Ancient Maritime Trade Between Ecuador and Western Mexico on Balsa Rafts: An Engineering Analysis of Balsa Raft Functionality and Design



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Ancient Maritime Trade Between Ecuador and Western Mexico on Balsa Rafts:

An Engineering Analysis of Balsa Raft Functionality and Design
Leslie Dewan and Dorothy Hosler
Keywords: Ecuador, Mesoamerica, Balsa raft design, Maritime trade, Pre-Columbian
Abstract:

By approximately 100 BCE Ecuadorian traders had established maritime commercial routes reaching from Chile to Colombia. Historical sources indicate that they transported their merchandise in large, ocean-going sailing rafts made of balsa logs. By about 800 CE the data show that Ecuadorian metalworking technology had reached the west coast of Mexico but remained absent in the region between Guerrero and lower Central America. Archaeologists have argued that this technology was most plausibly transmitted via balsa raft exchange routes. This paper uses mathematical simulation of balsa rafts' mechanical and material characteristics to determine whether these rafts were suitable vessels for long-distance travel. Our analysis shows that these rafts were fully functional sailing vessels that could have navigated between Ecuador and Mexico. This conclusion strengthens the argument that Ecuadorian metallurgical technology and other characteristics common to both regions were transmitted from South America to Western Mexico via maritime trade routes.


One key issue in New World archaeology concerns the extent to which the great civilizations of the Andes and Mesoamerica were in contact with one another prior to the European invasion. Metallurgy, for example, was introduced to western Mexico from the Andean zone around CE 800 (Hosler 1988). Archaeologists have argued that metallurgical knowledge and techniques were most plausibly transmitted north via a maritime route with a base in coastal Ecuador (Hosler 1988, Marcos 1977, Meighan 1969). The fact that no metal objects appear in the region between western Mexico and the northern Andean zone during the period under consideration strengthens the argument for a direct maritime transmission of metallurgical technologies from Ecuador to west Mexico.

We do know from archaeological data that by approximately 100 BCE Ecuadorian traders had established maritime commercial routes reaching from Chile to Colombia (Paulsen 1974; Rostworowski 1970). These traders transported their merchandise, which included metal ornaments, emeralds, and Spondylus oyster shells, in large, ocean-going sailing rafts made of balsa logs.1 Figure 1 shows a possible maritime transmission route of these trade goods and metallurgical technologies. Unfortunately, no remains of pre-Columbian rafts have been recovered in Ecuador or elsewhere.

[Figure 1]

The question concerning how metallurgy became established in Western Mexico, and whether it was established by South Americans traveling on the balsa wood rafts depicted in the historical sources is made particularly compelling because of the highly complex nature of metallurgical technologies. Metallurgy was invented independently in only two areas of the world, in the Near East, from which knowledge was introduced to China and elsewhere (Piggott 2006), and in the Andean zone of South America (Lechtman 1980). Hosler has pointed out (1988, 1994) that the earliest assemblages of metal objects found in Western Mexico (the Infiernillo sites, Tomatlán in Nayarit, and others) demonstrate that these west Mexican metalworkers were already skilled practitioners of the craft. They cast small bells using the lost wax method (widely employed in Colombia and Panama but rarely in Ecuador) and fashioned numerous cold-worked hand tools and ornaments such as rings, needles, and tweezers from an original cast blank, whose prototypes appear frequently in Ecuador and northern Peru. These activities—winning metal from its ore through smelting, lost wax casting and working objects to shape from an original cast blank—require mastery of an extensive body of technical knowledge about these materials. Such knowledge was likely imparted to west Mexican populations by Andean metalworkers who accompanied the maritime exchange voyages (Hosler 1988). Further, such metalworkers had to have lived with peoples in the mineral rich regions of Jalisco, Michoacan, Guerrero, Colima and Nayarit for a sufficient amount of time to transmit the critical aspects of this complex technology.



This paper assesses the argument for the maritime introduction of metallurgy from the northern Andes to west Mexico by modeling the mechanical and material characteristics of the balsa wood rafts to determine whether these rafts were suitable vessels for long-distance trade. Sixteenth and seventeenth century European invaders, who were sailors themselves, observed these craft and describe them in sufficient detail that we have used those descriptions as the data set for our model. To ascertain whether these craft could reliably have carried large quantities of goods between the two regions, we modeled mathematically four key aspects of their design to evaluate their aerodynamic and hydrodynamic properties, their buoyancy and cargo capacity, their functional lifetime, and the load-bearing capacities of their component materials.
Overview of Prior Research into Long-Distance Balsa Traffic along the Pacific Coast of South America

