Like most mathematical things, scale is a simple concept wrapped in a specific word with deep ramifications. As far as miniatures are concerned, scale is simply the ratio of lengths between two representations of a thing. If MiniCityArt made a print of a city block as big as the real city block, we’d call that 1:1 scale. Obviously, we’re not going to make a print that large! It’s a lot cheaper to build a 1:1 building out of concrete and steel than 3D printing filament, and a lot faster! Nevertheless, this begins our visual illustrations of scale and how it relates to 3D printing cities.

We would love to be able to print entire cities and make them affordable, but cities are big. Our perception of cities as being dominated by immense tall buildings ignores the fact that less than a few percent of the area of most cities contains those tall buildings. And the height of those buildings is minuscule in relation to the width of their host city. Let’s take Detroit, a city I’m very familiar with. Detroit is about 18 by 11 miles in size, noting that 11 miles is 58080 feet. A nice 12” (1 foot) print of the city would need to be 1:58080 scale to contain just the North-South extent of the city (1 foot on the model represents 58080 feet in real life). The tallest building in Detroit, the Renaissance Center, stands 727 feet tall. On our hypothetical model, that building would be only 0.15” tall (12 inches times 727 feet divided by 58080 scale ratio), or 3.8 mm. Would you even notice it?

So, instead of trying to print the entire city, MiniCityArt models focus on the downtown - where all the landmark buildings typically are! The first photograph below is a 6”x6” print of downtown Detroit at 1:20000 scale. There’s the RenCen on the right, adjacent to the river. You can see that there’s a little detail in the buildings, and smaller buildings and patches of trees are visible as clumps, but nothing smaller than that is apparent. And we’re covering nearly four square miles (6” is one-half foot, times 20000 is 10000 feet, which is about 2 miles) of Detroit’s nearly 140 square miles. A model of the whole city at this scale would measure about 5 by 3 feet.

Our 8” models are in 1:10000 scale, so one inch on the model represents 10000 inches in the real world (about 833 feet). The Renaissance Center (727 feet, remember) is a little less than that 833 feet, so we would expect the Renaissance Center in a 3D print of Detroit at 1:10000 scale to be a little less than one inch tall. Well, the image below shows one quarter of the area of the print above, and here at 1:10000 scale. So this is about one square mile, and now we can start to see air handling units on the roofs of buildings, more details in the buildings, some bridges, and even some individual trees and monuments and public artwork.

Let’s go even larger. Well - the print will stay the same 6”x6”, but the scale will change to 1:5000. This is the scale that we use for our 24”x24” 3D printed cities. Here’s where things get really interesting. Now we can see individual buses and even cars. Some light poles show up as thin sticks. Larger works of public art now have shapes, and even more architectural details are visible, including thin spires, walls, and fences.

We’re not done yet! The data that MiniCityArt uses is called LiDAR, which stands for Light Detection And Ranging. Airplanes fly overhead and project a swath of small laser pulses down at the ground. If a pulse hits anything which causes the light to bounce or reflect back up to a detector on the airplane, a record is made of the direction and time that it took the pulse to return. With precise knowledge of where the airplane is and of the speed of light, the device calculates a position for where that reflection occurred. The collection of those positions is a “point cloud”, and only contains the position of the “hits”, not what was hit. It could have been a patch of pavement, a blade of grass, a foamy crest of a water wave, or a person’s hat. And there are millions of these “points” per square mile, sometimes tens of millions.

This abundance of data gives us the ability to 3D print cities with incredible levels of detail. The final image below is the Renaissance Center and surrounding buildings printed at 1:2500 scale. This is the scale that we print our largest models at: anything over four feet in size. At this scale, every car is present. Most light and electrical poles, all fences, all trees and most shrubs. Every bus, truck, and boat. Recliners on urban roof decks are even here. This is about the limit of our data. At this scale, we could print the entirety of Detroit, but the full model would measure 38 by 23 feet (18 by 11 miles times 5280 feet per mile divided by 2500), and would take 6 years to print on a single 3D printer.

That sounds like a challenge.