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Incan Roads and Least Cost Paths

Ryan Connnaghan


This Project looks at the Inca road system to see what a comparison of the actual road paths and those generated using Tobler's function in a cost path can tell us about the origins of the road.  Specifically, I am attempting to see if this will tell anything about whether the Inca constructed the road, or if they were in place already.  I am using Arcmap for the least cost path, and comparing the results in Google Earth for some of the pathways.  


The Inca road system, or Qhapaq Ñan, is an extensive network of roads connecting different regions of the Inca empire, from Ecuador to Chile and Argentina. It is currently under consideration as a World Heritage Site by UNSESCO.  As part of this, 15,000 km of Inca roadways are being surveyed (United Nations Educational, Scientific, and Cultural Organization).  There has been a long debate over who constructed the roadways, and if they were in place prior to the Incan conquests, or if they were constructed to control the outer regions of the empire.  

Theoretical Approach and General Expectations

To begin this project, I digitized several roads from Hyslop(1984) The Inka Road System.  Of the 3 maps, 2 were roughly one degree on either side, while the northern road was 2 by one degree.  This scale, with one degree being roughly 111 km tall, and varying in width with latitude, makes the data quite coarse.  However, 90 meter DEMs were used, somewhat alleviating this problem.  

I am looking for several indications that the road was constructed by the Inca, or the previous inhabitants.  First, looked sites that pull the road away from the generated paths.  Either the road would be shifted toward a site occupied before the Inca conquest but not during their habitation, which would indicate the road was there first, or the road goes to a site established by the Inca, indicating that the road was placed by the Inca.  Though, this one can also indicate the Inca placed the site along the road on purpose after the occupation, as many of the Tampu were.

Ideally I wanted to find a settlement in place along a road that was far away from any Inca settlements, and was not anywhere near the idealized path.  I was able to find only one path that fell far from the least cost path, but there was no settlement associated with the change of course.  


I used the least cost path function to compare this generated path to several digitized maps and a GPS traced path of the actual Incan road.  By comparing the two, I hoped to find some differences that would show a path detoured toward a site that existed prior to the Inca Empire controlling the area.   

I began with a small test route until I figured out how to properly complete the Cost Path. 

Using Google Earth, I traced a section of road from Machu Picchu a short distance.  I chose this road because it was easy to see on Google Earth, and included many pictures so I could be sure I was still on the path, and not on a modern road.   This path also included a large elevation change.  In arcmap10, I could not get the program to take the hiking function into account.  It returned a circular map of time, with some minor variation along the cardinal points that was clearly not correct given the terrain. 

I did get the function to work in ArcMap 9.3.  Below are the results.

This is the cost path, in yellow, traced along with the actual path taken from google earth, in green, with the background of elevation.

And here is the same map, with the background being the path distance from the northern point.

Digitized Maps

Now that the function worked, I have digitized the map of the northern road from Hislop (1984:38).  The accuracy of this map is not great, and I have found differences against Google earth of .6 to 2 kilometers, though at the scale of the map from the book, a kilometer is about the width of the lines drawn on the map.  This is clearly not meant to be a very accurate map, but it was the best I had available.  

In the last week, I finally found a valid segment of GPS coordinates tracing the Inca trail leading to Machu Picchu.  This trail was foung on a hiking website,  A roughly 20 km segment lined up well with the short rout I had already looked at, so I knew the route was really on the Inca road.  In addition to that, pictures were taken at regular intervals along the path, showing it was indeed not a modern path.  

This path is the only one that had a different least cost path than the Inca road.  This bring into question of why the road diverged from following the least cost path.  Hyslop (1984:248) does speak of the roads having different purposes, such as military movements, governance or ceremony.  It is likely that given the small width of the road, that it was not often used militarily.  


Northern Road

The northern road in Peru is set over a mostly flat section of ground crossing several areas of desert.  This section of road is between Chan Chan and Tambo Real.  This area was dominated by the Chumu state, and many of the sites along this route have pre-Inca origins.(Hyslop 1984:40) 

Below is the digitized northern road in blue, and the least cost path in orange, over top of the DEM

The road has a break in it in the middle, and I calculated the cost path to the points in the middle to see if there was a reason for it.  The northern part of this road is very straight(Hyslop 1984:46).  Hyslop describes this section of road as running through Farfan, but the road is destroyed by the present day population site of Guadalupe, just to the northwest. 

Below is a map of the path distance with the roads. First a close up of the middle points, then the whole road. 

