Subject: Re: [harryproa] RE: Unstayed masts
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Date: 3/3/2014, 7:06 AM
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harryproa@yahoogroups.com.au

 

No sweat Rob, but i dont think we are talking about anywhere near 3-4times the glass and resin...

Rather than speculate, lets use some real numbers....

The rated  "E" of carbon used is 130Gpa in compression, whereas e-glass is 42Gpa. So the stiffness is ~3 times lower. If we compensate with added section diameter, in the area below the boom and through the highest load @ deck bearing, we should be able to match the deflection performance with a ~3 times stiffer section of slightly increased diameter. As stiffness is proportional to diameter cubed, we only have to increase the section size a little and we should match the deflection performance in e-glass at ~225mm diameter of same wall thickness - measured deflection at 1m above deck bearing. The actual deflection using an arbitrary but realistic design load of 10kN acting at center of pressure + 5.1m above deck is 27mm in carbon @ 165mm diameter VS 27.7mm in e-glass @ 225mm dia, both asasume a 10mm wall thickness. 225mm is a standard  storm water PVC pipe size too btw ... *wink*

Now to compare the strength, with UD e-glass its much closer match to carbon compared to stiffness. With 900mpa rated at 55% Vf, VS 1300mpa in carbon - i know some engineers use different numbers, but these are text book numbers from the same source so they should be at least comparable in relative terms. Highest stress at the deck bearing is 147 Mpa  for the e-glass section - well under the 900mpa compressive strength of e-glass. This means a safety factor of around 6. And in the carbon example, 287Mpa - also well under the rated strength of 1300mpa which equals a safety factor of 4.5. So this tells us the wall thickness could actually be reduced on the e-glass section and arrive at the same safety factor for each design. This so happens to occur at around 7.5mm wall thickness for the e-glass version.

So considering all of the above, lets look at the weight... the cross sectional area of the 225mm e-glass section, with a 7.5mm wall thickness is 20498mm^2. Whereas the 165mm carbon section in 10mm wall thickness is 19477mm^2 - again both at the deck bearing. So theres almost nothing in it in terms of volume. The density of UD glass epoxy is somewhat higher than UD carbon epoxy tho, teh same text shows a ratio of 1.6:1.9 or around 20% - so it ends up 20% heavier based on laminate density. This wont be bugger all extra resin tho, the density difference is in the fiber itself, as both values assume equal fiber volume fraction.

So the bottom 2 meters of mast, between say boom and bottom bearing - assuming no taper for ease of calculation, there is 9700cc volume in the 165mm carbon tube - which would weigh 9.700*1.6g/cc or  ~15.52kg. The bottom 2m of 225mm dia glass tube weighs is 19.475kg...

Price, 10kgs of carbon Vs 13kg of e-glass...

Dont even talk about what happens when you make a 225mm dia carbon section!!! Clearly it gets better again...

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