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Bending spars with a coke can
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Subject: Bending spars with a coke can
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From: Simo.Salanne@csc.fi (Simo Salanne)
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Date: September 1993
The following is a (very technical) article about carbon spars.
It consists of 5 parts:
- text
- a table of measured values
- three postscript files containing the results in
graphical form. I will post these as separate
files.
If you cannot view/print postscript or want a German translation
buy the latest Drachen Magazin 2/93, same stuff is published there.
(No I don't have the German version in computer; I wrote it in
English DraMa did the translation.)
If can view/print postscript and don't want German translation,
buy Drachen Magazin - it good, and part of it is published in
English.
Smooth Winds
Simo Salanne
===================================================================
Bending Spars with a Coke Can
=============================
My experiments, described in this article, were inspired by
David Lord's article in SKQ Vol. 3 No. 4, 1992, "Selecting spars
for a new kite design" and motivated by the lack of technical
data, which spar manufacturers don't seem to keep publicly
available. David measured spar deflections and calculated the
relative stiffness of several kite spar types used in U.S. From
my point of view his results had no practical value, because
any of the European spars, I use, were not included.
I am aware what Mark Cottrell says in his book "Swept Wing
Stunt Kites", 1990. According to Mark, by measuring the de-
flection only "flexibility" can be obtained - not a measure of
"stiffness". He also thinks that "to all intents and purposes a
single flexibility value is meaningless". However, Mark accepts
the approach when deflection is measured at number of differ-
ing loads, which, when presented as curve (deflection vs. load)
"yields (normally) a graph with nice straight line to start off...
The stiffness of the material is taken as being the slope of the
straight line portion of this graph." Hmmm..., Mark is searching
for stiffness of the material - in general.
By drinking a pint of beer is hard to say how strong beer is in
general, but one can estimate how strong this particular pint
was. Having more samples may confirm the first observation.
Having more samples may not confirm the first observation.
The Coke Can method can be considered as a case,
where the number of loads is two: a zero load and a load of full
can. Because two points is just enough to yield the straight line
part of the stiffness curve, I didn't bother by loading the spar
with two, three, four... cans until it breaks. The amount a 0.33
liter (360 g) can bends typical sport kite spar is in the same
magnitude the spar bends in normal flight.
I believe that measuring how much a spar bends on a suitable
load, gives much better basis to compare spars than relying on
how stiff it feels in my hands or how many consecutive national
competitions were won by flying XYZ-framed kites. One day, I
can go to a kite shop and buy individually measured spars,
with a tag telling the standard stiffness, measured in a way ap-
proved by KTA, AKA, STACK and me. Before that and so far,
David's tables and my bar charts have been most useful in
sparworks.
I processed the deflection values and weights into graphical
form, which is easy to use, e.g. when selecting a replacement
for a broken spar and original type spare spars are not availa-
ble. For example: you break an Easton A/C 3-30 spar and do
not have any replacement at hand. (When this article is pub-
lished it might be widely known, why it is hard to get Easton
spars any more). In diagram you can see that from European
brands both Beman Pro-15 and RCF-6 are very close to A/C
3-30 - just a little bit stiffer. AFC2200 could be used, too.
Measurement setup
-----------------
I measured the deflection of a spar under constant load as de-
scribed in picture. I placed two spars on a table, under a
weight, and hanged a 360g can on the other end of a spar in
my interest at 0.6 m distance from the edge of the table. The
deflection was measured between the spars. I measured at
least five samples of every spar type and calculated the aver-
age deflection.
A similar arrangement was used by David Lord, who used a
load of one pound and spar length of two feet. By using the
same reference spar (K75) my calculations should be compat-
ible with David's results within an accuracy for practical pur-
poses. K75 is glassfibre tube having diameter of 8.7/7.0 mm
and weight 33 g/m; have a look at standard Spinoff, there's
K75. In the table "Relative Stiffness and Weight of Spars" the
column "Rem." indicates which data is based on my measure-
ments (S) and which are from David's article (L). (Permission
to use David's data is granted).
Some of the figures are based on manufacturers data (M). Af-
ter it was agreed with DRAMA to publish my experiment, I
have been in contact with some manufacturers and spar dis-
tributors and managed to get their spar comparison charts or
tables. Unfortunately the charts and tables are not compatible
with eachother. However, I have used that information when
some spar size or type has not been available for measure-
ments. I have then scaled the manufacturers data by using
data from same chart for another spar, which I have meas-
ured. This kind of "indirect method" is tagged with M in remarks
column.