Several contemporary sailors have undertaken voyages attempting either to promulgate a theory of trans-Pacific migration or to recreate the voyages from Ecuador to West Mexico (Heyerdahl 1955; Smith 1999). During the last century the researchers Thor Heyerdahl and Cameron Smith experimented independently with balsa rafts' sailing abilities. Heyerdahl sailed the 45 foot balsa raft Kon-Tiki from Callao, Peru to Polynesia in 1947. The square rig used on Heyerdahl's raft does not replicate accurately the pre-European sail design and, furthermore, was capable only of sailing directly downwind. The fixed square sail used on his raft lacks the maneuverability to sail up or down the coast of Central America (Heyerdahl 1955). John Haslett and Cameron Smith attempted several ultimately unsuccessful voyages from Ecuador to West Mexico in the 1990s (Smith 1999, Haslett 2006). Their rafts were rigged with European-style lateen sails, which according to our sources were not used prior to the Spanish invasion (Johnstone 1980). In 2006, Thor Heyerdahl's grandson Olav Heyerdahl built a balsa raft that successfully recreated the Kon-Tiki voyage across the Pacific. This raft, called the Tangaroa, was rigged with square sails affixed to a yard that could be rotated about the mast. Although one piece of evidence—a 1538 sketch by the sailor Cristobal Rodriguez (Rostworowski 1970)—suggests early use of this rigging style, the bulk of the historical evidence indicates extensive use of crescent-rigged sails (Edwards 1965b; Zarate 2001 [1555]; Xeres 1985 [1534]; Estete 1992 [1535]).

Our assumptions about pre-Columbian raft design derive from sixteenth century first-contact written and pictorial accounts. As we show, sail design is crucial to raft functionality.
The Raft Model

A raft has to fulfill a specific set of requirements to be considered functional: (i) its components must exhibit the appropriate dimensions and material properties to withstand a given set of external stresses; (ii) it must be able to provide sufficient buoyant force to sustain the weight of its cargo and crew; (iii) its sail must be able to extract enough power from the wind to overcome the hydrodynamic drag caused by the local water currents; and (iv) it must have a service lifetime appropriate to its task. This paper uses the historical data set to address each of these requirements in turn.


By evaluating these four functional requirements in the raft model we constructed we were able to determine the feasibility of long-distance maritime travel between Ecuador and Mexico using balsa-wood sailing rafts. We also determined the rafts' dimensional limits, and thereby, their potential cargo capacities. Furthermore, comparing balsa rafts' functional characteristics to those of feasible design alternatives allows us to address the social and economic variables that drove the historically documented design choices.

The Data: Descriptions of Raft Design
Sixteenth and seventeenth century accounts of raft design provide information regarding the materials used to make balsa rafts, raft dimensions, the types of sails, and the design and dimensions of the steering mechanisms.

Agustín de Zárate, a Spanish chronicler who lived in Peru in 1543 while supporting Gonzalo Pizarro's rebellion against the king of Spain, describes the base of a balsa raft in his Historia del descubrimiento y conquista de las provincias del Perú (Zárate 2001 [1555]). He reported that the logs forming the base of the raft “are always of an odd number, commonly five, and sometimes seven or nine” (Zárate 2001:155 [1555]). His account then says the logs were laid out such that “the middle one is longer than the others, like a wagon tongue, ... thus the balsa is shaped like an outstretched hand with the fingers diminishing in length” (Zárate 2001:155 [1555]). Girolamo Benzoni, an Italian trader who encountered balsa rafts in Peru in the 1550s, corroborates this account in his 1565 Historia del Mondo Nuovo (Benzoni 1989 [1565]). He says that the rafts are “made of three, five, seven, nine, or eleven very light logs, formed in the shape of a hand, in which the middle one is longer than the others” (Benzoni 1989:223-224 [1565]).


Francisco de Xerez, who traveled with Francisco Pizarro on his second expedition to the west coast of South America, provides additional information about the raft base framework (Xeres 1985 [1534]). De Xerez sailed in a ship piloted by Bartolomé Ruíz, sent by Pizarro to explore the waterways of northern Peru in 1526. Near Peru's border with Ecuador they encountered a balsa raft “...made with crosspieces and underbody of some poles as thick as pillars, lashed together with line made of hennequen [Agave sisalana], which is like hemp. The upper works were of other thinner poles, also lashed with line, on which the people and merchandise rode so as not to get wet, since the lower part was awash” (Xeres 1985:66 [1534]). Agave sisalana, commonly known as sisal, is a fibrous plant still used today to make durable rope that is especially resistant to deterioration in seawater.
Miguel de Estete, who was on the same ship as Ruiz and de Xerez, described the raft as follows (Estete 1535 1992:66-68 [1535]):

