There’s nothing I love more than some back of the envelope calculations. And guessing games. Love those too. And I suppose the only thing better than either one of those is the intersection between guessing games and some fuzzy math! In this issue, we’ll look at some guessing games, and next week we’ll use the answer to estimate the size of a tree.
Guessing games
Last spring, I held weekly guessing competitions with the Field School kids. It started when we found a driftwood white cedar log and were trying to guess the age of the tree. I took a section home, smoothed out the surface, and then counted the rings with the kids. The following week a kid came up to me with a short section of a hemlock trunk. The contest was to guess how long it had taken the hemlock to grow 8″ in length (image above). We counted the rings at the top of the section, then the rings at the bottom and found the difference (5 years). The next contest involved a downed butternut tree. I cut a 6 foot section and carried it back to camp so the kids could guess its weight (98 pounds). The point is I like counting, I like guessing, and I like contests.
So just as our semester was wrapping up, I was inspired for our last guessing contest: how many leaves on a tree! The leaves were emerging on the various maples around camp, and it was already clear that two similar sized trees, here a sugar maple and striped maple both about 12’ tall and ~1⅛” in diameter, would have wildly different numbers of leaves. Our guesses ranged from 29 for striped maple and 36 for sugar all the way up to 500 for each. Interestingly, our guesses were all on the very low end of what would be the right answers (our average guess was 96 for striped and 122 for sugar, but most were below this, the median was 75 and 78, respectively).
Once the leaves had fully emerged, I then began the laborious task of counting every one of them. The grand total was 1,060 for the sugar maple and 306 for the striped maple. Of all the contests, we collectively did the worst on guessing for this one. While I’m not sure exactly why we were so off, three big questions came up for me:
- How does the total surface area of all those leaves compare to the total area that the tree’s canopy covers (a measurement foresters call crown area)? Put another way, is the tree more like an umbrella or a stack of layered umbrellas?
- Sugar maple produces lots of smaller leaves, usually 4-8 at each node on a twig while striped maple produced just 2 leaves, both of which are significantly larger than sugar maple leaves. Would the high number of small leaves on sugar maple provide a similar amount of coverage as the fewer large striped maple leaves?
- What’s the advantage behind sugar maple’s many smaller leaves?
To answer these questions, I’d have to do a bit of math, but more on that next week…
