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Sturgeon

The Matt Easton/Nikolas Lloyd Appreciation Thread

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I actually had assumed that this trope came from back when images (such as those taken by high-res cameras on satellites) could be much, much sharper than they could be displayed on a computer screen. So in that scenario, the "enhancing" bit is just getting closer and closer to the native resolution of the image.

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How much momentum does an arrow have? More to the point, how is the deflection of the shield supposed to reduce penetration when the momentum is only conserved by dint of stopping the projectile?

 

Momentum is conserved always, so when an arrow slows down, it is transferring its momentum to the target. Do the math approximating the penetration, and you'll get a good sense for how the arrow expends its energy penetrating the target, and from there you can calculate how much momentum it is losing. It's not difficult math.

 

Your shield won't move at all if the arrow breezes through it.

 

Maybe if your shield is made of paper stretched between dowel rods that is true...

 

It takes energy to penetrate a proper wooden shield, and that means the projectile is losing momentum as it penetrates. Where do you think that momentum is going?

 

 

This idea that things can flap around at less than a metre per second and somehow stop something moving at 50-100 metres per second shows a distinct lack of understanding. It's akin to sticking springs onto a metal plate and expecting it to become significantly better at stopping bullets.

 

You have just roughly described how NERA works. In other words, yes, turning an elastic collision into an inelastic collision significantly improves the effectiveness of armor. That is why professional tests of body armor ensure it is fixed to the ground before they shoot at it.

 

Again, the swinging has nothing to do with increasing the protection. The arrow will either penetrate or not (my experience is of the arrow penetrating to about the depth of the head) and will transfer momentum as it does so. The swinging will only substantially take place after the penetration event.

The only thing here that would increase protection would be for the shield to swing violently enough to change the path through the wood or to deform/shatter the arrow before it completes its penetration. Neither of which is going to happen in this case due to the relative masses of the objects and the velocity of the arrow.

 

Except that momentum is transferred instantaneously in an elastic collision, my friend, whereas the arrow's penetration through the shield is not instantaneous.

 

I'll wait here for my apology :P

 

I guess I didn't reply to this. See above for your deserv-ed smackdown. :)

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Momentum is conserved always, so when an arrow slows down, it is transferring its momentum to the target. Do the math approximating the penetration, and you'll get a good sense for how the arrow expends its energy penetrating the target, and from there you can calculate how much momentum it is losing. It's not difficult math.

Maybe if your shield is made of paper stretched between dowel rods that is true...

It takes energy to penetrate a proper wooden shield, and that means the projectile is losing momentum as it penetrates. Where do you think that momentum is going?

You have just roughly described how NERA works. In other words, yes, turning an elastic collision into an inelastic collision significantly improves the effectiveness of armor. That is why professional tests of body armor ensure it is fixed to the ground before they shoot at it.

Except that momentum is transferred instantaneously in an elastic collision, my friend, whereas the arrow's penetration through the shield is not instantaneous.

I guess I didn't reply to this. See above for your deserv-ed smackdown. :)

Sturgeon confirmed as necrolord.

Needless to say, I think you've either misunderstood my argument or just plain gotten things wrong (ERA, clamping soft body armour for tests etc). Luckily we don't need to have a backwards-and-forwards on this, because we can test it!

I'll make a static rig and a swinging rig and shoot it with arrows and darts. You do the same using mild steel or something and shoot it with bullets. Then we measure the average penetration depth for each rig and call it.

You game?

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I'll make a static rig and a swinging rig and shoot it with arrows and darts. You do the same using mild steel or something and shoot it with bullets. Then we measure the average penetration depth for each rig and call it.

You game?

 

My question for you is why do we need to test extremely well established physical laws?

I could test this very easily, but it would be essentially a waste of time. Even you seem to admit that the position I think you have (that elastic collisions work differently than physics say they do) isn't the position you actually have (which I presume would harmonize with the physical laws as we know them). So then, why would we need to test anything? We already agree, you seem to be implying, and I simply misunderstood you.

