Week 8 Lab Summary: Measurement

Brett Brzycki, Edward Marotta, Lily Petersen

This week’s lab focused on ancient methods of measurement using the groma and knotted ropes associated with Egypt. The knotted rope was an Egyptian measuring tool that created a right angle by dividing a rope into 12 equal segments with 13 knots that would create a 3-4-5 right triangle. However, the knotted rope was a small part of the lab, and the central tool of the lab was the groma. This device was a Roman surveying instrument that used suspended strings and weights to establish sight-lines and 90-degree angles. Alongside the groma, groups also used three green poles to line up three points in a line to create a new point in the line. Further, groups used a wheel-on-a-stick or a measuring tape to find distances between points.

The lab was divided across Monday, Wednesday, and Thursday. On Monday, groups prepared the knotted ropes and created 3-4-5 right triangles. On Wednesday, the groups constructed their gromas. Finally, on Thursday, the groups used these tools outside to create a Roman road, an augur grid, lay out a Roman colony, and measure an irregular area.

The goals of the lab were threefold: first, to test whether the groma and knotted ropes could effectively create straight lines and 90° angles; second, to understand the labor and coordination required to use these tools effectively; and finally, to gain a small experiential sense of what it felt like to survey in the ancient world.

Tools:

Knotted Rope:

Three people squat, each holding a corner of a piece of rope, creating a right triangle. — Knotting the rope at standard intervals

On Monday, every lab group took a length of rope that was approximately 33 feet in length, and knotted it roughly every 30 inches, so that we ended up with 13 knots and 12 sections. Many groups had to make their knots a little closer together, because their lengths of rope were not quite long enough. Using these knotted ropes, we were able to form perfect right triangles by having three people stand with 3, 4, and 5 segments between each of them. From this, we could then make squares or rectangles by maintaining the right angle while introducing another group member and changing the lengths of segments in between each other. The main purpose of this activity was to show how the ancient Egyptians were able to make such accurate right angle measurements, such as for the base of the pyramids at Giza.

Groma:

On Wednesday, every group was provided with the parts to make a groma, as listed below:

Individual Gear:

1 55″ pvc piece
a 3-piece pvc crossbar unit
1 4″ pvc piece

1 4-way divider
1 each 3-D printed top and bottom brackets
4 screws
yarn/string and something to cut it with
1 bead
1 steel plumb bob

4 10′ pvc pieces
4 3-D printed endcaps
yarn/string and something to cut it with
8 beads

4 3.75″ pvc shafts
8 pvc butt caps (4 with drilled holes)

Group gear:

Scissors / knives / razors
pens
sand / funnels
Screwdrivers

Using these, we then attached four small lengths of PVC pipe to form a perfectly perpendicular cross at the top of a post, from which we dangled lengths of string from each end of the cross, as well as the middle, that lined up to form two straight lines that could be used to plan out straight lines or right angles, as seen in the image below:

A man stands holding a pole with a horizontal cross affixed atop, with string dangling from each of the arms of the cross. — A completed groma.

Lab:

Road:

One person crouches in front of a groma and is lining up the strings, while another person, in the distance, is holding a stake in line with the strings. — Group 6 using a groma to create a straight line.

The first of the four activities that we did in our lab on Thursday was using the groma, stakes and flags to plan out a straight line, in order to replicate how the ancient Romans built their roads. This was accomplished by planting the groma at a point, allowing the strings to fall in a straight line, and then having a person with a stake stand directly in front of the line of string, adjusting until the person crouching behind the groma said that the stake was perfectly in line, and then planting it in the ground before sticking a flag in the location where the stake was. The hardest part was planting the first two stakes, but then after that point, it was much easier to tell whether the stake being used was in line with the other two, as they were easier to see than the strings. Using this method, we spent 30 minutes going in straight lines, and turning 90º when we met obstacles. All groups were able to go between roughly 200 and 500 feet in this time.

Grid-Making:

Bird-Sign:

Two people sit in the center of a grid demarcated by flags, while a third poses like a bird in the background. — Group 6 looks for bird signs, with Olivia as the Bird.

The second activity was the formation of a small square, with a center null point, in order to form four quadrants to attempt augury. Groups then looked for birds and noted what they saw. More research would be needed to understand the soothsaying traditions of Rome, but it was an easy precursor to developing a larger Roman colony.

Colony:

A diagram of perfect squares placed in a 4x4 grid with slightly wider divisions running between the middle squares, forming a cross shape. — Diagram of how a Roman colony was laid out

A grid of 2x2 squares is placed on a field with flags. — Diagram of how a Roman colony was laid out

The third exercise that we performed was the planning of a Roman colony. In this activity, our six groups dropped a zero point with the groma and then began to plan out the colony. There were two methods that emerged in our groups. The first method was to start from the zero point and to walk along the diagonals of each of the square plots, setting flags down at the appropriate lengths. The second method was to start with the roads around the square plots, following two parallel lines and marking out the corners of the plots. Our classmates felt very satisfied and that this process was really easy to do. The groma became cumbersome to some, and most preferred to simply mark out spots with stakes.

Measurement of an Irregular Place:

A schematic has been drawn on a grid, consisting of a large square from which right triangles have been greyed out. — Group 2’s calculations for measuring the area of the Mini Bald Spot

Our last activity was to attempt to measure the area of a building or location by marking out a square and cutting out right triangles. Groups measured a rectangle around the perimeter of a certain structure or building. Group 2 was able to finish removing triangles from their area by measuring out segments and then later subtracting the area by hand. Most groups noted errors in the measurements due to the angles of hills and uneven ground, especially since most of the line segments didn’t add up. There was ultimately a lot of confusion with this method, especially because irregular formations were exceedingly difficult to measure without guidelines.

In pursuit of the three goals of the lab, there were several complications, including strings snapping, wind moving the plumb lines, uneven ground, hills, sprinklers, communication across distances, and the need for multiple people to hold poles, place flags, steady the groma, and record measurements. A persistent issue that people discussed both in their reflections and in Friday’s class was the wish that groups could have consisted of six people instead of four. Many thought the groups could have worked more effectively if one person used the groma, two people measured the distances, and three people held the poles.

The four field activities showed the different strengths and limits of the ancient measurement techniques. In the road activity, many groups discovered that the groma was useful for establishing the first few points of a straight line, but once two reliable points had been established, the line could be extended more quickly by sighting from the existing flags and one string from the groma. The augural grid and colony exercise showed how right angles and straight lines could be expanded into larger planned spaces, but they also showed that the groma became irrelevant once the basic layout was established. Finally, groups measured irregular areas around campus, which revealed that it was actually difficult to subtract triangles to calculate an area because of the uneven landscapes and objects that blocked people’s vision. Bianca Lott’s reflection captures this feeling well:

“More broadly, the lab showed that ancient measurement was not simply about geometry: it was about adapting tools to imperfect real-world conditions like wind, uneven terrain, and human error. The Romans may not have had modern instruments, but they clearly developed methods that were remarkably effective when used collaboratively and carefully” (Lott, Week 8 Lab Journal: Measurement).

Overall, this lab showed that the groma and the knotted measuring rope were useful tools, but their effectiveness, especially the groma, relied on good conditions, careful planning, and clear communication. By creating Roman roads, an augural grid, a colony grid, and finding the area of an irregular space, the class gleaned an understanding of how ancient surveyors could create these large grids on any physical landscape, while, at the same time, experiencing the same small hardships that ancient workers had to deal with on a day-to-day basis.