“...these balsas are of some very thick and long wooden logs, which are as soft


and light on the water as cork. They lash them very tightly together with a
kind of hemp rope, and above them they place a high framework so that the
merchandise and things they carry do not get wet. They set a mast in the
largest log in the middle, hoist a sail, and navigate all along this coast.
They are very safe vessels because they cannot sink or capsize, since the water
washes through them everywhere.”
Figure 2 is a drawing of a balsa raft by the Dutch envoy Joris van Spilbergen, who published an account of his travels, Speculum Orientalis Occidentalis que Indiae Navigation, in 1619. Figure 3 is our model (made using the computer-aided design program SolidWorks) of the base of the raft, based primarily on Spilbergen's drawing, showing the balsa hull logs, crosspieces, and a set of thinner poles forming a deck, as well as centerboards and two curved masts.

[Figure 2]



[Figure 3]
Emilio Estrada and Clinton Edwards (Estrada 1955; Edwards 1965b), researchers who experimented extensively with the sailing capacities of balsa rafts, have maintained that the centerboards depicted in the Joris van Spilbergen drawing are a crucial design element, because balsa rafts have a large area in contact with the water and they present a fairly non-planar profile It would be impossible to sail one without a stabilizing mechanism below the waterline (Edwards 1965b). The Spilbergen illustration makes clear that balsa rafts were steered not with a rudder but with three sets of centerboards: one set in the bow, one set in the stern, and one set in the middle of the boat (Edwards 1965:351). Figures 2 and 3 show the centerboards' approximate placement on a balsa raft.
Based on a number of historical sources, Estrada and Edwards maintain that ocean-going balsa rafts had crescent-shaped sails, with backwards-curving leading and trailing edges (Estrada 1955; Edwards 1965b). These highly efficient sails would have given the rafts a considerable deal of maneuverability.2 As shown in Figure 2, a rope affixed to the top of the masts pulls on and curves the masts downwards, giving the sails their characteristic crescent shape. The degree of mast curvature could be adjusted to increase sail efficiency when sailing at different angles to the wind (van Dam 1987).

Stress Patterns and Resulting Constraints in Raft Components
A functional raft must be able to endure a given set of stresses without breaking or permanently deforming. These stresses, caused by the wind, water, rigging, and gravitational forces, limit the feasible dimensions of the raft's components. We examine first the stress patterns and resulting dimensional constraints in the raft's mast.
The Mast
Following the historical record, the mast is modeled as an encastered tapered beam set into the center balsa hull log, perpendicular to the deck (Estrada 1955, Edwards 1965, Edwards 1965b). Because the mast cannot rotate in its socket in the balsa hull log, setting it into the deck at an angle other than orthogonally would result in a highly turbulent, inefficient sail geometry at most points of sail (White 2003). Forming a mast out of a curved piece of wood would likewise inhibit sail efficiency and maneuverability. The masts in Figure 2 are each made of two separate pieces of wood (Edwards 1965b). It is possible that the masts were constructed out of two pieces of wood to facilitate repair of broken mast segments, or because of difficulty in finding a single piece of wood of adequate length for a mast. Nonetheless, it is appropriate to model each mast as a single curved beam, under the assumption that there was minimal slip between the two component pieces. We assume that the mast's wood has a modulus of elasticity of 10 gigapascals and a modulus of rupture of 100 megapascals, which are approximately average values for some hardwoods available in the Ecuadorian region (United States Department of Agriculture 1999: Table 4-5). The Kon Tiki and Tangaroa masts were made of mangrove wood, and Smith's rafts had masts made of guayacan wood. There is no historical data describing the types of wood used in pre-Columbian masts.
Stress on the Mast: Wind Stress and Rope Stress

Stress in the mast is due to two independent forces: the force of the wind on the sail, and the force of the rope that gives the tip of the mast its required displacement. Figure 4 is a free body diagram of the mast, showing the locations of the wind force (Fwind) and the force of the rope displacing the tip of the mast (Frope).