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Because:

1. If penetration were that easy to model using basic physics we wouldn't have to test things the whole damn time.

2. Fun

3. Settling arguments. We disagree about what will happen (I say that penetration shouldn't be significantly different whether you hold the shield tightly or limp-wrist it) so why not make sure?

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Because:

1. If penetration were that easy to model using basic physics we wouldn't have to test things the whole damn time.

2. Fun

3. Settling arguments. We disagree about what will happen (I say that penetration shouldn't be significantly different whether you hold the shield tightly or limp-wrist it) so why not make sure?

 

1. Penetration is not easy to model, but momentum is. 

 

2 & 3. The original question regarded bows and arrows and medieval shields. I have examples of neither. I should go out and spend money to test these things, just to win an argument with you that essentially concerns basic physical laws?

Gunshots are a lot more complex, and aren't the subject of the original question, so me shooting at wood could be instructive, or perhaps not. It's not even clear to me that doing so would represent an elastic collision at that point.

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1. Penetration is not easy to model, but momentum is. 

 

2 & 3. The original question regarded bows and arrows and medieval shields. I have examples of neither. I should go out and spend money to test these things, just to win an argument with you that essentially concerns basic physical laws?

Gunshots are a lot more complex, and aren't the subject of the original question, so me shooting at wood could be instructive, or perhaps not. It's not even clear to me that doing so would represent an elastic collision at that point.

It would be useful as a control, and to dispel the afore-mentioned 'armour plates on springs' misconception that people have. Plus, fun.

 

We don't need to exactly model a shield either, as this isn't about a specific design. It's about having a thin shield that normally wouldn't stop an arrow, and then making it stop one by allowing the shield to move in your hand. I think you could quibble a bit about wood versus steel versus leather or something, but beyond that the construction isn't the major issue.

 

Momentum also isn't the whole issue here, as it only matters in as much as it moves the shield around during penetration and makes it stop an arrow better. Which, again, is where I don't think you're going to see a difference given the relative masses of the arrow/shield and the velocity of the arrow.

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The "armor on springs" misconception that NERA designers apparently have, you mean?

Tell ya what, since you're the one who thinks it would be fun, and apparently you are a bit fuzzy on Newtonian mechanics, why don't YOU conduct this test? It would be very simple. Get two equal weight and thickness boards of uniform material (e.g. fiberboard), and fix one to the ground solidly, and allow the other to rotate about its center on a pole. Conduct some tests beforehand to ensure you have a board your arrow will juuuust barely perforate to give the clearest results.

Come back with your findings, and if they fly in the face of known physical laws according to the theory you insist is true but haven't really described yet, then we can think about peer-reviewing your test by replicating it, how's that sound?

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Momentum also isn't the whole issue here, as it only matters in as much as it moves the shield around during penetration and makes it stop an arrow better. Which, again, is where I don't think you're going to see a difference given the relative masses of the arrow/shield and the velocity of the arrow.

The movement of the shield, which can be described via momentum transfer, is the whole issue.

And exactly why do you think the shield cannot move fast enough to be relevant? Arrows are pretty slow, buddy, and it wouldn't take much velocity for a shield to A.) significantly soak up the momentum of the arrow and B.) move in such a way that the arrow's course of penetration was significantly disrupted, and keep in mind that those two effects would be related, as well.

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Because:

1. If penetration were that easy to model using basic physics we wouldn't have to test things the whole damn time.

2. Fun

3. Settling arguments. We disagree about what will happen (I say that penetration shouldn't be significantly different whether you hold the shield tightly or limp-wrist it) so why not make sure?

Alright Toxn, let's have some fun. I'm dusting off my Dynamics in Physics textbook and putting on my safety goggles for this bloodbath. 

 

When I'm done with classes for the day, I'm going to go home. I just so happen to own a bow, arrows, a target, and a place to hang said target. If you want a test, I'll give you a test. 

