Surveying Machu Picchu

A husband-and-wife team reveals the secrets of ancient Incan urban planning and design as being rooted in sound surveying.

By Kenneth R. Wright, PE and Ruth M. Wright, JD

An urban creation in the midst of an extraordinary tropical mountain forest in the Peruvian Andes, Machu Picchu survives as an example of the Inca Empire at its height. At 2,400 meters above sea level, its massive walls, terraces, and architecture appear as having been cut seamlessly from the continuous cliff-like rock ledges. The entire setting sits over the upper Amazon basin with its amazing diversity of flora and fauna.

Proficient in the surveying and arrangement of canals, terraces, stairways, and structures, the Inca laid out a community on a mountain ridge that was a gem of environmental and sustainable design.  And they did this without the benefit of the wheel, iron, steel, or a written language. The evidence of their surveying skills is embedded in the construction that they left behind for modern surveyors to examine.

As a husband and wife team—one a civil engineer and licensed surveyor and the other an attorney focused on the environment—we have spent the last 16 years studying the evidence at Machu Picchu to learn how the Inca developed this incredible site.

Just how the Inca performed their surveys and used their tools is still partly a mystery. At Machu Picchu we have examined a still-in-place survey stone and four stone-cut arrows pointing due south. At museums we have viewed a fine plumb bob made of solid silver found at Machu Picchu as well as Inca leveling instruments. While these surveying artifacts are interesting, the results the Inca achieved using these tools tell the real story of their remarkable surveying. 

Lost City of the Inca

Machu Picchu was a royal retreat built for the Inca Emperor Pachacuti beginning about 1450 A.D. The largest pre-Columbian empire in America, it was essentially abandoned 90 years later due to the Inca empire’s collapse at the hands of Spanish conquerors.

The site is about 870 miles south of the equator on the eastern slope of the Peruvian Andes near the headwaters of the Amazon River. Machu Picchu is laid out like a patchwork quilt on a mountain ridge between two prominent mountain peaks—Machu Picchu and Huayna Picchu. It is surrounded on three sides by the Urubamba River far below. 

Pachacuti selected the site despite the challenging site conditions presented by natural topography and environment. Nearly 80 inches per year of rainfall, precipitous slopes, landslides, earthquakes, and remoteness all made the construction of Machu Picchu difficult.  Nevertheless, the long-ago builders took the challenges in stride as they carefully laid out this royal estate.  The Inca’s advanced understanding of drainage, site preparation, and foundation design resulted in well-preserved remains at Machu Picchu that allow us to opine on how it was surveyed.

Math and Measurements

We know that the Inca employed the decimal system and that they had knowledge of mathematics. We also know that the Inca used body parts as units of measurement. Per a 1946 anthropology article, the following are units of Inca measure:

ckRok’ana: a finger
Yoku: the distance between the thumb and forefinger of an outstretched hand, about 5 to 5.5 inches
K’apa: a palm or 8 inches
Khococ: the distance from the elbow to tip of hand, about 18 inches
Rikra: the distance of an average man’s outstretched arms, about 64 inches
Sikya: half of the length of a rikra, about 32 inches
Thatkiy: a pace of about 51 inches
Topo: 6,000 paces or 4.8 miles
Wamani: 30 topos or 145 miles 

Field Evidence

Although the Inca left no notes, maps, or plats, there is plenty of field evidence of remarkable site layout and line and grade control at Machu Picchu. Construction of canals with the correct cross section and slope to carry a defined rate of flow required accurate measurements and computations, especially over long distances with nearly flat slopes and sometimes across valleys or aqueducts. 

Water at Machu Picchu was carried from spring water sources 2,500 feet to the urban sector via a small domestic water canal that is still functional after 500 years. The slope of the Inca canal at Machu Picchu varies from 2.5 to 4.8%. Its cross section ranges from 20 to 26 square inches. The alignment and slope of the canal across the steep and relatively unstable north face of Machu Picchu Mountain represents a major technical achievement. 

Engineering calculations tell us that the canal was designed with adequate capacity to accommodate unstable flow conditions and appropriate slope to carry low flows with reasonable efficiency.  Any surveyor who examined this feature would know that the resulting channel characteristics relied on competent surveys and disciplined field work.

Stairway of the Fountains

The Inca canal leads from the spring to a series of 16 fountains. The uppermost fountain is next to the royal residence so that the emperor could enjoy the purest water. An analysis of the elevation difference and length between the springs and fountain #1 reveals that it was an Inca surveyor who designated the location of the royal residence so that the first fountain would be at the emperor’s doorway. The other 15 fountains lie perpendicular to the contours in series below. 

Each fountain has an east-west orientation except for fountain #10, which was likely reversed to create special interest. Field testing of the fountains’ hydraulic characteristics showed that the fountains would operate satisfactorily, with a good jet for filling water vessels, at flows as low as 3 gallons per minute and as high as 26 gallons per minute, with an optimal flow of 7 gallons per minute. 

The elevation and location of each of the fountains and connecting channels are optimal to achieve these flows. Alongside the fountains is a steep walkway, known as the Stairway of the Fountains. The stairway splits in two around fountains #5 and #6 to create an interesting aesthetic and to allow access to the two fountains from two sides. The steps are functional and attractive with uniform risers; the Inca surveyors were able to measure horizontal and vertical distances and divide these numbers to achieve evenly spaced steps over the 180-foot distance and 85-foot vertical drop from fountain #1 to #16.

