See the attached screen dump of an excel sheet. It shows the automated calculations that produce an aluminium round tube with the exact same (bending) stiffness AND weight as a given round tube made out of carbon laminate.



All the numbers given in blue can be modified at random and an equivalent tube will be produced. This mathematic problem is fully determined, meaning that a solution (of equivalence) can ALWAYS be found. Although it must be said that not all produced wall thicknesses and outer diameters may be realistic because of other engineer considerations. Example ; a wallthickness of 0.1 mm is impossible to achieve by extrusion, a common production method for alu tubes.

The excel sheet allows all kinds of materials to be entered.

In the screen dump I've entered the typical material property values for aluminium and carbon laminate. A little further down I defined what could be typical dimensions of a carbon A-cat boom (0.04 x 0.002 mtr.). Clearly a fully equivalent boom can be produced in aluminium, both in weight and stiffness, when the extrusion has the dimensions 0.059 x 0.001 mtr

How stupid is this ?


For obvious reasons I left out cost-equivalence.

Obviously some mathematical model needed to be developped that could easily produce these results. Good engineers will do that, lazy engineers will just just think "whatever" and try to solve the design problem by throwing lots of money at it, covering their lack of skill by using exotic materials.


For reader who are interested in learning something more. The closer two materials are in their stiffness and density ratio the easier it is to produce an equivalent beam in both stiffness and weight. Pretty much any a-symmetry ratio (R_E/R_Ro) that is close to 100 % will make the use of one material over another unimportant. That is unless other considerations like cost, ease of production and stability of thin walls are not factored in. This a-symmetry ratio between aluminium and carbon is not particulary far from 100 %. This leads to the situation where it is relatively easy to find good alu alternatives to carbon laminates. A similar analysis can be performed for glass and kevlar fibres with respect to carbon.


A counter example : Lets compare dyneema lines to stainless steel cables. The asymmetry ratio is now about 700 %. Makes the carbon/alu ratio look like a minor league comparison.

Wouter