Stiffness vs. Flexibility
-------------------------
The relative stiffness is the deflection of the reference spar di-
vided by the deflection of target spar. E.g. relative stiffness of
AFC2200 is (47.8 mm) / (68.7 mm) = 0.70; means it bends
30% more than K75. This synthetic index could be called in-
verse relative flexibility, following Mark Cottrell's definition. I
have used relative stiffness to stay unconfusing with David's
article, which I do recommend. Usually a stiff spar is more desirable
than flexible. It is much easier to interpret the stiffness/flexibil-
ity index when "more" means "better". This works particularly
well in the bar diagrams, where relative stiffness is combined
with relative weight. Weight is naturally considered a "less"
means "better" matter in a kite. In diagrams the difference in
the height of relative stiffness and relative weight bars makes
a new measure marked by triangle. But I don't want to try nam-
ing it!
By measuring the spars, I found that variations in some spar
types were much larger than in some others. The smaller and
lighter, the more spread in deflection values.
Dave Lord's Scale Factor.
------------------------
Dave has developed a scale factor, which helps you
to scale kite designs:
Let's suppose you have a Speedwing which have RCF-6 frame.
You decide to build 25% larger Speedwing having similar
charasteristics. 25% means the leading edge will 1.25 times
longer. From the table you will find that RCF-6's scale factor
is 0.96. Calculate 1.25 x 0.96 = 1.2, which is the scale factor
of the spar you need for the larger Speedwing. From the table
you will find that both CarboFlex and RCF-8 have scale factors
of 1.20 and 1.21, respectively. Either of them will result to
a frame with similar bending charasteristics as you have
in you reference Speedwing.
Other way to work it out, is to study the table and then size
your new kite based on particular spar. Example: you decide
to use 4 mm AFC1580 to build a Speedwing "mini". How large
should it be? You take RCF-6's scale factor multiply
it by the scale factor of AFC1580: 0.96 x 0.67 = 0.64.
This means the "mini" should have a leading edge 0.64 times
the lenght of your reference Speedwing.
The scale factor can be derived from the formulas used to
calculate deflections of loaded beams. I bypass the theory,
and just give relation of scale factor S and relative
stiffness R.
S = R to the 1/4 power
or
4
R = S x S x S x S = S = S to the 4th power
Diagrams
--------
In diagrams spars are arranged by increasing stiffness. The
left bar is the relative stiffness and right bar the relative weight.
The triangle represents their difference.
Strength
--------
Relative stiffness does not tell anything about the"strength",
"durability" or "robustness" of a spar. A spar with a good rela-
tive stiffness might break in use more often than another with
a smaller relative stiffness. An example is RCF-6 and it's great
light brother RCF-6L. The 5 g/m lighter RCF-6L is 40% stiff-
er(!), but I have broken many more RCF-6L than RCF-6s.
(Did somebody say something about my flying style? But...I
am not Maxim!)
Price
-----
One important characteristic of a spar is the price. I am sure
your kite shop keeper will be happy to tell you everything about
this spar characteristic.
Missing spars?
--------------
What if your favourite spar is missing from table? The best way
is to send me five samples of it or encourage your supplier to
do it! The second best is as follows:
- Go to a super market and get some 0.33 liter can. Select
something you don't like, it's easier to keep the can unopened!
- Next you go to the self service weighing machine and weigh
the can.
Then, do the mesurement yourself. If your can weighs sub-
stantially different than 360 g, you should make a correction
when calculating the relative stiffness. Let's suppose your can
weighs 420 g and you measured a deflection of 61 mm. Then
relative stiffness = (420/360) * (47.8/61) = 0.91
and you can compare your spar to other spars in the table.
(Note: the average deflection of K75 was 47.8 mm when load-
ed by 360 g.)
Errors
------
I have done tens of measurements and entered the values into
a computer. I have checked and checked things out, a couple
of my friends proofread the article, but there might still be
some mistakes. Another possible source of deviation from
similar charts or tables is that manufacturers have made
changes in their products or product names.
Conclusion
----------
I have to confess: when the decision to publish my experiment
was made and the spar selection got larger and larger, I real-
ised the measuring setup takes too much time. I made a jig,
where the spar is suspended on two supporters (60,70 or 80
cm apart) and the weight (500..2500 g) hangs in the center
aligned with an adjustable mm scale. To measure a spar and
type the data into the computer takes now less than a minute.
I also changed my computer program so that the results
stayed compatible. Possibility to use different lenghts and
weights increased the accuracy, because mesurements can
be done on a suitable scale.
Stiffness and Weight of Sport Kite Spars
Stiffness and Weight of Sport Kite Spars 12-Jul-93
Outer
Spar Short Relative .... Scale Weight Diam.
