Using Engineering Principles to Reconstruct Leaf Shape

Using Engineering Principles to Reconstruct Leaf Shape: A Methodology to Predict Life Posture of Leaves of Extinct Plants — Marlene Hill Donnelly

This article appears in the 2010 Journal of Natural Science Illustration

Abstract: In reconstructing the elements of a convincing prehistoric landscape, some approaches require engineering equations while others depend on subtle nuances of personal observation. The reconstruction of a fossil taxon can be strongly supported with reference to a related extant species. Where no such living plant exists, visualization and imagination are not enough; creating models using structural engineering principles and in-depth field study of living analogs is vital to both accuracy and artistic authenticity. All images copyrighted by Marlene Hill Donnelly, unless otherwise noted.

 

INTRODUCTION

This was a genuine collaboration between art and science: questions about color and form had a significant part in directing research. All plant reconstructions were done for paleobotanist Jennifer McElwain of the Field Museum and University College Dublin. As an ecologist specializing in climate change, Jenny needed accurate landscape reconstructions of Late Triassic and Early Jurassic Greenland. The results provide a strong visual description of the long-term devastation of global warming.

All work was from fossils collected from the same site (different time beds) in Scorseby Sound. Plants were represented in the landscape in accurate relative populations. A sedimentologist determined whether the plant had grown in sand, mud, water or other environment. The final Triassic reconstruction was published in Nature Geoscience and the book Plants in Mesozoic Time edited by Carole Gee (Indiana University Press, 2010), and full-sized prints are on exhibit in the Field Museum and other natural history museums.

The creation of life reconstructions of fossil plants is fascinating and rewarding, but not always easy. Many extinct plants have related living analogs, which makes their reconstruction relatively simple. For example, the modern Ginkgo biloba is a clear relative of Ginkgoites and other extinct ginkgo genera; the extinct Dictyophyllum fern has a close living relative in the Dipteris (though the whole family was thought to be extinct until very recently!). In both cases fossils are basically “converted” to the modern growth form for reconstruction. Using the living plant as a template, I make a foil and wire model to pose in a life-like way, and off we go. All plants in the Triassic reconstruction fell into this category.

A new problem arises when a fossil plant has no living counterparts. In the new Jurassic reconstruction we had two such genera, Sphenobaiera (Fig. 3) and Czekanowskia (Fig. 4), two extinct genera from the Triassic. Though classified as ginkgoalean, their very unusual growth forms have no modern analog. How to proceed with the reconstruction in a way that would make the result reasonably reliable?

My initial attempts were firmly in the category of “winging it”—in other words, basically making things up. Following scientists’ suggestions and previous reconstructions, I made my usual paper, foil and wire model Czekanowskia (Fig. 1), which looked quite interesting but left me with serious misgivings. My doubts solidified when a visit to Hawaii brought me in contact with Casuarina, a plant superficially similar to Czekanowskia but botanically unrelated. Though structurally stronger (the Casuarina “leaves,” actually branches, are composed of jointed cylinders) they invariably drooped (Fig. 5), revealing my previous very rigid Czekanowskia reconstruction to be a physical impossibility. At this point I very much wanted to design an approach that would give at least the possibility of being correct!

ENGINEERING A SOLUTION

Consulting with the small army of mechanical engineers to whom I am related, it was suggested that I take an approach that used the principles of Modulus of Elasticity (the bending properties of materials) and Second Moment of Area, which addresses the position of the cross section of a structure relative to horizontal and vertical neutral axes (Fig. 6) to predict load capacity. The greater the distance from the neutral axes, the stronger the structure in that direction (see Fig. 6 diagram). It was emphasized that I would be able to reach a simplified approximation, a reasonable possibility rather than a scientific certainty.

The first step was to determine a modeling material with a Modulus of Elasticity similar to that of ginkgoalean leaf tissue. Weights were placed on a living Ginkgo leaf blade held loosely in a vice (Fig. 7) and the bending angle measured; the same weights were attached to a variety of papers and metal foils, which I had cut to the size and shape of the leaf (Fig. 8), in a search to duplicate the angle (Fig 9). The appropriate modeling material (laser printing paper) was cut to the size and shape of a Czekanowskia leaf and placed in the vice unweighted, where it drooped to a nearly vertical angle (Fig. 10).

The next step was to determine the affect of Second Moment of Area (Fig. 6). The necessary altered cross section was achieved by scoring the veins into the paper leaf with a BIC® fine point pen (with a mouse pad underneath for cushioning); the single vein present in Czekanowskia changed the flat cross section to a shallow “V” shape. This considerably strengthened the structure, allowing the distal end of the blade to rise noticeably (Fig. 11). However, the overall posture still sagged, because the mass of the blade is too large compared with the length and width of the pseudopetiole (the moment arm) to be overcome by cross section shape manipulation. The final model (Fig. 2) was much droopier than the first (made-up) model (Fig. 1), but had much more body than earlier, very limp reconstructions. My scientists were pleased: this reconstruction was consistent with the suggested hot climate of the Early Jurassic, which would encourage deeply dissected leaves that would dispel heat and still maintain an angle sufficient to catch enough light for photosynthesis, while not defying gravity.

The next challenge was to reconstruct Sphenobaiera, a ginkgoalean genus with amazing hand-sized (and hand-shaped) leaves. I had designed my original (purely conjectural) copper model (Fig. 12) with muscular rather flamboyant leaves, but the engineering modeling experience with Czekanowskia made me wonder whether Sphenbaiera needed to droop more as well.

