# Force applied to the human body

This is the basic premise of a physics question I have been attempting to solve over on the Physics SE. (I'm working on solving the actual science behind an old movie myth).

How hard a punch hits is determined by your hand's momentum, or the combination between mass and velocity. . . . What acceleration would Super Man need to achieve during his attack in order to impart enough force to punch his fist into/mostly through a human body?

Unfortunately, in order to solve this problem, I somehow need to figure out the amount of force needed for an object to enter/pass through the human body (by either passing through the sternum or directly below it). Since I have so far been unable to find anything helpful in online searches, and naturally I'm not about to test fire an object through human beings until I find the right amount of force, I'm asking for a little help from the experts on human biology... Does anyone know where I can find or how I can figure out this number?

As this is homework related I won't help with the math but I can help point you in the right direction.

Basically, you need to find the density of a human chest and then calculate the force required to "break" it. Looking into the average depth of the human chest we can see from this website, It comes out to be about 250 mm for British man.

The density of human muscle tissue is about 1.06 kg/liter. Average bone density is 1600 kg/m^3.

For now lets just assume that the heart and lungs also have 1.06 kg/liter as the density. This means we can calculate the overall density of the chest and the required force it can withstand.

The average surface area of a mans fist is .043 sq m.

Knowing the size of the fist and how much force the chest can take, we can from here calculate the penetration force needed to pass through the chest.

Granted this is gross approximations and doesn't account for surface area of the fist. You would need to find a better equation to be more accurate.

• This actually isn't homework, just a personal project related to a book I'm writing. (I have a superhuman character who was going to perform this feat, and I began to wonder about its plausibility/the related science.) Thank you for these numbers, it's a start, and more than I found on my own. In order to determine the overall density of the chest, do I need to figure out the ratio of bone to muscle and organs in the chest as well? – MarielS Apr 2 '19 at 8:38
• To be more accurate yes but there are a lot of variables to account for. For instance one assumption being made is that the objects do not compress. Skin and muscles can compress a bit which would increase the amount of force needed to pierce. Ballistics and penetration are rather large topics. Here is a [paper released in 2012 discussing simulations of depth] penetration(ias.ac.in/article/fulltext/sadh/037/02/0261-0279). – Hojo.Timberwolf Apr 2 '19 at 9:44
• Oh, And in general, the larger the surface area the less likey to pierce. This is becuase more area spread out requires more force to penetrate. One reason why characters in Grapler Biki or Fist of the North star Tended to attack with straight finders for stabbing. – Hojo.Timberwolf Apr 2 '19 at 9:46

For a very rough upper bound you could assume that the punch force is translated into 100% pressure on the bone, 100% traction on tendons/ligaments (and generally all tissues which contain collagene type 1 and aren't bone) and so on (which is obviously not true in reality where a punch from the side will generate a torque moment rather than a pressure).

The second step would then be finding the numbers for maximal pressure bone can take per mm^2 , maximal traction a tendon can take per mm^2 as well as the numbers for mass and volume of each in the human body.

These number exist so you can find them with enough effort.

The last step would be to decide which ratio you use for each (i.e. in the given area how much does each layer constitute) , this number (in reality) too exists most likely you can find it in some MRI studies.

So while you won't be able to get exact estimates (because they depend on the geometry of the person, constitution and infinite amount of other variables), you can get a very good upper bound by assuming that the force is translated into exactly the type of stress each tissue is supposed to work with!

Note also that you do not need to know the size/area of the attackers hands or the size of the impact area if you choose this method!