[Figure 4]
The magnitude of the wind force depends on the area of the sail. Assuming a ratio of 2:1 for sail height to sail width, based on historical sources, we obtain a correlation between the height of the mast and the force of the wind (wind load) that the mast would have to sustain. The wind forces on the sail that are transmitted to the mast can be broken down into two perpendicular components, lift force and drag force. Figure 5 shows the direction at which these forces act on the raft. The coefficients describing the lift and drag forces vary according to the point of sail (Larsson 1996). The sum of the squares of these coefficients is greatest when a boat's forward velocity is approximately 60 degrees from the apparent wind velocity, according to standard textbooks on yacht design (Larsson 1996; Marchaj 1988). The force of the wind on the mast is therefore greatest at this point of sail. These forces also depend on the magnitude of the apparent wind velocity. For our calculations, we set the velocity to 9 meters per second, which is approximately the highest magnitude the raft would encounter while sailing between Ecuador and Mexico, according to available wind current data (IRI/LDEO 2006).3

[Figure 5]



Mast Taper Ratio

The stress profile in the mast is also a function of the mast's taper ratio4 and the displacement of the tip of the mast, which varies as sailors change the tension on the rope as they pull on it. Increasing the taper ratio decreases the amount of force necessary to displace the tip of the mast by a given distance, but it increases the maximum stress. In particular, it causes a sharp peak in the stress profile in the upper portion of the mast. Decreasing the taper ratio flattens the stress profile and lowers the maximum stress. The mast must have some degree of taper, however, to decrease the amount of force necessary to displace the tip of the mast by a given fraction of its height.


We examined ratios of mast base diameter to mast tip diameter ranging from 1 to 10 in increments of 1, and we examined ratios of tip displacement to mast height from 5% to 50% in increments of 5%. According to this analysis, the maximum ratio of tip displacement to mast height that can be achieved without mast fracture is 20%. This displacement is possible on masts with a base to tip taper ratio of 2. Taper ratios and curvatures greater than these values result in localized stresses with sufficient magnitude to break the mast.


Safety Factors

The computer simulation written by L. Dewan in MATLAB determined the stresses along the mast induced by the rope and the wind for a range of mast heights and diameters. Because the maximum wind stress and rope-induced stress do not always occur in the same place, it is necessary to sum the stresses at each point along the mast, then take the maximum of this sum. A mast must be able to withstand the sum of these stresses.

Figure 6 shows a contour plot of the safety factors for feasible mast geometries. The safety factor is defined as the stress at which the mast breaks divided by the maximum stress present in the mast. According to Figure 6, given the constraints we have described, 1.5 is the largest possible safety factor the mast could sustain. This number is fairly low by modern standards; it is considered good engineering practice to include a safety factor of at least 2 or 3 for features as critical as a ship's mast. A safety factor is included because a well-designed mast must be able to withstand unanticipated stresses. These stresses would come most likely from unexpected gusts of wind, above and beyond the 9 m/s of wind the mast was designed to tolerate. Table 1 shows the approximate maximum wind gust velocity that the masts could endure, as indexed by their safety factors.
[Table 1]

Masts with a safety factor of about 1.4 could endure gusts up to 16 m/s before lowering their sails. It is highly likely that the Ecuadorian balsa rafts would have encountered unexpected gusts of this magnitude as they sailed, which suggests that the masts almost certainly were built with a safety factor of at least 1.4 (IRI/LDEO 2006).


Mast Height

Figure 6 relates a set of feasible mast heights and diameters but places no restriction on the maximum mast height. It is necessary, therefore, to look at another variable to determine the maximum mast height. This factor is the amount of force required to displace the tip of the mast a given distance. It is important to minimize the force required to displace the tip of the mast, because the degree of displacement of a crescent sail must be adjusted frequently to maximize its efficiency when sailing at different angles to the wind. If the necessary rope force is too great, it would be difficult to adjust the sail frequently because that would require more individuals pulling to generate sufficient force. We assumed that three sailors weighing about 60 kg each could apply their combined body weight, approximately 1800 newtons of force, to a rope tied to the mast tip in order to displace it.


The dashed line in Figure 6 indicates the mast dimensions that require 1800 newtons of force to displace the mast tip by 20% of its height. Masts below this line require more than 1800 newtons to generate the displacement and are therefore considered not feasible. The maximum possible mast height occurs near the intersection of the 1800 N bending force line and the 1.4 safety factor line. This intersection describes a mast approximately 7.5 meters tall and 0.16 meters in diameter. Stress analysis does not impose a lower limit on the mast height.
[Figure 6]

