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I modeled Hiccup’s arm as two segments, and focused on his forearm. It has a weight, it has the biceps pulling to keep it up, and it has the shield pressing it. These are represented by F_g, F_b, and F_n, respectively.
We can see the arm is at static equilibrium, so we can say that both net force and net torque is zero. There is another force, however, which is the force of the humerus, or the upper arm, pushing the forearm to keep it at equlibrium, represented by F_H. Our goal is to find the force of the biceps and the rest of the forearm.
Assuming his arm is completely rigid (doesn’t stretch or bend, etc. at this instant), we can use the zero net torque with the elbow joint as the pivot, making the torque created by F_H zero. I’m here going to assume that Dagur with his armor weighs about 100 kg and thus his weight 1000 N, and that he is putting half of his weight on the shield. Thus, F_n = 500 N. Assuming the mass of Hiccup’s forearm is 1.5 kg (not that big of a stretch, TBH), the force of biceps pulling on the forearm is 4102 N. That magnitude is enough to lift a 400 kg object.
Next, since we know F_B which is horizontal, we can use the vertical and horizontal components of the net force (which is zero) to get the vertical and horizontal components of F_H. Using the Pythagorean Theorem, this force has a magnitude of 4375 N. Further calculation shows that this is applied at an angle of 24.1° to the forearm (calculation not shown here).
Now, here is the issue: generating 4000+ N of force is… well, a bit ridiculous. I mean, this video shows a man doing a dumbbell curl with 105 lb (48 kg), but that’s just one rep, and he’s obviously prepared for this for a while to exert 4000+ N with his biceps. This is not something that is effortless.
I mean, you could argue it’s being supported by his other part: shoulder, back, etc. But this is one-handed, so this support pretty much ends at the shoulder. In other words, this is a wonderful way to ruin your shoulder for a while.
P.S. In the net torque equation, F_g is multiplied by sin 60, not sin 30.