[Navigator]

Hello, I have a structural questions.

Today, helmets are mainly monoblock. In ancient times, there were some types that were made flanking different parts, kept togheter by using a ridge.
Here, you can see an example:


You can see the central ridge, and eventually the pivots that keep the structure united.

To me it is quite logical that a monoblock structure is more restitent compared to one in which the shots are absorbed by some pivot. And this is a good reason for which today the helmets are monoblock. But, do we have models and studies that describe this from a mathematical perspective?


Thank you,
Navigator

[LuckyTran]

You should read up on stress concentrations and failure modes. You'll find them in introductory texts in solid mechanics.

[Navigator]

Ok, I have consulted some sourches (Performance Analysis of Motor Cycle Helmet under Static and Dynamic Loading, Design And Analysis Of Industrial Helmet and SOLID MECHANICS) according to them, here my explanation:

-------- START --------
As a matter of fact, the helmet purpose is understood as head protection, against penetration and shock/brain injuries. Thus, the purpose of protective helmets is to prevent head injury by decreasing the amount of impact energy that reaches the head, reducing the severity or probability of injury. So, the quality of the helmet is given by the ability to reduce the severity or probability of injury.

Besides resistance to penetration, the helmet is the initial shock absorber. We can highlight as follow the helmet responsabilities:
- spreading the impact load over a large area of the helmet, therefore reducing the concentrated stresses during an impact that reaches the head and increasing the amount of energy absorbed, by having a larger area of effective energy absorbing liner;

- prevent helmet penetration by pointed or a sharp object that might otherwise puncture/penetrate the skull;

- absorbing the initial shock in an impact.

We can consider that ridged and italic helmets cover more or less the same area (we can ignore for a while that the italic offer more protection for the neck), so, more or less, the defense against the penetration is the same. But, in the ridged one, there is a little problem near the same ridge. The ridged is made by flanked pieces, fixed by rivets. This means that near the ridge there is discontinuity and the impact is not distributed equally in different direction. So, the possibility that the metal is bent between rivets is higher than the probability to bend the metal of an italic helmet.

And, problem related, this discontinuity obstruct a correct spread of the shock on a larger area. One think is the ability of an italic helmet to spread the blow on the entire helmet surface, other is the the flanked pieces that circumscribe the impact area on a smaller area, thus reducing the amount of energy absorbed, that is leaving a greater energy to reach the skull, and finally the brain.

For these reasons, today the helmet are generally monoblock, the continuity of the medium, the helmet, allows to better distribute the impact of a blow, being it composite or metal.
-------- END --------

What do you think? Is there anythink wrong in my understanding of the problem?

Thank you

[flotus1]

You might find this kind of content interesting. Not exactly a scientific approach, but entertaining and interesting nonetheless: https://www.youtube.com/watch?v=Z1KJAeJj3Pc

Some issues that should not be overlooked when analyzing ancient designs:
1) They evolved over time. The helmet design in your image might have started out without the added side pieces. Then over time, people figured out that adding more protection below the ears could be beneficial
2) Manufacturing and cost. Creating such a complex shape without obviously fitting together several smaller pieces, each of them easier to manufacture, has not always been possible. Materials and techniques evolved over the centuries.
3) Motorcycle helmets and combat helmets are designed to protect from different things. A motorcycle helmet is supposed to prevent head injuries when falling from a bike. Thus it can afford to have a huge opening at the bottom end for easy entry.
A combat helmet is supposed to protect from stabbing, slashing and the likes. So having a huge opening in the chin and neck area would be detrimental. The side pieces provide good protection below the ears, but would make it impossible the get in or out of the helmet. Which is why they can be folded to the side.

[LuckyTran]

There's two different things going on.


1. Discontinuous materials don't transmit forces. They need to be connected somehow and this connection is almost always poorer than a contiguous piece of material. If you take your medieval helmet and make it also monoblock, say via 3D printing the entire thing in one piece, you'd still have a better helmet still than made by joining two plates. Continuity is a prerequisite for forces to transmit from one molecule onto another molecule at the molecular level. This is purely material science. 3D printing was not available in feudal ages, and that's why they had use very crude techniques.

