By Adam Kenvarg, Autodesk Sustainability Education Fellow
When doing design work, some people (engineers included) gloss over initial, basic calculations. Some see it as needless, others are intimidated. With such powerful software tools, why do we even need to do initial calculations? The main reason is ensuring that you can actually build what you propose.
Figure 1: Just because you can design something doesn't necessarily mean you can actually build it
I have often come across designs or concepts that hover between tremendously impractical and patently impossible. These designs are unfortunately not quick drawings on the back of a napkin, though; they are often long projects, either as part of a competition, school project, or research project. A great deal of time, effort, and in some cases embarrassment, could have been saved with some basic back-of-the-envelope calculations.
Pause and Ask: “Hey, Wait a Second”
Whenever you see a number that seems either too big or too small or too good to be true, you should pause. These are the places where basic calculations, and revisiting your assumptions and estimations, can be a great help.
For instance, in one funded research project for Engineers for a Sustainable World, a group of students were tasked with developing a solar energy storage system for developing countries. They settled on storing solar energy as potential energy by raising a large amount of water to a height and letting it drain down over time, generating electricity. This concept of pumped-storage hydropower is a very real and reasonable one. However, the scale needed to make it a viable solution to our power needs is truly immense. The students determined that they would need to raise 40,000 gallons of water to a height of 40 feet. This is where you can quickly use estimation to check if this design can reasonably be built.
Figure 2: A quick calculation of the weight of the water required
40,000 gallons of water would weigh approximately 160,000 kilograms (the actual number is 151,416 kilograms). To give a sense of scale, I looked up how much an elephant weighs. According to Wikipedia, the largest elephant ever recorded weighed 10,900 kilograms. This means that for this storage system to work you would need to raise the weight of about 15 elephants to a height of 40 feet.
This is obviously a lot of weight, and it would cost a lot of money to build a structure strong enough to support that, not to mention just buying a tank that large. I also wasn’t sure how big a tank that would be, so I looked up how big a tanker truck is. The largest in the US are about 9000 gallons. This means that you would need a tank as big as 4.5 very large tanker trucks. Here, this easy estimation shows that perhaps a better solution would involve using some cheap and easy to find car batteries to store the solar energy, instead of an expensive and complex water storage system. And, taking a deeper look at the user needs might help too. Perhaps people don’t even need electricity 24 hours a day in developing nations, but only enough to charge portable devices, such as cell phones, during the day. There are now many more ways to solve this problem, and they are more likely to be a path to success.
Figure 3: How much water is feasible to store in an elevated tank in the developing world? The equivalent of 15 elephants seems like a lot of weight, and 4.5 tanker trucks seems like a very large tank.
A different team, who was analyzing the feasibility of using solar panels to help power cargo ships, did a good job of basic estimation that yielded useful results early in the design process. Their analysis found that the solar panels required to power a cargo ship would greatly outsize the ship requiring them, making the plan impossible using current or near future technology.
Figure 4: The area of required solar panel arrays, with the ship in the bottom left for scale
The blue area in this picture represents the area of solar panels required given 24 hours a day of clear skies and full sunlight (which is clearly impossible). The red represents the required solar panels given 6 hours a day of the same conditions. Even if their numbers are somewhat off we can still reach the same conclusions: From these simple representations we can see that we will need to look for other ways to power ocean-going freighters.
The Impossible Light
Figure 5: A pretty design; but will it work?
Another example of forgetting to do some basic calculations is the Gravia Lamp, the runner-up in the Core77 / Greener Gadgets Design Competition in 2008. The Gravia was designed to slowly lower a 50 pound weight over 4 hours, powering a light that could illuminate a room. While this sounds like a great idea, the basic physics were impossible.
Many people did analyses of what was wrong with the design, but this one is perhaps the best (please note that it does contain some potentially offensive language). A simple calculation of the potential energy stored by lifting a weight (mass * the acceleration of gravity * height) shows that the even using a theoretically perfect light with no losses in a 100% efficient system would only produce a tiny fraction of what the design promised. This means that no matter how efficient LEDs get no light source could ever make this design work. The laws of physics simply prevent it, regardless of technological improvement.
If It Won’t Work, It Won’t Get Built
Skipping basic background estimation and calculation may save you a small amount of time and headache early in the design process, but it can cost you greatly in the long run. Using good estimation techniques and basic calculations can ensure that your work ends up being useful, rather than something doomed to sit on paper or in a computer forever.