Density is a material characteristic we all know well. It hides itself within materials though, so we end up not thinking about it very often. We even have jokes about it because of this unintentional veil. “Which weighs more: a ton of feathers or a ton of bricks?” The goal of the “joke” is to trick someone into saying “a ton of bricks” because of course bricks weigh more than feathers! This joke is particularly tricky because it intentionally omits half of the importance of density. Density is defined as mass per unit volume. In our joke setup, we have learned we have an equivalent mass of feathers and bricks. The trick of the joke is the volume. We have no information on the volume of bricks or feathers we have! The mind gravitates to this omission and begins to make assumptions. One has typically held a feather and a brick and will typically make a misguided conclusion to similar volumes of each. Let’s be nerds together and see specifically how this joke works.
The density of a typical brick is 1.992 grams per cubic centimeter. This written out way already brings some clarity to what density is. A cube made of brick that measures 1 centimeter on all sides will weigh 1.992 grams. The density of a typical feather is about 0.0025 grams per cubic centimeter. Aha! This means cubes of the same size of bricks and feathers will weigh vastly differently. Let’s rearrange things to shed light onto our joke.
We defined density earlier as the following:
We can use some math to move around this relationship and discover the following:
Now we can plug in our values for density (1.992 brick, 0.0025 feather) and mass (1 metric ton = 1,000,000 grams) to determine the following volumes:
This means that in our joke, we have 800 times more volume of feathers. This is why the weights are equal and why the joke works: because of density.
Why is this all important?
Density is only one of many characteristics of materials, metal included. It is a consideration that must be factored into the material design of a component. Let’s say that we are designing an item that has a hypothetical set of needs in which titanium and aluminum share similar benefits. For the sake of our example, let’s say that we are designing an aerospace component with a particular corrosion requirement and set of dimensions, but functionally nothing else. Let’s hop onto the internet and find the densities! Keeping the same units, aluminum has a density of 2.7 and titanium has a density of 4.5. Now we must ask ourselves what this difference means to our component. After all, every other characteristic of both aluminum and titanium meets our needs in our hypothetical scenario. This example is, however, an airplane. Components made of either material may function properly, but a plane should be designed to be light to promote, well, flying. This means that although equally functional, an aluminum component is a more optimal option because it minimized the component weight.
Isn’t titanium lighter than aluminum?
Rarely are engineering problems so simple. The lack of simplicity makes the above statements confusing. Isn’t titanium lighter than aluminum? It must therefore be denser, right? We’ve seen empirically in the above density values that this is not true. Titanium is denser than aluminum. To better see why this still all makes sense, let’s add a strength requirement to our made-up component and remove our dimensional requirement. Now we must factor in corrosion, strength and weight. Titanium is significantly stronger than aluminum. This means that to achieve the same strength as an aluminum counterpart, we will need less titanium. So much less in fact that usually the final weight of an equivalently strong titanium product is lighter than the aluminum one! Our understanding of density holds up. Our concept of density as a usable characteristic is also maintained.
Why is the density of an alloy important?
These examples highlight why density is an important consideration. In fact, all characteristics of a material have a potential to be considered in some capacity when designing an item. The largest example of control of this understanding is composites. In the aforementioned examples, we saw the design considerations that density can play. In one, we could reduce dimensions to meet similar strengths, and in the other we had important differences in our item weight. Composites aim to blend characteristics from multiple materials into one single unit. This differs from an assembled component as composites are integrated in such a way to be considered one material. Density, as we now know well, defines each material’s weight within the composite. Therefore, all the desired characteristics of the composite and chosen materials is referenced against density if weight is of any concern. As an example, titanium could be easily used to strengthen a composite while adding minimal weight.
This is likely the most you’ve ever thought about density. We can see how important it is though. It is a measure of how much stuff is actually in a given space. As the world of engineering pushes components to be smaller and lighter, and for products to have more features in less space, the concept of density is perhaps more relevant than ever. Materials used in our advancing products must be more specific to their needed functions. Materials today aim to waste less – more purpose in less space. The understanding of density permits engineering to this need.