Tail Musculature Reconstruction
Of the three musculature cross section reconstructions used here the 'slim' model (Figure 4.1,
Figure 5.1-5.3) is comparable to the classic bone-delimited models used, e.g., by
Carpenter et al. (2005) and
Arbour (2009), and the simple elliptical model of
Allen et al. (2009), with the bone sized 22% of the muscle cross section area. The 'medium' model has 14% bone surface area, and the 'croc' model has 7.5%, close to the value determined for Alligator (Figure 4.2-4.3). The latter model lies within the variations for soft tissue extents of the accurate models of Allen et al. (2009). Inspection of X-ray and CT scans of various reptiles confirmed that normally, the soft tissues in the tail of healthy individuals extend beyond the bone by at least 15-20%, more often 30 to 40%, measured in dorsal view, similar to the values in the 'medium' model. In crocodiles and alligators, the muscles can extend to 190% of the bone structure laterally, while the rate in the dorsoventral axis is usually close to 130%. These results diverge somewhat from those of
Allen et al. (2009), but may depend on individual variations of the specimens studied. The large amount of musculature on the tails of crocodiles may be connected to the fact that they use their tails for swimming.
In sum, the 'slim' model should be discounted as unrealistically conservative (see
Allen et al. 2009,
Persons 2009), possibly having only half the correct muscle cross sections. Calculations based on it suffer not only from unrealistically low muscle diameters and thus force estimates. Smaller muscles result in lower moment arms (see examples in
Figure 4.1-4.3, 4.5). Because torque is the product of force and moment arm, torque estimates for the 'slim' models may be as low as 25% of the real value. The 'medium' model probably is the best conservative approximation, while a crocodile-like model may overestimate the muscle volume of Kentrosaurus. However, non-avian dinosaurs relied mainly on the m. caudofemoralis for locomotion (Gatesy 1990),
so a large m. caudofemoralis and an accordingly large axial musculature should be expected. Because thyreophorans very likely used their tails as the primary means of defense (e.g.,
Carpenter et al. 2005), it is possible that their musculature was similarly or even more developed then that of extant crocodylians.
Mass Estimates, COM Position, and Motions
Kentrosaurus shows the typical COM position of quadrupedal dinosaurs, with the greater part of the weight supported by the hindlimbs. The percentage of weight supported by the hindlimbs is high for a quadruped at 80% to 85%, comparable to many basal and some derived sauropodomorphs (Henderson 2006;
Mallison 2010b). For Stegosaurus a similar COM position was found by
Henderson (1999), and the generally similar body proportions of other stegosaurs indicate that this pattern is true for the entire group. Due to the short moment arm from the COM to the hips, lateral acceleration of the entire body was probably easily effected, allowing rapid pivoting around the hind foot with relatively little exertion.
The large moment arm between the forelimb and the COM, combined with the high flexibility of the tail, lead to modest lateral accelerations of the anterior body in all CAE models. A stiff tail would induce a large amount of rotational inertia to the trunk if halted suddenly, but the tail of Kentrosaurusas modeled here moves laterally only at its base. Continuous flexion along the tail means that the distal half is moving mostly anteriorly in relation to the animal's trunk just before reaching extreme deflection, so that the resulting transferred moment can easily be taken up in the forelimb. In none of the simulation runs it is necessary to broaden the stance in the forelimbs to increase the moment arm by choosing a sprawling posture to achieve stability. However, impacts of the tail on a very large (>200 kg) and thus inert target at high speeds tend to create large lateral accelerations, in some simulation runs achieving 7g laterally, which is sufficient to topple or laterally shift the model unless correcting motions were taken in the forelimbs or hindlimbs. These events require extreme forces in the shoulder and elbow. Under such circumstances a sprawling forelimb position would have been a significant aid in stabilizing the posture, explaining why the maximal forces in the shoulder and elbow were possibly not caused by locomotion. More detailed modeling of such impacts and target-missing tail swings will be needed to clarify the exact forces and accelerations involved.