Sail Area and Raft Length
The stresses in the mast provide an upper limit on possible mast heights. The mast height limits the maximum sail area, which in turn limits the potential size of the raft. It is necessary to determine the possible sizes of the raft base, because these dimensions factor into the raft's cargo capacity and buoyancy. Capacity and buoyancy are analyzed more explicitly in the following section.
The wind generates lift and drag forces on the sail, as shown in Figure 6. The forces that drive the raft in the desired direction are a function of these lift and drag forces, which are calculated using appropriate lift and drag coefficients. The forward driving force decreases as the raft sails closer to the wind.
While the wind force drives the raft forward, the hydrodynamic drag force always acts opposite to the raft's direction of motion. Setting the forward driving force and the hydrodynamic drag force equal to each other describes a raft that is moving forward at a constant velocity. The resulting equation5 gives the raft's maximum wetted area as a function of its sail area. We converted wetted area to arrive at raft length. Assuming that the length of a typical Ecuadorian raft was 1.5 times longer than its width, following Figure 2 (Edwards 1965b), a raft with two seven meter masts, the tallest possible mast heights given our computations, would be able to propel an 11 meter long raft.
The Centerboards
The raft's three sets of centerboards are also subject to dimensional constraints. They must withstand the stress generated by forces that push the raft perpendicular to the desired direction of motion. The magnitude of this perpendicular force is a function of the wind lift and drag forces.

Estrada and Edwards (1955) built model balsa rafts in the 1950s to test centerboard steering methods. Removing some of the bow centerboards swings the bow away from the wind, as the force of the wind on the sail causes the raft to pivot along the stern centerboards; removing the stern centerboards swings the stern away from the wind (Estrada 1955; Dewan 2004). We also found this to be the case in a 3 meter long model raft we launched in the Charles River in 2004 (Dewan 2004).


For a given below-water depth and width, thicker centerboards experience a lower maximum stress. However, the boards must also be thin enough to fit in the gaps between the balsa hull logs. The centerboard geometries tested in our simulations ranged in thickness from 0.01 to 0.10 meters, with a below-water depth of 2 meters and width of 0.5 meters. The maximum stress in the centerboards is on the order of a few hundred kilopascals for all tested geometries. For example, the side force generated by a raft with two 7.5 meter masts sailing 60 degrees from the wind would generate a maximum stress of 320 kilopascals in a centerboard with thickness of 0.05 meters. The modulus of rupture of native hardwoods is on the order of 100 megapascals (United States Department of Agriculture 1999:Table 4-5), thus there is little chance that this side force could approach a magnitude high enough to snap a centerboard.
In addition to steering the raft, the centerboards also minimize the velocity at which the raft drifts perpendicular to the desired direction of motion. Increasing the below-water centerboard area lowers this perpendicular velocity. However, increasing this area also increases the raft's hydrodynamic drag.
Setting the perpendicular force on the raft equal to the force the water exerts on the centerboards ensures that the raft is not accelerating perpendicular to the desired direction of motion. This equality describes a relation between the raft's forward velocity, its perpendicular velocity, and the centerboard area. The raft's sideways velocity should be less than 1/10 of its forward velocity. A raft with two 7.5 meter masts would require about 12 square meters of centerboards below the water to maintain this velocity ratio. Our model's calculations assume centerboards with below-water depth of 2 meters and width of 0.5 meters.

By analyzing the stress patterns in the raft's components we are able to determine the raft's size constraints. The mast height limits the raft's sail area, which in turn limits the size of the raft base and the necessary number of centerboards. Knowing the size of the raft's base allows us to determine its cargo capacity.




Raft Buoyancy and Cargo Capacity
Another step in the analysis approximates the cargo mass that a balsa raft could carry. These calculations assume that the base of the raft is approximately 11 meters long by 7 meters wide. These dimensions represent the maximum feasible raft size according to our model. Balsa logs of this length would have a diameter of approximately 0.9 meters when stripped of their bark.
The quantity of goods that the raft could carry is a function of the mass of the balsa hull logs and deck risers, hardwood crossbeams, decking, mast, and number of crew members. A raft of this size would need at least six crew members: three manning the sails, and one person on each of the three sets of centerboards.

If the hull logs were 75% submerged, the raft could carry approximately 30 metric tons of goods. This below-water value is a conservative estimate; none of the relevant historical sources describes the degree to which the logs were submerged. This calculation assumes that the rafts were built using dried balsa wood, which has a density of approximately 150 kilograms per cubic meter, rather than with green wood. The logs provide less buoyant force the longer they are in use because of waterlogging, decomposition, and damage by marine borers. This decomposition is discussed in greater detail in a following section.



Raft Interactions with Varying Wind and Water Currents
The wind and ocean currents on the west coast of South and Central America vary significantly from month to month, making certain times of year particularly amenable or inhospitable to sailing either north or south. We investigated the monthly variation in these conditions and determined at what times of year a balsa raft would be able to sail north from Ecuador to Mexico or south for the return voyage.

