By Richard Bleil
A friend of mine was watching the Tranformer movie Bumblebee as we sat side by side on a flight today. As I glanced over, a question struck me; I wonder what the average density of Bumblebee is in the robotic form.
Density is a “physical property”. There are only two types of properties, physical and chemical, for any matter. They correspond to the two types of changes, physical and chemical. A “Physical Change” is one where we change the material at hand without fundamentally changing what it is. For example, phase changes like melting or boiling are physical changes; as we melt ice or boil water, fundamentally we have water, just at the three different (main) phases of matter, solid, liquid and gas. We can break something, which will produce smaller pieces, but we haven’t changed what it is. I tried to break a credit card today (as I did not have scissors), but it was too malleable (bendy), not brittle enough to break.
On the flip side of the coin are chemical changes. In a chemical change, we fundamentally change what we have into an entirely different element or compound. Iron rusts to form some type of iron oxide (actually, it’s more complicated than that but we’ll roll with it). Since rust is fundamentally different from iron, the question of if an element rusts or not is a chemical property. Whether or not it burns is another chemical property, since a burnt turkey is fundamentally different from an unburnt one, where we will pretend like “unburnt” is actually a word.
Density is a physical property. It tells us how much mass (quantity of matter) we have per some given volume. For example, water (to a good approximation if you’re close to room temperature) is about 1 g/mL. That means if you have 1 milliliter of water, it has about 1 g of matter in it. Since it does not correspond to any kind of chemical change, density is a physical property.
Okay, density is mass divided by volume. To figure out the density of Bumblebee, we must know the mass (related to but different from the weight) and volume. Volume will at best be an approximation as he is an irregular shape.
In ancient Greek, the King was related, as I understand it, to a philosopher named Archimedes. The concept of density was well-known, but volume was difficult to measure for all but the simplest shapes. The King had reportedly given a known mass of gold to a jeweler and commissioned a new crown. When it was returned, the King wanted to know if the jeweler had stolen any of the gold. Certainly, it was the correct mass, but the jeweler could have taken, say, 100 grams of gold and substituted it with 100 grams of a cheaper metal and the mass would be the same, but the density would not. Alchemists of the day were proficient enough to be able to extract out anything that was not gold, but in so doing would destroy the crown whether or not the jeweler had stolen gold, which defeats the purpose of the commission. So, he challenged Archimedes to figure out the conundrum.
Presumably, Archimedes struggled with how to determine the volume of the crown without melting it down. After a long fruitless day, he decided to go to the public baths. That day, the bath attendant overfilled the bath, and as he sat in it, some of the water sloshed out. He realized that the volume of water the sloshed out equaled his own volume, and was so happy he ran down the street naked shouting “Eureka! Eureka!” which apparently meant “I found it! I found it!”
What would you assume a man means when running naked shouting “I found it”?
Today, water displacement is a common way to determine the volume of an unusually shaped object. Measure the volume of water, add the object, and measure the new volume. The difference is the volume of the object. But, personally, I’m not about to ask a huge battle hardened robot to take a bath, are you?
So, back at the oddity at hand. When asked, Michael Bay said that Bumblebee is 17.5 ft tall, which is about 5.9 m (or 590 cm). Looking at the photos, I’m going to guess (and this is only an approximation) that Bumblebee is about one third as wide as he is tall (about 200 cm), and maybe a third as thick as wide (let’s say 70 cm). Now, volume is length times width times height, so Bumblebee’s volume is about (590*200*70=) 8,260,000 mL (8,260 L). This is roughly 2,200 gallons.
Now, we need a mass. In the movie, Bumblebee turned into a VW bug, which had a weight of about 1,700 lbs, or 790 kg. Let’s assume that the VW bug was about 2/3 empty space (around the engine block, trunk, etc.), so we can assume Bumblebee has a mass of, oh, let’s say 3 times this, or roughly 2,400 kg. This is 2,400,000 g.
Thus, the density of Bumblebee is 2,400,000g/8.260,000mL, or roughly 0.3 g/mL. To put this into some kind of perspective, water has a density of 1.0 g/mL, which is more than 3 times the density of Bumblebee in the robot form. In other words…in water, Bumblebee would FLOAT!!!!!!!!!!!!