Terminal Ballistics of Stone-Tipped Atlatl Darts and Arrows: Results From Exploratory Naturalistic Experiments

1.1 Theoretical Concepts in Dart and Arrow Terminal Ballistics

Weapons like the atlatl and dart (Figure 1), bow and arrow, or thrown spear (javelin) can be designed with different tasks and targets in mind, such as harpooning sea mammals, stunning small game with blunt tips, penetrating through body armor, and delivering a lethal dose of poison to the blood stream (Knecht, 1997). In this study, we are principally concerned with situations where these weapons are designed to incapacitate prey by creating a deadly, incised wound. Such penetration events are unavoidably complex affairs with many variables involved. Here, we attempt to summarize for the reader the key ballistic variables of penetration, which we use in this study, along with research questions we seek to answer.

Figure 1

A typical Basketmaker atlatl and dart from the North American Southwest; replica of the White Dog Cave (WDC) system photographed near its place of origin: Marsh Pass, AZ.

First, effective projectiles have sufficient kinetic energy (KE = 1/2 m × v ²) and momentum (P = m × v) to penetrate, but questions arise as to which of these variables better explains the penetration of projectiles and knives in soft tissues (Ankersen, Birkbeck, Thomson, & Vanezis, 1998; Hetherington, 1996; Tomka, 2013). Kinetic energy is a measure of the work a projectile can do to a target by damaging or penetrating it and thereby creating new surface areas within it (Anderson, LaCosse, & Pankow, 2016; Atkins, 2009, p. 12; Kneubuehl, 2011). However, greater P reduces the effect that forces (F = m × a) of resistance and drag have on how rapidly a projectile decelerates (a = ∆v/∆t). Tomka (2013) has compiled requirements for both minimum KE and P from modern bowhunting and applied them to stone-tipped darts and arrows (Tomka, 2013). We assess the explanatory power of these variables for penetration in Section 3.4.

Archaeologists have drawn from concepts in bullet terminal ballistics to understand javelins, darts, and arrows (Cotterell & Kamminga, 1990; Hughes, 1998), but these weapons travel at what ballisticians consider low velocities (<250 m/s), where simplified fluid models of bullet penetration lose relevance (Carlucci & Jacobson, 2018, pp. 377, 599). Unlike bullets, javelins, darts, and arrows use sharp tips and edges to efficiently fracture (pierce/cut) their targets, such as the ductile and often fibrous structures in biological tissues (Anderson, 2018; Atkins, 2009).

Important variables of armatures (attached cutting/piercing heads) for modeling their drag through fluids are the drag coefficient (a dimensionless shape factor) and the tip cross-sectional area (TCSA; Hughes, 1998; Kneubuehl, 2011). A closely related measure to TCSA, sectional density (SD = m/TCSA), has long been recognized as affecting bullet penetration (Atkins, 2009, p. 209; Kneubuehl, 2011, pp. 65, 94). However, the tip cross-sectional perimeter (TCSP), which is used to calculate the wound surface area (WSA = TCSP × wound length) of a bullet or arrow wound (Friis-Hansen, 1990; Kneubuehl, 2011), is found to better predict stone-tipped dart and arrow penetration depth in homogenous target simulants (ballistics gel, pottery clay, and target foam; Grady & Churchill, 2023; Pettigrew & Bamforth, 2023; Salem & Churchill, 2016; Sisk & Shea, 2009; Sitton, Story, Buchanan, & Eren, 2020). The surface area (SA) of an armature is also found to produce significant results in clay (Pettigrew & Bamforth, 2023; Sitton, Stenzel, Buchanan, Eren, & Story, 2022). However, these homogenous targets are not scalable to soft tissues; they tend to produce greater friction on larger surfaces and do not adequately capture the effects of sharper tips and edges, whereas sharper armatures with larger TCSA/P may perform significantly better than smaller, duller ones when penetrating leather and fresh pig carcasses (Karger, Sudhues, Kneubuehl, & Brinkmann, 1998; Pettigrew & Bamforth, 2023). This points toward potential problems using TCSA/P to predict stone-tipped dart and arrow penetration through carcasses. The following rhomboidal equations are used to calculate TCSA/P of stone armatures (Hughes, 1998; Sisk & Shea, 2009):

Forensic research on knife wounds for investigating crime scenes may be more applicable to questions of dart and arrow performance than bullet penetration. Force of penetration through skin, which is generally regarded as the most resistive soft tissue on a body, can serve as a relative measure of knife thrusting efficacy (Ankersen et al., 1998; Gilchrist et al., 2008). Forensics specialists find the sharpness and geometry of the very tip of a knife to be the most important predictor of stabbing force through skin, while trailing edge sharpness is important, to a lesser degree, for widening the cut and continuing penetration through subcutaneous tissues (Ankersen et al., 1998; Gilchrist et al., 2008; Knight, 1975; O’Callaghan et al., 1999). Additionally, soft biological tissues are ductile materials that deform under load, absorbing energy from impact, but given their specific strain-rate sensitivity they can stiffen more quickly during high velocity impacts, thereby reducing the energy spent during penetration by a knife or bullet (Anderson, 2018; Ankersen, Birkbeck, Thomson, & Vanezis, 1999; Atkins, 2009; Fenton, Horsfall, & Carr, 2020; Hetherington, 1996; Knight, 1975; Nayak et al., 2018). Therefore, sharpness and velocity are theoretically the most important predictors of cutting force through soft tissues.

