Woodchuck

How much wood could a woodchuck chuck if a woodchuck could chuck wood?

Well, if a woodchuck could chuck wood, we can assume based on the average size of a woodchuck (about 3 tons) and the inverse square law that his or her teeth would typically be 3 inches long. Assume a wear rate of 1 mm per 5000 logs chucked for hardwoods, or 1mm per million logs for extremely soft wood like balsa, with pine somewhere in between, let’s estimate it at 1 mm per 20,000 logs. This is of course assuming an ISO standard sized log of roughly half an el, not an ANSI standard log of 0.001 furlongs.

From here we can calculate that (again, if a woodchuck could chuck wood(), it would take, on average, 3 million logs to wear down that woodchuck’s teeth. So we can be confident that, if the woodchuck could chuck wood, it would be able to chuck 3 million logs. However, this does not take into account the time a woodchuck’s teeth would grow during the time it chucked all those logs. First we need to calculate the likely growth rate, which for a rodent the size of the average woodchuck is likely to be 1mm per day.

Studies have indicated that it takes approximately 75 seconds to chuck a piece of hardwood, while balsawood can be chucked in less than a second and softwoods such as pine take a minute to chuck. (We’re still assuming the woodchuck could chuck would here. If it couldn’t chuck wood, this would all be moot.) Assuming only wood chucking by the woodchuck as a means of wearing down its rapidly-growing rodent teeth, it becomes clear that by the time a woodchuck finishes chucking enough wood to wear its teeth to nothing, its teeth will already have grown sufficiently to make up for the difference, regardless of whether it chucks hardwood or softwood.

So one could say a woodchuck could chuck an indefinite amount of wood (if a woodchuck could chuck wood).

Except, of course, that leads to another consideration: If a wood relies solely on chucking wood to check the rate of growth of its teeth, and that wood is comparable to balsa, its teeth will grow without bounds, eventually becoming too long for the woodchuck to successfully chuck wood (if it could chuck wood in the first place). At this point we can conclusively say such a woodchuck could not chuck wood.

So we must assume a woodchuck could not chuck wood indefinitely unless some of that wood is hardwood, making it possible to keep the rate of wear and rate of growth in balance.

But we’re still not taking into account calories or sleep. Woodchucks are not spherical, despite what some researchers have suggested, and do not in fact exist in vacuum either. Well, they could, but prior research on other rodents suggests that if a woodchuck were to be found in vacuum, it would not be in a position to chuck wood, as it could have asphyxiated before it could begin.

So we need to calculate: how much sleep does a woodchuck need, if it spends all its waking hours chucking wood? Data here is scant, as the author is unaware of any rigorous studies on this subject, but we can extrapolate from studies on metal chucks, for which drills typically need to be charged for an hour after 2 hours of continuous use. As woodchucks cannot simultaneously rest and take in energy, we must therefore assume that for every 2 hours a woodchuck chucks wood, it must eat for 1 hour and sleep for another. This gives us an upper bound on how many hours per day a woodchuck could chuck wood of 8 hours per day full-time. That makes 40 hours a week on average, though if it could chuck wood full time, it could also theoretically chuck wood on weekends too, perhaps as a side gig. That means it could still chuck wood 8 hours a day.

So given sufficient food and water supply, and a balance of wood hardnesses such that the growth and wear rate of the woodchuck’s teeth remain balanced, we can in fact still assume a wood chuck could chuck wood indefinitely until it dies of old age (assuming, of course, that if could chuck wood in the first place).

And that brings us to the final consideration: What is the average lifespan of a woodchuck? And how old is it before it can reasonably be expected to be able to chuck wood? According to BS. et. all, the oldest known woodchuck lived to be 87, though its teeth fell our two years prior to its death. We can assume that it could not chuck wood for the last two years of its life. The average woodchuck’s teeth have matured sufficiently to chuck wood by the age of three weeks. So assuming ideal conditions under which a woodchuck could chuck wood for as long as possible, we can assume roughly 8 hours a day for 85 years, giving us roughly 248200 hours’ worth of potential wood chucking. (8x365x85. Conveniently, 21 leap days is very close to the three-week maturation period required for the woodchuck to begin chucking wood.)

Side note: there have been objections raised to the ethics of insisting that a woodchuck spend all its waking hours chucking wood or eating. Please be assured that this research remains hypothetical, and by the time we’re ready to begin real-world experimentation, all such studies will be done under the observation of the American Humane Society to ensure that the woodchucks involved lead long, happy lives. This will likely result in fewer total hours of woodchucks chucking wood, but we can extrapolate how many hours they could have chucked if they’d been so inclined.

Anyway, we have an upper bound of 24800 hours for each woodchuck to chuck wood. That means we need to once again consider the time taken to chuck different hardnesses of wood. A continuum exists along which a mix of hardnesses of wood provided can counteract 24 hours of tooth growth over 8 hours of wood chucking by the wood chuck, assuming that the food it eats during off-hours does not contribute significantly to tooth wear. Optimizing for the number of logs chucked while fitting this curve gives us a peak at 40% hardwood, 40% balsa and 30% pine, from which we can calculate an average of 41.9999 logs chucked per hour, giving us our answer:

Under ideal conditions, if a woodchuck could chuck wood, said woodchuck could chuck 1 million 41 thousand 5 hundred and 1/4 ISO-standard logs over its liftime.

This of course assumes standard air pressure and gravity. If we were to transplant a woodchuck and a sufficient number of logs to another planet, or perform the experiment in free-fall, we would have to account for different rates of tooth growth at the very least. In fact, one would have to consider whether, in a weightless environment (assuming a regular supply of wood to chuck and chucking the chucked wood out the airlock), a typical woodchuck could gain sufficient purchase to chuck wood in the first place, which brings us back to the question of just how much would this wood cost before chucking, why do we want it chucked, and can the woodchuck chuck wood in the first place?

Clearly, further research is needed to answer these questions.