Generally when you write something, especially a blog, you need to start off with a hook to draw the reader in: an anecdote, a quote, a compelling question—basic high school English class stuff. To that end, I was trying to think of a clever way to start this blog post, but then I realized: I don’t need anything clever. The subject matter is a good enough hook. So here it is: we dropped pumpkins from the top of a parking garage and we have video footage.
There. Did I hook you, draw you in? I suppose at this point you could just scroll to the bottom of the page and watch the video, but I hope you’re wondering, “Why on earth did they drop pumpkins for a PTC Mathcad blog?” Well, there are three answers to that question. First, I know very few people who will not be interested in watching pumpkins explode on impact. Second, it’s almost Halloween, so doing something with pumpkins seemed apt for the season. Third, we didn’t just drop pumpkins for the sake of dropping pumpkins; we ran an experiment.
You may not know this, but PTC Mathcad can actually do quite a lot in Design of Experiments (DOE). In a broad range of disciplines, it is very important to understand which factors within a design have the greatest impact on the end result, whatever that may be. But it can often be very tedious and expensive to run all of the necessary experiments for all of the factors. And even then, you don’t really get a picture of interaction effects between factors (i.e. sometimes two factors are insignificant in their own right, but together they may have a rather large effect). By using various DOE methods and algorithms, you can get a picture of the significance of various factors, and their interactions, without running a complete set of tests.
I’ll do my best to explain with our pumpkin experiments, but first, I need to add a disclaimer: This is a very basic, even simplistic, example of DOE. PTC Mathcad’s capabilities in this realm are extensive, far beyond what I could accomplish in a blog about plotting dropping pumpkins. You can find more information and better explanations at a recent blog post written by my colleague Thomas Devaraj. Also, to keep things simple, we don’t explore interaction effects in this blog post.
Now, we need to answer two questions: what is the “end result” we want to test against, and what factors might influence that end result? In the case of these pumpkins, we want to look at splatter radius—how far from the impact point does the largest significant piece of pumpkin shrapnel go? And the factors to test against are size (in terms of weight), drop height, and whether the pumpkin is intact or has been hollowed out.
In order to really get a full understanding of these factors, we can use the fullfact function, which tells us that we need to conduct eight different runs.
The columns for A, B, and C give either -1 or 1. This corresponds to high and low values to be used in testing. In our case, factors and lows/highs are as follows:
A: Size – ~6 lb (-1)/~24 lb (1)
B: Hollow or not – hollow (-1)/ full (1)
C: Drop height – 3rd floor of parking garage (-1)/ 4th floor of parking garage (1)
For a full experiment, we would need to conduct eight runs, meaning eight pumpkins. While I would have had more fun throwing eight pumpkins off a parking garage, it’s a little costly (imagine the cost of running a complete experiment for 10 or more factors—that would be 100 or more tests!).
Instead, I can use different methods to reduce the number of runs while still giving good information. A couple of methods are fractional factorial (using the fractfact function in PTC Mathcad) or taguchi. Giving a comparison of the two methods is well beyond the scope of this blog, but you can read more here.
We decided to use the Taguchi method, which gave us the four runs that we would do for this experiment. That’s half the cost and effort of the full experiment.
Running the tests, we found the following results for splatter radius.
To get an idea of the impact of each factor from these results, we use the quickscreen function.
I can visualize these results by pulling the data from this matrix Q and plotting them on an Effects Plot, where the slope of the line for each factor gives the significance of that factor in pumpkin splatter radius.
You’ll notice some interesting things here. By comparison to the other two factors, the height at which the pumpkin was dropped does not have a very large effect. Size has by far the greatest effect. How can we explain these results? Well, more testing would have to be done to get a more clear understanding, but we can definitively say that if you want a large splatter radius when you drop a pumpkin (I think now is when I’m obligated to say, “Kids, don’t try this at home”), you should get the biggest pumpkin you can find and hollow it out.
For my part, I was surprised most by the need to hollow out the pumpkin. Truth be told, there isn’t much inside. Pumpkins are already pretty hollow. Just seeds and fibers. But based on the small, full pumpkin thrown from the 4th level, which didn’t really explode much, we were able see that the reason it held together so well appeared to be that those fibers did a lot to keep the pumpkin intact.
Why doesn’t height seem to be much of a factor? Hard to say. There’s no way they reached terminal velocity in the descent. Again, we’d need to do further testing, but in any event, the results indicate that height is not as important as the size of the pumpkin and making sure to hollow the pumpkin out.
Okay, here’s the video. I hope you have almost as much fun watching as we did doing the actual dropping.