Bending Spars with a Coke Can

This is a (pretty technical) article about sport kite carbon spars. It was first published in Drachen Magazin 2/93. Then it was published in rec.kites: 
Date:   Thu, 27 May 1993 09:00:32 -1000
From:   salanne@convex.csc.FI (Simo Salanne)
Organization: STACK Finland
Subject: Bending Spars with a Coke Can
and placed in the rec.kites archive (ftp.hawaii.edu).

In 1995 I converted the article into HTML-format and published in the Web. The article text content is still the original. The spar table has updated to the current measurements. Postscript diagrams are replaced by one Radar-chart in GIF-format.

Smooth Winds

Simo.Salanne@csc.fi
References:

  1. Mark Cottrell, "Swept Wing Stunt Kites", 1990.
  2. David Lord, "Selecting spars for a new kite design", SKQ Vol. 3 No. 4, 1992,.
  3. Simo Salanne, "Mass-stab", Drachen Magazin 2/1993.
  4. Michael Graves, "Spars, Making your best picks...", KiteLines Vol 11. No. 2, Winter-Spring 1995.

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 deflection 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 approved 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 available. For example: you break an Easton A/C 3-30 spar and do not have any replacement at hand. (When this article is published 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 described 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 average 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 compatible with David's results within an accuracy for practical purposes. 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 measurements (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). After it was agreed with DRAMA to publish my experiment, I have been in contact with some manufacturers and spar distributors 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 measurements. I have then scaled the manufacturers data by using data from same chart for another spar, which I have measured. 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 divided 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 inverse 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/flexibility 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 naming 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. The derivation of the formula contains many inline images, think twice before selecting this link, if you have a slow connection!.

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

The Radar-chart diagram represents relative stiffness and weight in graphical (and very compact) format. The spars are sorted by increasing stiffness. Due to scaling and space reasons most flexible and stiff spars do not appear on the chart, just in comparison table table. Spars are identified in the diagram by abreviated name, for the full name see the comparison table.

Strength

Relative stiffness does not tell anything about the "strength", "durability" or "robustness" of a spar. A spar with a good relative 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% stiffer(!), 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:

Then, do the mesurement yourself. If your can weighs substantially 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 loaded 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 realised the measuring setup takes too much time. I made a test bench, 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.

Spar Comparison Table