Archaeologists have suggested ways to measure the piercing/cutting efficacy of knapped stone projectile points from macroscopic features, including frontal angle, tip thinness, and leading edge sharpness (Ahler & Geib, 2000; Friis-Hansen, 1990; Grady & Churchill, 2023). These features are challenging to measure on knapped stone points, which are variable in form and shape, but significant correlations are suggested to occur between blade ratio width:thickness (BladeW:T) and the lateral edge angle, as well as blade ratio length:thickness (BladeL:T) and tip thinness (Ahler & Geib, 2000, p. 805), and we may also suspect a correlation between blade ratio length:width (BladeL:W) and frontal angle. In these blade ratios, length is measured from the widest point along the cutting edge forward to the tip, while width and thickness represent maximum values. Importantly, however, sharpness can fail to correlate with macroscopic edge or tip angles and is primarily attributed to the microscopic radius of the edge (Atkins, 2009; Reilly, McCormack, & Taylor, 2004; Stemp, Awe, Prufer, & Helmke, 2016; Valletta, Smilansky, Goring-Morris, & Grosman, 2020). Aside from these metrics, rougher grained materials such as quartzite, or finer grained materials such as obsidian, have varying degrees of relative durability and sharpness (Loendorf et al., 2018).

In addition to armature efficacy, velocity, KE, and P, archaeologists recognize that penetration improves when armatures cut a large enough hole in skin to reduce drag on the armature’s haft and the trailing shaft (Friis-Hansen, 1990; Guthrie, 1983; Hughes, 1998). Friis-Hansen (1990) presents two measurements of this effect: the perimeter ratio (PR = TCSP:shaft circumference [SC]) and the area ratio (AR = TCSA:shaft cross-sectional area [SCSA]). When PR > 1, the armature cuts a sufficiently large hole for the haft and shaft to follow, but larger armatures can increase the cutting work performed, so the AR should be as small as possible to reduce resistance relative to the “strength” (and presumably KE and P) of the shaft (Friis-Hansen, 1990). These ratios must be balanced along with a large enough TCSP to achieve a sufficient wound surface area (WSA). This balancing act is the basis for the cutting index (CI = PR:AR; Friis-Hansen, 1990). Importantly, Friis-Hansen’s method seems to measure armature thickness at the haft (referenced herein as TCSP_h and TCSA_h) rather than on the armature itself. Hafting can significantly change armature geometry (of Folsom points, for instance) in ways that are not necessarily equivalent across armature types and may have a dramatic impact on their penetrating efficacy, suggesting that TCSA/P should reflect hafted geometry (Ahler & Geib, 2000). In the following analysis, we test the effectiveness of both TCSA/P and TCSA/P_h calculated from the above equations, as well as when these variables are more accurately measured from 3D models of hafted armatures (TCSA/P_hPV; Section 2.2).

Last, darts and arrows sometimes have a pronounced transition from main shaft to foreshaft. We present the shaft ratio (SR = foreshaft:main shaft diameter) as a measure of drag at these transitions. Additionally, in this study, the center of mass (CM) represents the balance point on the shaft measured as a percentage of the overall length of the shaft back from the tip. A greater distance between the tip of a dart or arrow and its CM means that the tip has more leverage to alter the trajectory of the shaft when highly resistive targets are encountered (namely, bone), inducing yaw and drag (Ashby, 2005).

2.1 Targets

The four experiments involved a ca. 100 kg hog in summer of 2015, two goats (hereafter Goat1 [38 kg] and Goat2 [40 kg]) in winter of 2019–2020, a 23-year-old ca. 450 kg female bison (Bison1) in summer of 2020, and a 2-year-old ca. 450 kg male bison (Bison2) in summer of 2022. Ranchers provided estimates of the weights of the bison and hog while goats were weighed by the rancher. All animals were raised for consumption and humanely killed by the ranchers immediately prior to the experiment. Following university guidelines, we consulted the IACUC committee at the University of Colorado Boulder, who informed us that this procedure did not require IACUC approval as the experimenters themselves did not handle live animals (Althea Lantron, email correspondence, 2019). The carcasses were butchered after the experiments, meat was salvaged for consumption, and the skeletons cleaned for analysis. While butchering Bison2, skin thickness was measured by the four experimenters using calipers at one location over the abdomen and two locations over the thorax. Because the compliancy of skin makes thickness measurement dependent on the force applied by the instrument (Fenton et al., 2020), the experimenters took measurements independently (blind), which were then averaged.

Carcasses are imperfect analogs for living bodies, yet are significantly more realistic for studying wound ballistics than homogenous flesh simulants (Bartlett & Bissell, 2006; Fenton et al., 2020; Humphrey & Kumaratilake, 2016; Nicholas & Welsch, 2004). This is particularly true for low velocity cutting projectiles, which as discussed above, behave very differently than bullets and lack a comparable research program to identify a viable flesh simulant as for firearms (e.g., Maiden, Fisk, Wachsberger, & Byard, 2015). Consequently, carcasses currently provide the best standard for testing darts and arrows, but not without challenges.