For the discussion of tail swings, the combination of the under-muscled 'slim' model and the lowest specific tension value, 20 N/cm2 (Figure 6.1), will be ignored, because it suffers
from a multiplication of errors, not only addition (i.e., if half the correct
moment arm is multiplied by half the correct force, the resulting torque will be
only 25% of the true value), that make the final results unrealistic. The unrealistically low muscle cross section results in too low a calculated force, which is then multiplied with the moment arm that is also too low because of the anorexic reconstruction. Although a specific tension of 20 N/cm2 is a realistic value, it is at the lower end of the range reported for muscles of larger animals, and thus cannot ameliorate the effect of the double error introduced by the 'slim' musculature reconstruction. Similarly, models using specific tension values greater than 50 N/cm2 are discounted here as well (Figure 6.4,
Figure 8.4), because recent experimental studies consistently find values below 60 N/cm2. Although it is certainly possible that values between 50 N/cm2 and 60 N/cm2 as found by
O'Brien et al. (2010) or values below 20 N/cm2 (e.g.,
Maganaris et al. 2001) are also correct, using the 20–50 N/cm2 range eliminates the highest and lowest extremes of the reliable values. The combinations of the 'medium' and the 'croc' model with a specific tension value of 20 N/cm2 to 39 N/cm2 are considered to provide the range of best estimates here.
All other models reach top speeds of at least ~ 40 m/s, and the arc covered at over 10 m/s is greater than 75° (Figure 6.2-6.3,
Figure 8.1-8.3). Using the lowest specific tension value of 20 N/cm2, the two realistic musculature reconstructions, the 'medium' and 'croc' models, arc greater than 90° at 10 m/s and nearly 40° above 20 m/s (Figure 7.1,
Figure 8.1). At this speed the spikes could penetrate deeply into soft tissues or between ribs and were able to shatter bones. Using 50 N/cm2, these models top 60 m/s, arcing over more than 80° at over 20 m/s (Figure 7.3,
Figure 8.3). Impacts at this speed, creating localized pressure over 5 kN/cm2, would have been sufficient to cause serious, likely fatal injury independent of the exact body part hit and the exact geometry of the impact, because the failure parameters of even relatively strong bones are exceeded (e.g.,
Ono et al. 1980).The best estimate models suggest top speeds between ~ 50 m/s and 55 m/s, and high speeds (> 20 m/s) across arcs greater than 60°.
Penetrating impacts at 10 m/s created forces greater than those sufficient to fracture a human skull (Ono et al. 1980), and thus were probably hard enough to pierce integuments and fracture bones close to the surface such as ribs or some facial bones, the latter even of large theropods. At 20 m/s the impact energy was probably sufficient to drive the spikes deeper, despite the increasing diameter. Because the tail tip spikes of Kentrosaurus are very slender, their diameter increases little with increasing penetration depth, so that deeper penetration requires little additional force. The cross section area of importance is therefore that directly behind the apical diameter increase. Due to the flattened shape, the cross section area here is roughly 9 cm2 in MB.R.3803 on both spikes (~ 10 cm2 including a thin keratin layer), while those of the longer spikes mounted on the exhibition mount in the MFN (MB.R.4842and 4843) are slightly larger, at 13 cm2 and 13.5 cm2, respectively. This means that the tail tip moving at 40 m/s, a value achieved as top speed by all realistic models and across a significant arc by the 'medium' model for a specific tension of 50 N/cm2 and the 'croc' model for 39 N/cm2, the spikes were able to crush bones equivalent to a human skull.
When striking the torso, however, the lance-like shape makes it likely that the spikes would slip on ribs and push through the intercostal musculature. Even below 20 m/s the models predict impact forces sufficient to cause deep penetration if only soft tissues are hit. Once the body wall of the trunk was perforated, the spikes could slip deeply into the lungs or intestines against little resistance, causing massive and probably lethal soft tissue damage. Strikes at the posterior end of the ribcage, where no sturdy girdle elements are in the way, and where ribs tend to be less stout in dinosaurs, would be especially effective. Probably even more dangerous were hits on the neck. Less deep, because of the slightly greater resistance of muscles, but still incapacitating injury probably occurred on the tail base (comparable to that of the Allosaurus caudal described by
Carpenter et al. ) and limbs.
As shown by Carpenter et al. (2005), penetrating strikes create a high risk that spikes become lodged in the target body and subjected to high bending moments. This possibility causes a high risk of fracture, even more so in the slimmer Kentrosaurus spikes than in the sturdier osteoderms of Stegosaurus.