To the south of the fountains is the main drain that effectively splits Machu Picchu’s urban sector from its agricultural sector.  It is the drainage focal point for the site, receiving gravity drainage from both the north and the south. The grade of the drain and its capacity are just as a modern surveyor and engineer would have planned it.  A sharp rock juts from the north wall of the main drain, which we judge to have been a control point for field surveys.

Temple of the Sun and Garden Terraces

Adjacent to fountain #3 is the Temple of the Sun, also known as the Torreón. This feature is a different type of example of Inca surveying because of the special alignment of its east-facing window. The temple is a D-shaped building with a carved ceremonial rock inside.

As the sun rises on the winter solstice (June 21), a string weighted by a plumb bob hanging from the center of the window lintel casts a shadow that aligns with the even edge of the ceremonial stone. Astronomical knowledge and careful alignment by the ancient surveyors is made evident to visitors to the Temple of the Sun each June.

Machu Picchu’s agricultural terraces cover 12 acres in total. Beautiful, functional, proportional, they’re perfectly sloped for shedding water towards drains without soil loss. Certainly the Inca surveyors had their hands full ensuring that retaining walls as much as 20 feet high would be in the right place. Most of the terraces at Machu Picchu are linear, the surveying for which was well conducted. 

The terraces below and west of the guardhouse would have presented a special surveying challenge, however, because they are gracefully curved to hug the terrain.  To achieve these uniformly arced terraces, the Inca surveyors would have had to consider the hillside stability, its concave shape and slope, as well as the placement of the Inca trail and guardhouse.

Artisan’s Wall Staircase

Of all of the staircases at Machu Picchu, it is the Artisan’s Wall staircase with its 60 granite steps that is the most uniform. The staircase commands the view from the Temple of the Three Windows and is even more magnificent as you draw closer.  Good surveying led to this masterfully built set of stairs, the subject of thousands of travel photos each year.Overall, the Inca had 18 distinct styles of wall construction. The grand stone walls built by the Inca at Machu Picchu and other Peruvian archaeological sites have a 10% batter, a vertical angle of about six degrees. This provided the stability that has helped these walls endure for five centuries. Using the decimal system made it easy for the stoneworkers to follow the rules of the designers’ plan of ten vertical to one horizontal.

Cave of the Sun

The Intimachay, or Cave of the Sun, is located northeast of the Temple of the Sun. The altered and embellished cave has a window that archaeoastronomer David Dearborn concluded was designed to admit the light of the rising sun during the December solstice, a significant day for the Inca.  On December 21, the sun’s rays rise over a dip in the ridge of a mountain two miles distant and enter the window. If you stand in the interior of the cave you may be astounded to see a bold ray of sunshine coming from the far-off notch, penetrating a narrow tunnel, and casting a beam of light on the slanted rock at the back of the cave. How the ancient surveyors were able to align the tunnel with the sun through a distant notch on this special day taxes the imagination.

The building construction details and layout at Machu Picchu demonstrate consistent imperial Inca design standards. You can recognize Inca design throughout the empire because of its geometry and uniformity. Central plazas, streets built on a grid, gravity flow water supplies, and good use of special views were standard for the Inca. 

At Machu Picchu, however, these survey principles were modified and enhanced to meet the environmental and physical conditions of the ridge-top site.  The result is that, in the 21st century, Machu Picchu enthralls its visitors with the perfection of its relationship to its surroundings. 

Survey Tools

Inca survey tools that we have seen are a silver plumb bob (that American academic, U.S. Senator, and explorer Hiram Bingham found at Machu Picchu in 1912), level instruments at the Inca Museum of Cusco, and several pointed stone survey markers at various Inca archaeological sites including Machu Picchu.

Bingham discovered all kinds of tools left at Machu Picchu by its ancient workers, including the unique, precious metal, silver plumb bob, perhaps used to mark the June solstice at the Temple of the Sun. Also, the Inca Museum of Cusco features Inca and pre-Inca artifacts, including leveling devices that can be viewed by the public. They are vessels that hold water, often with handles, and Incan surveyors used them to create a true horizontal plane much like surveyors the world over used in antiquity.

The sharp rock along the main drain (mentioned earlier) is a remaining embedded stone Inca survey marker at Machu Picchu. It would have been used as a reference point for layout of not only the main drain but the entire hillside south of the main gate. Likely there were many other such reference points during construction; why this survey marker was preserved remains a mystery.
In different places at Machu Picchu we have seen four arrows carved in stone, pointing south. One of the arrow stones is at the summit of Huayna Picchu pointing south to Salcantay Mountain, which the Inca considered holy. Surveyors used the cardinal directions routinely and were master astronomers throughout Andean pre-Columbian history.

How did the Inca, with primitive equipment, integrate the royal estate into the landscape so well? Professional surveyors, who have their own reasons to marvel at Machu Picchu, understand it began with the surveying. The Inca were able to maintain grade and line control in their canals, develop proper hydraulic conditions for their fountains, develop long, even staircases, and orient structures to precise astronomical phenomena—and each other—because they were good surveyors.

Standard ancient surveying practices of measuring altitudes, horizontal angles, and distances on the land surface—and positioning proposed construction or engineering works—clearly have a long, proud history. A Machu Picchu visit for any land surveyor today will certainly add to the pride in their profession.

Kenneth R. Wright is the founder of Wright Water Engineers, a 50-year-old Denver-based company that focuses on water resources engineering.

Ruth M. Wright is an attorney and former Colorado legislator with a long interest in planning and engineering.  She is author of The Machu Picchu Guidebook. 

» Back to our October 2012 Issue