Hi, I’m attempting a new construction method for a hollow board and I made a model. Right now the model is 11inches long and a half inch thick. I’d like to do some weight tests on it but I am extremely terrible at math and I need an equation so I can convert my strength to weight ratio to a full size board. Can anybody help me. And no, I haven’t looked in the archives because I wouldn’t know what terminology to search for. If there is stuff in there, could somebody point me in the right direction? Thank you all.

first, how are you finding the strength of your model? are you planning on doing a destructive test? i’m afraid that you’re in for some heavy-duty mechanics ahead…

What I was going to do was apply weight until it starts to show noticeable damage or until it crushes.

Hooboy…like the man said, this one doesn’t have an easy answer. And so many variables in there - what would your model scale up to ( 11 inches to X inches, materials thicknesses, not just overall thicknesses, etc ) so that you wind up with a helluva lot of mechanics and mathematics, not just a simple formula.

http://ocw.mit.edu/OcwWeb/Civil-and-Environmental-Engineering/1-050Fall-2004/CourseHome/index.htm might give you an idea of what you’re up against. And that’s an intro course.

Now, having said that…depending on what kind of course you’re in ( and I wouldn’t try this in a senior-year engineering school project ) … there may be a cute way to attack this problem empirically.

Assuming your materials sizes are to scale ( lets say 1/8 scale - a 7’ 4" or so board in full-size, shall we?, so that what would be 1" thick materials or layers in the full-sized version would be 1/8" thick in your model, etc ), this is something I might try.

Make a similar model using ‘normal construction’ - the lightest aircraft model cloth you can find, foam of normal weight and standard resin. Test both models to deflection and destruction. Then, test a full-sized surfboard ( which is what you base your conventional model on) to similar ( scaled) deflections and destruction. This would give you a baseline equation or constant that’d spit out some worthwhile information.

For instance, if your conventional model deflected 5% at 10 lbs force and the conventional surfboard deflected 5% at 400 lbs force, you have a constant you can multiply in, 40 in this case.

Applying that same constant to what force deflects your new construction method model 5% ( multiply the force times 40 ) gives you some predictions of what it’ll do full-sized. Not necessarily right, mind you, but at least you have someplace to go from.

Hope that’s of use. For further info, you might look at http://www.nist.gov/ and www.nasa.gov - both have considerable experience with scale model testing of structures.

doc…

You may get some results, but I’m not sure how accurate they would be. Scaling things down or up for stress test purposes doesn’t always work. The mechanical properties change too much and the maths needed to accurately plot the actual stresses could be a nightmare, especially if you aren’t math oriented in the first place.

I think when it comes to hollow boards, the best teacher would be time and experience.

The aeronautical engineer I worked with helped me with fins, but even in his vast experience he had no idea of the actual stresses on a fin. It only took a few disintergrating fins to make him realise. But I must admit that in the end, after much trial and error, we had hollow light fins that didn’t fall off.

Sorry mate, I just don’t trust the math too much.

I’m a mathmagician. i’m not sure my expertise would be of use for your question.

Doc, your knowledge of all things surfcraft is very humbling, and also makes me want to read till my eyes burn

hi,

stress equations for a plank are pretty easy

s = Mc/I

s= max stress (top and bottom)

M=moment (F*L/4 for 3 point bend)

c= max distance to neutral axis

I=moment of inertia of the X-section (b*h^3 /12 for rectangles)

I’m sure it looks confusing, But do a google search

for things like:

flexure stress in beams,

beam strength calculation,

bending stress. etc.

But the best place to find it all is chapter one of any Mechanics of Materials text book.

let me know when your ready for more.

-bill

Jeez, man, I’m just this beat up old boat carpenter who’s partially trained as an engineer. And always been kinda interested in stuff - including mathematics, though these days I kinda flame out at much beyond kitchen math, y’know?

I kinda envy you. Heee- making the numbers dance, working through the toolbox of mathematics to see what you can apply to the question, yeah, what little I did I enjoyed hugely.

Now, the thing about beam deflection calculations, beam bending stress, all that sort of stuff, is that there is always a k in there. A constant or constants that varies with the material used and the structure, which for Monkstar’s purposes here can be treated pretty much as one and the same. Given that k, you can plug it into the formulas and it’ll spit out the appropriate numbers for beam deflection, amount it’ll bend and all that good stuff.

Unfortunately, that needs standardised testing, kinda like NIST (www.nist.gov the National Institute for Standards) was set up to do and still do, among many others. In great big labs, with sophisticated gear that’s nicely calibrated…and chances are that’s not available. So, you gotta wing it.

That’s okay - still looking for useful information on how this structure compares to conventional construction. And to do that, you gotta compare 'em, scaled down.

It struck me that ‘noticeable damage or until it crushes’ isn’t really going to give anything that’ll give any numbers that can be plugged into a formula. But what will would be, basicly, weighting the thing with its ends set on a couple of blocks, so that you could see how much it bent under a certain load.

And that can give some pretty neat results. Now, rather than just making a little, conventionally made model of a surfboard to test alongside the new structure of Monkstar’s ( which I am gonna call M from here on in) what I’d do is use a couple of pieces of wood of reasonably precise dimensions and known species too.

Then, set up your blocks and your weights and all that, with maybe a machinist’s dial indicator in there someplace ( like this cute little sucker ) to measure how far your test samples are bending on a very small scale. Record all this, see what it takes. For a surfboard-like structure, I’d think that a deflection of much more than 5% of the overall length would be pretty close to breaking or buckling. Given an 11 inch model, you’d be looking for deflections ( how much it’s bent down ) on the order of 0" to a half inch. Make your other test samples the same length.

Test and record your data. Now for the fun part - well, maybe not for anyone but ChasingLefts and me on a good day.

Not only can you plot these on a graph, deflection per weight, but if you take the numbers you got for the wood samples of a known species( for which that constant k I mentioned before is known) then you can manipulate the formulas to give you a very, very approximate value of k for the new and old surfboard construction methods. And suddenly the way surfboards bend, flex and break is more predictable.

Whaddya know…while it’s not the NIST lab, some applied math and relatively unsophisticated testing can do some pretty neat stuff.

hope that’s of use

doc…

hi Doc,

The k you are refering to is

E: modulus of elasticity

effectively how much stress develops in a material for a given abount of strain (stiffness).

You’re correct that you need to look up or measure E for each of the materials in the design.

As suggested, a 3 point bend test with a means to record weight and deflection would do the trick , if you could not find the desired properties in MATweb (or you didn’t believe them).

-bill

Hi Bill,

Yes, that’s exactly what I was trying to think of, been a while since I futzed with beam design.

best regards

doc…

Wow! A lot of info there. I think I’m just going to go with the “Build a full size one and see if it works” method. The materials I’m using are relatively cheap so it’s not too much of a big deal if it doesn’t work. Thanks for all of your (confusing) help.