If the tips of the spikes were drawn across a predator's body, the effect would depend on the exact angle. If there were sufficient pressure, the high speed and sharp tip would lead to gouging injuries, with the spike tip cutting into soft tissues and potentially fracturing thin, superficial bones. The keels on the spikes may indicate a keratin sheath that exaggerated the keels, making the outside shape more blade-like (H. Larsson, personal commun., 2010). However, the keels were proportionally small in tail spikes, and in the tail tip, spikes mostly are not ridges sticking out, but only sudden changes in curvature (Figure 3.2), so that this possibility remains speculative, and is ignored here.
Slashing hits are potentially lethal where large blood vessels run close to the surface of the body without being protected by thick bone, e.g., on the skull and neck. Sheet-like muscles such as the m. trapezius are at the risk of being totally severed, while thicker muscles can be harmed badly as well, so that loss of limb function is a realistic danger. Slashing impacts likely were rare, because the strike geometry requires that the target is at exactly the right distance to the stegosaur. A little further away and the tail misses, a little closer and the impact becomes a blunt strike. However, if such hits occurred, the calculated impact energies were certainly sufficient to cause dangerous wounds.
Given the angled attachment of the spikes on the tail, this type of impact is the most likely. Among this category, those strikes must also be counted in which the tip of the spike initially penetrates, but at a shallow angle, so that almost immediately a large area comes into contact with the target.
Blunt strikes distribute the energy of the impact on a larger force than penetrating strikes, reducing the peak pressure. The larger the area, the lower the pressure on any specific point. The effective contact surface of a stegosaur tail spike may have been as large as half the total lateral aspect, roughly 120 cm2 (Figure 1,
Figure 3). In a blunt strike, the spike would therefore not penetrate the integument. Instead, the spike would be brought to a halt in contact with the target's surface, transferring probably not only the kinetic energy of the tail tip, but that of the entire distal part of the tail. However, because the tail consists of not just one rigid block, but a system of links embedded in muscle, the deceleration would result in some internal motion. Combined with the absence of penetration this means that the contact time between spike and target would be relatively long, giving bones close to the surface time to break due to bending, not due to being crushed locally by a point impact.
In the interest of traffic safety, a number of studies have been performed in which impactors of various weights were used to cause blunt trauma in human cadavers at speeds typical for auto accidents, usually under 10 m/s.
Viano et al. (1989) used a circular 23.4 kg impactor with a 177 cm2 impacting surface at speeds of 4.5 m/s, 6.7 m/s and 9.4 m/s in lateral impacts, causing rib fractures and occasionally pubic ramus fractures.
Talantikite et al. (1998) used smaller impactors (12 kg and 16 kg) of the same size and a narrower speed range (6 m/s to 8.5 m/s). During 11 tests on human cadavers they recorded between three and eight broken ribs, with between three and 16 separate fractures (Talantikite et al. 1998, table 5). Both studies also recorded occasional liver ruptures (Viano et al. 1989;
Talantikite et al. 1998). Impacts of the 23.4 kg impactor at 9.4 m/s are roughly comparable to a 10 m/s blunt impact of a Kentrosaurustail tip spike, while those of the lighter impactors create lower forces on the thorax than a spike hit would. In summation, it is reasonable to assume that at least similar injuries occurred during tail impacts on targets with rib sizes similar to humans.
This means that even at modest speeds, the tail of Kentrosaurus could cripple small and medium-sized theropod no matter what angle the tail tip spikes impacted. Large predators with a thick integument probably suffered only minor injuries at low impact speeds. However, a doubling of the impact speed to 20 m/s means that the impact force is also doubled, while at 40 m/s the force is quadrupled, so that all tail strike models deemed realistic could cause multiple rib fractures even in large theropods. For example, the anterior dorsal ribs of the abelisaurid theropod Majungasaurus crenatissimus (Depéret, 1896)
Lavocat, 1955 measure less than 30 mm across the base of the shaft (O'Connor 2007) and are thus less than four times as strong as human ribs, which have an average greatest shaft thickness of roughly 12 mm (e.g.,
Abrams et al. 2003). Other structures of similar robustness could also be broken by blunt strikes, such as scapula blades or facial bones.
Aside from breaking bony structures, the impact of a club can cause other potentially lethal injuries, e.g., the rupture of internal organs or blood vessels, or severe muscle damage. Strikes to the skull can result in concussions or intracranial lesions.
