I have microCT scans of different feather shafts (non-circular, not really hollow, with clear heterogeneity in material composition); I want to get accurate calculations of the 2nd moment of area without the standard assumptions of regular geometry. I'm leaning towards the BoneJ plugin for ImageJ, and would love thoughts on this or any other suggestions.
Because there are also differences in resolution between feathers (feathers of different sizes were scanned in the same container), I am also wondering if relatively lower resolution of the smaller diameter feathers is a limitation for either calculating or automating.
If you know porosity (f) of the shaft, then you may try to find I_ij as an integral over cross-sectional area (A) of f*x_i*x_jdA; here 0 < f < 1and i,j = 1,2. This is a quick , though not very accurate, way to estimate I_ij.
Great - thank you so much! Calculating the error is a good idea-- one I hadn't considered ...
Lindsey, you may also want to look into the software Mimics if your goal is finite elements analyses. http://biomedical.materialise.com/mimics
The software isn't cheap, but it can compile CT scans and has a plugin for making finite element models that can be spit out directly into other engineering software. I also believe for bone it can also use the density values from the CT scan and apply variable material properties (more dense areas of bone would be stiffer for example). You could probably also apply this to your feather shafts.
BoneJ is easy, cheap, and seems to be vary accurate. Charlotte A Brassey had a good suggestion of using calipers to check your results. The Slice Geometry tool will give you minimum and maximum diameters that you can compare to what the calipers give you. With that data, you can try different thresholding functions in ImageJ and see what gives you the best binary image from the scans.
The check of convergence for increasing resolution proposed by Charlotte looks nice, but the criterion of convergence in the form "your values plateau and increasing resolution doesn't affect your property any more" is a little bit not precise. In such case its a good ideas to use a Grid Convergence Index (GCI) criterion by Roache
http://www.taoxing.net/web_documents/p4enew.pdf
http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html
http://www.dynamore.de/de/download/papers/forum08/dokumente/I-I-03.pdf
It is primary used to check the convergence of mesh in Finite Element Method, but can be used as well to check the convergence of you results with CT scan.
In short, you need three scans with increasing resolution and corresponding values of moments of inertia. With Roache method you can extrapolate results and estimate exact value of moment.
I hope it will help.
I don't know if it will help for your specific purpose.
If the feathers have 3-order (or higher) rotational symmetry then it will help a lot.
www.mecsym.org
Cutting the feather across at its maximum cross-sectional area
would help find the greatest bending moment and should occur where the
cross-section is greatest. The wall thickness will be part of your calculations,
as is the distance between opposing walls. The greatest distance
between walls should apply to the direction of greatest applied force,
and bending moment, while the smallest distance between walls
will correlate to the lowest applied force.
By comparing to circles, ellipses, rectangles, and squares, and by
considering the strength of the materials that make up the shaft of the
feather, it should not be too complex.
Remember Nature places materials at the optimum locations to
maximize the strength, while minimizing the weight.
Drive shafts on cars are constructed in a similar fashion, as
are signposts, Lamp posts, trees, power poles, etc.
Feathers are cantilevers, wide at the base, and progressively
more narrow as they approach the tip.
Only if you careful cut through the feather. The art is to cut it without
crushing or splitting it, or changing its shape.
Maybe a diamond saw????
Michael Clark. If you are answering my question, what I mean is if somebody can post or send to me one (or some) typical section(s).
You need a cammo suit and a big net, and welding gloves.
then put out some bird food and.......
I would avoid eagles.......They might object more than a smaller birds
about having their feathers pulled out.
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