can be quite significant. Just as an example, take the scenario where the cutting depth is 0. With no work output done by the chisel, 100% of the KE in the chisel has now been lost to these factors.

And the momentum is zero as well, so we're not better off thinking mementum alone.

To answer the other comment about 40%. If we wanted to get the same force applied, and assuming the depth of cut is the same too (big if). The speed of the mallet would have to be sqrt(2), or about 1.41, hence the 40%.

If you want the same initial momentum in both cases, then the velocity would need to be twice. The claim that momentum correlates to the cutting depth is a big assumption as well.

Neither description is likely to be accurate, this is an inelastic collision after all.

[Michael Bulatowicz]

And the momentum is zero as well, so we're not better off thinking mementum alone.

To answer the other comment about 40%. If we wanted to get the same force applied, and assuming the depth of cut is the same too (big if). The speed of the mallet would have to be sqrt(2), or about 1.41, hence the 40%.

If you want the same initial momentum in both cases, then the velocity would need to be twice. The claim that momentum correlates to the cutting depth is a big assumption as well.

Neither description is likely to be accurate, this is an inelastic collision after all.

Let’s continue with your example of the two mallets of 1 versus 2 units of weight and let’s add the condition of identical force. Let’s further take the linear approximation of F = E/d, where d is still the distance travelled by the mallet head center of mass during the impact, E is the kinetic energy, and F is the force. Additionally, F = M * a, where M is the mass and a is the acceleration. For a constant force, d = 1/2 a * t^2, where t is the time over which the force is applied.

So, we have M * a = 2E/(a * t^2) = M * V^2 / (a * t^2) and therefore t = V/a = M*V/F = p/F, where p is once again momentum. So, for the same force, the mallet with 2 units of mass applies that force for twice the time duration, and further, the time duration is based on momentum, not energy—even though the two are deterministically related and the force is identical.

[Justin Allen]

And the momentum is zero as well, so we're not better off thinking mementum alone.

To answer the other comment about 40%. If we wanted to get the same force applied, and assuming the depth of cut is the same too (big if). The speed of the mallet would have to be sqrt(2), or about 1.41, hence the 40%.

If you want the same initial momentum in both cases, then the velocity would need to be twice. The claim that momentum correlates to the cutting depth is a big assumption as well.

Neither description is likely to be accurate, this is an inelastic collision after all.

Transfer of momentum wouldn't be zero. At least a part of the chisel would be moving (with or without the mallet attached to it). Motion would stop when the chisel deformation has absorbed all of the transferred energy. Or, in the case of a rigid body, it would bounce off the surface (if your fingers weren't holding it in place). In the second case, not all of the KE would be lost, but none of it would be converted to work.

Momentum is conserved across both elastic and inelastic collisions. Kinetic energy is not in inelastic collisions.

Kinetic energy (like all forms energy), is a state of the system. It has the ability to be converted to work. That doesn't mean that all of it is.

[Eric Brown]

One thing you are not taking into consideration is the shock that transmits through the handle. That is energy taken away from the mallet head. It is also absorbed by the hand. Usually heavier mallets have heavier handles also. Less energy would be transmitted. You also are not considering potential damage to the hands/wrists. A person who is new to the craft probably should start with the lighter mallet for control. Exceptions if the person has been doing other work where they have strength already.

[Jim Koepke]

Slightly off topic but since we are talking mallets, does it matter which way the grain is facing on turned mallets? It seems to matter with baseball bats.

This should be easy to visualize. A piece of wood is more pliable to bending flat with the grain than it is against the plane in which the grain is running. Like a board, a bat is more likely to flex, giving up some power, when hitting a ball flat against the grain than when it is being hit in line with the grain.

This is the same with hammer and shovel handles. This makes me very picky about how the grain is running when selecting a new hammer or shovel.

jtk