Tail Swing Times
Despite the threat to attackers posed by the tail, Kentrosaurus was apparently not immune to attacks, especially by predators that were fleet of foot. Collision speeds are much lower near the base of the tail than at the tip, so that a quick dash just after the tail had passed could have allowed a predator to get close enough to the tail base to be safe from lethal or serious injury. A return of the tail on the reverse swing takes between 1 s and 4 s in the 'torque' models, depending on the applied torques, giving ample time for a well-timed sprint across the 3 m distance between the hips of Kentrosaurus and a safe spot just outside the tail's reach. Also, the tail covered only the posterior aspect, so that the anterior body and neck were unprotected (Mallison 2010a). Of this area, as much as 90° may have been covered at speeds sufficient to cause lethal injury ('croc' model, 50 N/cm2,
Figure 8.3). However, this means that three quarters of the stegosaur were exposed to attacks unless the animal reacted timely to a threat and rotated the entire body so that the 'danger zone' of possible high tail speeds faced the threat. Defensive action thus required a good overview of the immediate surroundings. The 360° circumferential visibility required a maximally extended and thus vulnerable neck, while lateral flexion of the neck resulted in a large dead area created by the body (Mallison 2010a). In any case, rapid pivoting of the entire body was required to bring the tail to bear, facilitated by the extremely posterior COM position.
An important point about the times for strikes calculated here is that the tail is already in a maximally lateroflexed position at the beginning, thus positioned for a full-power strike. Another advantage of this prepositioning is that it allows the muscles of the extended side that will have to perform the strike to be maximally stretched. The passive part of the muscles' force production curve can thus be used to generate a high torque and rapid acceleration quickly. Essentially, part of the force required to perform a rapid strike can be delivered by the muscles of the contralateral side of the tail and stored in the stretched muscles. Extant monitor lizards and crocodylians sometimes prepare for defensive action in this way. Komodo dragons (Varanus komodensis) occasionally even run away holding their tails off the ground and strongly lateroflexed and strike at pursuers when they come into range (pers. obs.). The time to preposition the tail must be added to the times calculated here if an attempt is made to judge the time interval between two swipes of the tail, i.e., the time window available to a predator to get close.
Comparison to Previous Works
A comparison of the results presented here to those of
Carpenter et al. (2005) and
Arbour (2009) is difficult. The torque values calculated here are significantly higher than those found by
Carpenter et al. (2005) for Stegosaurus and
Arbour (2009) for ankylosaurs, due to the extremely low estimates of muscle cross sections in these studies. However, because
Carpenter et al. (2005) and
Arbour (2009) incorrectly used the half-width of the reconstructed tail, represented by the distance between the horizontal tail midline and tip of the transverse process, the assumed moment arms do not conform to the musculature reconstructions, and may in fact be close to the actual values (see
Figure 4 on moment arm position versus muscle size), so that the overall error in Carpenter et al.'s and Arbour's calculations is much smaller than that of the 'slim' model used here. Additionally,
Carpenter et al. (2005) miscalculated several values, resulting in a roughly 10-fold increase of the estimated pressure at impact in their Method 1 (Carpenter et al. 2005, p.336), and used an incorrect physical formula (Pressure is defined as Impulse per Area instead of Force per Area,
Carpenter et al. 2005, p. 340). Also, the motion range of the tail was estimated very low, with an average limit of below 2.5° per intervertebral joint (Carpenter et al. 2005, p. 340) between osteoderm plates and total rigidity assumed within segments (Carpenter et al. 2005, p.338, contra ibid, figure 17.6a). Illustrations of Stegosaurus caudals in
Gilmore (1914), and
Galton and Upchurch (2004) and personal inspection of mounted skeletons in the NMS and DMNS do not indicate a significantly reduced lateral mobility compared to Kentrosaurus.
Carpenter (1998, figure 5a) showed a hypothetical Stegosaurus tail without osteoderms at maximum flexion, in an overall curve generally similar to that found for Kentrosaurus at 5° by
Mallison (2010a). Larger amount of soft tissues than assumed by
Carpenter (1998) and
Carpenter et al. (2005) would allow more motion, and it is also not clear why mobility should be possible in only one single joint, and not a group of two or three joints at the overlap points of osteoderm plates. Biomechanically, such a system with no motion in most joints and significant motion in one single joint should lead to differing joint morphologies, which are not visible on any known skeleton.