The same approach—using the appropriate laser print paper and scoring it according to venation—yielded satisfying, if surprising, results. Because Sphenobaiera leaves are so much larger than those of Czekanowskia, Second Moment of Area kicked in to permit a much more rigid leaf. Strength increases at a factor of the fourth power relative to length, meaning that a leaf section twice as wide as another would be two to the fourth power, or sixteen, times as strong (Figs. 13 and 14). Essentially, the larger Sphenobaiera leaf could hold itself up at any angle whatsoever, unlike the smaller and structurally weaker Czekanowskia. A nearly vertical posture would still be at risk in strong winds, so I did not get too carried away designing aggressively upright leaves (Fig. 15), but my original model (Fig. 12) proved to be a reasonable possibility in this case.

THE SIMPLE APPROACH

To summarize the methodology of designing a reconstruction without the benefit of a living species to use as reference, the following steps offer the most direct and time-saving approach. They take much less time to do than they did to explain, so don’t get discouraged!

1 Determine the appropriate model material to use for the design process by testing the characteristics of different papers and foils against the bending properties of leaf tissue for known related species. Begin with a living leaf (still attached to a twig, in water to prevent wilting) secured in jeweler’s vice or similar device.

2 Weight the leaf with a known quantity (I used a piece of a kneaded eraser, just enough to bend the leaf to approximately 45º).

3 Trace the leaf and cut templates from a variety of papers and foils.

4 Weight these model leaves with the same piece of kneaded eraser and watch for an angle that duplicates the living leaf to determine the correct paper to use for the model.

5 Score veins into this paper leaf with a BIC® fine point pen; a mouse pad makes a good scoring surface.

6 Place the model leaf in vice to test rigidity and find possible life angles.

This approach, which takes advantage of engineering principles to pose plant structures in accordance with the basic laws of physics, allows the paleo artist to reconstruct fossil plants that lack living analogs in a reasonably reliable way. It removes much of the guesswork, increases satisfaction for both artist and scientist, and in the end saves a great deal of time.

BIOGRAPHY

A third generation professional artist, Marlene Hill Donnelly is Scientific Illustrator in the Department of Geology at the Field Museum in Chicago. She holds degrees in zoology and art, has received many awards for her work, and is co-author with Peggy Macnamara of Painting Wildlife in Watercolor (Watson-Guptill). Her freelance clients include the major museums, publishers and organizations, and many zoos and aquariums. Marlene has taught botanical and natural science illustration at the Art Institute of Chicago, Field Museum, Morton Arboretum, Chicago Botanic Garden and at GNSI workshops.

FIGURES

Fig.1 - the first Czekanowskia model.
Constructed from my usual foil and wire, it is pure guesswork, based on scientists’ suggestions and on other reconstructions.

Fig. 2 - Final Czekanowskia model.
Through the use of solid engineering principles we can reasonably assume that the living plant at least could have looked like this.

Fig. 3 - Sphenobaiera fossil leaf (Field Museum).

Fig. 4 - Czekanowskia fossil leaf (Field Museum).
These long, deeply dissected leaves have no modern counterpart.

Fig. 5 - Casuarina sketch.
This unrelated but superficially similar plant hinted strongly that the first Czekanowskia reconstruction was a physical impossibility. Graphite on paper, 4 in. x 7 in.

Fig. 6 - Second Moment of area.
The second moment of area addresses the position of the cross section of a structure relative to horizontal (x) and vertical (y) neutral axes. The greater the distance from the neutral axes, the stronger the structure in that direction (therefore, the cross section on the left can support a higher load than the cross section shown at the top). This is an extreme simplification of a very complex structural engineering principle! The modern Ginkgo petiole (diagrammed on the right) is an efficient “support beam.” But there is no evidence that Czekanowskia or Sphenobaiera had similarly differentiated petioles. My problem was to determine how the mechanics of these extinct plants supported their leaves at a sufficiently reasonable angle to efficiently catch light.

Fig. 7 - Ginkgo leaf in a vise.
The living leaf is weighted so that it bends to a moderate angle; the specimen is fully hydrated to maintain its bending properties

Fig. 8 - leaves cut from different materials.
Seeking an appropriate modeling material, I cut ginkgo leaves (using a living leaf as a template) from an assortment of papers and foils.

Fig. 9 - Paper leaf in a vise, weighted identically
(see Fig. 5). Tests of different papers yielded one with a similar moment of elasticity to the living Ginkgo leaf, meaning that it bent to approximately the same angle with the same weight applied.

Fig. 10 - Czekanowskia leaf cut from the appropriate paper.
This unscored leaf flopped loosely.

Fig. 11 - Paper Czekanowskia leaf.
Scoring a single vein into paper gave it considerably more body, but it still could not stand anywhere near the vertical. This is Second Moment in action!

Fig. 12 - Sphenobaiera copper model.
It was in scoring the veins into this early model that I noticed that the leaves became more rigid with every score. My enquiry into engineering principles was launched!

Fig. 13 - Sphenobaiera paper leaf in a vise, scored.
The larger leaf, scored into a strong shape, is an example of Second Moment in action.

Fig. 14 - Second Moment of area, part 2.
Once again these are cross sections of structures. An increase in length “L” increases the strength of the structure to the fourth power for the load in the z axis (which is perpendicular to the x and y axes, but not shown in the diagram). Our Sphenobaiera pseudopetioles (diagrammed on the right) were twice as wide those of Czekanowskia (diagrammed on the left), and so Sphenobaiera pseudopetioles were 16 times stronger than Czekanowskia pseudopetioles on the z axis.

Fig. 15 - Sphenobaiera illustration.
Transparent gouache on paper, 14 in. x 9 in. ©2008 Marlene Hill Donnelly.

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