Legolas: prince of the Woodland realm, one of the nine members of the Fellowship of the Ring, uniter of several peoples of Middle Earth, and a stranger to any basic principle of physics. Among many other traits, one of the characteristics that sets elves apart from any other inhabitants of Middle Earth is their ability to literally tread lightly — almost without a trace. Director Peter Jackson reminds us of this trait frequently in both The Lord of the Rings film trilogy and The Hobbit film trilogy. The first evidence of this ability can be seen when Legolas is able to walk on top of accumulated snow while the company is journeying over the Pass of Caradhras in The Fellowship of the Ring (2001). In The Return of the King (2003), Legolas can be found climbing a Mûmakil by nimbly swinging from arrows that are lodged into the animal’s hide. In the film adaptations of The Hobbit, there are several moments in which Legolas’s apparent weightlessness is exploited further, however none can top the scene where he somehow runs up a series of falling stones.
All of these examples lead me to think that Legolas doesn’t just tread lightly, he must actually be an incredibly lightweight human being. How lightweight? Well, this is what I am here to explore.
It is quite possible that by asking this question I am spoiling the mystery and intricacy of the story. I am sure the real answer to this question is more along the lines of: elves weigh as much as any taller-than-average individual weighs, but they are learned in many arts and skills that the common man would naïvely define as magic. When it comes to the world of Middle Earth, I would say that is an appropriate answer. However, I am a human physicist living in 21st century Earth, and I can never watch The Fellowship of the Ring without thinking “I gotta figure out how much this guy weighs”. So here goes.
The only example from Legolas’s aforementioned feats that is also found in J. R. R. Tolkien’s writing is the incident on the Pass of Caradhras. In this part of the story, the Fellowship is attempting to cross the Misty Mountains. [Figure 1]
The Fellowship found that their path was quickly becoming shrouded in snow by an antagonist — to the point where the members of the company considered turning back. While the company were strategizing about how they would continue their journey amidst the challenging climate, Legolas interjects:
“Legolas watched them for a while with a smile upon his lips, and then he turned to the others. ‘The strongest must seek a way, say you? But I say: let a ploughman plough, but choose an otter for swimming, and for running light over grass and leaf, or over snow — an Elf.’ With that he sprang forth nimbly, and then Frodo noticed as if for the first time, though he had long known it, that the Elf had no boots, but wore only light shoes, as he always did, and his feet made little imprint in the snow.” — J. R. R. Tolkien, The Lord of the Rings, Book 2
So, Tolkien confirms that Legolas is able to walk on top of freshly fallen snow with little to no footprints. With this information, Legolas’s weight can be approximated by solving for the maximum amount of force that snow can withstand. A paper by J.B. Jamieson and C.D. Johnston titled “In-Situ Tensile Tests of Snow-Pack Layers” provides an illuminating plot of the tensile strength of snow. [Figure 3] Tensile strength is the amount of force per unit area that an object can withstand while being pulled or tugged upon before collapsing. In the plot provided by Jamieson and Johnston, tensile strength is provided for several types of snow microstructures.
By Frodo’s account of the adventure, the snowfall began and quickly escalated during their journey, which leads me to conclude that the snow microstructure was closer to what Jamieson and Johnson would consider ‘partly settled grains’. According to Figure 3, the mean tensile strength of snow for partly settled grains is approximately 1.7 kN/m².
If tensile strength is defined as force per unit area, then the maximum amount of force that the snow can withstand should equal the tensile strength multiplied by the area that the acting force is applied over. In this case, this is the area of Legolas’s footprint. In order to calculate the area of Legolas’s footprint, I have approximated the shape of a foot to an ellipse, and approximated the size of one of Legolas’s feet to be 5 cm wide and 25 cm tall. The origin of these measurements stem from my assumption that elves are tall yet elegant. Having large feet does not seem advantageous when it comes to nimble fighting styles and general stealth, yet being taller than average requires a well-sized foot in order to maintain balance from a torque standpoint.
Figure 4 provides a breakdown of the area calculation of Legolas’s footprint, and concludes that both of his feet, in total, take up approximately 0.0196 m².
Armed with the approximate tensile strength of snow, and the area of Legolas’s footprint, an approximation for Legolas’s force due to gravity (weight) can be calculated using the following equation:
(tensile strength) * (area of footprint) = weight
1.7x10³ N/m² * 0.0196 m² = 33.3 N
Legolas’s weight is 33N, and his mass can be calculated by using the formula:
F = mg, where g is the acceleration due to gravity: 9.8 m/s².
m = (33.3 N) / (9.8 m/s²) = 3.4 kg = 7.5 lbs
My estimate concludes that Legolas weighs, at most, 7.5 lbs. Is this reasonable? Absolutely not, but we are talking about an immortal elf that makes no footprints in the snow and among other things can communicate through telepathy and see incredibly far, so one could say that the whole situation is not reasonable. As mentioned at the beginning of this investigation, it is entirely possible that J. R. R. Tolkien intended for elves to weigh the same as any other human of their size and instead would claim that elves are able to use their connection to nature to tread lightly. However, if I were asked to explain this phenomenon, I would confidently conclude that Legolas weighs 7.5 lbs.
I still have no physical explanation for this, however:
…maybe some things are best left a mystery.