Type Name Stiff. Weight Fact. g/m mm Rem
================================================================================
Reference spar: Glassforms K75 K75 1.00 1.00 1.00 33 8.7 S/L
--------------------------------------------------------------------------------
AFC 1580 AFC1580 0.20 0.33 0.67 11 4.0 S
AFC 1700 AFC1700 0.26 0.37 0.71 12 4.3 L
AFC 1800 AFC1800 0.32 0.40 0.75 13 4.5 L
Beman Superlight Shaft 13 BeSPL13 0.37 0.44 0.78 15 5.0 M
AFC 1880 AFC1880 0.38 0.45 0.79 15 4.8 L
AFC 1960 AFC1960 0.45 0.49 0.82 16 5.0 L
Beman Pro-Competition 13 BePRO13 0.49 0.49 0.83 16 5.0 M
RBJ 5.5 mm RBJ5.5 0.49 0.57 0.83 19 8.0 S
Beman Superlight Shaft 14 BeSPL14 0.54 0.53 0.86 18 5.5 M
Glassforms Prospar PS-15-278 PS278 0.57 0.63 0.87 21 7.1 M
Clearwater C252 C252 0.60 0.41 0.88 14 7.1 L
Advantage 250/2 ADV/2 0.60 0.49 0.88 16 7.3 L
AFC 2200 AFC2200 0.70 0.66 0.91 22 5.6 L
Exel Strong RCF 6 RCF6S 0.70 0.96 0.92 32 6.0 S
Beman Pro-Competition 14 BePRO14 0.71 0.54 0.92 18 5.5 M
Beman Superlight Shaft 15 BeSPL15 0.71 0.63 0.92 21 5.9 M
SkyShark IIIp SkyS3p 0.74 0.39 0.93 13 R
Easton Aluminum/Carbon 3-30 A/C3-30 0.75 0.62 0.93 21 6.6 L
Glassforms Procomp CP-15-278 CP278 0.84 0.54 0.96 18 7.1 M
AFC 2300 AFC2300 0.84 0.69 0.96 23 5.8 L
SkyShark Vp SkyS5p 0.84 0.48 0.96 16 R
Exel/Vlieger-Op RCF 6 mm RCF6 0.85 0.66 0.96 22 6.0 S
Beman Pro-Competition 15 BePRO15 0.88 0.63 0.97 21 5.9 M
Beman Superlight Shaft 16 BeSPL16 0.92 0.66 0.98 22 6.3 M
Beman Strong Shaft 15 BeSTR15 0.92 0.71 0.98 24 5.9 S
Easton Aluminum/Carbon 2-71 A/C2-71 1.00 0.62 1.00 21 7.1 L
AFC 2400 AFC2400 1.00 0.76 1.00 25 6.1 L
SkyShark VIIp SkyS7p 1.01 0.57 1.00 19 R
Clearwater C253 C253 1.06 0.57 1.02 19 7.5 L
Advantage 250/3 ADV/3 1.06 0.75 1.02 25 7.7 L
Glassforms Prospar PS-16-306 PS306 1.11 0.88 1.03 29 7.8 L
Beman Strong Shaft 16 BeSTR16 1.11 0.77 1.03 26 6.3 M
Beman Pro-Competition 16 BePRO16 1.14 0.74 1.03 25 6.3 S
Clearwater C312 C312 1.17 0.51 1.04 17 8.7 L
Easton Aluminum/Carbon 4-49 A/C4-49 1.19 0.70 1.04 23 7.2 L
AFC 2540 AFC2540 1.26 0.88 1.06 30 6.5 L
Exel Ultra RCF 6 RCF6U 1.26 0.51 1.06 17 6.0 S
Advantage 250/4 ADV/4 1.42 0.93 1.09 31 8.1 L
Glassforms Procomp CP-16-309 CP309 1.43 0.76 1.09 25 7.8 L
Glassforms Prospar PS-19-352 PS352 1.54 0.98 1.11 33 8.9 L
Clearwater C313 C313 1.86 0.76 1.17 25 9.1 L
Clearwater C382 C382 2.03 0.58 1.19 20 9.0 M
Phoenix/CarboFlex 8 mm CFlx8 2.10 0.93 1.20 31 8.0 S3
Exel/Vlieger-Op RCF 8 mm RCF8 2.17 0.96 1.21 32 8.0 S
Glassforms Procomp CP-19-352 CP352 2.30 0.84 1.23 28 8.9 S
Exel/Vlieger-Op RCF 9 mm RCF9 3.08 1.05 1.33 35 9.0 M
Clearwater C383 C383 3.25 0.78 1.34 26 10.9 L
Exel/Vlieger-Op RCF 10 mm RCF10 4.73 1.20 1.47 40 10.0 M
Exel/Vlieger-Op RCF 11 mm RCF11 5.75 1.35 1.55 45 11.0 M
--------------------------------------------------------------------------------
S = Based on measurements by Simo Salanne
L = Based on measurements by David Lord
M = Based on manufacturers data
S3 = like S but only 3 samples
R = Based on manufacturers comparison data
with Advantage
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