Breaking a Face with Physics

Writer's scene...

Our hero, Det. Jesus De La Cruz is undercover and in the middle of a tenuous meeting between two drug lords being held in a mechanics garage. Everything is going as smoothly as a meeting between two hyper-aggressive alpha leaders can when a third party enters the fray. In a three sided war, it's no holds barred.

His name is shouted from across the room. Cruz turns and the right side of his face connects with an engine block. The force knocks him off his feet, the back of his head colliding with the concrete floor. Lights out. End of scene.

X-rays will show fractured cheek bone and eye socket, damage to the jaw. Our hero's career as an undercover cop is over.

Engineer Calls Time Out....

The question is not WOULD a face and engine colliding ALWAYS results in so much damage to our hero, but COULD it? Is it feasible?

To answer the questions, we need to know...

  1. How much does an engine block weigh?
  2. How fast was it moving, which is really asking could it generate enough force to fracture bone?
  3. How much force is needed to break bone?

To answer these questions, we get to play with physics. We are specifically interested in calculating force and the laws of nature governing momentum. These laws explains how things will behave when they collide with other things. A few notes here: don't be intimidated by the math. We aren't doing anything expect multiplying and dividing, adding and subtracting. Second, we aren't trying to be exact. We aren't designing the next Mars rover, after all. We are using the laws of physics to position the people and scene of the story to create the outcome needed to keep the story going.

Doing some basic research. An engine can weigh between 300 and 600 lbs. Since I'm trying to break a face and I don't care what the make or model of the vehicle is, I'll use the 600 number. The force needed to break bone depends on the bone, the angle of the blow, how healthy the bone is and how well protecting the bone is. A post on curiosity.com noted science that said a femur (thigh) bone can stand up to 4,000 Newtons. Ribs can take about 3,300 Newtons. I couldn't find numbers on a face, so I'll use the 3,300 Newtons. Now, all we need to do is connect the 600 lbs of metal and fluid to the 3,300 Newtons needed to break bone.

Before we do anything, we have to straighten out the units. We need to be in one system if this is going to work. We'll use the metric system because the math is easier.

Weight is how hard gravity pulls on the mass of an object. This means the 600 lbs is a measurement of force in the Imperial (aka U.S.) system. To translate to metric, we multiply by 4.44822162 (seriously), to get 2,669 Newtons. Dividing by gravity (9.8 m/sec^2) get us to the mass of the engine of 272 kg.

To generate force, we need something to move. How fast does either our hero's face or the engine need to be traveling to generate 3,300 Newtons on impact? We're going to use a formula here. Again, don't be intimidated. A formula isn't anything more than an explanation of how things relate to each other, kind of like a recipe.

Banana Split = 1 banana + 1 cup whipped cream + 3 strawberries + 3 scoops ice cream

Here, Force = mass of the object times the velocity divided by the stopping time. We'll write this Force = mass * velocity / stopping time. We need Force to be around 3,300 Newtons or  we have to change our scene.

We'll start with our hero since, well, people move. Assume the engine block was stationary, just hanging there, and our hero runs into it, could he break his face?  A 180-lb man has approximately 82 kg on mass on planet earth. Running at rate of 6 miles / hour equates to 2.68 meters/second. The force our hero absorbs will be his momentum when he hits the engine divided by the time it takes to stop. The strike will be instantaneous so let's use a tenth of a second. The math then is 82 kg (mass) * 2.68 m/s (velocity) / 0.1 sec (stopping time) = 2,200 Newtons. Painful, yes, but he haven't broken his face.

In many auto mechanic garages, a shop hoist is a simple crane that lifts the engine straight up with movement limited to the rough dimensions of a car. In such a limited space (say 6 feet or 2 meters), the top acceleration is 1 m/s every second. Force then calculates as 272 kg (mass) x 1 m/sec (velocity) / 0.1 sec (stopping time) = 272 Newtons. Enough to cut, bruise, knock over, but not close to the bone breaking 3,300 Newtons.

A shop hoist won't work for the story. We have to get creative. What if our garage owner installed a bridge crane that reached across his four bay garage. Maybe he was really into cranes or got a good deal at Cranes-R-Us. Who knows? Doesn't matter to the sotry. What does matter is the crane was bigger and was motorized. After some basic research on larger bridge cranes, I couldn't find information on their top speed (apparently, not a priority of crane suppliers). So what do we do? Quit? Heck no, we make an assumption (aka guess). Let's assume the hoist was capable of moving along the rails at a rate that was a slow walking pace for a man, say 3 miles / hour, which is 1.34 m/s. The engine, then, moving at full speed and striking a still man can create a force of 272 kg (mass) x 1.34 m/s / 0.1 seconds = 3,650 kg-m/sec^2 or 3,650 Newtons. Just enough to call it feasible.

This means in our scene the engine has to be in motion to get the desired result. Congratulations, we just broke his face and the scene can continue.

Here are a few of the resources I played with in developing the background for the scene and this post. Check them out!

https://curiosity.com/topics/how-much-force-does-it-take-to-break-a-bone-curiosity/

https://sciencing.com/mass-weight-7721316.html

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