Help with physics of carbon fiber guitar case suspension system

[nickcc]

I'm developing a range of carbon fiber cases for guitars, violins and laptops.

The cases have a suspension system of high density closed cell foam pads which hold the instrument where it is strongest eg base of the body, where the neck joins the body.

It has been suggested that it would be better if the pads had a top layer of of 1/2" of soft foam which could more easily distort and in the event of the case being droppped ie creating a crumple zone.

I would like to better understand the physical laws which apply in the event of the case being dropped.

I understand that the kinetic energy of the case is calculated from the formula E = (1/2) mass × speed2. This would seem to suggest that the lightness of carbon fiber will gives an advantage over heavier materials as less energy build up during a fall - is this so?

And the guitar being lighter than the case will have much less kinetic energy to dissapate...so will a 1/2" layer of soft foam be of any value as a crumple zone?

I wonder if to be effective a 1/2" layer would have to be very soft - so soft that it would not hold the instrument securely enough in normal use.

I would be most grateful for any comments that would help my understanding of the physics so I can make an informed decision on the design.

Nick

 

[Mech_Engineer]

There a few things to consider. First, how far is it falling from, so you know how fast it's going when it hits the ground. PE=m*g*h for that, and when paired with the equation for kinetic energy you get (the m's cancel) g*h=1/2*v^2 or v=(2*g*h)^(1/2).

Now the important point to consider is the fact that it doesn't matter how much energy is dissipated, but instead how FAST it is dissipated. For this reason, carbon fiber would be particurally bad for absorbing an impact because it would deform only a very small amount, which means the instrument inside would be subject to a very strong acceleration which could possibly cause damage to the instrument. With a thick layer of soft foam around the instrument, it would be subject to much smaller accelerations, helping to prevent damage.

Also, it doesn't matter how much the case will weigh, only how much the instrument weighs.

 

[nickcc]

Thank you - I'm grateful for this - some light begins to dawn.

I don't understand your use of term 'acceleration' in the situation where the case has come to a sudden halt. Could I use de-celeration and still be right?

I also don't understand why the weight of the case doesn't matter - surely a heavier case will mean the whole thing hits the ground with more kinetic energy ? Would you expand on this for me?

And it would be helpful to understand more about the soft foam. To help musicians travel more easily they need the most compact case possible - so adding really thick foam could be a problem.

Maybe it helps if I give more details. An acoustic guitar weighs around 5lbs, my case weighs 10lbs. Let's assume a drop of 6 feet onto concrete.
Can you give me some idea of the forces at play on the guitar when the case hits the ground and what thickness/softness of foam would reduce the acceleration sufficiently to reduce potential damage?

Thanks

 

[Mech_Engineer]

I don't understand your use of term 'acceleration' in the situation where the case has come to a sudden halt. Could I use de-celeration and still be right?

In engineering terms, it is all acceleration. "Slowing down" is just acceleration with a negative value (deceleration). You can use whatever terminology you like though.

I also don't understand why the weight of the case doesn't matter - surely a heavier case will mean the whole thing hits the ground with more kinetic energy ? Would you expand on this for me?

The case will hit the ground and decelerate itself, however the instrument is being held inside the larger case and the acceleration it is subject to will be dependent on how much the case holding it will "give." The more the case gives, the less net acceleration the instrument will see. So say you drop two guitars, one on 2-mm thick linoleum and one on 12-mm thick carpet. The guitar on linoleum will be subject to about 6 times the acceleration of the guitar on carpet. See the correlation? The thicker the insulating material (assuming the entire thickness is used) the lower the probability of damage.

And it would be helpful to understand more about the soft foam. To help musicians travel more easily they need the most compact case possible - so adding really thick foam could be a problem.

Well, this is really just a best-effort type of excersise I suppose, and "thick" is very relative. But, given the circumstances, a half-inch of foam would give a LOT more insulation from damage than being directly supported by rigid carbon fiber. You might consider adding about an inch of foam only where the instrument is being supported, assuming the foam were compressed to about a half-inch of thickness once the instrument is securely placed in the container. This way, you will have gone from a fraction of an inch of deflection with the carbon fiber (bad) to a full half-inch (or could be less if you want) of foam. This will really help insulate the instrument from damage.

The full calculations for determining exactly how much acceleration an object will see are simple but will have a lot to do with material properties and impulse. Perhaps you should do a little reading on collisions and conservation of energy. Also, read a little on material properties of foams.

 

[Danger]

Nick, you might also want to look into Sorbothane (or whatever name they're marketing it under now). It's just about the most shock-absorbant substance on the planet. I believe that it's available as insole liners for high-impact sports shoes. Edmund Scientific used to sell it in sheets. Maybe you can find some and experiment a bit.

