More than a safety line: jump-stabilizing silk of salticids

Yung-Kang Chen, Chen-Pan Liao, Feng-Yueh Tsai, Kai-Jung Chi

Abstract

Salticids are diurnal hunters known for acute vision, remarkable predatory strategies and jumping ability. Like other jumpers, they strive for stability and smooth landings. Instead of using inertia from swinging appendages or aerodynamic forces by flapping wings as in other organisms, we show that salticids use a different mechanism for in-air stability by using dragline silk, which was previously believed to function solely as a safety line. Analyses from high-speed images of jumps by the salticid Hasarius adansoni demonstrate that despite being subject to rearward pitch at take-off, spiders with dragline silk can change body orientation in the air. Instantaneous drag and silk forces calculated from kinematic data further suggest a comparable contribution to deceleration and energy dissipation, and reveal that adjustments by the spider to the silk force can reverse its body pitch for a predictable and optimal landing. Without silk, upright-landing spiders would slip or even tumble, deferring completion of landing. Thus, for salticids, dragline silk is critical for dynamic stability and prey-capture efficiency. The dynamic functioning of dragline silk revealed in this study can advance the understanding of silk's physiological control over material properties and its significance to spider ecology and evolution, and also provide inspiration for future manoeuvrable robot designs.

1. Introduction

Many animals jump as a means of locomotion and to overcome obstacles or gaps, escape from danger, mount hosts or prey and launch into flight [1]. Jumping has been of biomechanical interest for many decades, particularly concerning energetics and take-off. Various mechanisms have evolved in jumpers to obtain sufficient kinetic energy for take-off or further destinations, including longer limbs with larger muscles, elastic energy storage and catapult mechanisms for rapid power output [26]. However, jumpers also face challenges to maintain in-air stability and smooth landing, because falling may lead to injury or extra energy costs in returning to the canopy. Besides adjusting the centre of mass (CoM) close to the vector of propulsive thrust at take-off to avoid later body rotation [7,8], some jumpers actively use dynamic control for in-air stability. Two mechanisms have previously been proposed to counteract unwanted torque in the air: using the inertia of swinging appendages [912] and aerodynamic forces from flapping wings [6,7]. Take-off mechanisms and stability control that evolved in nature have led to significant progress in bioinspired designs for manoeuvrable jumping robots [11,13].

Jumping spiders, members of the family Salticidae, are diurnal hunters known for their acute vision, remarkable predatory strategies and jumping ability [1417]. They jump for prey capture, escape and rapid point-to-point movement. Before take-off, they attach dragline silk to the substrate, presumably as a safety line as proposed for orb-weaving spiders [14,18,19]. Unlike other arthropods, spiders have no extensor muscle in their major leg joints and use rapid increase of hydraulic pressure in the hind legs to launch a jump [14,20]. Parry & Brown reported an occasion of somersaulting after a salticid's dragline silk was broken [21], implying silk's functioning towards motion control [22].

Dragline silk is widely used in spiders for various mechanical functions. Besides being a safety line (or lifeline) for unexpected falling and as a guide to return to the starting position [14,18,23], it is also used by spiders for locomotion (ballooning) [24], braking while jumping through air or fishing on water surfaces [21,22,25] and as a framework for web construction [14,19]. Ranked among the toughest materials known [26,27], spider silk has drawn substantial attention to the molecular basis for its remarkable properties and ultimately for its potential applications [2830]. The dragline's outstanding tensile strength and toughness are important in its role as a safety line [19], whereas its unusual torsional properties may prevent an abseiling spider from swinging or rotating, a movement that might attract predators [31]. To serve as a useful safety line, new silk has to be produced during the spider's fall to prevent it from breaking [32]. Although rapid spinning might stiffen the silk and hence provide a greater resistant force, the falling spider most likely stops itself by using an internal friction brake [33], presumably the ‘valve’ of the spider's spinning system [34], that clamps onto the passing silk.

Most studies on spider (and even insect) jumping have focused on take-off mechanisms or overall jumping performance, but few have discussed body rotation and stability after take-off. Among jumpers, salticids are unique because they attach dragline silk to the substrate before take-off. Although dragline silk has been observed in braking and motion control during spider jumping [21,22], the dynamic functioning of dragline silk in spider locomotion remains less examined [32,33]. A thorough understanding of the natural uses of silk not only allows us to explore its significance in salticid biology but also provides biological inspiration for future manoeuvrable robot designs.

