Impact differences in sledge hammer sizes

[Groveton]

The bright spot about being ignorant is you don't realize how complicated a question can be.

Original question: Two sledge hammers, one is 10lb with 5.062 sq in striking face.
One is 16lb with 8.265 sq in striking face.

I was asking for the difference in force between the two.
Things being equal: handle length, speed, head material, striking material.
Then questions arose about impact time (steel vs. wood) head material (soft steel vs hard steel) and speed (pick one. Don't really care. How fast can you swing it from over your head to 1' above the ground?)
My mind went south. To the beach.

All this for a simple article I'm writing on using the correct tools.
I'm rephrasing my question.

Is there something that will give me a percentage difference in the impact per square inch?
I know it's not a simple ratio of different weights, as the impact faces are different.

I've killed a lot of electrons looking for an answer to this.
Anything you have would be appreciated.

 

[256bits]

With a sledge hammer you are more concerned with the kinetic energy that you impart to the head by swinging it. With a 4 pd hammer and a 16 inch handle you can swing with one hand. With a 16 pd head the length of handle would be long enough to swing with 2 hands and if you do it right you can put your whole body movement behind the swing. Look up kinetic energy.

The face is larger for heavier heads necessarily because you do not want to crush the top surface of what you are swinging against, but that is relative. The sledge hammers used for the railroad have a pointed head similar in size as the 'nail' being driven into the wooden ties.

 

[haruspex]

No, it's the momentum that matters here. Typically a sledge hammer will make an "inelastic" collision with its target. That means the hammer can be treated as coalescing with the target, not bouncing off. A lot of energy is dissipated as heat, and the effect on the target is dictated by conservation of momentum. So the more momentum the hammer has, the more the effect.
E.g. compare a 4pd hammer at 30mph with a 16pd hammer at 10mph. The former will have more energy but the latter more momentum.

But you also have to take the mass of the target into account.
If a hammer mass M1 strikes a target mass M2 at speed U then the speed of the target (and hammer) after impact is M1*U/(M1+M2). Suppose the intent is to drive a pile into soil. How far it goes in after impact does depend on the kinetic energy (of hammer+pile). I.e. it depends on (M1*U)^2/(M1+M2).
The effort you had to put into swinging the hammer is the kinetic energy you gave it, proportional to M1*U^2. So you could say the efficiency is the ratio of the two, M1/(M1+M2). (Yes, I know I've consistently left out a factor of 1/2 here.) In practice, there'd be other considerations, as you say, including the nonlinear energy costs of muscles.