 

[turbo]

I know that weight is a consideration for traveling musicians, and I have had my share of battles with the airlines. You are considering entering a very elite field in case-construction, though. First off, my dreadnought (hand-made by Augostino LoPrinzi in the mid 70's) is not going to be exactly the same in dimensions as a 1950's Martin D-28 or any other desirable guitar. The people who want your cases will want them to fit perfectly, so you'll have to produce several versions of each (very expensive) case shell, and be prepared to hand-fit the interiors. Good luck getting a violinist to loan you their Strad or getting a bluegrass mandolin player to loan you their Gibson F1. I'm not trying to discourage your from an admirable enterprise, just pointing out that the form-fitting of the shock-absorbing layer needs to be very precise and you can't always "wing" it.

How can you deal with this? I would suggest that you could devise some membrane to wrap around the instrument, and encase it in a non-expanding material of some type with which you could make a cast of the instrument around which you could pour shock-absorbing foam in a preform that would fit the sturdier foam with which you intend to line your carbon shell.

Good luck

 

[Mech_Engineer]

Another important thing to consider-

Your case will basically end up being "rated" for a certain height fall, based on the thickness of your impact absorbing material. At a certain height the entire thickness of the foam will be used to cushion the fall, but any higher and the foam will be completely compressed, and the acceleration the instrument sees (and the force it is subject to, this is the key) will ramp up significantly.

You'll need to decide exactly how far a fall you need (or want) the instrument to survive, and then choose a foam thickness based on the weight of the instrument and an acceptable acceleration the instrument itself can handle. This will all be dependent on the effective spring constant of the foam used, and the thickness of the layer holding the instrument. It is possible you could also experiment with multiple layers of increasing density foam to build a "progressive spring-rate" composite layer. Actually, a progressive spring rate composte layer sounds like the best approach for this application.

 

[nickcc]

Thank you - all your replies are immensely helpful. I'm doing some research on Sorbothane.

Does anyone know of other materials that have excellent shock absorbing properties? I seem to recall reading about some material made of micro balls within a viscous material - does that ring bells with anyone?

turbo-1 all the custom fitting you refer to will be done by adjusting the size and position of the suspension system blocks within the case.

 

[turbo]

turbo-1 all the custom fitting you refer to will be done by adjusting the size and position of the suspension system blocks within the case.

Your last request makes me wonder if you might be able to line the cases with a cloth envelope containing Styrofoam balls (like a bean-bag chair) perhaps with Velcro closures so more balls could be added as they deform over the years.

 

[nickcc]

I too like the progressive layers of foam idea and have had this in mind for some time.

There are no agreed ratings for guitar cases etc and so what I am looking for is first an understanding of the physics and second some tests that will make sense to musicians - eg dropping a case down some stairs, piling lots of luggage on top.

Turbo-1 thanks for your styrofoam balls idea - the engineer I am working with had a similar thought. Musicians tend to be very conservative and I suspect this solution may be too radical for them. Also I like the elegance of suspension system route.

However I now have a question about the suspension system - am I right in thinking that if the instrument is held in only three places all the forces of acceleration which occur on impact would be concentrated on those three points or (depending on how the case lands) two or even one of those points ? If this is the case would an instrument be better protected from impact if there were more points of support?

 

[Danger]

Since the total impact transmitted to the instrument will be the same, then the load per unit area will definitely be lower with more support points. That is not necessarily desireable, though, if the points that you add are significantly weaker.
Just as a throw-away suggestion, have you considered using an adjustable elastic harness rather than solid padding?

 

[Mech_Engineer]

However I now have a question about the suspension system - am I right in thinking that if the instrument is held in only three places all the forces of acceleration which occur on impact would be concentrated on those three points or (depending on how the case lands) two or even one of those points ? If this is the case would an instrument be better protected from impact if there were more points of support?

Yes, quite true. The more contact area you have, the more distributed the decelerating force is over the area. It would be wise to utilize as much surface area as is possible without adding too much weight, depending on the fragility of the instrument being protected. Also consider though, that the more surface area you have in contact with the instrument, the softer you will want the foam to be...

 

[FredGarvin]

What about a formed bladder that is filled with air or any other gas?

 

[nickcc]

I think systems involving bladders/gas etc would be expensive, complicated and likely to scare off musicians who like simplicity.

Tonight I have been looking at various sources on impact absorbing materials. It seems that EPS and EPP have the best impact absorbing performance - considerably better than polyethelenes.

The challenge is to protect the instrument from crushing forces (which makes a minimal suspension system a good idea) AND from impact forces which makes a more diffuse support system desirable.

If the case is dropped any distance it is likely to fall on one of its edges rather than on the top or bottom. If we make this assumption then it might be good to have suspension system blocks on the upper and lower faces of the guitar and around the sides of the body of the guitar a fitted enclosure of something like EPP.

Does this make sense and if so does it seem a good solution?

 

[Mech_Engineer]

The challenge is to protect the instrument from crushing forces (which makes a minimal suspension system a good idea) AND from impact forces which makes a more diffuse support system desirable.

The fact that the case will be made out of caron fiber will make it crush proof, not the "suspension" system. Carbon fiber when made properly and with enough layers is VERY strong. That being said, you will want to think a little about where the stresses will be highest in a crushing situation, and make sure you reinforce those areas.