To examine the functioning mechanisms of dragline silk as an in-air stabilizer for spider jumping, we (i) analysed the motion of normal and non-silk salticids throughout jumps that were recorded using high-speed videography, (ii) estimated instantaneous silk force from kinematic data, (iii) associated body motion with the magnitude and direction of silk force, and (iv) summarized these findings in the context of silk's material properties and physiological control for silk production.

2. Material and methods

2.1. Animals

We used 27 completely intact samples of Adanson's House Jumper (Hasarius adansoni) collected near Taichung City to study the role of silk during spider jumping. Spiders were kept individually in captivity at room temperature (21–24°C), supplied with water and fed with three or four fruitflies two or three times a week. Each subject underwent four experimental sessions during eight weeks of captivity. The first session commenced after a week of acclimation in the laboratory, with intervals between sessions being longer than a week. Among the subjects collected, five did not attach dragline silk at the take-off stage during the initial experimental session and remained non-silk throughout the whole experimental period, whereas the other 22 subjects consistently left dragline silk attached to the take-off stage during all experiments and to substrates during daily activity. Owing to the small size of these spiders, we were not successful in blocking the silk glands with wax to create experimentally manipulated non-silk spiders. Instead, we used the natural non-silk spiders as controls. There were no other observed differences in feeding or activity between the two groups. During the experiments, all subjects, normal and non-silk, were able to climb onto an elevated platform of height of 18 cm and jump onto a lower stage 7.5 cm away (figure 1a). The body mass (BM) of each subject was measured using a laboratory scale immediately after the experiments. Body length (BL) was measured from images as the sum of cephalothorax and the abdominal lengths. The cephalothorax is typically used as a measure for BL because abdomen size can change considerably with physiological condition. But here, we report total length here as it affects the amount of drag as well as the silk's moment exerted on the body.

Figure 1.

Schematic of the experimental set-up and mechanical analyses. (a) Take-off and landing platforms. (b) Body orientation depicted by the cephalothorax (θC), abdomen (θA) and body angles (θA−C = θAθC). The angle bisector (θB) represents the mean body direction. (c) Free-body diagram of a salticid jumping at velocity (v) and subjected to drag (FD) and silk forces (FS), with directions θv, θD and θS, respectively. Drag acts in the opposite direction of velocity. The angle between the silk and the abdomen is θS−A. The area used for calculating drag is that which is projected onto a plane normal to the instantaneous velocity vector. Legs (not shown) have a surface area similar to that of the body.

Although no differences were found in feeding and behaviour between the two groups, to assure that the non-silk condition did not affect jumping performance we compared body size and jumping ability of 15 normal and four non-silk subjects whose jumps were recorded successfully for kinematic analyses. Normal spiders had BMs of 19.95 ± 4.71 mg and BLs of 6.1 ± 0.3 mm (n = 15), and the non-silk spiders had BMs of 21.14 ± 2.83 mg and BLs of 6.0 ± 0.2 mm (n = 4; table 1). To compare body condition between silk and non-silk subjects, we conducted a one-way multivariate analysis of variance (MANOVA). Results suggest that the body size (BM, BL) was not significantly different between the two groups (ΛWilks = 0.94865, F2,16 = 0.4330, p = 0.6559; electronic supplementary material, figure S1). Jumping ability was assessed using take-off velocity (vi; table 1) because it mechanically determines the distance of a jump. We examined whether the two groups had similar vi values by fitting with a general linear mixed model (GLMM) where silk condition was set as a fixed factor (value of 1 for silk, 0 for non-silk), an individual was treated as a random factor nested within the silk condition, and BM and BL were assigned as covariates. Results suggest no significant difference in vi between the two groups (T17 = 0.9844, p = 0.3387; electronic supplementary material, table S1). Because no observed differences in feeding, behaviour and physical condition were found between the two groups, the four abnormal non-silk producing subjects were otherwise considered normal and healthy for the purposes of this study.

View this table:
Table 1.

