Cutting stone with a pendulum saw: operation and results

Using the built pendulum saw described above (Figure 4), I attempted six experimental cuts (Table 1) on a hard limestone block from a quarry in Pennsylvania (USA), in lieu of Greek limestone and conglomerate. The goals were threefold: first, to test the effectiveness of different blade shapes; second, to investigate the method for making the deepest incisions on antae and pillar bases; and finally, to document, measure and compare the experimental cut marks to known heights of the built pendulum saw.

Table 1.

Results of experimental cuts with a pendulum saw.

In the experiment, two sawyers operated the pendulum saw, standing on opposite sides of the device and pulling the saw back and forth with a rope (Figure 5a & b; Video 1 in the online supplementary material (OSM)). Water and sand served as a lubricant and abrasive respectively while cutting (Video 2 in the OSM). An initial block weighing 11.3kg was attached at the lower portion of the pendulum to increase friction. The weight was later increased to 18.1kg through the employment of two blocks.

Questions concerning blade shape stemmed from uncertainty over whether the curved cuts were made by a similarly shaped saw or primarily by the motion of the pendulum swing. Four non-serrated blades of pure tin-bronze were thus tested (Figure 6): an elongated, curved blade (0.39m long × 0.15m high); a triangular blade (0.15m wide × 0.2m high); a short, straight-edged saw (0.15m long × 0.17m high); and a longer, straight-edged saw with slightly rounded edges (0.38m long × 0.095–0.14m high). A metalsmith from Crete manufactured these bronze blades using sand moulds (cf. Maragoudaki & Kavvouras Reference Maragoudaki and Kavvouras2012: 205). While Aegean Bronze Age saws are typically 1–3mm in thickness (Shaw Reference Shaw2009: 49–50), the experimental blades were 5mm thick. This difference stems from the difficulty in manufacturing blades thinner than 4–5mm using sand moulds (E. Maragoudaki pers. comm.). Although several rounds of annealing could reduce blade thickness, the experimental blades were annealed only once. They were heated to 600°C for one hour, immersed in cold water and then hammered. Ideally, this procedure would have been repeated to increase blade strength and to reduce thickness, yet the single annealing proved sturdy enough to cut limestone. The blade dimensions are somewhat arbitrary; the generous height ensured that the blades were reusable, as the deterioration rate was unknown prior to experimentation. A saw from Andronianoi on Euboea measuring 0.557m × 0.077–0.09m and one from Prosymna measuring 0.217 × 0.039m (Maragoudaki & Kavvouras Reference Maragoudaki and Kavvouras2012: 201) indicate that the experimental blades are within the length range of preserved Mycenaean saws, although these particular examples were designed for woodworking.

Figure 6.

Four experimental saw blades.

The long, curved experimental blade generated concave markings (Figures 7–8). This saw successfully made three incisions, each stopped artificially at a different point to ensure variety in cut depth and length (Table 1: cuts 1, 4 & 5; Figure 9: 1–3). The angles of these cuts were homogeneous and nearly vertical, thus notably different from the angled incisions recorded at Boğazköy-Hattusha (Seeher Reference Seeher2007: 35, fig. 10). The experimental pendulum saw might be capable of cutting at an angle if the pendulum were placed and secured diagonally, but further work is required to test the efficiency of this position. These three experimental cuts, ranging from 0.56–0.85m in length and 25.5–48mm in depth, resemble the dimensions of the Tiryns saw cuts, which are typically 0.6–0.8m in length and 30–60mm in depth (Seeher Reference Seeher2007: 38–40). The cutting speed with a curved blade was recorded for one incision (Table 1: cut 5): a depth of 25.5mm was reached after 45 minutes. The first nine minutes produced a starting groove 3mm deep; afterwards, sawing progressed at a steady rate of 7.5mm every 12 minutes. During these 12-minute segments, water and sand were added at two-minute intervals.

Figure 7.

Curved saw cut (0.85m long) produced by a curved saw.

Figure 8.

Limestone block after experimental cutting; a) the curved saw made an 0.85m cutting; b) the triangular blade created a wobbly incision.

Figure 9.

Lengthwise sections of experimental saw cuts: 1) cut 1 (complete), produced by a curved blade, cut length = 0.85m, greatest cut depth = 48mm; 2) cut 4 (nearly complete), produced by a curved blade, cut length = 0.765m, greatest cut depth = 41mm; 3) cut 5 (partial), produced by a curved blade, cut length = 0.56m, greatest cut depth = 25.5mm; 4) cut 6 (partial), produced by an elongated straight blade, cut length = 0.685m, greatest cut depth = 19mm.

The triangular blade and short, straight blade (Table 1: cuts 2 & 3) were ineffective for use with a pendulum machine. Wear on the triangular blade revealed that only its tip—0.025m long—touched the stone. This blade created a wobbly groove on the limestone surface (Figure 8), thus eliminating it as a possibility due to its inability to form a straight cut. The short straight blade also proved to be useless, as its corners repeatedly stuck into the stone and prevented the pendulum from swinging back and forth.