The terrain is generally flat as it runs along the coast.  Here, you can see the hills to the north and east affecting the cost.  Along the coast, it gradually adds up, but the hills are shown with  lighter areas where the slope increases the cost. 

Canar to Azuay road

This section of road runs near the Pan-American Highway, but takes a much different path.  I thought this would be a place where I might see some variation between the least coast path and the actual road.

Once I ran the cost path, it followed the general path of the road, with some minor variation on the southern portion.  Below are the two paths, the Inca road in green, and the least cost path in red.
The least cost path generally follows the Inca road, and does not deviate toward the Highways path as I thought it might.  As the Highway is built for cars and not pedestrian traffic, Tobler's function will not accurately predict the path, as the costs are different.  I did not realize how different it would be.

Uspallata Road

This section of Inca road follows a valley and runs along the river. Again, the Inca road and the least cost path matched up very closely.  

Below is the map of the roads, red for the least cost path, and blue for the Inca road, and they are placed over the DEM. 

Below is the cost path, and as you can see, the road is forced to the right greatly by the steep slopes on either side of the valley.
The red least cost path line also shows it's tenancy to go straight along one of the cardinal directions over flat terrain, while the actual road most likely follows slight variations in terrain.

GPS trail to Machu Picchu

This trail is approximately 20 Km long, and follows a path along the ridge line.  I believe there may be a second trail close to the least cost path, but I cannot say from using Google Maps alone. 

Below are the paths, yellow being the least cost path, and pink the GPS trail, over the path distance raster.


And here below is the same over a 1 arc second DEM, showing the GPS trail following the ridges, and the least cost path following the valley. 

In the end, they both enter the site on the same trail, and there is a path where they both converge leading up the hill into the site.  


The Northern Road.

This road's relatively flat terrain allowed the least cost path to match up very closely to the Inca Road.  This road was also visible in sections on Google Earth, and it showed the accuracy of the scanned map compared to Google Earth. The road was off by about a kilometer in some places.  I should note that while I am confident I can see the actual road, I cannot be sure.  The region has many paths crossing it, and one path lines up with the direction of the road very neatly, but is off to the east of this digitization. Below you can see a section off by about .6 Km from Google Earth

Other areas are further off than this section, and in areas, there is no sign of the road.  This road seems to have the right details, with 2 clear sides and a middle clear of debris.  However, at this resolution, that is how many of the roads appear. 

Canar Road

This section of road I thought would hold the potential to show a wide difference in cost path and the actual road, due to the route the Pan-American highway takes in this area. The black and white line shows the highway, while the line with green down the middle is the Inca road.
As the least cost path was very close to the actual road, this shows the the highway must have been built using a different set of variables, or is connecting places that I do not know about.  The requirements for the highway are different than hiking, but I was hoping the road might deviate to a certain settlement.  

Uspallata Road

The road here follows the valley, and the cost path follows the Inca road very closely.  One part would cross the river, but if I had added a restrictive layer on the rivers, this would have most likely kept the least cost path on the one side.  I thought that this map would line up closely because of the restrictive nature of the valley.  The steep sides on each side keep the road toward the valley floor.  

One interesting point on this map is the northern section, that shows the least cost paths tendency toward the cardinal directions.  While running the function on Arcmap 10, it failed to implement the proper functions, returning a near circular path distance, with slight deviations toward the 8 cardinal points.  It appears that this is part of the way the function is implemented, and that it will have a tendency to run longer distances along the points.  While I don't think it affected the results much in this case, it is an important point to know.  


The GPS trail was the only one to take a completely different path.  The GPS trail stays toward the top of the mountains, while the least cost path follows the valley floor.  There does appear to be an Inca road along this path, and it is possible that the route followed by the hikers was not the route that would normally be followed from that starting location.  It is likely this was a route taken by those approaching from the southern valley. I also ran a view shed analysis from Machu Picchu to see if the site was visible from the path, but I was not able to find a section could be seen from the site.

There was one section of the cost path that is interesting.  Here is a close up on the area near Machu Picchu climbing the last slope.  The thicker orange line is the GPS trail, while the yellow line is the least cost path.  The white line is a trace of the actual trail leading up the hill. 

 Instead of following the steep path in white up the side, the least cost path crosses the slope at an angle, and even appears to switch back at some points.  I am not sure if this is an error in the DEM causing the deviation, or the way the least cost path runs. 

The GPS trail was very nice for it's accuracy to the trail, and the level of detail it provided in contrast to the course data from the digitized maps.  

