So, I recently finished reading Halo: Envoy, and some particularly interesting showing of Spartan strength has inspired me make some consistent as possible calcs on the Strength of a Spartan-II in armour. While yes, there are lower and higher showings of Spartan strength (most of which are unarmoured), I decided to focus on the strength displayed when in their armour, and when they’re noticeably straining doing so, rather than babbling over the warthog flip for the thousandth time in the Halo community.
The Fall of Reach: Monolith feat:
There’s an excerpt in The Fall of Reach, where 3 Spartans, and 1 wounded Spartan (James-005) manage to push a gargantuan an cracked quartz monolith, sliding the brunt of its weight across itself to eliminate some Mgalekgolo. Take note of how these same creatures can backhand 3.5 tonne warthogs several metres away, implying an extreme level of weight from the monolith.
Now, let’s just break down the concept of friction. It’s a resistive force that prevents two mediums (typically an object to the normal force of the ground) from sliding two objects freely amongst eachother. In basic high school physics, this concept is often ignored when determining the work of an object. This resistance is known as the coefficient of friction, with the symbol µ. In physics, steel has a coefficient (meaning the ratio of resisting force from the object itself to the ground) of around 0.6 of gravitational force. Assuming the coefficient of friction was equivalent to steel, the kinetic friction to move something of this size would be approximately 60 percent of the force required to lift. However, The monolith was the density of quartz, with the dimensions of a 6x3x3 metre, M12-sized pillar (it seemed very wide, considering 4 Spartans could squeeze themselves along one face), this would weigh around 140 tonnes - if we were to believe the gravity was equivalent to Earth’s.
What we need to do now is multiply the weight of the object by the resistance coefficient of quartz, otherwise known as silicon dioxide. In most instances (and likely with something of this size), this will be around 0.9 to 0.4µ, kinetic, as it is functionally similar to glass. The coefficient of friction will be equivalent to 0.9 times the force of gravity on the top crystal (where the highest range of frictional force would likely be), divided by 0.1µ with the quartz proportional to the ground. With a straightly cut crack, this would require the following formula:
µ = Ff/Fn
Where Ff is the steel (or perpendicular force), and Fn is the quartz monolith
µ = 0.4 / 0.9
= 0.44.5µ. This would be equivalent to a strong human pushing something similar without wheels that weighed 224.7 kilograms, or the average man pushing 157 kilograms.
Now, a vertical pushing force will be similar to that of a bench-press, so comparing the two may seem at least decently reasonable. If we were to assume that the force of gravity was that of Earth’s, then the monolith will have an applied 1,372,000N.
Plugging in this with the coefficient of friction, we can determine the kinetic force necessary to move the monolith from it’s initial positioning.
F = 1,372,000 * 0.44.5
= 609,777.8N or around 60.9 tonnes of combined pushing strength. The average man can push with an approximate force of 600N
However, we must account for the fact that James-005 had a missing arm at the time, and did not participate in the initial displacement of the monolith. Because of this, there will be 6 arms coming into contact with the face of the monolith. Therefore, each Spartan was applying:
609,777.8 / 3 = 203,259N
Meaning each Spartan was applying a bench-press equivalent of 20.7 tonnes. If I recall correctly, the visual source for this monolith varied in dimensions, though initially appearing cuboid in shape, making an apt representation of these numbers. It must also be noted that said quartz slab only managed to move a “little bit”, meaning that if they attempted to upthrust this kind of force in a bench press, they likely would fail and be crushed by the weight. Realistically, this number would be a more feasible contrast to a 15-18 tonne successful bench press.
Evidence of Tank-rolling:
Many people have a tendency to rebuttal the claims from Frank O’Connor, the Franchise Development Director at 343 Industries, in that Spartans can overturn an M808 Scorpion - believing his statement to be mere hyperbole on his part.
However, I’d like to point out that his assertion seemed more in line as indicative of their abilities, given he stressed the idea of said gameplay capabilities being the few instances where the physical strength of Spartan IIs can be demonstrated, even aligning it with the other superhuman performances and not isolating the idea of such. What would be an exaggeration on his part, was the statement of Spartans lifting the tank in similar positioning to a bench-press.
Now, according to Grimbrotherone, overturning a tank is again, not out of the question for a Spartan’s canonical abilities. Because of these two statements, let’s look at the required leverage to succeed with such a feat., shall we?
Leverage from one side of the vehicle would equate to half of the centre-mass of the symmetrical vehicle. Using the formula to calculate mechanical leverage, this would come to weight x distance from weight to fulcrum = lifting force x distance from lifting force to fulcrum
138,000 * 3.9 = Lifting force * 7.8
To tip the entire vehicle from it’s peak force, you would need the strength to overcome it’s weight at a 45 degree angle.
Weight x 3.9 = Lifting force * 7.8
Lifting force = 0.5 * 646,800(0 degrees). The force on the M808 Scorpion is 646.8 thousand newtons, when on a planet with the equivalent gravity of Earth.
At 45 degrees, this will come as:
Weight = 646,800 * Cos (45)
= 646,800 * 0.525
= 339,570
The lifting force will therefore be:
= 0.5 * 339,570
= 169,785N, or around 17 tonnes of lifting force coming from each Spartan.
To appropriate for a lower-end interpretation, let’s measure the weight of the the newest model, the M820 Scorpion tank, which weighs 35 metric tonnes with a gravitational force applied of 343,000 newtons. I’d be hesitant with the number’s given from Halo Waypoint however, as it states the Grizzly to be 5 tonnes lighter than the Scorpion, despite it’s larger size and heavier armament directly scaled from the M808.
= 343,000 * 0.525
= 180,075
The lifting force will now be:
180,075 * 0.5
= 90,037.5 newtons, or a 9 metric tonne lifting force. In contrast unaugmented individuals, this will make a Spartan 150 times stronger than the average man, and 90 times the strength of a notably healthy human male.