Body size, jumping kinematics and mechanical energy during salticid jumping (mean ± s.d.). BM, body mass; BL, body length; θi, direction of take-off velocity; vi, vf: velocity at take-off and landing, respectively; D, distance travelled; Tair, Tland: duration of the aerial phase and landing phase, respectively; Δv, change of velocity between take-off and landing. Subscripts X and Z denote horizontal and vertical directions, respectively. Ei, mechanical energy at take-off; ΔE, change of mechanical energy between take-off and landing. Mechanical energy (E) was calculated as the sum of the kinetic energy and potential energy, and the latter was set to zero for take-off.

2.2. Kinematics of spider jumping

In nature, salticids might jump to destinations of different heights and distances up to 25 times their own BL [14,22]. Here, we considered only subhorizontal jumps to a lower destination to simplify analyses. We designed and constructed a jumping platform with a narrow take-off stage (approx. 3 × 5 cm) at a height of 18 cm (figure 1a). Each subject was released at the stage bottom to climb up the slope to the take-off stage and jumped onto a destination within the salticids' 10 cm field of view [14]. Because the destination stage was the only obvious target within the covered aquarium, in most cases, the subjects jumped onto it without stimulation; otherwise, the subject's escape reaction was provoked by short blasts of air. During each experimental session, the subject was made to jump three times. The whole jumping process of each subject was filmed with a high-speed video camera (MotionPro X3, Integrated Design Tools, IDT) at 1000 frames per second (fps) using image acquisition software from Motion Studio (IDT). Graph paper was used for scale to calibrate jump lengths. High-speed images of spider jumping were analysed using motion analysis software TEMA v. 2.6 (Image Systems). The position of the tip of the cephalothorax (head), the cephalothorax–abdomen joint or pedicel (middle) and the end of the abdomen (tail) were tracked for each subject (figure 1b).

The trajectory of the spider's middle, assumed to be its CoM, throughout a jump was smoothed by a cubic polynomial using Origin v. 8.5 (OriginLab Corporation) to reduce tracking error. Velocity v(t) and acceleration a(t) were then calculated as the first and second derivatives, respectively, of the position function. The body orientation of each spider was analysed as follows: the directions of the cephalothorax and abdomen were their angles relative to the horizontal plane (θC and θA, respectively), and the cephalothorax–abdomen angle bisector (θB) was used to represent overall body direction. Hence, head orientation can be quantified as θC and body posture as the cephalothorax–abdomen angle (θA−C = θAθC; figure 1b). Before take-off, the spider attached a dragline silk to the substrate, and the location of the attachment point could be identified from the high-speed image at the moment when the subject contacted its tail to the ground. Silk production and attachment were confirmed by checking the substrate after each jumping trial. The silk stayed straight throughout a jump (as seen in some frames of electronic supplementary material, movie S1), and therefore we could calculate the silk angle (θS) and the silk–abdomen angle (θS−A) from known silk–attachment positions to obtain the association between silk and spider (figure 1c).

2.3. Kinetics of spider jumping

During jumping, the spider's acceleration (a) is determined by the net force it experienced, which is composed of gravity (mg), drag from the air (FD) and silk force (FS)Embedded Image 2.1where m is the spider's mass and g is gravitational acceleration. Therefore, the instantaneous FS can be calculated with known a(t), mg and FD. Given an air density (ρ) of 1 kg m−3 and viscosity (μ) of 18 × 10−6 Pa s, a spider with length l = 0.6 cm jumping at velocity v = 0.6–1 m s−1 would have a Reynolds number (Re = ρlv/μ) of 200–400. For this range of Re, pressure drag (FD) can be estimated as followsEmbedded Image 2.2where Cd is the drag coefficient, A is the projection area facing the direction of the spider's motion and v is the instantaneous velocity of the spider's CoM calculated as the first derivative of the fitted position function. The direction of drag is opposite to that of CoM's velocity (figure 1c).

The Cd of a sphere based on the frontal area is 0.5; but for Re < 1000, Cd is calculated as follows [35]Embedded Image 2.3Hence for Re ∼ 200–400, Cd for a sphere should be 0.75–0.92.