First, carcasses must be fresh. Skin cells may remain representative of skin in vivo if tested within 6 h of death (Fenton et al., 2020), and a prior experiment on samples of in vitro cadaveric skin did not begin to record differences in penetrating force until 110 h after death (Careless & Acland, 1982), although other physiological changes in underlying tissues and bodily fluids also occur that may affect penetration into a carcass. To our knowledge, the specific effects these changes have on the penetration of low-velocity cutting/piercing projectiles remains largely uncharacterized. However, another study that tested obsidian and bone-tipped projectiles in a controlled fashion against a reindeer carcass did not document noticeable changes in penetration over 3–4 h after death (Wood & Fitzhugh, 2018). Our experiments occurred within 4–6 h after death.

A second concern is how to support the carcass. The hog and Goat2 were lain on boards supported by sawhorses and secured in place by means of ropes around their legs (Pettigrew, 2015), but this method compresses the abdomen, which can increase tension of abdominal skin and reduce forces required to penetrate it (Knight, 1975). Goat1 was suspended between two poles by means of ropes tied around the neck and to a small metal rod placed through the skin immediately above the tail, but the suspension of the carcass caused it to jostle and swing upon impact, significantly affecting the penetration of slower and heavier projectiles. Both bison were laying on the ground on all fours, held upright with boards against the back (Figure 2). We suspect this presented a more realistic target, as many shots in the past occurred on sleeping animals (Cundy, 1989; Hill & Hawkes, 1983), or animals that had been injured by being driven over cliffs (Brink, 2008).

Figure 2

The general layout of a carcass experiment (Bison1). At least 4 participants are needed: to fill the roles of photographer, shooter and flight camera operator, recorder, and velocity camera operator. The latter assists the shooter with measuring penetration and placing shot markers. More hands speed up the process and ensure better results. Photograph by John Whittaker.

In the appendix, we present a statistical comparison of the variability between the carcasses and how this informs our analysis. In sum, Bison2 (the 2-year-old bull) and the hog presented denser and more resistive targets than Goat2 and Bison1, while dart shots in Goat1 were problematized by the reduced inertia from hanging the relatively light carcass.

2.2 Arsenal

Most preserved atlatls and darts in North America come from the arid Southwest (Figure 1) and some from the Ozark bluffs. These artifacts and our attempts to replicate them have been described in detail elsewhere (LaRue, 2010; Pettigrew, 2015, 2018; Pettigrew & Garnett, 2015). Many details of the arsenal to be described, including details of experimenters, description of methods used to measure 3D models, and photographs of each hafted armature are provided in the appendix and the supplementary database with this article.

Weaponry used in these experiments included 11 atlatls (both archaeologically derived replicas and more generalized forms, Figure A1, Table A1) and three bows of black locust (Robinia pseudoacacia) based closely on southeastern (Catawba and Cherokee) bows that drew 20–23 kg at 70 cm of draw (Figure A2). Eighteen main shafts included 11 darts and 7 arrows of river cane (Arundinaria gigantea), Tonkin cane (Pseudosasa amabilis), coyote willow (Salix exigua), and green ash (Fraxinus pennsylvanica; Figure A3). Foreshafts were attached into sockets in main shafts. The experiments deployed 178 armatures donated by flintknappers (Figures A4–A8). Following Kay (1996), the armatures were dipped in methyl violet to facilitate observing impact damage. Not all armatures would be considered highly efficient (e.g., thin, aerodynamic, and sharp), or matched to ethnographic or archaeological dart and arrow sizes, as the goal was to represent a range of weapon efficacy.

All armatures were thoroughly measured and photographed before and after hafting. Hafted armatures used on Goat2 and both bison were photographed for photogrammetry, allowing detailed measurements of cross sections, mean edge angles, and surface areas (SAs; Figure 3). From these models, cross-sections were obtained using ParaView. Edge angles were obtained using a stand-alone program described by Valletta et al. (2020), with h1 factors set to 1.8–3 depending on armature size. Mean values from both edges were averaged to arrive at MeanEdge. SAs were obtained on models trimmed directly below the haft using the “Compute Geometric Measures” filter in Meshlab and subtracting the foreshaft cross-sectional area. In an earlier version of this study, calculations of the drag coefficients of hafted armatures were also attempted through computational fluid dynamics, although this method was cumbersome and produced insignificant results and was not continued for Bison2 (Pettigrew, 2021, pp. 74–125).

Figure 3

Showing the comparison between hafted TCSA/P derived from photogrammetry (TCSA/P_hPV) and from rhomboid equations (TCSA/P_h) alongside screen captures of two 3D armature models. For armature 33, a model trimmed below the haft for measuring SA and the locations of edge angle measurements is also shown.

Most archaeological notched armatures belonging to Late Archaic or “Basketmaker” kits in the intermountain US were hafted with hide glue and sinew (Cosgrove, 1947; Frison, 1965), and some from the Ozarks with bark (Pettigrew, 2018), while we assume stemmed or lanceolate points were typically hafted with additional glue or mastic. Experimental armatures were hafted following these procedures, using elm (Ulmus spp.) bark, sinew from deer and elk, hide glue, and pine (Pinus spp.) resin mixed with organic matter and charcoal. A limited number of beveled points used on the hog were hafted with artificial sinew and modern adhesives (Pettigrew, 2015).