The elongated straight blade with rounded corners produced cut 6 (Table 1; Figure 9: 4). After making an initial groove 1mm deep, this saw fashioned a curved cut 19mm deep after 24 minutes of operation. The cutting speed was noticeably faster and more efficient than the curved saw blade, progressing at a rate of 9mm every 12 minutes, while also producing a longer cut. When assessing experimental cutting speeds, one must acknowledge that several variables today differ from those in antiquity. These include the skill and experience of the workers, the saw blade's thickness, the abrasive used (e.g. emery sand would have been better than sedimentary sand) and the type of stone.

The experimental saw created long, curved incisions. Yet it remained unclear how the pendulum saw made deep cuts on antae and pillar bases, as the wooden bottom of the actual pendulum would eventually hit the stone. The solution became apparent after considering the aforementioned base in the House of Columns at Mycenae (Figure 3). If a blade were appended to the pendulum's side, as Seeher (Reference Seeher2007: 40, fig. 19a, Reference Seeher, Pirson and Wulf-Rheidt2008: 7, fig. 12b) hypothesised for a saw at Tiryns, the sawing device—through a multi-stage process—could reach the lowest parts of the block. The saw would initially (Figure 10: 1) cut until the pendulum end prevented the blade from progressing. Unwanted portions of the block were then chiselled or hammered away to provide sufficient space for the pendulum to descend again (Figure 10: 2). After removal of this excess stone, the saw could continue cutting without hindrance (Figure 10: 3; Video 3 in the OSM). The half-finished base from Mycenae (Figure 3), and perhaps a threshold from Tiryns (Küpper Reference Küpper1996: pl. 13.3), preserves evidence of this procedure in progress. Rivets (bolts in the experiment) securing the blade protruded slightly from the blade side (Video 4 in the OSM), so that the pendulum saw cut the stone at a slight angle (Figure 10: 3–4). This process would be repeated with the entire pendulum moved to lower rungs (Figure 10: 4) to fashion a block's lower end. This procedure might account for the heterogeneity of Mycenaean pendulum cuts, including the imperfect vertical profiles of sawn antae and bases (Küpper Reference Küpper1996: pls 5–12), even though the experimental cuts only produced near-vertical sections.

Figure 10.

Multi-stage process for how the pendulum saw made deep cuts on antae and pillar bases (drawn by Giuliana Bianco).

A final issue investigated by the experiment was whether a pendulum's height corresponded to the arc of a curved cut. Küpper (Reference Küpper1996: 21–25) proposed that the radius of the pendulum's swing (thus providing an estimated size for the device) was between 3 and 8m high for various cuts, the largest figures corresponding to threshold marks. To check the reliability of such calculations, the length and depth of the experimental saw cuts were compared to the known pendulum heights. Using basic geometry, the radius of a circular segment can be calculated if the arc width and arc height are known. Using Pythagoras's Theorem, the equation is: arc radius = $\ \frac{{{\rm{arc\ height}}}}{2} + \frac{{{\rm{arc\ widt}}{{\rm{h}}^2}}}{{8( {{\rm{arc\ height}}} )}}$ . Restated with the dimensions of a curved saw cut, the formula is: pendulum radius = $\ \frac{{{\rm{cut\ depth}}}}{2} + \frac{{{\rm{cut\ lengt}}{{\rm{h}}^2}}}{{8( {{\rm{cut\ depth}}} )}}$ . The calculated pendulum radii based on the experimental cut measurements are listed in Table 1. The known pendulum saw heights, taken from the deepest point of each cut to the height of the horizontal bar, are also provided. None of the calculated radii match the measured pendulum heights. It is worth highlighting cut 6 (0.685m long × 19mm deep) made by the elongated straight saw (Table 1; Figure 9: 4). Based on the arc radius formula ( $\frac{{0.019}}{2} + \frac{{{{0.685^2}}}}{{8\,{\times}\,0.019}}\ $ = 3.097), the dimensions of this cut indicate an expected radius of 3.097m, which is 1.589m longer than the known pendulum length of 1.508m. The experimental cuts and calculations prove that a pendulum saw using an oval notch creates imperfect segments of a circle.

Küpper (Reference Küpper1996: 17–21, fig. 12.2) suspected that an oval notch would cause variability, which led to his cumbersome solution of lowering the block, rather than the pendulum apparatus, during cutting. From his detailed illustrations, it appears that Küpper assumed that the curved saw marks at Mycenae and Tiryns were parts of true geometric circles (1996: figs 133–41). If that were the case, calculation of the original height of the device—that is, the pendulum radius—would be possible based on the length and depth of curved cut marks. The experimental cuts and profiles presented here (Figure 9: 1–4), however, illustrate the difficulty in determining whether a curved saw mark represents part of a circle. For instance, would experimental cuts 5 and 6 (Table 1; Figure 9: 3–4)—seemingly symmetrical—have been identified as circular segments if their pendulum radii were not already known? This challenge is even greater if only a small portion of the saw cut is preserved.

An unavoidable conclusion is that Küpper's calculations for pendulum radii (especially those of extreme height), which have puzzled scholars (Seeher Reference Seeher2007: 32), are greatly overestimated. Küpper's work on the pendulum saw, however, remains valuable; he identified pairs of cuttings on blocks that reflected similar pendulum lengths (Küpper Reference Küpper1996: 17–18, figs 132–35). While his estimated heights may be inaccurate, the relative relationship of the markings to each other, and the prospect of paired cuts, should not be disregarded. Küpper's observation of paired incisions made from a common height, in my opinion, supports the existence of a device that allowed for incremental pendulum-height adjustments.