Hi, my name is James and welcome to Code/Switch, today I want to talk about a magic item from Pathfinder called a feather token, specifically the tree variety. I’ve had someone ask about the force with which one of the tokens erupt, and if it was actually significant.
Figuring this out was a little more complicated than I thought at first, because I ended up having to make some assumptions. First, let’s lay out what we know. A feather tree token takes a standard action to use and once used creates a tree that’s 60 feet tall, has a 40 foot diameter of foliage, and whose trunk is 5 feet in diameter. To give a good estimate on the force the tree token provides we have to assume the following; the length of a standard action, the type of wood, and that the force it generates is not in excess of what it needs to erect itself to full height. Also, I’m going to ignore that globe of foliage and just focus on the trunk. The foliage ball is nearly impossible to find the density of and its large surface area will make our numbers look paltry.
The first assumption is the length of a standard action. In Pathfinder a turn is about 6 seconds, so I had to divide a turn into lengths of time that would allow 2 move actions and a swift action, or a move, swift, and standard action. Using that requirement I reason that a standard action is 3.5 seconds, a move action is 1.5 seconds, and a swift is 1 second. While not perfect, it gives a reasonable time-frame for our tree token to sprout. Also, if we go by the “rules”, the effect is instantaneous, in which case this tree just appears magically with infinite force, and I can’t calculate that.
I also assumed that the type of wood was red oak. The feather tree token grows an oak, but doesn’t specify species, and I just chose red oak because I like the shape of its leaves. Also, red oak is popular I guess.
To figure out the force this tree needs we have to figure out how big the trunk is, how much it weighs, and how fast is grows during the process of using the item. A 60 foot tall cylinder with a 5 foot diameter has a volume of 1178 feet3. Red oak wood has a density of 45lb/ft3, giving our tree trunk a weight of 53,015 pounds, about 26.5 tons. Interestingly, there’s a formula to estimate tree-age, and you multiply the diameter in inches by the species growth factor, which for red oak is 4, which would make our tree roughly 240 years old, surprisingly in the 200-400 year range the tree generally lives, yay real life accuracy! Next we have to find our trees speed, it grows 60ft in 3.5 seconds, giving us an average velocity of 17.14 ft/sec. Using the kinetic energy formula we find out growing tree pushes with 242,119 foot/pounds of pressure or just over 1681 pounds per square inch (psi) [also 11,590,087 newtons/square meter for metric].
1681 PSI is a lot of force, while bone is strong, that’s likely enough force to break bone, taking into account which bone, angle, etc. This video from Seeker goes more into the forces needed to break bones, but safe to say our tree makes the minimum requirement. This force is also likely to be able to lift thatch roofs and other sub -1,500 pound objects up to the trees maximum height. So, as it turns out, the feather tree token does produce a significant amount of force, who knew? You can find me and the rest of the KD crew at our Discord!