Six experimenters launched darts at carcasses (Table A2). Having multiple shooters helps reduce fatigue and improves representation; some (Dust and Shield Chief Gover) could launch heavy darts with accuracy and force, while others (Whittaker, Garnett, Hashman, and Pettigrew) were practiced in lighter equipment. The atlatlists have extensive training and could direct shots straight at the target with comparable velocity to a larger sample of individuals using a variety of atlatl and dart equipment (Whittaker, Pettigrew, & Grohsmeyer, 2017).

2.3 Data Collection

Although our methods evolved and improved to some extent, we used the same general protocol over five experiments (for additional details, see Pettigrew, 2015, 2021; and for a similar protocol, see Schoville, Wilkins, Ritzman, Oestmo, & Brown, 2017; Smith et al., 2020). The range from shooter to carcass was 10–12 m, which fits with ethnographic accounts of atlatl and bow hunting (Cundy, 1989; Hill & Hawkes, 1983; Pope, 1918). Two high speed cameras filled the roles of “flight camera” (set near the shooter and aimed at the carcass to capture projectile flight and impact) and “velocity camera” (set near the target and capturing impacts orthogonal to the trajectory; Figure 2). To assist calculating velocity and deceleration in the open source Tracker video analysis program (https://physlets.org/tracker//; Figure 4) and observing shaft orientation during impact, shafts were marked with various reflective and colored tapes that terminated under socket whippings to reduce drag during penetration. These markings included a scale to calibrate the video and bright points to track prior to and during penetration.

Figure 4

A screen shot of Tracker. Initial deceleration penetrating skin is averaged from the two values at t = 0.033 and 0.035 s.

For the hog experiment, a Casio EX-F1 was the flight camera and a Casio EX-ZR1000 was the velocity camera, but for subsequent goat and Bison1 experiments, the EX-F1 became the velocity camera and a Kron Technologies Chronos 1.4 became the flight camera. In the final Bison2 experiment, two EX-F1 cameras filled the roles of both flight and velocity cameras, which simplified data collection by a smaller crew of four experimenters. More powerful cameras improve resulting data but are generally more challenging to operate, making the experiment more difficult to carry out and more prone to user error.

In the hog experiment, the EX-ZR1000 camera (filming at 240 frames/s and 512 × 384 pixel/inch resolution) allowed armature tips to be tracked and the video to be calibrated after the projectile impacted and the scale became clear (Pettigrew, 2015). Using the EX-F1 in subsequent experiments (filming at 600 frames/s and 432 × 192 pixel/inch resolution), markings on dart shafts can be tracked in flight when sufficient light, a solid backdrop, and clear markings are present, while arrows are scaled to the length of the shaft and the nock or tip tracked across the backdrop.

In the hog and Bison2 experiments, velocities were also obtained from radar using a Bushnell Velocity Speed Gun and a Stalker Pro II + radar gun, respectively. We used radar to tabulate initial velocity for several shots in the hog experiment and to validate velocities calculated from video in both the hog and Bison2 experiments. Details of the agreement between radar and video are provided in the appendix. In sum, velocities derived from the EX-F1 camera were in strong agreement with radar, while velocities derived from the EX-ZR1000 were more variable due to its lower resolution.

In addition to impact velocity, we tabulate deceleration during penetration through skin and subcutaneous tissues of the bison and goats by averaging 1–3 deceleration values from Tracker over 0.003–0.007 s. The number of deceleration values we chose depended on the penetration duration; larger armatures mounted on darts took longer to traverse skin than arrows, (for e.g., Pettigrew & Bamforth, 2023). Tracker calculates deceleration using a finite differences algorithm over four tracked points to reduce error in marker placement (Brown, 2021). Nevertheless, some error is expected in deceleration given the short duration of the impact event and the sensitivity of deceleration to precise marker placement. Shots on the hog could not be included in the deceleration analysis due to limitations of the EX-ZR1000 camera, which did not allow precise tracking of markers on shafts over brief impact events.

2.4 Data Analysis

In postprocessing, high-speed videos from the flight camera are analyzed sequentially to document precise shot placement (Figure 5) and compared with notes taken during the experiment to choose shots for inclusion in the statistical analysis. For the following analysis, shots were chosen that were not problematized by several factors: skewed impact, significant bone impacts (indicated by damages to stone and bone along with shallow penetration and rapid deceleration), cutting through a prior wound channel in skin, or penetration more than half the length of the shaft completely through the carcass. The latter effect can result in high outliers in a statistical analysis, since over much of the penetration depth the armature is no longer encountering soft tissues. This was a problem of some shots with heavy dart shafts in the Goat2 experiment.

Figure 5

Showcasing four dart-bone impacts mapped onto a screen capture of Bison1 from the flight camera. Armature 33’s history is given in text and Figure 6 (shot 270); armature 108 impacted with 28.5 J and penetrated 6.5 cm, stopping at the scapula (shot 272); armature 136 impacted with 64 J, decelerated at −1,135 m/s² entering the skin, and struck a vertebra with 41 J after penetrating 15 cm (shot 291); armature 170 impacted the 10th rib with 67 J and failed to penetrate (shot 294).