Because non-silk salticids were subjected only to gravity and drag during jumping, we could determine the most appropriate Cd by comparing their velocity change in the horizontal direction (ΔvX(t)) to what is predicted using Cd = 0.5–2.0. This range covered Cd equal to 1, which has previously been used for some jumping insects [36]. The Cd leading to the best prediction was then used to calculate the drag experienced by normal spiders. Reference area A is empirically defined as the frontal projection area (FPA) of the spider in the moving direction, and was calculated as the area projected onto the plane normal to the instantaneous velocity vector (figure 1c). Because body postures changed throughout the aerial phase, we treated each body segment (cephalothorax and abdomen) separately, approximated its projection as an ellipse and calculated FPA using segment length, width and angle relative to the projection plane (figure 1c). The projected area of the body's transverse plane was also included. The maximum FPA of eight legs (measured from top view) was comparable with that of the body. We assumed that the legs and body had a similar projected area because they usually had a similar orientation during jumping.

2.4. Estimating drag and silk force

We treated horizontal (x-direction) and vertical (z-direction) motions separately in our analysis. To demonstrate the relative contribution of dragline silk on spider motion, we first compared the kinematic variable (velocity change in x-direction, ΔvX) between empirical data from normal spiders to predictions for the non-silk conditionEmbedded Image 2.4where vX0 is the initial velocity. Forces acting on the subject, as described in equation (2.1), can be decomposed into x- and z-directionsEmbedded Image 2.5where aX(t) and aZ(t) are the instantaneous accelerations in the x- and z-directions, calculated as the second derivative of the corresponding position function fitting the original data. Drag and silk forces in the x- and z-directions can be calculated asEmbedded Image 2.6where drag, silk forces and directions are shown in figure 1c. Therefore, the prediction of ΔvX(t) for the non-silk condition can be made (equation (2.4)) using acceleration calculated from equations (2.5) and (2.6) with FSX = 0Embedded Image 2.7where the drag force FD can be calculated using equation (2.2) and Cd determined as described in section 2.3.

Finally, the instantaneous silk force FSX can be calculated using equation (2.5) with known mass, empirically obtained acceleration aX(t) and calculated drag FDX. FS was further calculated with known silk direction (equation (2.6) and figure 1c).

2.5. Statistical analyses

The mean and standard deviation of jumping kinematics, body orientation and mechanical energy were calculated to assess the jumping performances of normal and non-silk subjects (for variables, see tables 1 and 2). Besides comparing body size and take-off velocity (see §2.1), we also performed statistical analyses to compare the aforementioned variables between the two groups. We used SAS/STAT software, v. 9.3 of the SAS System for Windows [37] and R [38] with package ‘nlme’ [39], and set p < 0.05 as the criterion for significance.

View this table:
Table 2.

Body orientation and its change at different stages of salticid jumping (mean ± s.d.). Statistical results for comparisons between the two groups are presented in table 3 and electronic supplementary material, table S3. θC, θA−C denote cephalothorax and body angles representing the body orientation as shown in figure 1b. ΔθC, ΔθA−C denote change of cephalothorax and body angles.

To examine whether silk has effects on the aerial phase of jumping, we conducted separate comparisons for translational and rotational variables using two-way nested multivariate analysis of covariance (MANCOVA), with silk condition (value is 1 for silk, 0 is for non-silk) as a fixed factor and individual (nested within silk condition) as a random factor. We used transformed dependent variables if the distribution of residuals of a MANOVA/MANCOVA/GLMM was significantly non-normal. In the MANCOVA test for the translational variables of flight duration (Tair) and velocity changes (ΔvX, horizontal; ΔvZ, vertical), we considered the following covariates: body size (BM, BL), initial velocity (vi), jumping distance in two directions (DX, DZ), take-off angle (θi) and modifications of these variables (see electronic supplementary material, table S2). In the MANCOVA test for the rotational variables of body orientation at landing (landing θC and landing θA−C), we considered two extra rotational covariates (take-off θC and take-off θA−C; electronic supplementary material, table S3). If the overall effect of silk is significant in the MANCOVA test, then we fitted the dependent variable to a GLMM and selected the best model by stepwise selection with Akaike information criterion (AIC).

