# Designing a LEGO skyscraper – part I

What exactly is involved in designing a LEGO model of a real skyscraper ? I wish I had a knack for doing it by eye – intuitively figuring out how wide (in terms of studs) and tall (in terms of brick heights) the model needs to be just by looking at pictures of the real building. I am sure some people can pull it off but this approach is clearly a hit-or-miss for many others (which is the only way I can explain all the models I have seen that are badly out of proportion compared to the real building).

Being an engineer, I tend to rely on a more rigorous approach based on math (very simple math as it turns out) instead of using just my eyes and intuition. The first step is picking the scale that works best for the model. The scale is just the relative size of your model compared to the actual building – expressed as a ratio. So a 1/100 scale simply means that your model of a 500 foot tall building would stand exactly 5 feet tall. Now, this 1/100 ratio applies to all the dimensions in the model – not just the height. And so if the actual building is 100 feet wide, your model would have to be 1 foot wide or it would not have the right proportions (it would either look too skinny or too squat compared to the real building).

There is obviously a trade-off associated with scale. The bigger the scale, the more accurately you can represent all the elements of the original building in your LEGO model. But too large of a scale can also result in a massive, unwieldy model with a prohibitively high piece count and cost. On the other hand, using too small of a scale can force you to compromise on accuracy (probably more than you would find acceptable). I try to find the sweet spot with my skyscraper models – a scale that is somewhere between the tiny scale used in the LEGO Architecture series and the huge scale used for the models you would find in a LEGO Miniland. In fact, the scale I pick is usually the smallest one that would allow me to accurately represent the floor count and the window count of the original building.

Let me use the Empire State Building as an example – to show how I arrived at the 1/230 scale I ended up using for my model of this building. The first step is getting the dimensions of the real building and here Google Earth proves to be very useful.

As you can see from the 3D view in Google Earth, the Empire State Building tapers as it rises and there are 7 distinct sections that make up the building. The largest section is the main tower (as I call it) which spans 42 stories (floors 30 through 71) and I am going to use that to determine the scale of my model. Not everyone is aware of this, but you can use Google Earth to make very precise measurements. I can zoom into a specific area in the 2D view and hit the ruler icon to make a measurement. I did this on my phone and measured the footprint of the main tower to be 184 x 134 feet.

Next I take a closer look at the window configuration in the main tower. On the longer side the main tower has windows arranged like this

-xx-xxx-xx-xx-xx-xx-xx-xxx-xx-

(where x represents a window) with the middle portion recessed. There are 2-wide and 3-wide banks of windows but one nice thing about this building is that all the individual windows have the same width which is also similar to the spacing between the different banks of windows. So if we were to represent each window using one stud, the longer side of the tower would be 30 studs wide. The shorter side has 7 banks of 2-wide windows

-xx-xx-xx-xx-xx-xx-xx-

and that adds up to a total of 22 studs.

Next we figure out what scale we would be using if we have 184 feet represented using 30 studs. Here are some of the key dimensions of a LEGO brick – it is 0.8 cm wide and 0.96 cm tall. Three plates are equal to a brick in height and so each plate is 0.32 cm tall.

If each stud is 0.8 cm wide, 30 studs would be 30 x 0.8 = 24 cm wide. We need to convert the width of the real building into metric units as well. 184 feet is roughly 5608 cm (1 foot = 30.48 cm). So our scale ends up being 24/5608 or roughly 1/230. We arrive at roughly the same number if we use the dimensions of the shorter side (134 feet) and the 22 studs we would be using to represent it in our model (22 studs = 17.6 cm, 134 feet = 4084 cm. The scale is 17.6/4084 = 1/230).

Once we have the scale, it is easy to know how tall our model will be – just divide the total height of the Empire State Building (1454 feet) by 230 and you get 76 inches (6 feet, 4 inches). Next, we need to figure out how tall each floor of the building will be in terms of brick heights (actually I prefer to use the smaller unit of plate heights). In most older skyscrapers, each floor is typically 12 feet tall. This is also the number you get when you divide the total height of the building (1250 feet which is the roof height not including the spire) by the number of floors (102). So the main tower should be 42 x 12 = 504 feet tall. It turns out this estimate is close enough to the actual measurement of 502 feet from the drawing at this link.

So how many plates does 12 feet translate to ? 12 feet are equivalent to 12 x 30.48 = 366 cm which in our model should translate to 366 / 230 = 1.59 cm. This is equivalent to 1.59 / 0.32 = 5 plates. It is important to keep this in mind when we design the model. We may be tempted to just use 2 brick heights (6 plate heights) per floor to make our lives easier but that would just make the final model 15 inches taller than it needs to be (the proportions just would not look right).

Now, not everyone has the wherewithal to build a model that is over 6 feet tall using (as it turns out) 20 K pieces. So what do you do if you want to build something smaller ? Then, it’s basically a matter of balancing your target size/cost for the model with the compromises you are able to live with in terms of accuracy. The first model I built when I got into this hobby was actually a smaller version of the Empire State Building. It used a smaller scale (1/360). Here I used 19 studs for the wider side of the main tower instead of 30 and one of the compromises I had to make was to use a single stud to represent each of the 2-wide and 3-wide banks of windows. Clearly I was not happy with what I had to give up in terms of accuracy with this model and that is what led me to build the bigger, more accurate version that I now have.