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First published online August 22, 2008
Journal of Experimental Biology 211, 2832-2840 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.014191
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The scaling of safety factor in spider draglines

Christine Ortlepp and John M. Gosline*

Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver BC, Canada V6T 1Z4


Figure 1
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  		Fig. 1. Overview of bungee jumping spiders. (A) A spider bungee jumping with pre-made silk of length xo. The silk attachment point is marked with a red star. When the silk starts to take the load of the spider, xo below the attachment site, the silk is stretched {Delta}x before the spider comes to a stop. (B) Worst-case scenario in which the spider falls 2xo before silk is loaded.

 

Figure 2
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  		Fig. 2. The solid line shows the form of Eqn 5, which indicates the effect of breaking strain on the minimum static safety factor required for bungee jumping. The gray shaded area below the solid line represents strain–safety factor combinations that would fail during bungee jumping. For example, a strand of Kevlar would require a static safety factor of at least 58, while natural rubber would only need a static safety factor of approximately 3 to survive a bungee jump.

 

Figure 3
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  		Fig. 3. Sample data from several silk tests to failure from juvenile and adult spiders. Salticus scenicus are shown in blue and Araneus diadematus in black. Note the difference in shape of the stress–strain curves for the two species.

 

Figure 4
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  		Fig. 4. Breaking strain is normally distributed (P=0.47), with a mean (±s.e.m.) 0.249±0.009, for combined data from both A. diadematus and S. scenicus. There is no statistically significant trend with log-transformed spider mass (M). The least-squares regression best-fit for the combined data was {epsilon}max=0.237–0.008logM, r2=0.02, P=0.35.

 

Figure 5
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  		Fig. 5. Silk tensile strength ({sigma}max) plotted against spider mass (M). There is no statistically significant trend of tensile strength with log-transformed spider mass. The least-squares regression best-fit for the combined A. diadematus and S. scenicus data sets was {sigma}max=1.14x109+3.99x10–6logM, r2=0.0002, P=0.96.

 

Figure 6
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  		Fig. 6. Cross-sectional area (A) plotted against spider mass (M) with a least-squares regression applied to log–log transformed data from A. diadematus and S. scenicus. Area scales as A=5.86x10–9M0.739, r2=0.90 for A. diadematus, and A=1.38x10–9M0.77, r2=0.83 for S. scenicus.

 

Figure 7
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  		Fig. 7. Breaking force (Fmax) scales with mass, (M), as Fmax=11.2M0.786, r2=0.96, s.e.m. of the slope=0.027 for A. diadematus, and as Fmax=0.363M0.66, r2=0.87, s.e.m. of the slope=0.13 for S. scenicus (solid lines). The pre-web first-instar A. diadematus were excluded as outliers and fall well below the extended best-fit line (dotted line). The static safety factor (SBW) determined from the force-mass scaling relationship, is shown as broken lines, where the black line indicates data for A. diadematus (SBW=1.14M–0.214) and the blue line indicates data for S. scenicus (SBW=0.037M–0.340).

 

Figure 8
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  		Fig. 8. Static safety factor (SBW) plotted against spider mass for pre-web first-instar A. diadematus, adult A. diadematus, and S. scenicus. Adult A. diadematus have safety factors of 4–6 whereas small individuals can have safety factors as large as 30. Note that the first-instar spiders are well below the values predicted by the scaling relationship. Safety factors for S. scenicus approach 1 for adults.

 

Figure 9
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  		Fig. 9. Graph of static safety factor (SBW) against breaking strain as in Fig. 1 but scaled for the silk data. Curves for bungee jumping (solid line) and a worst case (broken line) were included to predict whether silk of a known SBW and strain at failure would support a spider successfully under these conditions. Silk with properties that place them in the gray area below the solid line would not survive a bungee jump, while only silk above both lines would survive a worst-case scenario.

 

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© The Company of Biologists Ltd 2008