The west coasts of Ecuador and Central America experience a torrential rainy season. The severity of these weather patterns would preclude any sailing. The rainy season in Ecuador lasts from January to April, and the rainy season on the Pacific coast of central America and Mexico occurs from approximately May to October. A balsa raft would not be able to sail during these times of year.

We performed analyses to determine the feasible times for sailing during the dry season. The size of the raft determines the months it can be sailed. Larger rafts have both larger sails and a larger wetted area. They can therefore extract more power from the wind but are also subject to a larger drag force from the water. We first analyzed the aerodynamic and hydrodynamic characteristics of a raft base that measures 11 meters by 7 meters with two 7.5 meter tall masts. We modeled the monthly variations in the raft's interaction with the changing wind and water currents. This modeling allows us to determine the times of year at which the raft could be sailed in a particular direction.
Charts showing the monthly averages of ocean surface current velocity in the year 2000 and charts showing the monthly averages of wind current velocity during this same time period were obtained from Columbia University's International Research Institute/Lamont-Doherty Earth Observatory Climate Data Library (IRI/LDEO 2006).
The ocean surface current charts indicate the highest velocity water currents that the raft would have to overcome. These currents generate a hydrodynamic drag force on the raft. The magnitude of the drag force depends on the apparent velocity of the raft with respect to the surface of the water. The directions, magnitudes, and locations of the three largest hull drag forces were recorded for each month.

Using the wind charts, we determined the wind speed and direction in the vicinity of the largest hydrodynamic drag forces. Estimating the lift and drag coefficients for the particular point of sail, we calculated the wind driving force pushing the raft in the desired direction. We then compared this wind driving force to the hydrodynamic drag opposing the raft's motion. The raft can overcome an ocean current at a time of year when the component of the wind force pushing the raft forward has a greater magnitude than the water drag force opposing its motion.


We then examined the wind current charts separately to determine whether wind forces alone would be strong enough to prevent the raft from sailing at certain times of year. Assuming that the raft can sail within 60 degrees of the wind, there is no time during the year in which the wind currents alone are great enough to prevent the raft from sailing either north or south. Figure 6 shows the components of the lift and drag forces, which can be resolved into driving and side forces, that act on the mast and are transmitted to the raft, as well as the water drag that opposes the motion of the base of the raft.
A raft with two seven meter masts could sail south to north from September to January or in June. Sailing in this direction would be easiest in December or January. A raft with the same dimensions could sail from north to south from January to March or in September. Based on the wind and water currents, sailing in this direction would be easiest in late March.
We performed similar analyses for rafts with different dimensions. Larger rafts have both larger sails and a larger wetted area. They can extract more power from the wind, but they also experience a larger water drag force. In general, the magnitude of the increase in wind force is significantly greater than the increased water drag, so that larger rafts with larger sails have significantly greater leeway in what times of year they can sail. This again is constrained by the torrential rainy seasons that disallow sailing during these periods.
A 6 meter long raft with a single 6 meter mast appears to be the smallest that could travel in both the south-north and north-south directions. The corresponding minimum mast height for a two-masted raft is approximately 5 meters. These rafts would be able to sail north only in January-December, and south in late March. Even at those times, the net forward force on the raft is fairly small, so that the raft has very little leeway in navigation. Given our discussion of the time required for Andean metalworkers to introduce metallurgical technologies, our opinion is that South American voyagers most likely remained in Mesoamerica for the duration of the year.

Based on this analysis, it seems likely that the rafts that made the journey had two sails, because the additional sail area greatly increases the power the rafts can extract from the wind. The maximum mast height, as determined in the previous section, is 7.5 meters, and the minimum mast height for a two-masted raft is 5 meters.