As discussed in Section 1.1, initial penetration through skin provides a way to gauge the relative efficacy of a cutting weapon. Recording deceleration through skin also increases the sample of shots through soft tissues, as impacts with bone deep within a carcass or penetration significantly through are no longer problematic for a statistical assessment of penetrating performance. We therefore use deceleration of hafted armatures through the outer carcass (skin and subcutaneous flesh) to analyze armature efficacy.

The following shot groups met the above criteria and are isolated for analysis: For modeling penetration, 72 shots with darts and 12 with arrows are available across the carcasses, 50 of which had armatures modeled by photogrammetry. For modeling deceleration and force in the goats and bison, 52 shots with darts and 9 with arrows are available, 53 of which had armatures modeled in photogrammetry. Shot data are provided in the supplementary database.

The large amount of data from these experiments were incorporated into a Microsoft Access database and analyzed in JMP (SAS Institute Inc., 2022), as well as in R (R Core Team, 2022). We used subset regression as well as simultaneous multiple regression with the backward and forward selection procedures to find models that balanced statistical significance with simplicity of interpretation and offered the best test of which possible ballistic variables best explain weapon efficacy.

3.1 Qualitative Assessment of Atlatl Dart Penetration

Prior to addressing the questions set out in Section 1.1 it will be beneficial to present a qualitative assessment of four atlatl darts that struck Bison1. This will help lay the groundwork for understanding the results of the analysis and the important and interconnected features of dart and arrow terminal ballistics. Figure 6 showcases these four shots:

Figure 6

Showcasing the terminal ballistics of four dart shots on Bison1. Black boxes in graphs contain averaged deceleration (−m/s²) at marked intervals. Deceleration of shot 271 is cut short as the most proximal velocity marker entered the carcass.

Shots 270 and 271 were made by Pettigrew with a light Basketmaker dart main shaft (#1; e.g., Figure 1) and penetrated the thoracic cavity. Shots 290 and 293 were made by Shield Chief Gover with a large river cane main shaft (#7) that penetrated behind the diaphragm. Armatures 108 and 136 were of Burlington chert, 33 of Brazilian agate, and 170 of obsidian.

In shots 270–271 with the light Basketmaker dart (#1), armature 108 decelerated 150% more rapidly and penetrated half as deeply as armature 33, despite having greater velocity and nearly equal mass. Armature 33 skipped off the side of the ninth rib on entry, causing light edge flaking and slightly changing its orientation. On exit it encountered the eighth rib, removing the tip with a longitudinal fracture and producing more flaking on the opposite edge. Both impacts produced hardly a mark on ribs. Nevertheless, and despite low initial energy, the dart carrying 33 penetrated completely through the thorax, 50 mm through skin on the other side, while there is no indication that 108 hit bone until its next shot (Figure 5).

Shots 290 and 293 with the heavy cane dart (#7) produced similar results. Armature 170 penetrated entirely through the bison (180 mm out the other side). Given the length of the point, this dynamic penetration event through outer skin and tissue can be observed over four frames of the velocity video. Subtle deceleration occurred as the point entered skin (at time 0.06 in Figure 6) and the quickest deceleration occurred when the bulky haft contacted skin upon entry. Tabulated deceleration for this shot is an average of these values. Deceleration was more rapid when 136 encountered skin and was nearly matched on its next shot (Figure 5 caption).

This pattern of finer grained armatures significantly reducing deceleration was repeated with other shots as well. A corner notched point (#28) of Brazilian Agate mounted on the same Basketmaker dart (#1) decelerated at −576 m/s² penetrating intercostal tissues of Goat1 (one of few darts to penetrate Goat1 effectively) and a corner notched point (#55) of Indian Agate (a tough and grainy material, one of three test armatures made by artisans in India and sold in the US as souvenirs) on the same dart decelerated at −1,552 and −1,607 m/s² on two sequential shots that penetrated intercostal tissues of Goat2. These armatures had precisely the same maximum width and thickness (and subsequently the same TCSA/P), and both were corner notched points hafted with sinew. The discrepancy in their deceleration must be due to other aspects of armature efficacy, namely, tip and edge sharpness.

Additionally, Figure 6 shows how force can drop considerably (20–80%) through less resistive internal organs, but these forces also capture drag on the trailing shaft. The shots with the replica Basketmaker dart (#1) are particularly useful for considering drag, since Basketmaker darts often have a shoulder at the socket where the removable foreshaft is attached. Armature 108 (Figure 6, shot 271) was mounted on a 9 mm diameter foreshaft, 5 mm smaller than the full diameter of the main shaft socket. The second sharp decline in its velocity occurred the moment the shouldered socket contacted skin. Armature 33 was mounted on a slightly larger (11 mm diameter) foreshaft. Consequently, deceleration is slightly more rapid as the foreshaft penetrates but less rapid when the socket hit skin, and it still penetrated 235 mm past the socket.

3.2 KE and P

We can now address the first research question: Does KE or P better predict penetration of darts and arrows with stone cutting armatures in soft tissues? Both darts and arrows can carry highly variable amounts of KE and P. For darts, increasing these factors is achieved primarily by increasing their mass. In these experiments, across a total of 231 dart throws with recorded velocities and made by 6 different atlatlists, dart mass is strongly correlated with KE (R ² = 0.8318, p < 0.0001) and P (R ² = 0.9521, p < 0.0001).