Finally, we examined silk's effect on landing duration (Tland) using a GLMM, also setting silk condition as a fixed factor and individual as a random factor. Covariates for this model included the body size (BM, BL), landing velocity (vf), jumping distance (DX, DZ) and body orientation at landing (landing θC and landing θA−C; figure 2a and electronic supplementary material, movie S4). We selected the best model by stepwise selection with AIC.

Figure 2.

Body orientation during spider jumping. (a,b) Change of body orientation, θA, θB and θC as shown in figure 1c, in a normal and a non-silk spider during the take-off (T), aerial (A) and landing (L) phases. Animation of these two events is shown in electronic supplementary material, movies S4 and S5. (c) Relationship between spider's body angles (θA−C) and head orientation (θC) at take-off (filled circles, open circles) and landing (filled triangles, open triangles; solid symbols denote 44 trials from 15 normal subjects, and open symbols denote 13 trials from four non-silk subjects). (Online version in colour.)

3. Results and discussion

3.1. Silk's effects on jumping kinematics and body orientation

To discern dragline silk's functional significance as a safety line and in-air stabilizer, we first analysed the kinematics of 57 jumps from 19 female jumping spiders (H. adansoni), among which four subjects stopped producing silk before experiments. Table 1 summarizes the results of jumping performance, velocity changes and mechanical energy dissipation. Table 2 summarizes head orientation and body angles at take-off and landing, as well as changes that occurred during aerial and landing phases. Because no measurable difference was found between normal and non-silk spiders in body size, take-off velocity and mechanical energy (§2.1; table 1 and electronic supplementary material, table S1 and figure S1), observed differences in jumping mechanics could be attributed to the existence of dragline silk. Table 1 suggests that despite similar jumping performance (distance DX and height DZ), normal spiders stayed in the air longer (Tair) and decelerated more horizontally (ΔvX) than those without silk. Equipped with dragline silk as a safety line, normal spiders lost significantly greater mechanical energy, accounting for 76% of the original mechanical energy, which is significantly greater than the 33% that was lost by non-silks (table 1).

We examined the extent that silk affects spider jumping during aerial and landing phases by conducting separate comparisons of two-way nested MANCOVA using various sets of covariates. Results suggest a significant overall effect of silk on various translational (Tair, ΔvX and ΔvZ; ΛWilks = 0.4927, F3,15 = 5.15, p = 0.0120) and rotational variables (landing θC and landing θA−C; ΛWilks = 0.3533, F2,16 = 14.64, p = 0.0002) for the aerial phase of jumping. We further constructed GLMMs to discern silk's contribution to them (Tair, ΔVX and ΔVZ in electronic supplementary material, table S2; landing θC and landing θA−C in electronic supplementary material, table S3). For the landing phase, the model suggested a significant effect of silk on landing duration (Tland) (T15 = −2.3367, p = 0.0337; electronic supplementary material, table S4). Table 3 summarizes the coefficients of silk condition for each kinematic-dependent variable in its corresponding GLMM and the differences in empirical data of the two groups (tables 1 and 2). Because the value for silk condition was set to be 1 for silk and 0 for non-silk, each coefficient represents a suggested difference that silk made for that dependent variable by the model, which took the effects of covariates into account.

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Table 3.

Coefficients of silk conditions for various kinematic variables fitted by a general linear mixed model (GLMM) after AIC model selection. Silk (yes, 1; no, 0) was considered a fixed factor and individual (nested within silk condition) as a random factor. Each set of model used different combinations of covariates. The differences in empirical data of the two groups are also presented for comparison.