While this is an Incan trail being followed, it is not necessarily the path that would have been taken given the starting point.  it is possible that the path is actually a road leading north, and one leading west, from a starting point to the south.


There were certainly some areas where a study of just these maps was limiting.  River crossings, and their costs, were not taken into account.  Certainly some areas were easier to cross than others, either a shallow area to ford or a narrow area to build a bridge over.  Without a better knowledge of these factors, I left them out of the analysis. 

Tobler's function is meant to be used for hiking, where I am looking at roads.  This implementation of the function took into account only the topography, and did not take any other terrain considerations into account.  Certain types of terrain would limit road construction, or increase its cost.  Areas of swampy land, or hard rock across a slope that would limit its ability to be cut into, would be examples of variables that were not looked at. 

To increase the accuracy of the function toward the actual roads, I believe several things can be done.  First, giving a value to the river crossings could keep the program from needlessly crossing the river.  I also think you could edit the values of the hiking function toward walking on roads over hiking trails. The road may have different values for going over or around a hill.  The cost of hiking across a slope, in the function, is the same as flat terrain.  Cutting into this hillside to construct a flat road may make constructing the road on level ground at the bottom of the hill a more attractive option.  Switchbacks are also not taken into account at all, and many can be found in the road system when it meets a steep slope.  Such a steep slope is listed as impassable by the hiking function.  I'm not sure if this is correctable in the way the function is run in Arcmap. 

For the digitized maps, the accuracy of the digitized road placed into Google maps is at times off 1-2 kilometers.  this is most likely a combination of digitization error, an unspecified coordinate system(I used UTM84), some error in the original survey, and the coarseness of the data.  In addition to this, in the areas that I could clearly find on Google earth, these digitized maps do not take into account the small variation in the roads.  While these maps gave a good idea of the rough path of the road, it does not follow the variations the paths take, and it is maps at this scale that most likely leads to the idea that Inca roads are often straight. 


What do the results mean in terms of the larger question? What might be future directions for research?

In the end, I believe that a least cost path analysis will never really be able to say if the road was built by the Inca, and not a pre-Inca group.  It does give a good fit for where their roads should be, but there is no guarantee that some other reason for a detour is needed.   Without an extensive set of sites with their chronology of occupation both before and after the Inca occupation, you cannot conclusively say who built the roads.  It is likely the Inca used existing roads and paths, and that they improved the roads and network.  The locations of Tampu, and their association with the Inca, may show a formalization of the road, with their placement approximately a days travel from one another.(Hyslop 1984:chapter 20) . You can see new Inca settlements with Inca road leading to them, Showing what a true Inca road looks like, you can not say that anything that appears similar is a road build by the Inca.  It is unlikely the Inca would destroy a road or path to create their own, but would improve right over the existing network.

Hyslop (1984:274) talks about the difficulty in obtaining archaeological evidence for older roads that were built over by the Inca.  This is, unfortunately, likely the best method for truly saying who constructed the first road there.  It is likely that any roads were built, at least partially, over paths between older settlements.  The hiking function does show an approximate fit for walking between sites, where it is likely that individuals would take the easiest path they could.  Old paths would be covered with stone, leaving little to see of the old path.

So, while the cost path may help identify paths that were in place prior to the Inca conquest, it will not prove that the road was built only by the Inca.  Dates for the location would help determine if the road was constructed, but still cannot say if the path was created by the Inca or just improved upon.  I believe the only way to say if the road was constructed by the Inca is to conduct and excavation of the road, and attempt to date the construction.  

The question I originally proposed is also more complex than I originally anticipated.  The area was home to many groups at many levels of complexity.  Some had formal road systems already, and large urban centers connected in networks.  Others were much smaller, but it is likely that many areas at least had beaten paths to get between them.  By their design, the least cost paths are routes that individuals would use to travel and trade.  But how do you tell who is responsible for the roads if they are used by each group who lived in the area over time.  Does a path built over by the Inca count as an Incan road?  Or is it only an Incan road if they forged a new path where none had existed before. To define who built the Inca road, you will first need to define what you count as an Incan Road, which is a more complex problem that I realized

References Cited

Hyslop, John

  1984The Inka Road System.  Academic Press, New York

United Nations Educational, Scientific, and Cultural Organization

 2012Main Andean Road - Qhapaq Ñan.  Electronic Document.  Accessed May 1, 2012


  2012Inca Trail (Cuzco - Machu Picchu).  Electronic Document.  Accessed April 29, 2012

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