Balsa Wood Durability in a Marine Environment
The balsa hull logs are the most important factor limiting the raft's functional lifetime. Balsa wood decomposes very quickly due to its low density, and it does not naturally contain chemicals such as silicates that repel microorganisms, insects, or mollusks that would damage it. Balsa, like other woods, decomposes more rapidly in salt water than in freshwater because of the larger numbers of wood-consuming invertebrates that live in salt water. Teredo navilis, the common shipworm, causes the most significant damage to a balsa vessel (Lewis 1983). Teredinids, which live throughout the Atlantic and Pacific, are wood-boring mollusks that subsist entirely on cellulose. While some researchers believe that shipworms were introduced to South America on Spanish ships in the sixteenth century (Kristensen 1979), it is possible that the mollusks were native to the region. Because shipworms' effects on raft viability are so pronounced, we elected to assume that they were extant in South America prior to the Spanish invasion. Some sources argue that balsa logs were likely coated in tar to decrease the extent of shipworm infestation (Haslett 2006). Though sources of tar are present on the Ecuadorian coast, there is no archaeological evidence that tar was used in raft building, therefore we do not include it in our calculations.
The data describing balsa decomposition in a marine environment come from the study Fouling and Boring of Glass Coated Plastic Balsa Blocks conducted by J.A. Lewis in 1983. Both the balsa blocks in Lewis' experiment, which were partially coated with a glass-plastic laminate, and the partially submerged balsa hull logs of an Ecuadorian raft have approximately the same ratio of surface area to volume (Lewis 1983). Since these ratios are the same for both balsa geometries, the balsa blocks and the balsa logs decompose at approximately the same rates. According to Lewis, the blocks lost 16% of their volume over the course of six months. Assuming that the 7000 km round trip between Ecuador and Mexico takes about four months, a raft would lose about 10% of its balsa wood during each round trip, if it was kept out of the water between the outbound and return trips.
This hull log degradation greatly affects the weight of cargo the rafts can hold. The shipworms not only decrease the logs' buoyancy as they destroy the balsa wood, but the wood weight loss also significantly decreases the wood's modulus of rupture. Though the balsa hull logs are not subjected to significant stresses in calm seas, the waters off the west coast of Central America are frequently and unpredictably very rough. The waves induce the maximum stress in the raft base when the raft is supported by two wave peaks close to the bow and stern. Though water can flow through the raft base, fast moving waves could temporarily hold the raft in this position.
Undamaged balsa wood with 25% moisture content has a modulus of rupture of about 15 MPa (United States Department of Agriculture 1999:Table 4-5). This value is high enough so that it does not place a realistic upper limit on a raft's cargo capacity. According to an analysis of the effect of termite damage on wood strength, losing 10% of the wood weight decreases the modulus of rupture by about 75% (DeGroot 1998). A damaged balsa log with its modulus of rupture decreased by this amount would not be strong enough to support a large cargo in rough seas.
After four months in the water, the time for one round trip between Ecuador and Mexico, an 11 meter long raft would be able to hold 10 tons of cargo, or one third of the maximum cargo capacity of a new raft. After two round trips the raft could hold only 5 tons. From this analysis, it seems likely that the rafts were not in use in the water for more than eight months. It would be inefficient to send a raft and crew so long a distance with so small a cargo.

Feasibility of Long-Distance Trade
A balsa raft between 6 and 11 meters in length, equipped with two masts of heights between 5 and 7.5 meters, would be able to sail nonstop between Ecuador and Mesoamerica. Rafts in this size range have a cargo capacity of between 10 and 30 metric tons.
Assuming that the raft could sail at 4 knots, a fast walking pace, and that it traveled about 12 hours per day, it would take between six and eight weeks to complete the 3000 kilometer voyage between Ecuador and Mesoamerica. The prehistoric Andean traders would most likely have left Ecuador in early December and arrived in Mexico in late January, taking advantage of the favorable wind and water currents. The rafts could travel south again in March, at the earliest. Leaving in late March would have allowed the sailors to avoid the rainy season in Ecuador, which ends in April. It is far more likely, however, that the sailors elected to remain in west Mexico throughout the hurricane season, particularly if some of them participated in activities having to do with ore mining, smelting, and metalworking, which required long term interactions with western Mesoamerican peoples.

Our analysis shows that prehistoric balsawood rafts were fully functional sailing vessels that could have sailed between Ecuador and the west coast of Mexico. This study greatly strengthens the argument that maritime trade was a prime mechanism for the transmission of Ecuadorian metallurgical technology and other South American cultural elements from South America to Western Mexico. We also know that the sailing vessels were capable of making at least two round trip voyages between the two regions before they became inoperable. This is a critical element in the argument, because balsa wood is unavailable in western Mexico. The craft needed to be seaworthy for the return trip, which suggests that the voyages were likely undertaken by two or more rafts, one perhaps carrying balsa logs for replacements.


Our study demonstrates that information obtained from mechanical and materials engineering analysis constitutes a powerful tool in archaeological and historical studies.

ENDNOTES
1. Spondylus shell was sacred in the Andean region and especially in the Andean highlands, where it was used for rainmaking ceremonies. Because Spondylus requires a warm water habitat, it cannot survive in the waters off the coast of Peru, which are governed by the extremely cold Chile-Peru (Humboldt) current. It thrives however, in the warm waters from the Gulf of Guayaquil north to the Gulf of Mexico. The cultural importance of this shell made the acquisition, processing, and exchange of Spondylus a major economic activity in the Andean region.