2. The other is the solid mechanics or structural design problem. Certain shapes are better than others. Here you can talk about the purpose of the ridge and how it can absorb an initial impact and spread it over an area. For the same applied force, different shapes or structures can transmit different amounts of the force to certain places. Certain structural designs can have a lesser maximum stress within the material. If the material strength is exceeded, they break.

In term of mathematics. The solid mechanics part can be described by Laplace's equation and the Korteweg-de Vries equation and other more complicated pde's. Laplace's equation will tell you the distribution of stresses. The KV equation describes the evolution of impact waves. And so on.

[Navigator]

Originally Posted by flotus1

You might find this kind of content interesting. Not exactly a scientific approach, but entertaining and interesting nonetheless: https://www.youtube.com/watch?v=Z1KJAeJj3Pc

Some issues that should not be overlooked when analyzing ancient designs:
1) They evolved over time. The helmet design in your image might have started out without the added side pieces. Then over time, people figured out that adding more protection below the ears could be beneficial
2) Manufacturing and cost. Creating such a complex shape without obviously fitting together several smaller pieces, each of them easier to manufacture, has not always been possible. Materials and techniques evolved over the centuries.
3) Motorcycle helmets and combat helmets are designed to protect from different things. A motorcycle helmet is supposed to prevent head injuries when falling from a bike. Thus it can afford to have a huge opening at the bottom end for easy entry.
A combat helmet is supposed to protect from stabbing, slashing and the likes. So having a huge opening in the chin and neck area would be detrimental. The side pieces provide good protection below the ears, but would make it impossible the get in or out of the helmet. Which is why they can be folded to the side.

Thank you for the reply, the point is that I am searching for a scientific approach. But I will reply for other points.
1. Both evolved. Gallic evolved in the Italic and Ridged seen some pieces removed and added. Buth the concept at the base of the Ridged did not evolve, (well... it become even worse because often in was made by flanking 4 parts and not only 2). But, consider that the ridged was knewn since long time, it was not a novelty.
2. Yes, obviously these are points to be considered (and to me its quite obvious that the ridged is easier to make), but I am interested in a comparison for what concern the ability to defend the soldier.
3. effectively, I have used sources concerning industrial helmets, motorbike and working helmets. And all the points I have highlighted are perfectly applicable to the comparison I am interested.

Anyway, please consider that I am mainly interested in understanding and evaluate the structural working of these helmets.

[Navigator]

Originally Posted by LuckyTran

There's two different things going on.


1. Discontinuous materials don't transmit forces. They need to be connected somehow and this connection is almost always poorer than a contiguous piece of material. If you take your medieval helmet and make it also monoblock, say via 3D printing the entire thing in one piece, you'd still have a better helmet still than made by joining two plates. Continuity is a prerequisite for forces to transmit from one molecule onto another molecule at the molecular level. This is purely material science. 3D printing was not available in feudal ages, and that's why they had use very crude techniques.

2. The other is the solid mechanics or structural design problem. Certain shapes are better than others. Here you can talk about the purpose of the ridge and how it can absorb an initial impact and spread it over an area. For the same applied force, different shapes or structures can transmit different amounts of the force to certain places. Certain structural designs can have a lesser maximum stress within the material. If the material strength is exceeded, they break.

In term of mathematics. The solid mechanics part can be described by Laplace's equation and the Korteweg-de Vries equation and other more complicated pde's. Laplace's equation will tell you the distribution of stresses. The KV equation describes the evolution of impact waves. And so on.

Thanks for the reply. The first point is what I have understood reading that papers/books, and is the reason for which I think that the ridged approach is considered to have less quality than others (Goldsworthy - The Complete Roman Army).

Thanks also for the second point suggestions