 

But I can assure you that the next post is going to contain a proper definition of force balances, sheering, penetration, and a bit of material analysis.

 

In a sense, you're basically telling every single physicist since Newton that they are wrong, and backing up your claim with "Well it makes sense to me like this." 

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Alright Toxn, let's have some fun. I'm dusting off my Dynamics in Physics textbook and putting on my safety goggles for this bloodbath.

When I'm done with classes for the day, I'm going to go home. I just so happen to own a bow, arrows, a target, and a place to hang said target. If you want a test, I'll give you a test.

But I can assure you that the next post is going to contain a proper definition of force balances, sheering, penetration, and a bit of material analysis.

In a sense, you're basically telling every single physicist since Newton that they are wrong, and backing up your claim with "Well it makes sense to me like this."

Well I am a biologist.

Please do the test and write up the results. I will do the same.

Edit: since tone is hard and you and Sturg seem to want to impute an adversarial one on my part, I should emphasise that I really am keen to have actual answers rather than snide arguments from first principles. You would do me a service by providing them.

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The movement of the shield, which can be described via momentum transfer, is the whole issue.

And exactly why do you think the shield cannot move fast enough to be relevant? Arrows are pretty slow, buddy, and it wouldn't take much velocity for a shield to A.) significantly soak up the momentum of the arrow and B.) move in such a way that the arrow's course of penetration was significantly disrupted, and keep in mind that those two effects would be related, as well.

Since you're not interested in testing, feel free to do the math.

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I think you're taking this kind of the wrong way. Re-read Oedipus's last sentence for me. Note that both he and I think you're making a simple grade-school physics error. Maybe you're not, and we've misunderstood you, but besides saying "you've misunderstood me" and leaving it there, you've given us no indication of what we're missing in your argument, here.

Given that, pretty much demanding that we conduct (again, grade-school-level) physics experiments to satisfy you, or that we "do the math" (which math? A force diagram, or some penetration model? If the latter, what kind?) doesn't exactly light our fires, if you know what I mean. If we sound dismissive or uncooperative, that's why.

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I think you're taking this kind of the wrong way. Re-read Oedipus's last sentence for me. Note that both he and I think you're making a simple grade-school physics error. Maybe you're not, and we've misunderstood you, but besides saying "you've misunderstood me" and leaving it there, you've given us no indication of what we're missing in your argument, here.

Given that, pretty much demanding that we conduct (again, grade-school-level) physics experiments to satisfy you, or that we "do the math" (which math? A force diagram, or some penetration model? If the latter, what kind?) doesn't exactly light our fires, if you know what I mean. If we sound dismissive or uncooperative, that's why.

Eh. I'm fully capable of making grade-school errors in physics, although I'd hope that this is a high-school level error at least.

I'm keen to test it anyway, and will get back to you in that front.

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For (hopefully) clarification, here is something I sent to Oedipus:

"I'm not claiming that momentum isn't conserved, just that in this case there won't be much difference. Remember that in both cases the collision will be inelastic, it's just that in one the guy is bracing the shield and in the other it's swinging free.

My intuition here (which I fully admit may be wrong) is that, in the first case, the arrow penetrates and transfers momentum as it does so and the user gets a shock to the arm as it moves. In the second the arrow still penetrates (to significantly the same depth) and transfers momentum, but the mass of the person holding it isn't involved so the shield swings impressively and the user feels like it has cushioned the blow somehow.

The key thing, as far as I understand, is that the shield only begins moving significantly after the arrow has already done its thing, as momentum transfer does not happen instantaneously in the real world and things need to accelerate up to speed.

So the penetration path and angle will not change enough to really make an otherwise non-protective shield protect you."

I could also add that the situation might be very different depending on the relative masses of the projectile and target, and the speed of the projectile. At some point you're going to enter a region where Newtonian penetration is a valid approximation of the event, while at another point the collision becomes essentially inelastic. In between it is all, sadly, a muddle.

 

Edit: gah, I mean elastic.