We can start by checking the fit between KE, P, and total penetration (MaxPen). Eighty-four shots with darts and arrows that penetrated soft tissues of the five carcasses are presented in Figure 7. KE provides a better overall fit with MaxPen than P for these shots. The fit with MaxPen is made stronger by removing the arrows (KE, R ² = 0.3537, p < 0.0001; P, R ² = 0.3093, p < 0.0001). Arrows were used predominately in Goat1 and Bison1 experiments and therefore met less resistance than a large sampling of 72 shots with darts that also included impacts to the more resistive Bison2 and hog.

Figure 7

Momentum (P) and KE as predictors of penetration depth (MaxPen) and wound surface area (WSA) of darts and arrows in soft tissues.

Clearly the ability of KE or P to explain the variance in MaxPen is limited by differences between the carcasses and other ballistic variables separating the different projectiles. Arrows as a group traveled at higher velocities and had smaller hafted armatures and shafts than darts, although overlaps occurred in the TCSA/P of large arrow and small dart points (Table 2). Darts, being fitted with larger points than arrows, produced substantially larger wound surface areas (WSAs; Table 2). Consequently Figure 7 demonstrates a stronger fit between KE and WSA than MaxPen, a topic we return to in section 3.5.1.

Two specific shots with the light Basketmaker dart shaft (#1) demonstrate that lower than the recommended KE for bowhunting (Table 1) can cause lethal wounds in bison: The shot with armature 33 on Bison1 (Figure 6) and a shot that closely reproduced it in Bison2 using the same main shaft and a nearly identical Brazilian Agate armature (#41), which had been shot once into Bison1 without hitting bone and was rehafted to the same foreshaft as armature 33 for the Bison2 experiment. This armature (#41) struck intercostal tissues at 26.4 m/s (KE = 33.2 J, P = 2.51 kg-m/s) and penetrated 228 mm into the thorax of Bison2. In all likelihood both of these shots would have been highly lethal. However, these shots did not directly encounter bison ribs, which presented substantial barriers to all stone-tipped dart impacts. In contrast, in the hog experiment, a medium cane dart shaft (#5) that approached the KE requirements to hunt an animal of that size (Table 1) could break through ribs and penetrate the width of the thorax, while Basketmaker darts performed poorly when encountering hog ribs (Pettigrew, 2015). Notably, even light darts that fall well short of the KE requirements can surpass the P requirements for hunting large African game with arrows (Table 1).

Last, the fit in Figure 7 shows how KE, a measure of the ability of an armature to do work on the target by creating new surfaces within it, better explains penetration across our sample. However, the reduction in deceleration that comes with greater P is demonstrated in Figure 8 across 63 shots with darts and arrows isolated for deceleration analysis in the goats and bison. Arrows averaged 64% greater velocity than darts but were much lighter (Table 2) and consequently were more easily affected by changes in force. Larger or duller armatures will therefore have a greater negative effect on the penetration of light and fast arrows than on slower and heavier darts or javelins.

Figure 8

The reduced effect of greater resistance force (F) on deceleration (a) for projectiles with greater momentum (P).

3.3 Assessing Armature Efficacy

In this section, we treat the next question regarding the variables of armatures used by archaeologists that capture their penetrating efficacy. We test these variables against both penetration depth (MaxPen) and the resistance force penetrating skin (F).

3.3.1 TCSA/P

To cross-validate TCSA/P as predictors of penetration, we start by plotting TCSA/P against 72 dart and 12 arrow shots through soft tissues of the hog, Goat2, and both bison. If larger TCSA/P affects the ability of stone-tipped darts and arrows to penetrate in a meaningful way, a negative correlation should occur, but TCSA/P shows positive correlations with penetration (Figure 9). These positive correlations between TCSA/P and MaxPen become significant at the p = 0.05 level once the 12 arrow shots are removed (TCSA, R ² = 0.0812, p = 0.0152; TCSP, R ² = 0.0888, p = 0.0110). This correlation occurs because larger dart points were usually fitted to heavier shafts that carried more KE, penetrated deeper, and produced larger wounds. However, visible in Figure 9, TCSA/P also fail to explain penetration depths within groups of projectiles of similar mass and velocity (p ≥ 0.2362). For 19 shots with light Basketmaker darts, variation in TCSP explains almost none of the variability in MaxPen (R ² = 0.0256, p = 0.5125). Considering comparable targets, we obtain similar results for 11 shots with Basketmaker darts that impacted Bison1 and Goat2 (R ² = 0.0045, p = 0.8440), and 18 shots with heavy dart shafts 7 and 13 on Bison2 (R ² = 0.0446, p = 0.4002). For similar results on the hog, see Pettigrew (2015).

Figure 9

Shows the fits between TCSA/P, penetration depth (MaxPen), KE, and mass (m) of 84 dart and arrow shots across the hog, Goat2, and bison.

Using the thickness measure at the haft (TCSA/P_h) does not improve these fits, nor does plotting the area or perimeter ratios (AR or PR) against MaxPen. We may note, however, that only four armatures failed to meet Friis-Hansen’s (1990) requirement of PR > 1 to cut the shaft free from friction. These were four Folsom points hardly wider than the shafts carrying them, which continued to experience high forces of drag after penetrating the skin of Bison2. The two lowest penetration depths recorded in the CaneH (heavy dart shaft 7) category in Figure 7 were made with two of these armatures (# 231 and 237).

