I don't have the time to refute everything you just said, but that is completely false. It is a fundamental misunderstanding of what force and acceleration is. I learnt in middle school physics that any change of velocity (speed) is an acceleration.

I was using the layman definition that I already told you of, I was speaking in terms of penetration, I thought you were too but apparently not. I gave the official definition and the laymen definition that's been going on in the net, I assumed you knew which one I was using considering I was clearly speaking in terms of penetration.

That's one of the few things taught in middle school physics which is absolutely accurate. Any acceleration of an object is caused by a force. I also specifically explained that the force that hurt you isn't the force that causes the deceleration in flight, it's the force that causes the arrow to decelerate rapidly upon hitting something (technically, the reaction force of Newton's 3rd). I can't explain this any more clearly than that to you.

In that case you are talking about shock, not penetration. I thought you were talking about penetration. You should have figured that out as I said:

*force is hardly the optimal way to calculate penetration power of an arrow.*
If you are talking about shock then that's a different story, but I was talking about penetration.

You don't understand the very basic physics, please try and learn it, and don't press points about the physics until you do.

Also please stop trying to lecture me on physics, you're wasting your time and embarrassing yourself further. I have 10 years education in physics, including two masters and a PhD in it, and am writing this post from my office in a physics research institute. You're one of the posters I respect the most on here but you seem to be deliberately losing credibility as fast as you can.

Which part of my equation is wrong then? I used the exact same equation you provided, and the result was given. If you have a different result for energy and momentum than show it. If you have a different result for impact area, such as proving that the test hit the armor with something BESIDES an unhardened bodkin, than show it. All you did was assume a lot of things about the test that wasn't correct. Whether you have a PHD in physics doesn't change that.

In summary, the test used a cherioballista which could shoot a 102 g bolt at 47 m/sec (113 joules and momentum of 4.8).
When the same cheiroballista was tested against the lorica segmentata, it used a 70 gram bolt with an unhardened bodkin arrowhead at a distance of 50 meters. Judging from the picture, the arrowhead have an angle of roughly 30 degrees which is not atypical for an arrowhead.

The lorica segmentata was set up on a "dummy legionary" with at least some padding.

The lorica segmentata had steel girth hoops of 1.25 mm thick, whereas authentic ones would have girth hoops closer to .7 mm thick, and the metallurgy would be equivalent to "mild steel".

The test penetrated the first girth hoop, and severely dented the overlapping one underneath it.

-You brought up force, and you are using it to talk about shock. I thought you were using it to talk about penetration, which is why there is a misunderstanding. In fact, you should have figured it out because I already told you

*"I gave you the alternative "layman" version because the ***official definition is hardly the best way to calculate the penetration power **of an arrow, as it's just a combination of acceleration and mass."

-But besides that, you provided the equations for energy and momentum, which is exactly the same equations I used. Show me just where my calculations are off, don't just wave your PHD in my face. Show me precisely where the calculation are off. Did you use the same equation to get a number (102 gram bolt, 47 m/s) besides 113 joules and a momentum of 4.8?

-You talk about the importance of impact area, I already told you that the armor was impacted by an unhardened bodkin point, which is not exactly an atypical arrowhead. How in the world do you think an unhardened bodkin point caused an atypical impact area compared to other generic arrowheads? Don't throw your PHD in my face, explain precisely why you would think an unhardened bodkin point hitting the armor would have an atypical impact area compared to generic military arrowheads. In fact bodkin points are one version of generic military arrowheads.

For someone with a PHD and a physics office, I expect

more hard data and less vaunting. So far you listed the following variables:

Force <---- I'm talking about penetration, you admit you are using it to talk about something else. Ergo irrelevant.

Impact area <------ I already told you that the arrowhead was an unhardened bodkin, you have not explained how that would give a different impact area than other generic military arrowheads, especially considering bodkins are one type of generic military arrowheads

Energy <----- I used the exact same equation you used, if you arrived at a different number then show it.

Momentum <----- I used the exact same equation you used, if you arrived at a different number then show it

Impact Energy <----- I may have used initial energy rather than impact energy, but this means I'm being generous to the armor being tested. This is because initial energy of an arrow is greater than impact energy, and if you don't know that then I would doubt your PHD or even high school degree for that matter.

I may not be a major in physics, but I do have an advanced math degree with my own share of physics so I'm sorry, but your PHD in itself won't impress me. Show me the actual math to impress me, because so far I haven't seen you do any calculations to prove your point. So why don't you show some actual hard data, I'm not hiding behind my degree why are you? So hard data/calculations otherwise the loss in respect is mutual.