Physics of BJJ: How to Break my Arm

Physics of BJJ: How to Break my Arm

Brazilian Jiu-Jitsu (BJJ) is a ground based martial art that utilizes grip, position and superior technique to control and neutralize a resisting opponent. BJJ famously advocates that a smaller, weaker person can effectively defend against a larger, stronger opponent by using leverage to maximize the amount of force applied against certain parts of the human body. One technique that reflects this principle is the jūji-gatame, otherwise known as the basic armbar, which is presented in a step-by-step representation below. 

The armbar, one of the first submissions you learn in BJJ, uses your entire body to apply an immense amount of downward force to your opponents elbow. Your legs are used to stabilize your opponent to prevent them from escaping. This position isolates a single arm, making your opponent’s elbow a leverage point that is planted against your groin. By the process of laying down and thrusting your hips up, the force is enough to bend the elbow past 180°. Grabbing the hands of your opponent maximizes the amount of leverage and force that can be applied to the leverage point, easily hyper-extending the elbow, thus neutralizing your opponent while inflicting a substantial amount of pain. 

So how much force is required to actually break an arm of a resisting opponent? In particular, how much force is required to break my arm? We can rephrase the question to ask, “What is the minimum amount of torque to overcome the torque of the bicep exerting on the arm in the opposite direction?” To test this, I went to the gym and found the max weight to maintain a dumbbell from an arm extended position with my elbow rested at the edge of a table. My max weight was 70 lbs, or approximately 30 kg. Assuming that the distance from my elbow and the tendon of my bicep is approximately 5.0 cm, the length from my elbow to my knuckles is approximately 35.0 cm, and the angle at which my tendon connects to my arm is slightly less than 180° (i.e. 175°), we can calculate the torque of my biceps to be 102.9 N*m, disregarding the weight of my arm. Therefore, with my arm in the straightened position, can resist a torque of 102.9 N*m before it breaks.