Notably, 55 hafted dart and arrow armatures were modeled with photogrammetry and provide accurate TCSA/P values measured in ParaView (TCSA/P_hPV; Figure 4). Comparing these values against TCSA/P_h demonstrates the potential inaccuracy of the equations. TCSA_hPV averages 22% larger and ranges up to 61% larger than TCSA_h, while TCSP_hPV averages 6% larger and ranges up to 34% larger than TCSP_h. Armatures with wide blades and narrower hafts (especially corner notched varieties) tend to have TCSA/P_hPV values closer to the equations, while lanceolate types (e.g., Clovis, Dalton, and Cody types) tend to diverge from the equations (Figure 4). Paired t-tests found statistically significant differences between TCSA_hPV and TCSA_h (t[54] = 8.0636, p < 0.0001) and between TCSP_hPV and TCSP_h (t[54] = 8.0865, p < 0.0001). However, while mean TCSA_hPV is 42.5 mm² larger than TCSA_h, mean TCSP_hPV is only 3.4 mm larger than TCSP_h.

Testing the more accurate TCSA/P_hPV measures against MaxPen, 44 shots with darts (those which have modeled armatures) on Goat2 and both bison were compared, but a weak positive correlation between TCSA_hPV and MaxPen remains (R ² = 0.1248, p = 0.0217), and no fit occurs between TCSP_hPV and MaxPen (R ² = 0.0659, p = 0.1009). By comparison, a slightly stronger positive correlation occurs between the surface areas of the modeled hafted armatures and MaxPen from the same shots (R ² = 0.2296, p = 0.0013). Repeating the above analysis on penetration within projectile groups and targets, no statistically significant fit is found for the accurate measurements from 3D models.

Another way to assess the effect of armature size on penetrating efficacy is to compare the fit between KE and the WSA (Figure 7). This fit is stronger than between KE and MaxPen, suggesting that larger points tend to produce larger wounds but at the cost of penetration depth. However, this effect is most pronounced in distinguishing arrows from darts, while less change occurs in the distribution of darts (Figure 7). Here the higher velocity of arrows may also be increasing their penetrating efficacy, which we consider in the next section.

3.3.2 Force Penetrating Skin

Many factors must be involved in how rapidly projectiles decelerate while penetrating soft tissues, but which factors stand out in a broad comparative analysis? In Section 3, we demonstrated qualitatively how armatures of different materials can have a substantive impact on how rapidly darts decelerate, and consequently, how much force they experience penetrating skin. A statistical assessment of this effect is shown in Figure 10 with a broad comparison of 52 dart shots through the outer skin and tissues of Goat2 and both bison (arrows are excluded due to their different ballistic profiles, which we describe more below).

Figure 10

Force (F) of 52 hafted dart armatures by material that penetrated skin and outer tissues of Goat2 and both bison.

Some of the variance in Figure 10 can be explained by the targets. In studies of knife penetration in cadavers, Knight (1975) found that knives met less resistance in intercostal skin where skin is naturally pretensioned between ribs, relative to thinner but more elastic abdominal skin. However, abdominal skin is easier to penetrate when it is artificially pretensioned (Knight, 1975). In Figure 10, the two lowest outliers in Novaculite and the lowest outlier in Indian Agate resulted from impacts to the abdomen of Goat2, which was compressed (pretensioned) by the scaffold. Other shots, including the highest outlier in novaculite, and all shots in the Buffalo River group, impacted thicker intercostal and abdominal skin of Bison2. Nevertheless, two materials most prominently represented by shots in Bison1, Brazilian Agate, and Burlington Chert had similar mean TCSPs (50.8 and 57.3 mm for Brazilian Agate and Burlington, respectively), but Burlington averaged 114% greater force penetrating skin. Similarly, the two lowest forces in obsidian in Figure 10 impacted thicker intercostal skin of Bison2, and despite relatively high mean TCSP (68 mm), still experienced among the lowest force in the sample.

The lowest mean forces in this sample were experienced by Brazilian Agate and obsidian points, respectively, despite their size differences. However, for 53 dart and arrow shots with modeled armatures, TCSA/P_hPV and surface area (SA) show significant positive correlations with force (TCSA_hPV, R ² = 0.4854, p < 0.0001; TCSP_hPV, R ² = 0.3188, p < 0.0001; SA, R ² = 0.3650, p < 0.0001). But if arrows are removed, for 44 shots with darts, these fits lose some predictive power (TCSA_hPV, R ² = 0.3230, p < 0.0001; TCSP_hPV, R ² = 0.1137, p = 0.0252; SA, R ² = 0.2376, p < 0.0008). As was the case for explaining MaxPen, these armature size measurements are insignificant for explaining force within ballistically similar categories of the 53 darts and arrows (Figure 11). TCSP is generally accepted as the better predictor of stone point penetration in homogenous target simulants (Grady & Churchill, 2023; Pettigrew & Bamforth, 2023; Sisk & Shea, 2009; Sitton et al., 2020), but TCSA_hPV, is more sensitive to increases in the size of a hafted armature, as indicated by its stronger fit with the overall projectile mass (R ² = 0.8096, p < 0.0001) than the fits between TCSP_hPV (R ² = 0.6133, p < 0.0001) or even SA (R ² = 0.7265, p < 0.0001) and mass.