2. A 1535 sketch by Girolamo Benzoni (Benzoni 1989 [1565]) shows fishermen paddling a balsa raft rigged with a fixed square sail. A raft rigged in this style can sail only directly downwind (Romola). Because prevailing winds never blow directly south from Ecuador to Mexico, this type of craft could not have been used for transport between the two continents.
3. Calculations at the end of this section take into account the larger, unexpected gusts of wind the raft might encounter.
4. The taper ratio is defined here as the ratio of the mast's base diameter to the mast's tip diameter.
5.

REFERENCES


Benzoni, Girolamo. 1989 (1565). Historia del Nuevo Mundo. Madrid: Alianza.

DeGroot, Rodney, Robert Ross, and William Nelson. “Nondestructive Assessment of Wood Decay and Termite Attack in Southern Pine Sapwood.” Wood Protection. 3(1998):25-34.

Dewan, Leslie. 2004. Performance Characteristics of a Three Meter Model Balsa Raft. MIT UROP Report. MIT UROP Office, Cambridge. (unpublished manuscript).

Edwards, Clinton. 1965. Aboriginal Sail in the New World. Southwestern Journal of Anthropology. 25:351-358.

——— . 1965. Aboriginal Watercraft on the Pacific Coast of South America. Berkeley, California: University of California Press.

Estete, Miguel de. 1968 (1535). Noticia del Perú. Lima: Editores técnicos asociados.

Estrada, Emilio. 1955. Balsa and Dugout Navigation in Ecuador. The American Neptune 15:142-149.

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Hosler, Dorothy. 1994. The Sounds and Colors of Power: The Sacred Metallurgical Technology of Ancient West Mexico. Cambridge, Massachusetts: MIT Press.

International Research Institute/Lamont-Doherty Earth Observatory (IRI/LDEO). Climate Data Library. Columbia University, New York. 2006.

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Lechtman, Heather. 1980. “The Central Andes: Metallurgy Without Iron.” in The Coming of the Age of Iron. T. Wertime and L. Muhley, eds. Pp. 267-334. New Haven, Connecticut: Yale University Press.

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Xeres, Francisco de. 1898 (1534). Verdadera Relación de la Conquista del Perú. Madrid: Cronicas de América.

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Figure 1. Possible maritime transmission route of metallurgical technology via balsa raft (dashed line).
Figure 2. 1619 drawing of balsa raft by Joris Van Spilbergen. Speculum Orientalis Occidentalis que Indiae Navigation (from Edwards 1965b), indicating a sailor manipulating a crescent-shaped sail and sailors manipulating centerboards.
Figure 3. CAD model of raft base, indicating relative sizes and locations of tapered masts, balsa hull logs, and centerboards.




Figure 4. Free body diagram of the forces acting on the raft's mast. The mast is modeled

as a tapered cantilevered beam, encastered at the deck end.

F
igure 5. Components of wind and water forces acting on a raft.


F
igure 6. Mast safety factors as a function of mast height and base diameters. The mast is modeled as a cantilevered beam (encastered at the raft's deck) with a 2:1 taper ratio and enduring 9 m/s winds. The dashed line indicates the geometries that require 1800 newtons of force to displace the mast tip by 20% of the mast's height.

Table 1. Approximate maximum endurable gust velocity, assuming a mast configuration with a given safety factor.





Safety Factor

Maximum Gust Velocity (m/s)

1.0

9

1.1

10

1.2

11

1.3

12

1.4

16

1.5

18




List of Figure Captions:

Figure 1. Possible maritime transmission route of metallurgical technology via balsa raft (dashed line).
Figure 2. 1619 drawing of balsa raft by Joris Van Spilbergen. Speculum Orientalis Occidentalis que Indiae Navigation (from Edwards 1965b), indicating a sailor manipulating a crescent-shaped sail and sailors manipulating centerboards.
Figure 3. CAD model of raft base, indicating relative sizes and locations of tapered masts, balsa hull logs, and centerboards.
Figure 4. Free body diagram of the forces acting on the raft's mast. The mast is modeled

as a tapered cantilevered beam, encastered at the deck end.


Figure 5. Components of wind and water forces acting on a raft.
Figure 6. Mast safety factors as a function of mast height and base diameters. The mast is modeled as a cantilevered beam (encastered at the raft's deck) with a 2:1 taper ratio and enduring 9 m/s winds. The dashed line indicates the geometries that require 1800 newtons of force to displace the mast tip by 20% of the mast's height.


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