Our study reveals that a jumping spider with dragline silk has a more dynamically stable body posture and smoother landing (see electronic supplementary material, movies S1–S3). After take-off, increasing body angles in spiders of either group imply initial rearward torque (figure 2a,b), consistent with other salticids reported previously [21,22]. By contrast, wandering spiders pitch forward, probably because of the different relative position of CoM and leg extension mechanisms [40,41]. To counteract this initial pitch moment and prevent in-air rotation, previous studies suggest that spiders could adjust leg movement or use silk to reverse body orientation towards the ends of long jumps [21,22,40]. But here we show that normal salticids underwent multiple pitch reversals (see electronic supplementary material, figure S2a and movie S4) to land at shallower body angles (figures 2c and 3 and table 2). The GLMM suggests that non-silk spiders would land with a head angle (θC) 40.97 ± 7.08° greater than normal ones (table 3 and electronic supplementary material, table S3). Among 44 jumps from 15 normal subjects throughout the aerial phase (Tair = 116 ± 13 ms), six jumps underwent three pitch reversals, 23 jumps had two reversals, 13 jumps had one reversal and two jumps had none. For jumps with two or more pitch reversals, the first occurred at 32 ± 8 ms after take-off (approx. 31 ± 11% Tair) and the second at 85 ± 21 ms after take-off (approx. 72 ± 14% Tair).

Figure 3.

Landing motions of normal and non-silk jumping spiders, recorded using a high-speed video camera (a,b filmed at 1000 fps; c filmed at 600 fps). (a) The spider with silk kept a stable body orientation and leg–ground contact throughout the landing phase (with duration Tland). (b,c) Non-silk spiders landing upright hit the ground with their abdomens shortly after the leg contact (shorter TL−A), and underwent faster forward rotation. They can even slip and tumble due to unfavourable initial leg–ground contact (as shown in (c), three out of 13 events), which defers the completion of landing (longer Tland). The arrow and circle in (a,b) indicate the tip of the abdomen and the leg, respectively, at the beginning and the end of the landing phase.

By contrast, non-silk spiders underwent greater rearward pitch (in-air ΔθC) and landed more upright with greater variation in orientation (landing θC), implying less predictable body postures (figures 2b,c and 3; tables 2 and 3; electronic supplementary material, table S3 and movie S5). Consequently, they required greater forward pitch to complete a landing (ΔθC during landing) and might even slip or tumble due to inappropriate foot–ground contact (figure 3b,c). Compared with normal spiders, the bodies of non-silks hit the ground much earlier and hence were subject to greater impact forces. Although the spider is less likely to be injured by impact owing to tumbling [42], a non-silk spider landing unstably needs more time to complete a landing (Tland) than a normal spider (51 ± 29 versus 10 ± 2 ms) before proceeding to capture prey (figure 3 and table 1). The GLMM suggests that the decrease of Tland due to silk alone was 13.11 ± 5.61 (table 3 and electronic supplementary material, table S4). The other factor with significant effect on Tland was θC at landing (see electronic supplementary material, table S4). With a coefficient of approximately 0.3, a difference in landing θC between the two groups (approx. 50° in table 2) would lead to Tland being approximately 15 ms longer in non-silk subjects. These results suggest that dragline silk can function as a body stabilizer to prepare salticids for a predictable, optimal landing posture, and hence is critical for these agile and efficient hunters.

3.2. Relative contribution of drag and silk force

During jumping, the spider experiences mg, FD and FS (equation (2.1). We discerned the relative contribution of dragline silk on spider motion by comparing empirical kinematic data to what was predicted for the non-silk condition. Hence, the deviation of empirical data from predicted values shows the effect of silk force. We treated horizontal (x-direction) and vertical (z-direction) motions separately in our analyses. In the x-direction, acceleration aX(t) was −0.7 ± 0.6 m s−2 for non-silk (n = 4) and −3.2 ± 0.7 m s−2 for normal spiders (n = 15). In the z-direction, aZ(t) was −9.3 ± 0.5 m s−2 for non-silk and −8.5 ± 0.3 m s−2 for normal spiders, suggesting that drag alone contributed a force of approximately 5% of body weight (BW), whereas silk contributed an additional force of approximately 8% BW. Therefore, the vertical motion of spiders was predominantly determined by gravity, and the effect of drag or silk was negligible in the analyses.

