Safety question: joules to pounds per square inch

[triple f]

Hi there,

I am the administrator for an airsoft group based out of the Chicagoland area. Many of our members currently use mesh safety goggles of the sort used in arboriculture, wood chipping, and concrete cutting. These goggles do not have a specific impact rating (though the manufacturer does claim they are resistant to high velocity impacts), but the tensile strength of the stainless steel wire they are made from is rated at 65,000 pounds per square inch (as per the manufacturer). The projectiles our airsoft replicas fire never exceed 1.49 joules of energy (.20 gram projectile @ 400fps).

Is there anyone here who could tell me if there is a way to calculate how many pounds per square inch 1.49 joules will exert? I'm trying to calculate the relative impacts these goggles can take.

Thanks,
TF

 

[cesiumfrog]

Can't really be done. At least, to convert the impact to a pressure as you request, you would need to at least know the duration of impact. If the impact were "instantaneous", the pressure would be "infinite". The simple mathematical models and basic material properties aren't enough to fully determine behaviour under these situations. I would suggest testing the goggles by firing into them at point blank (and experimenting with artificial weaknesses in the goggles, or heavier and faster projectiles). I'd also suggest contacting the manufacturer of the safety goggles, who likely have some kind of data available on their effectiveness.

 

[triple f]

Thank you for your reply.

We performed a series of bench tests on mesh goggles firing .20 and ,25 gram bbs at 400 fps from pointblank range into them. The goggles stood up to the punishment without fail, or even deformation. The tests were reassuring, but I just wanted another (more scientific) level of assurance.

I also contacted the manufacturer. They told me they do not have impact data for the lenses, since they are not meant to satisfy ANSI certification. They were the ones who said the wire used in their construction had a tensile strength of 65,000 pounds per square inch.

Hypothetically, is there some way to approximate the duration of the impact in question (since I don't have hard data)? I'd still like to figure out if the science supports our assumptions.

Thanks,
FFF

 

[russ_watters]

Well, with a stress-strain graph for that type of steel, you could calculate the deformation before failure and from that calculate the time and energy of the impact.

 

[triple f]

LOL! Sorry, I hope I didnt misrepresent myself as having a grasp of physics, because I dont. Everything Russ just wrote went right over my head...

 

[AlephZero]

You can't do anything much with the "65,000psi tensile strength" data directly. If you take one piece of wire and try to stretch it by pulling it, the force to break it should be more than 65,000lb times the cross section area of the wire in square inches.

But you are not stretching one piece of wire, you are bending and stretching a whole grid of wires, and the curved plastic lens is also absorbing some the energy itself and transmitting the forces from the projectile into the wires.

Since you have a high speed impact, the speed that the forces are transmitted through the structure will be significant, and for a fairly thin, curved structure, there isn't a simple formula to calculate that speed.

The material properties may also depend on the speed of deformation (in simplistic terms, ductile materials like steel tend to be stronger if you deform them quickly, because the internal flaws take a finite time to get large enough to cause a failure.

Also, the way the projectile deforms or breaks up could have a big effect on what happens.

It is possible to calculate all these effects with the right software and the correct material data (rather more than a single tensile strength number) - but it's not easy, and in any case the computer models would need to be verified by testing before the results were believable.

So the most practical way to go is do some tests under realistic "worst case" conditions. Increasing the severity of the impacts till you do get some failures would be a good idea, to see how much safety margin you have.

 

[AlephZero]

For amusement only, here are a few very crude calculations. They only give orders of magnitude. They are ***NOT*** useful for any sort of safety analysis!

* Velocity of projectile = 4800 in/sec
* Assume the goggles deflect 0.1in on impact - they may well spring back to the original shape, this is not a permanent deflection.
* Assume constant deceleration of the projectile (highly unrealistic!)

Standard formulas for constant acceleration: s = at^2/2 and v = at

So the duration of the impact is t = 2s/v = 2*0.1/4800 = 42 microseconds.

Average deceleration is a = v^2/2s = 1.15*10^8 in/sec^2 = 300,000G

* Mass of projectile = 0.2g

Average impact force = 0.2*300000gf = 60 Kgf =130 lbf.

From the impact duration, any mechanical vibrations of the goggles at frequencies up to 1/24*10^-6 = 24 KHz will affect what happens - you can't do a realistic calculation on the basis of statics.

To repeat, the above are NOT meant to be accurate.

 

[triple f]

Thank you very much Aleph, Russ and Cesium. I didnt get the answer I was hoping for, but I still very much appreciate the answer(s) I got.

We'll try increasing the severity of impacts until we achieve failure. If we achieve it on several pairs of goggles, we might be able to figure out an average maximum fps limit.

Thanks again,
TF

 

[cesiumfrog]

It's a troublesome thing. You don't want to be responsible for testing the safety of the goggles. After all, they're probably strongest front on, but what if (just for one example) a shot from the side somehow gets under the goggle? Will you then be responsible for the eye damage? This is of course why the manufacturer will not make any guarantees (beyond whatever is necessary to access the intended market).

On the other hand, your lack of concern for the rest of the face suggests that the projectiles aren't really that dangerous. If it isn't likely to puncture skin or chip teeth, then the goggles are probably a completely sufficient precaution. If it's just your friends wanting to shoot each other, they need to choose for themselves a level of risk, and accept that. On the other hand, if you're organising for other people to play a game (which inevitably implies an expectation of safety) then you're negligent if you do not provide safety gear that is thouroughly tested, certified and adequate. Either way, back-of-the-envelope calculations won't do you any good when something happens that you hadn't correctly considered.

 

[triple f]

Just want to clear up a few statements so there's no misunderstanding:

You don't want to be responsible for testing the safety of the goggles.

I am not vouching for the goggles, only testing them to satisfy our curiosity. Everyone who participates signs a very detailed waiver and release of liabilty form, so responsibility is squarely on the participant's shoulders.

but what if (just for one example) a shot from the side somehow gets under the goggle?

Not possible. Our safety requirement stipulates that all eye protection be full-sealing. BBs can therefore NOT slip through from the underside.

your lack of concern for the rest of the face suggests that the projectiles aren't really that dangerous. If it isn't likely to puncture skin or chip teeth, then the goggles are probably a completely sufficient precaution.

A .20 gram projectile traveling at 400fps will break unprotected skin (at close range) and possibly even teeth (again, at close range.) The group suggests members wear full face protection but it isn't required (though most of the members do.) Those who eschew face protection in favor of comfort do so fully cognizant of the risks- they are over 21 and willing to assume responsibility. The eye protection requirements, however, are never optional (you can fix a broken tooth if you have to, but you'll never get an eye back.) FYI- many of the mesh safety goggles available for airsoft incoporate a paintball type mask

if you're organising for other people to play a game (which inevitably implies an expectation of safety) then you're negligent if you do not provide safety gear that is thouroughly tested, certified and adequate.

Nah, that isn't true. The organizer doesn't have to provide safety equipment to the participants. The organizers set the requirements and standards and the members meet it on their own. Not even the companies who put on airsoft games commercially provide the participants with safety equipment. Like I said before, everyone who participates also signs a waiver assuming all the risk and liability.

This has all been tremendously off-topic and I apologize for that. I just wanted to set the record straight in the interest of clarity. Thank you for your on-going support of my question.

TF