Tuesday, May 10, 2011

Flex modelling - whats the point?

BoardOff Design Tool has had a great response with about 30 downloads so far!

Thanks to some comments from users on another the use/value of the flexmodel tab is becoming clearer.

The flexmodel tab in BoardOff is an attempt to model the flex of the board when bent at the middle and at the tip under different loads. The theory needed to do this is well developed in the theory of composites and the theory of beams and in many cases further simplifying assumptions can be made that are theoretically justifiable.
Q:  So whats standing in the way of the model accurately predicting the flex in a board in advance of building it?
A: the big variation in the properties of the materials you use ii) small parameter variations due to construction variations and errors to which the flex is highly sensitive e.g core thickness, and concave, resin modulus variation due to ambient temperature.

So, if there is so many uncertainties in the material properties what is the value of attempting to model it if its predictive power for the next board is limited? I believe that the real value lies in the ability to quantify what impact changing a parameter will have on the flex of the board and hence which parameters the flex is most sensitive to 'all else being equal'. While it may not be possible to guarantee that your next board will flex 10cm at the tip under a 20kg point load, you will be able answer questions like:

'All else being equal'....
i) if I increase the concave by 1mm what would that do to the flex?
ii) If I use 10mm core instead of a 12mm how much will the flex change?
iii) To increase the flex should I remove a layer of glass of reduce the core width given the accuracy of my setup?
iv) What difference will tapered tips make compared to a step profile in the tips?
v) If I change the orientation or type of reinforcement I use how will that affect the flex?
vi) What sized paulonia stringer would I need to end up with the same flex I would get using the 'carbon stringers' like the Bro-kite masters?

These can all be read off the model to allow you to develop rules of thumb by which to build the boards. For example the models show that the flexural rigidity of a foam core board at a given point is is proportional to the core thickness squared and linearly dependant on the thickness of the laminate. So taking 1 layer of glass off a 3 layer layup ( each side) will reduce the flexural rigidity by 33% (for equal weight and orientations of reinforcement) where as changing the core thickness by 10% changes the flexural rigidity by 21%. One 'rule of thumb' to come out of this is that for each 1.5mm of core thickness you take off you may need to add 1 extra layer of glass based on your previous laminate schedule.

These rules of thumb are what typically develop with the board builders experience but this modelling exercise helps to speed the process up and deepens understanding of why production boards are built the way they are and may challenge some wives tales.

The modelling exercise is far from complete with the model primarily being for flex affects. However, two of the other quantities of interest are the maximum stress and strain in the board. The holy grail of this model is to predict strength. Unfortunately this is very difficult and I suspect the rules of thumb will have to incorporate big margins of safety.

The situation with tensile strength is not as bad as it is with compressive strength. Tensile strength is less sensitive to variations in construction than compressive strength is. The reason being that failure under compression is rarely because the compressive limits of the material are reached but more often that local imperfections in the laminate or bonding layer of core surface etc lead to concentrations of compressive forces and delamination of the laminate. In this way the compressive limits are rarely reached before the board breaks. The challenge is further increased by the 'micro failures' in the laminate that accumulate over time and change the properties.

The first step in this process is simply to see whether the magnitude of the forces predicted by the model are of the right order of magnitude and if not, discover why not. Then ideally you would create some test pieces with all sorts of variations in materials construction technique and do destructive tests on them. From this one could create a set of margins of safety that could be applied to design decisions.

Finally, and for me most importantly, it absolutely fascinating to learn about this stuff. The fact that its applied to kiteboards is all the better but being fascinating is almost enough in its own right.


  1. Hi Matt,

    A quick question. Was reading your blog and observed that in april blog u indicated that the flexual rigidity is proportional to the core thickness cubed (^3) (1mm core thickness change was equal to 28% flex change on 10mm core), however here you are indicating that the relation is squared(^2). Could you elaborate, did i miss something...?

  2. Hi MirsadC. Thanks for the really good question - and I'm very happy to hear someone is reading it!!!!

    Its a case of both are right but it depends on which part of the core you are thinking about. Flexural rigidity is the product of elastic mod. and 'I', the secod moment of inertia. 'I' relates the shape of the cross-section only and E relates only to the properties of the material that its made up from. I for a rectangle is width*height^3/12. So if you are talking about the core material withouth any laminate on the outside (no fibreglass etc) then the flex. rig. is proportional to the height cubed.

    If you talking about just the 'shell' of reinforcement on the outside of the core then for this thin 'shell' of laminate has an 'I' whose largest term is core thickness squares times the thickness of the laminate 'shell'. This is because you can find the I of a complex shape by simply adding or subtracting the I of its components. I for a shell is then

    w*(c+t)^3/12 - (w-2t)*c^3/12; where c is core thickness and t is laminate thickness

    when you expand this out the c^3 terms cancel and you get c^2wt as the largest terms.

    The 'E' for pvc foam compared to the E for fibreglass is so small it is effectively zero for flex calculations so the core felx. rig is due just to laminate shell. Woodcores have an E can't be ignored and so the flex rig of a wood core is the sum of the flex rig for the core (proportional to c^3) and the reinforcement (c^2t).

  3. much obliged!

    It is all much more clear now :).