A quick search finds that three potential answers to the woodchuck conundrum are already in existence. One traditional reply holds that, “A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood”. While clever, this doesn’t really answer the question that is being asked. It’s specific in what it’s saying, but vague in how it’s of any use in the real world; like a Rishi Sunak budget. The second potential answer is that a woodchuck can’t chuck wood. This too is not good enough in that it essentially denies the existence of a problem that it should be trying to solve. Like a Rishi Sunak budget. The third potential answer is much better. In 1988, Richard Thomas (a wildlife technician, which is probably a thing) calculated that if a typical woodchuck burrow is 7.6 to 9.1 metres long, and the volume of dirt the woodchuck had to move to dig that burrow was translated into an equivalent volume of wood, then the woodchuck could move approximately 323 kg of wood. Much better; or at least it would be if we were asking, how much wood could a woodchuck move if the ground was made of wood? As it is, we’re left with some unsubstantiated numbers which nobody can really explain the relevance of. Which reminds me of something.
So let’s start by defining our terms. To “chuck” can mean several things, although we can safely discount most of them. It’s unlikely that the rhyme is about a woodchuck ending a relationship with some wood. Even if it were, I couldn’t find anything about paraphilia in rodents or if they could choose to abandon the object of their paraphilia, so it’s unlikely I could get an answer to that. Now if you’ll excuse me, I need to have my computer destroyed. Similarly, we can assume that we’re not trying to work out how much tree a woodchuck can vomit, as like rats and indeed most rodents, woodchucks can’t vomit (although there is one report of them vomiting due to red squill poisoning). Top tip: sit behind the woodchuck if you go on a rollercoaster. Overall, it’s likely that we want to know how much wood a woodchuck could throw if it was able to.I was unable to find any reports of woodchucks throwing anything, never mind wood, so decided take the data from human wood chuckers and extrapolate. Arguably, the best example of humans throwing large amounts of wood in an environment where this bark flinging is measured can be seen with the Scottish athletic feat of tossing the caber. Here the tosser (the definite proper technical term, so shut up) attempts to throw a large wooden pole (typically made from larch wood) so that it turns end over end in a straight line. The straightest end over end toss scores the most points. It’s essentially extreme timber filing. A typical caber is 5.94 metres tall and weighs 79 kg. According to the Guinness Book of World records, the largest caber ever tossed was 7.62 metres long and weighed 127 kg. This is pretty impressive, but I would argue that for “how much wood” we need a large amount of wood to be chucked several times in a set period.
The most caber tosses in three minutes is 14 and was achieved by Kevin Fast (a strong reverend) in Canada in 2013. Kevin used two 5.02 metre long cabers, each weighing 41.73 kg. Unsurprisingly, Kevin is famous as a multiple Guinness World Records title holder. Woodchucks, also known as groundhogs, are famous for other things. Woodchucks, also known as groundhogs, are famous for other things.
Using a fairly basic equation for Power (Work/Time, where Work = Force x Distance), we can work out that in completing his one caber’s worth of his magnificent feat of tossing, Kevin transferred 55.29 Watts.
Height lifted (Kevin’s height) = 1.75 metres
Force (Mass [41.73 kg] x Gravity [9.80665 metres per second2) = 409.23 Newtons
Time (180 seconds/14 tosses) = 12.86 seconds
Power = (409.23 x 1.75)/12.86
Power = 55.69 Watts.
In woodchucks, the forelimb (their woodchuck arms for woodchucking) contain 44 muscles, with two groups, the lattissimus dorsi and pectoralis superficialis being the largest. Apparently, woodchucks have great pecs. In being specialised for digging, the highest individual power available from woodchuck forelimb muscles is 4.0 Watts. The height of a woodchuck is 0.8 metres and we’ll give our marmot friend the same amount of time to chuck his wood as we gave Kevin.
So, if Power = (Force x Distance)/Time
Then, 4.0 = (Force x 0.8)/12.86
And Force = (4.0 x 12.86)/0.8 = 64.3 Newtons = 6.56 kg.
Adjusting for scale, this means the best woodchuck woodchucker can throw a 6.56 kg of 1.99 metres length 14 times in three minutes. This is both an answer and an adorable image.
To check our calculations, we can work out maximum woodchuckage in another way. We know that Kevin Fast weighs 136.078 kg and can therefore estimate his lean body mass to be 74.57 kg. I used the Hume Formula for this. Other formulae are available, although all are just estimates and in fact, none of them are probably suitable for a man such as Kevin who is likely more muscular than the average pastor. Since skeletal muscle is, on average, 54% of lean body mass, we can estimate that Kevin has 40.72kg of muscle.
For woodchucks, their body mass is typically about 3.13 kg in the Spring and 4.20 kg in the Summer. a woodchuck definitely wouldn’t stand for a ludicrous “beach body” advertising campaign. Given that in Spring, adipose tissue is 40.31% of a woodchuck’s body mass (56.10% in Summer) and skeletal muscle is 52.41% of lean body mass (56.10% in Summer), then a woodchuck will typically have 0.98 kg of muscle (1.00 kg in Summer).So in the Spring, Kevin has 41.09 times the muscle mass of a woodchuck, and 40.27 times the muscle mass of a woodchuck in the Summer. This is assuming that as non-hibernating mammal, Kevin’s weight and adipose proportions don’t fluctuate as wildly as woodchuck’s do. Muscle strength is proportional to cross sectional area, so it is perhaps more relevant to state that woodchucks have 6.41 times and 6.35 times smaller cross sectional area of muscle than Kevin in Spring and Summer, respectively. Correspondingly, this means that a muscular woodchuck vicar could toss a 6.51 kg caber of 1.98 metres in length in the Spring and a 6.57kg caber of 1.99 metres length in the Summer. In the Winter, it would probably be asleep. You’ll note that this is satisfyingly similar to our original estimate.
So in conclusion, depending on the season, a very strong woodchuck member of the clergy could chuck a 6.6 kg stick of wood that was nearly 2 metres long 14 times in three minutes. In addition, if on that occasion it saw its shadow, it would mean six more weeks of maths.