Quite some time ago I had Morris make me up a clamping caul
"template". Basically it's a 48" long piece of Masonite with a curve
cut on one edge to a radius of 2000.5 (inches, I believe). The goal
was to have the ends be 1/8" higher than the center when place on a
flat surface. Well just recently I got around to making the actual
cauls themselves. I had a bunch of baltic birch rippings left over,
so I laminated three pieces together and template routed the curve
into one edge. The finished dimensions are 1.5 x ~3 x 40". I made
them 40" because that maximized usage of material, and because I
needed them for a 36" round table top. I ended up making six of them,
and they really worked like a charm. I used them in pairs, top and
bottom, but I suppose if you had a really rigid bench you could just
use one on top to push it flat. In that case, though, maybe you'd
want them a bit wider - say 4" or so.
And, for those who think it ridiculous to go through the trouble of
obtaining a CNC'd template to make a clamping caul.....you're probably
right! To me a fair curve seems like it should apply more even
pressure across the width of the panel, so that's why I wanted it.
I'm glad they did the job. The nice part about having a good template is
that it can be used over and over.
Afterward I wondered if a catenary with that same 1/8" chord height
might apply more even pressure...
Thank /you/ for helping keep the lights on. :)
It's not difficult, but I usually write a simple C language program to
write the bulk of a part program - so as to take advantage of the
increased precision available.
The mathematical description (actually, several of 'em) can be seen at
I'm not sure the difference in behaviors of arc and catenary would be
Take your choice, a catenary is a special case of a parabola where
only the weight of the cable, chain, rope, etc defines the curve.
x^2/a^2 + y^2/b^2 = 1 is the basic formula for a parabola. where the
values chosen for a & b define the curve.
On Mon, 8 Jun 2009 17:48:21 -0700 (PDT), Jay Pique
Assuming a caul with uniform stiffness - EI is constant along the
length of the caul - to get uniform pressure along the clamping
surface, the shape of the caul should be:
Y = Ymax * ( 1 - 3.20 * [ (X/L) - 2*(X/L)^3 + (X/L)^4 ])
where X is distance along the caul, L is the length of the caul
between the clamps at each end, Y is the chord height at any point
along the caul before applying the clamps, and Ymax is the maximum
chord height at the clamp location at each end.
The clamping pressure exerted by the caul - force/unit length. - is
Q = 76.8 * EI * Ymax / L^4
where Q is the clamping pressure, EI is the caul stiffness (E Young's Modulus of the caul material, I is the cross section moment of
inertia) and Ymax is the maximum chord height of the unloaded caul at
the clamp positions.
Increase the pressure exerted by the caul by any combination of:
1) increase the maximum chord height
2) increase the caul stiffness
3) decrease the length of the caul between clamp positions.
<snip of complex formulas and other stuff I don't understand>
Sweet fancy Moses, Tom - did you just pull that off the top of your
head?! Thanks for sharing - I may have to get Morris to translate it
into a real live caul sometime!
Now that you see what a total PITA beam deflection calculations are
along with the incorrect assumption that the beam is supported on
knife edges unless cantilevered, you can understand why stress
calculations are used with a serious safety factor derate to CTA, for
Plus the fact that the algebraic equations result from integration of
the governing differential equations which are themselves linearized
because the actual non-linear equations frequently do not have a
closed form solution in any but the most trivial cases.
All of engineering mathematics is an approximation of the real world
but the nice thing about it is that the linearized versions of the
equations generally yield conservative results when compared to
numerical solutions of the non-linear equations. One of the
linearizing simplifications that is non-conservative with respect to
deflections is ignoring the contribution of shear deformation. That
particular effect isn't usually introduced in undergraduate level
Your point about the assumptions underlying the model is well taken.
The simplifying assumptions are rarely a true and exact picture of the
real world. That's why it's called "Engineering Approximation" and why
"Safety Factors" (civil engineering) or "Margins of Safety"
(aeronautical engineering) are always applied to any critical stress
In response to a question asked in another post: No, I didn't recall
that from memory. I believe Albert Einstein is credited with the
advice to never try memorizing something that you can easily look up.
I went back to an old Strength of Materials text from my undergraduate
days in the '60s. The case of a uniform beam, simply supported, with a
uniform distributed load is one of the introductory examples of beam
The most dominant design factor is the eyeball.
It's got to look good in the shower.
Look at the columns on some of the monuments in Washington DC.
Ever see a school building with anything smaller than an 8WF35 floor
Still remember my design engineer's comment about bracing ribs on the
bed of a threading machine used in a steel mill to thread seamless
"I could use 3/4 thick ribs, they are certainly strong enough, but
1-1/4 ribs look better, and after all, we sell this equipment by the
I hear you!
But since I spent most of my working life in the aircraft industry,
the "pound" was the arch-enemy! Had to be "hell-for-stout" and light
as goose down. Which is why we talked in terms of safety margins
rather than safety factors and tested all major structure to failure
to verify/validate the analysis.
OTOMH, don't think so (if I understand the question).
_IF_ the caul were perfectly rigid, the force would be distributed
normal to the surface uniformly between the two ends irregardless of the
The real-world difference is how much flexure is in the caul and the
mold and how much bending there is between the applied pressure points.
(At least that's the way I initially see it w/o actually writing the
free body diagram...)
Assuming the intent is to apply uniform pressure over the length of
the caul, use the deflection curve of a uniform beam, simply
supported, and uniformly loaded along the length. Since the beam
equations are linear - or at least approximated by linear equations -
the deflection curve would be a good approximation of the shape of the
caul that would give a uniform clamping pressure.
The assumptions aren't rigorously met since the caul doesn't have a
uniform cross section if one side is straight and the other is curved,
nor is it likely that the material's modulus of elasticity will be
perfectly consistent at every cross section along the length of the
Haven't run any numbers but I'd guess the difference in results from
using a circular or parabolic arc and the results of the beam
deflection equations wouldn't be worth worrying about.
I've made clamping cauls with a fair curve on my jointer by raising the
outfeed slightly above the cutter height and keeping pressure on the
infeed table as I pass the stock over the blades. Having the outfeed
table slightly higher than the blades causes the stock to ride up
causing the curve.
The trick is then getting the table back to the proper height to produce
straight cuts. To do this I mark the table at the ways before changing
the height adjustment.
If you're not sure of the outfeed table height there is one sure-fire
way to adjust it dead-on.
Take about a three foot piece of stock that is known to be flat.
Joint about an inch or two and stop. Turn the piece around and start
from the other end and joint the entire piece. If you can still see
the cut from the first end the outfeed table is too high. If you have
totally cut off the cut from the first end the outfeed table is too
low. If you can barely see evidence of the first cut the outfeed
table is, as Goldilocks said, "just right."
Screw a 1 x 2 to the edge of a straight board at the ends.
Push the middle of the 1 x 2 toward the board and
secure it with a third screw. Run the whole stack
through a tablesaw, ripping the bowed edge straight.
Unscrew the 1 x 2, watch it pop into a long curved
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