#4
Post
by Dennis La Varenne » Mon Oct 25, 2010 4:26 am
Daryl,
Thank you for the interest you have shown in the article.
My insistance of keeping the two outer halves of the limbs as non-bending levers is an assumption on my part derived from my reading and investigation of this bow design which, in fairness I should have kept a record of and inserted as footnotes in the paper for others to follow up on if they desired to see where I drew my conclusions about its design and the cleverness of its design from. I did not and that is a cross against my name.
The most current thinking among the bowyering community internationally rightly or wrongly, has accepted as orthodoxy that this stiff outer lever principle is the basis of the design, and I have followed that orthodoxy because the reasoning behind it makes good sense to me and has two practical benefits in allowing a reasonably short/medium length bow to have a moderately more shallow string angle coupled with low outer limb mass which is beneficial toward higher limb speed and hence arrow speed.
Of course, you are quite correct in considering that there is not the slightest reason that this bow cannot also be made with bending outer limbs like any other flatbow design. The lower outer limb mass would still be maintained, but at the expense of a slightly greater string angle at full draw, which, depending on the n-n length of the bow, may or may not be significant. But, if one wants to build this design of bow as short as possible for simple handiness, the non-bending outer lever principle will have a positive value in terms of minimization of finger pinch and stacking.
You are also right in your inference that it is not necessary to build these bows to mathematical model to be successful in making one. Clearly our European neolithic ancestors did not and nor do we. However, using the mathematical methods explained by Dave Clarke in his series on Using Maths to Build Bows, does allow bows to be built to a blueprint within the elastic limits specific to the particular piece of wood we have in our hands, and, also not to be dismissed, to be able to make analytical models of various bow designs and make predictions with considerable accuracy on how they will bend and where to distribute the bending loads to best effect.
Maths is a valuable tool we now have to apply to our ancient craft both retrospectively to analyse the mechanical advantage of any particular design compared to any other design. Applied mathematics is the reason we can understand the cleverness of the Holmegaard design because it allows us to understand how the distribution of bending loads inherent to this design can allow maximum performance from an all wood bow compared to other bow designs extant in that same period, principle of which, in my view, is low outer limb mass to allow maximum arrow speed coupled with shallow string angle in a moderately short bow. Maths explains the WHY of this design in detail.
I have insisted in the body of the text that the inner bending section of the limbs of this design should be both parallel in width and thickness. In my introduction to the revised 2010 edition, I describe how this in not necessary, and how, using mathematical modelling based on distribution of bending load within the elastic limits of any piece of wood where the modulus of rupture is known, that there actually should be either tapering of width or thickness or a combination of both. Before I got my head around what Dave Clarke was explaining, together with some of the maths explained in Robert Elmer's 'Target Archery' and some other publications on using applied maths in bowmaking, I found that keeping the inner limb parallel in both width and thickness the most expedient way in which to tiller this design successfully, and I recommended this technique on that basis.
This recommendation on my part does not preclude any other tillering method and the success of any technique is that you end up with a functioning durable bow. Applied maths can be thought of as a finessing of the design for optimum performance for the most economical use of materials. I would be the last person to decry the work of any bowyer who produces an obvious Holmegaard design bow which functions. That would be just plain arrogance on my part, because we all know that cats can be skun in a number of ways.
I have recently come on a web discussion (again I did not note down the URL) that the characteristic Holmegaard design with which we have become familiar is most probably a deviant non-typical variant of a more common design from the same area which does NOT have the characteristic mid-limb steps and another discussion on paleoplanet which purports pretty convincingly to me that the only genuinely typical design of this bow is from another archaeological site called Mollegabet. The well known artefact from the Holmegaard site does NOT have the characteristic mid-limb steps with 'define' this design. So, the worms are now crawling from the opened can.
Nevertheless, among trad bowyery, we have been presented with a design of bow with or without mid-limb steps depending on the extent of one's archaeological PC perspective which has clear mechanical benefits and which design seemed to get lost over time until it was resurrected in the 1920s by the likes of Clarence Hickman, Paul Klopsteg and Forest Nagler who decided to investigate just what made a bow do what it does and why using applied maths. They ended up re-discovering that the most mechanically efficient designs were flatbows of firstly isosceles pyramidal shape followed by a more practical shape which had nearly parallel sided limbs for around half their length with sharply tapering outer limbs - very reminiscent of the various Holmegaard artefacts.
Our Holmegaard ancestors were pretty bright people and they managed to hit upon a design which, according to Tim Baker and Paul Comstock and others endured for something like 4,000 years then seemed to drop out of the archaeological record thereafter for whatever reason. Clearly intuition based on experience allowed some cleaver neolithic bowyer to come up with the bow based on empirical evidende, but is is largely due to applied maths that we are now able to understand the benefits of the design as well as we do today. We don't need maths to build these bows quite obviously, but it allows us to understand WHY the design is so good.
Dennis La Varénne
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