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I'm finishing up the momentum and force paper currently and I'll post examples and results. 

 

But in the meantime, yes, Sturgeon has said what I would have said. 

 

And for the record, I was a biologist before I went back for chemical engineering. 

What sort of biologist? I mean, we're all molecular biologists now, but still.

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So the penetration path and angle will not change enough to really make an otherwise non-protective shield protect you."/quote]

What makes you think that momentum transfer won't be effectively instantaneous for a projectile moving at just 100 m/s?

And yeah, if your shield sucks, it won't stop a shot. That doesn't mean the swinging motion isn't reducing the penetration of the shot.

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   “Again, the swinging has nothing to do with increasing the protection. The arrow will either penetrate or not (my experience is of the arrow penetrating to about the depth of the head) and will transfer momentum as it does so. The swinging will only substantially take place after the penetration event.”

 

 
This is your original postulate. You claim that “the swinging” (in regard to the movement of the object that has been struck) has nothing to do with the arrow penetrating.
 
You've since cleared up a bit of what you have stated. You now say that there wont be an appreciable difference in penetration given a swinging vs stationary object (shield). That the difference would be purely academic, which you could be very correct on! However, you are also correct in your statement that nothing in real life is instantaneous. 
 
Again, true, depending on the relative reference. And in this case, your very point of penetration not being instantaneous is what makes a "swinging" object not be penetrated as far. I'll get to that later on, but I wrote up a bit on momentum and forces in case anybody was interested in getting a summary of Physics 1. 
 
So we’ll first have to get some definitions going. 
 
 
FORCE: Force is defined in physics as that which tends to change the momentum of a body containing mass. Force is proportional to the rate of change of momentum. That is, Force is the derivative of momentum. SI Units are the Newton
 
In other words, Force is the product of a constant mass and an acceleration. Acceleration is the change of velocity with respect to a change in time (dV/dt!) 
MOME NTUM: Units are Kilogram per meter second (Kg*m)/s. Or, they can be said as Newton-Seconds (The seconds will cancel, since the Newton is a unit of force. In other words, taking a mass and multiplying it by the velocity will give us a momentum. Momentum is a conserved quality, much like Force.
 
NET FORCE is the total amount of force exerted by a body in motion. It is the change in momentum divided by the change in time. We can actually determine the net force acting upon an object by using force balances and setting a proper coordinate system. 
 
So let’s start by doing some modeling. No, not that kind of modeling, Sturgeon. Put your shirt back on. 
 
We’ll start by modeling an elastic collision. The definition for such is as follows. 
 
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms.
 
Let’s assume that we have two objects, on a single dimensional frictionless plane. Object A has a mass of 5 Kg and object B has a mass of 10 Kg. 
 
Object A is moving toward B on this plane at a speed of 1 m/s
 
Calculating the momentum of A gives us the following 
 
A  = 5 Kg*m/s, 
 
Sadly, they will collide. Not so sadly, they are hypothetical and we can do terrible things to hypotheticals without consequence. 
 
After the collision, we find that the new velocity of block A is -0.2 m/s
 
Since we know that momentum is a conserved quantity, and there are no other forces, frictional or otherwise, in this 1-D plane, what will happen after they collide?
 
(Assume right is positive direction and left is negative as you’re looking at the screen)
Initial momentum of system = 5 Kg*m/s
Pinitial = Ptotal before collision (P here is how we denote momentum
PofA + PofB = Ptotal after the collision
We can combine them into the following. 
5 kg*m/s = 5 Kg * -0.2 m/s + 10 Kg * VfinalB
Solving for the final speed of block B after impact, we find it to be 
Vfinal for block B is now 0.6 m/s
 
Newton’s third law tells us that forces acting upon each other are equal yet in opposite directions. So the force on one is equal to the force on the other. 
 
Overall momentum will be conserved.
 
Let’s look at once more example. What if block B was moving?
 
Let’s give B a positive velocity of 0.4 m/s. 
 