Figure 11

The fits between TCSA/P_hPV, SA, and F within categories of ballistically similar projectiles.

There are other variables involved in armature efficacy that we attempted to measure using blade ratios and edge angles. To see which of these variables help explain force, we fit a multiple regression model testing the same 53 shots with darts and arrows and the following predictors of force: Exp (carcass), Material (armature), v, TCSA/P_hPV, SA, BladeL:W, BladeL:T, BladeW:T, and MeanEdge. As a rule, an effective model should contain no more than one of the cross-sectional size metrics. The best model includes TCSA_hPV (p < 0.0001), Material (p = 0.0040), and MeanEdge (p = 0.0130) and explains 74% of the variation in force (R ² = 0.7399, R ²adj = 0.6532, p < 0.0001). The standardized coefficients for TCSA_hPV (β = 0.74) and MeanEdge (β = 2.8) indicate that they both have a positive effect on force. If we attempt to replace TCSA_hPV with the more preferred TCSP_hPV measure, the latter is insignificant and the best model includes only Material (p = 0.0044) and velocity (p = 0.0002) and explains 62% of force (R ² = 0.6214, R ²adj = 0.5078, p < 0.0001). The parameter estimates indicate that velocity (β = −6.75) has a negative effect on force. We will avoid listing every parameter estimate for Material categories, which clearly need larger samples to validate.

Although the “blade ratios” (BladeL:T and BladeW:T) have been suggested as indicators of armature efficacy (Section 1.1), in our sample, none of these ratios correlate with force (p-values > 0.2650) and BladeW:T only predicts 12% of the variance in MeanEdge measured on the 3D models (R ² = 0.1197, p = 0.0111).

3.4 Modeling Stone-Tipped Dart and Arrow Efficacy

In this final section, we attempt to answer question 3 by modeling the most important variables of stone-tipped dart and arrow penetration and wounding potential in soft tissues. For this, we isolate 48 shots with darts and arrows on the goats and bison that are appropriate for both penetration and deceleration analysis and have 3D modeled armatures for accurate measurements of cross section, surface area, and edge angles.

In Figure 9, the correlations between TCSA/P, mass, and KE show how causal factors in the data are problematized by multicollinearity (multiple correlations between variables). However, multivariate procedures can assess the relative contributions of many correlated variables. Figure 12 presents a heatmap of the correlations between 17 ballistic variables: MaxPen is positively correlated with mass, P, KE, TCSA_hPV, and SA, and most negatively correlated with F, SR, and PR_hPV. However, in addition to other problematic correlations, the three armature and shaft ratios (AR, PR, and SR) also correlate negatively with KE and P. This is because heavier darts tended to be fitted with lanceolate armatures (e.g., Clovis) that produced smaller ARs and PRs relative to wider notched forms, which were more commonly mounted on lighter cane darts. Additionally, darts with larger SRs (representing shouldered main shaft sockets) were most common on replica light Basketmaker darts (e.g., armature 108 in Figure 6). For 19 shots with Basketmaker darts across the hog, Goat2, and both bison, the SR retains a significant negative correlation with MaxPen (R ² = 0.3595, p = 0.0067), showing how a large enough SR (>1.25) can stop penetration when the shouldered socket contacts skin, which was especially noticeable on the hog (Pettigrew, 2015). But large SRs are not present among the higher energy cane and composite darts to allow direct comparison.

Figure 12

A heatmap showing correlations from multivariate analysis of 48 shots with darts and arrows. All cross-sectional measures (TCSA/P, AR, PR, SD) are obtained from 3D models of hafted armatures (TCSA/P_hPV).

Ten of these ballistic variables can be compared in a partial correlations matrix (Table 3). A partial correlations matrix displays the relationships between pairs of variables after adjusting for the impacts of all other variables in the matrix, thus providing a means of controlling for the confounding effects of related variables on each relationship. Prior to adjusting for confounding variables, MaxPen has the strongest positive correlations with mass, KE, and TCSA_hPV, and the strongest negative correlation with the SR. After adjusting for confounding variables, MaxPen has a significant negative correlation with force, while KE and SD_hPV have significant positive correlations at the p ≤ 0.10 level.

To model penetration of these 48 shots, the following predictors are included in a multiple regression against MaxPen: KE, P, F, TCSA/P_hPV, SA, SD_hPV, AR_hPV, PR_hPV, SR, CM, and MeanEdge. The best model includes KE (p < 0.0001) and force (F; p < 0.0001) and explains 49% of penetration (R ² = 0.4917, R ²adj. = 0.4691, p < 0.0001). From this regression we can use the following formula to predict penetration: MaxPen = 357.41 + 4.96(KE) − 1.28(F).

Finally, we may recall that in Section 3.4 KE had an even stronger fit with wound surface area (WSA) than with MaxPen (Figure 7). Performing the regression using the same variables as above as predictors of WSA, we again find that the best model includes KE (p < 0.0001) and F (p = 0.0006) and explains 58% of the variability in WSA (R ² = 0.5845, R ²adj. = 0.5660, p < 0.0001). We can use the following formula to predict wound size: WSA = 1244.34 + 37.60(KE) – 6.03(F).