In contrast to previous notions interpreted from jumping trajectories [22], our results suggest that drag cannot be neglected especially in determining horizontal motion. Even without silk, velocity change deviated from the ideal condition of no drag (figure 4a), and approximately 33 ± 11% of a spider's initial mechanical energy was dissipated (table 1). To estimate Cd, we compared the empirical results of ΔvX of non-silk spiders (−0.08 ± 0.05 m s−1; n = 4; table 1) with those predicted using Cd = 0.5– 2.0 (figure 4a). Empirical data from non-silk spiders suggest that ΔvX is best estimated using Cd ∼ 1.5 (ΔvX = −0.08 ± 0.03 m s−1), which is greater than suggested for a sphere at a similar range of Re (Cd = 0.75–0.92 calculated using equation (2.3), for Re = 200–400). Hence, assuming that jumping spiders (or insects of similar size) are spherical in shape will underestimate the drag experienced. Figure 4a suggests that a different Cd yielded the best prediction of ΔvX at each moment, presumably owing to varying body shapes throughout a jump.

Figure 4.

Velocity change and external forces throughout a spider's jump. (a,b) Velocity change in the x-direction is based on empirical data (red lines) and predictions using drag coefficients Cd = 0.5–2.0 in normal and non-silk spiders. Without drag, the horizontal velocity would not change (i.e. ΔvX = 0), as indicated by the horizontal lines. For non-silk subjects, on average, a prediction for total ΔvX calculated using Cd ∼ 1.5 yields the best fit to the empirical data (n = 4; the best fit in this case occurred at Cd ∼ 1.125). In normal spiders, deviation of empirical data from predicted values suggests the effect of silk force. (c) The relative contribution of drag and silk to the total force exerted on a normal subject throughout a jump (same subject as in (b)).

Using the same criteria to calculate drag for normal spiders allowed us to demonstrate silk's relative effects on spider motion, as indicated by the deviation of empirical data from predictions (figure 4b). To quantify the instantaneous FS, we first considered the horizontal direction (equation (2.5)) to estimate the x-component of silk force (FSX) from acceleration aX(t) and FDX. The latter was calculated from FD and its direction (equation (2.6) and figure 1c). FD for each event was calculated using Cd = 1.5, the FPA facing the direction of the spider's motion and the instantaneous velocity of the subject's CoM (equation (2.2)). Finally, we used the known silk direction θS to calculate FS (equation (2.6) and figure 1c). Our results suggest that the mean FS is 50.4 ± 11.1 μN (26 ± 4% BW; n = 15) throughout the aerial phase.

The relative contribution of drag and silk forces exerted on a subject varied with time (figure 4c). Silk force was dominant and kept at approximately 80% of total resistant force during the first half of jumping; however, during the last quarter of jumping, silk's influence declined to approximately 20%, and resistance was dominated by drag. For the normal subject reported in figure 4b,c, 67% of the initial mechanical energy was dissipated by braking, in which drag and silk friction contributed comparably (32% and 35%, respectively).

3.3. In-air stability control with adjustable silk force

Temporal patterns of changes in body and silk angles (θA and θS−A) and resistant forces (FD and FS) reveal how dragline silk is used to adjust body orientation and stabilize jumping (figure 5). After take-off, the subject elevated its head with θA increasing from approximately 180° to 220° owing to the initial rearward pitch moment, but the silk–abdomen angle θS−A decreased to approximately 140° until the first pitch reversal (forward rotation) occurred about 10 ms later, as opposed to being towards the end of a jump as previously reported [22]. Analyses suggested that the maximum silk force FS ∼ 79.6 ± 15.8 μN (42 ± 11% BW; n = 15) occurred at take-off and remained almost constant until the abdomen angle θA returned to approximately 180° (approx. 70 ms after take-off in figure 5). During this time, FS acting on the tail provided a moment MS = FS . sin θS−A, maximum at 60.3 ± 28.4 nN m, to rotate the abdomen forward about the pivot (middle) of the body (figures 1c and 5). The abdomen continued to pitch forward below 180° but with less amplitude than before, whereas the slightly decreased FS began to provide a moment with the opposite direction to slow down forward pitch until the second reversal (approx. 107 ms in figure 5). Subsequently, the subject pitched rearward again to approach horizontal towards the end of the aerial phase, during which FS decreased drastically and provided little moment on the tail. During the stage of last reversal, drag FD instead increased to decelerate the subject (figure 4c). Such varying of silk force is presumably controlled by the valve of the spinning system [34].

Figure 5.

Body orientation, silk orientation, silk force and moment throughout a spider's jump. Abdomen angle (θA) and silk–abdomen angle (θS−A) fluctuated about 180° and were out of phase during the course of jumping. The direction of the abdomen and silk is shown on the high-speed images at take-off, pitch reversals (at approx. 32 ms and approx. 107 ms after take-off) and the end of the aerial phase.