I don’t know about you guys, but I don’t like it when two things move. How about we adjust our reference frame? Let’s do a moving reference frame. We focus in on block B, which is moving at 0.4 m/s. That means that, to the observer, block B is no longer moving (But we secretly know it is.)
But now, Block A appears to be moving slower. In fact, it appears to be moving at 0.6 m/s (1-0.4!). So what kind of momentum are we going to be imparting into block B when they DO collide?
 
(0.6)(5) = 3 kg*m/s!
 
So because the second object was moving in the same direction as the initial block, it received LESS momentum! Since mass didn’t change, it is clear that Velocity played a major part.
 
This is an important consideration we must remember as we move into our next part.
 
Now that I’ve beaten that to death, let’s talk about what happens with something more tangible. How about an arrow? What if it’s an inelastic collision? First, we’ll define what exactly that means.
 
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction.
 
So what does any of that mean?
 
2bJPVw2.gif
 
In the most extreme case (which this is), one object completely sticks to another, imparting all of its momentum.
 
In the case of an arrow penetrating an object, the depth of penetration is function of many different variables. Penetration requires one object to push the particles of another object out of the way. In doing so, the object doing the penetrating experiences many forces. Forces which are dependent on parameters.
 
(Writing those sentences made me grin with sophomoric delight.)
 
Material properties of the arrow tip, material properties of the object being struck, momentum of the arrow and the object, frictional forces (Which are tied to material properties), etc.
 
When an arrow strikes a target in an inelastic collision, the tip doesn’t simply bounce away. The tip of the arrow pushes particles out of the way, and does so based on the arrow’s momentum (along with a butt-ton of other stuff). However, the arrow is equally pushed back against by the object it has struck. In fact, every particle that the arrow is attempting to push away is robbing the arrow of forward momentum. 
 
But it’s not instantaneous. This arresting of the arrow takes time. Not much, but it does.
 
Kinetic energy is not conserved during an inelastic collision. That’s an important thing to remember. Also, the impulse time is different (aka, longer) during penetration. Forces are active over a longer period (no longer instantaneous, as was the case in elastic collisions) during penetration.
 
This time difference is what gives rise to the penetration qualities of swinging vs stationary objects. 
 
At the moment the arrow strikes an object to the moment it stops within the object, momentum is exchanged. Within that time frame, the forces acting opposite to the arrow’s forces (friction within the object) create a force that will push a free (aka not stationary) object in the same direction as the arrow. 
This acceleration of the second object robs the arrow of forward velocity, as in our second example from above. 
 
If the velocity is lower, the penetration overall is lower. Again, holding all factors constant and only allowing velocity to change, we can build a model to prove this (Don’t make me do this in Matlab, please, I beg of you. It’s the weekend damnit.)
 
This does not occur in a stationary object, where the friction forces are not split between moving the struck object AND stopping the arrow, in a sense (This is an oversimplification of force diagrams don’t you dare call me out, Collimatrix)
 
So in summary, there are about 19348 (Rounding) factors that can effect penetration of one object into another. Holding most of them constant and watching how velocity of a penetrating object changes with respect to a reference frame of the struck object will show that allowing the struck object to use part of the force imparted by the penetrating object to begin a positive movement along the same direction as the penetrating object will lower the penetrative distance and still conserve momentum. 
 
Which might be the longest sentence I’ve ever written. 
 
 
Sources: 
 

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If there's a typo, deal with it. It's my weekend, but I hope that clears a few things up. I think Toxn and Sturgis-man and myself are looking at the same thing from three different directions.

 

Also, to answer your question, my biology focus was on molecular genetics and creating plasmids for shoving into CHO cells and then putting together bioreactors for large scale cell culture to produce antibodies. So immunology and genetics and a bit of bioengineering. Also did testing for a biopharma company for a while before going back to school for engineering. 

 

Also, it's currently sleeting outside so I don't think I'll get to the actual experiment today.

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