Bending spars with a coke can

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

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

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 

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 

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
        R = S x S x S x S = S  = S to the 4th power


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.


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!)


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.)


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. 


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

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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