Throughout the aerial phase, θA and θS−A fluctuated about 180° out of phase for multiple cycles (figure 5), revealing the first evidence that dragline silk provides a counteracting torque for dynamic pitch control during spider jumping. After take-off, a constant and greater silk force controls the first pitch reversal and diminishes fluctuations in later body rotations. Decreasing silk force, and hence moment, towards the end of the aerial phase could prevent the body from further rotation (pitch reversal). Consequently, silk that is almost aligned in parallel to the abdomen could be more effective in braking.

In a jumping spider, silk force could result from material extension or an internal brake [33]. The latter might be served by the valve of the spinning system clamping onto newly produced silk as proposed for orb-weaving spiders [32,34]. Silk force exerted on a descending orb-weaving spider ranges between 0.1 from silk spooling and 2.2 BW from a fully activated internal brake [33]. Although our estimated silk force of 10–80 μN (approx. 0.05–0.4 BW), presumably owing to varying activation of the internal brake, cannot fully stop a jumping spider, it effectively decreased its landing velocity and reversed its body rotation (figures 2, 4 and 5 and tables 2 and 3).

Under complete braking, dragline silk is held tightly and subjected to external forces from the spider's momentum change during jumping. The efficiency of such a safety line can be evaluated using safety factor (SF), which is a ratio of a material's loading capacity to the actual load experienced. From a reported strength (1.19 GPa) [32] and measured cross-sectional areas of dragline silk of two threads (514 ± 73.2 nm each in diameter measured from SEM images, n = 14; Chen & Chi, 2010, unpublished data), the maximum force that silk could sustain is about 490 μN. To stop our subjects having a mass of 20 ± 5 mg jumping at a mean acceleration of 9.18 ± 0.84 m s−2, the force exerted on the silk would be 180 ± 44 μN, about 0.9 ± 0.2 BW (n = 15). Therefore, the average SF of dragline silk during jumping is 2.7. At a force that is twice the mean, SF would decrease to about 1.4, similar to what was reported previously for dragline silks from orb-weaving spiders [32]. Despite the fact that reeling speed during jumping (up to 1000 mm s−1) is an order of magnitude greater than the maximum used in forced silking (0.1–100 mm s−1) or natural descending, the mean stress that we estimated on silk fibres during jumping (434 ± 105 MPa) is similar to the range of stress reported for forcibly silked fibres from Argiope trifasciata at various speeds [43,44]. During salticid jumping, both the mean silking force and silk diameter were about an order of magnitude smaller than what was measured during the forced silking from the orb-web spiders.

4. Conclusions

Dragline silks, renowned for their superb properties, provide multifaceted functions that shape spider ecology and evolution. Here, we demonstrate that the dragline silk of salticids not only works as a safety line for deceleration but also, more importantly, works as a body stabilizer throughout the jump. With acute vision, remarkable predatory strategies and jumping ability, dynamic stability further enhances prey-capture efficiency in hunters such as salticids. In addition to using the inertia of swinging appendages and aerodynamic forces from flapping wings, we propose herein a newly discovered third mechanism for in-air stability control found in nature. Dragline silk, in accordance with varying adjustable forces for pitch reversals, can stabilize the spider throughout a jump. Counteracting torque from adjustable silk tension provides biological inspiration for future manoeuvrable robot designs.

Funding statement

This study was supported by the National Science Council (NSC) of Taiwan to K.-J.C. (grant no. 96-2112-M-005-002-MY3). An early stage of this study was conducted when Y.-K.C. participated in the NSC High Scope Programme and the National Taiwan Science Education Centre (NTSEC) Young Scientists Development Programme.

Acknowledgements

We thank M.-C. Shih, M.-H. Wu, I.-M. Tso, E.-C. Yang, J.-R. Roan, H.-Y. Tzeng, H.-D. Huang and the Shih-Roan-Chi Joint Group for assistance and discussion, and the anonymous referees for helpful comments and suggestions.

  • Received June 26, 2013.
  • Accepted July 17, 2013.

References

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