Best? Strength to weight ratio is your criteria? First, you will have to redefine your criteria. You know, "Define Best". Are we talking axial strength, bending strength, bending stiffness, etc. Second if you have conducted a search, within the search you have already a "local best" choice, you just have not accepted it as such yet... Maybe better still exists outside of your initial search.
Strength to weight ratio is attractive, but what strength do you need and and how do you get to lightness? Bending strength? Impact strength? Torsional strength? Then there is how much must you have and what is the trade for weight in your application? As a long lived and successful product engineer, I know that tradeoffs exist toward the best product. You seem to have already fixed the laminate with the exception of core density, that sets most of the weight of the thing. The guy who invents a decent core that is lighter than air will have something. You will do your project many favors by reconsidering your fiber weight and core thicknesses - you will achieve more this way than by seeking out the absolute lowest density core and accepting whatever other negatives come with it.
I am thinking that adhesion to your resin, low assembled mass, adequate bending and shear stiffness of the assembly, and some level of assembled strength must all be there, but these are all scales with a variety of results. And you get to pick which one you want to end up with. I suggest some sample part fabrication and then assessing their sturdiness to see if they will survive in your build and use environment.
Much of the outside of many sailplanes is the fiber reinforcement you are suggesting. And they already have cores that work well to make a sturdy long lived structural sandwich. Usually around 6mm. For faired racing bicycle, I suspect that this might be quite good, long lived, sturdy in use, etc. And heavier than you will like too. If this is to be a more targeted machine, for racing or record setting, I will suggest that lower mass can be achieved with lighter facings as well as thinner and lower density foam products in exchange for it requiring more care in build and handling. In fact, you might even build a sturdier set of fairings for general use, training etc, then a lighter one and spares for competition work... Again though, it comes back to "Define Best". Then you get to fabricate and test and decide...
Almost all of the foams out there will go compound curve by a cycle of gentle warming and pressing over forms. They each have their own temperatures to do this...
9mm core is pretty thick. My airplane uses 6 pcf PVC foam in about that thickness for much of the structural shell of my airplane, with a design dive speed of 268 knots. Please explain - not for me, but for you - why your velo needs as much or more skin stiffness for its non-structural fairing than the structural skin of an airplane designed to go over 300 mph? It seems to me your defined "needs" are over specified, and can undergo significant adjustments. For instance, you 9 mm core will weigh as much as or more than your laminated facings. Then there are lighter foams, some down to 1.5 pcf.
And you get to choose where on the scale of lightness vs sturdiness you want to be...
Billski
