This appears (I don't know why adamantine is different, perhaps my tests there need to be peer reviewed) to work at predicting the velocity required to completely fracture armor (or metal skin) of standard (low) thickness:

This function doesn't show contact area or thickness yet. I think Pirate Bob found earlier that the round-to-100 rule applies to the contact area and thickness scaling for this function. I used a fudge factor of 2 to make the results work in the case where contact area was larger.

"Completely fracture" means the velocity at which you see the smooth sigmoidal transition in deflection and appearance of tearing damage.

While this equation is definitely a start, it is does not fully describe the results from my last post for copper bolts vs. iron and bronze at varying IMPACT_FRACTURE. I found that for iron armor, momentum=IMPACT_FRACTURE/22436-12.453 and for bronze, momentum=IMPACT_FRACTURE/22294-15.426 (multiply the fits for forces by copper bolt mass=1.3395). While the coefficients of IMPACT_FRACTURE are close to 22500, the difference is significant. Also, the offsets are really not close to those predicted by IMPACT_YIELD/45000.

1) How do you define the location of the transition? I define it as the force/momentum where non-bruise wounds occur 50% of the time. Maybe you (and/or Toady) are actually defining it based on some other threshold?

2) Shouldn't your equation strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD describe this same transition? (Edit - it appears that is actually something different, and the equivalent thing would be the momentum/strain needed for 100% fracture? Can you confirm this?) If so, then we should expect the momentum at fracture also be a function of IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD. It's possible that some factors (like 1/IMPACT_FRACTURE, for example) might cancel out, but it's also quite possible that the final equation becomes very complicated (which I think is likely given that simple linear fitting doesn't seem to quite work). Also, how sure are you of the accuracy of strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD? Should I try to confirm this over a wide range of impact parameters?

3) Have you done anything more towards figuring out what determines the strain on the material? Assuming (2) is true, this would be extremely informative for figuring out armor protection. I could do this myself now that you got me to use the right version of DFHack, but it seems likely you've already been working on this. If I was going to do it, I would imagine setting SHOOT_FORCE such that the strain was about half of its maximum value, and then seeing how the strain changes when different parameters are varied. This has a huge advantage over deflection testing,

~~ as you get an exact numerical output of how the strain changed from a single hit~~(Edit - the result is not really "exact", as there is variation in the strain you get at a given bolt momentum - not clear if there is actually a great advantage over looking at deflection). In other words, if (2) is true and you don't plan to do this, let me know and I will try.

I really, really need to put up my full data for all materials at contact area 2 and 10. I'm sorry I didn't do this earlier, as it would have helped you a lot when working on the relationship between momentum for injury and impact parameters. There's just a lot of it and I'm not 100% sure the best way to represent it. I'll try for a spreadsheet of the raw data on DFFD if nothing else. If you could tell me what % serious wounds you are looking at for your equation that would be helpful, as then I could make a table of that. I am also running more simulations varying IMPACT_FRACTURE with IMPACT_YIELD set to zero right now, which hopefully should shed some light on the relationship between momentum required to cause injury and the impact parameters.

Edit:

I looked at the data for IMPACT_YIELD=0, and this data perfectly fits to momentum=IMPACT_FRACTURE/22500 for iron, bronze, and adamantine over the whole range from 1 to 6 times the vanilla IMPACT_FRACTURE. The fit is perfect in all cases to within the error of the measurements. This means that the offset and the corrections to the slope must be some function of IMPACT_YIELD, possibly multiplied with other factors (like IMPACT_STRAIN_AT_YIELD).

I have posted the complete results for this and varying IMPACT_FRACTURE at vanilla values of IMPACT_YIELD for iron an bronze on

DFFD. And it is late, so I need to go to bed. Sorry, I will really try to post my older data soon

.