[Superman].

An attempt is made to explain the ability of Superman to jump high buildings and deflect bullets. It is hypothesised that these powers come from a superhuman density of muscle and this theory is tested and found lacking. Introduction In Superman's first comic book appearance it was said that he could “easily hurdle a twenty storey building...and that nothing less than a burning shell could penetrate his skin”[1]. Superman's humanoid appearance suggests a (albeit super-­‐) humanoid physiology. This paper will investigate muscle density as the source of both his superhuman strength and his ability of bullet deflection. Discussion For Superman to jump a 20 storey building – approximately 100m in height – he must leave the ground at a vertical speed of 44ms. This assumes that acceleration remains constant, that the vertical speed at the peak of the jump is 0ms, that there is no effect from air resistance and that (at this point in his mythology) Superman is not immune to gravity. In order to reach this speed, from a stationary start, over the distance Superman travels between his initial crouch and take off (taken to be 0.5m), an acceleration of approximately 2000ms is needed. The force required for this acceleration is, F = 2000m (1) where m is the mass of the object being accelerated. This force is assumed to have come solely from Superman's leg muscles. Humans muscles are composed of many microfibres, each one capable of producing approximately 0.3μN of force[2]. In practice many factors may affect the strength of a muscle including its shape and the proportions of different fibres present, but, for the purposes of this paper, the muscle strength is proportional to the number of fibres. As, visibly, Superman's muscles are no larger than a similarly sized human's, if his physiology is similar to humans then he must have a greater muscle density. In humans, muscle density is averaged at 1.06gcm[3]. In a similar way to the calculation of Superman's required force, it can be shown that human legs are capable of providing a force of approximately 800N[4]. Assuming all other things are equal, producible force will be related to muscle density, ρm, by, F = kρm, (2) where k is a constant of proportionality that can be calculated from the above values as approximately 750Nmkg. Again, all other things being equal, and assuming that muscle density is constant within all muscles in the body, this muscle density will relate to the total mass of the body. Using average human data; mass and the percentage volume of each type of tissue[5], mass can be found, in kg, by, m = 46 + 32ρm. (3) where 46 denotes a weight term for all tissues that aren't muscles and 32 litres is the volume of muscles in the average body. Can Superhuman Muscles Stop Bullets, February 6, 2011