Amount of energy, roughly, needed to kill with blunt force trauma

[Jake Sparre]

Basically, I have been trying to solve my own fictional equation of the amount of weight/mass needed to be dangerous or lethal from roughly 400 feet in the air. I have tried multiple equations and what not to come to no answer besides the answer to the amount of kinetic energy. This does not yield the stress value, or even tell me the amount of stress a human or animal could withstand. I understand it is an odd question, and logically I think 5 pounds dropped from 400 feet would be lethal, but the math would yield the proper answer.

 

[berkeman]

Basically, I have been trying to solve my own fictional equation of the amount of weight/mass needed to be dangerous or lethal from roughly 400 feet in the air. I have tried multiple equations and what not to come to no answer besides the answer to the amount of kinetic energy. This does not yield the stress value, or even tell me the amount of stress a human or animal could withstand. I understand it is an odd question, and logically I think 5 pounds dropped from 400 feet would be lethal, but the math would yield the proper answer.

Welcome to the PF.

What is the context of your question? Why is this something you want to calculate?

 

[berkeman]

BTW, 400 feet is high enough that most objects will be at terminal velocity when they strike the person. The obvious most serious injury is a head injury, which can result in death within a couple of minutes (due to internal brain hemorrhage).

That's why hard hats are required in most construction sites where objects can fall and hit workers on the head. See the discussion about head protection with hard hats starting on page 16 of this OSHA document:

https://www.osha.gov/Publications/osha3151.pdf

 

[rkolter]

Basically, I have been trying to solve my own fictional equation of the amount of weight/mass needed to be dangerous or lethal from roughly 400 feet in the air. I have tried multiple equations and what not to come to no answer besides the answer to the amount of kinetic energy. This does not yield the stress value, or even tell me the amount of stress a human or animal could withstand. I understand it is an odd question, and logically I think 5 pounds dropped from 400 feet would be lethal, but the math would yield the proper answer.

In a perfect world, you could drop a mass at 400 feet up, and have it hit the ground about 5 seconds later at about 50 meters per second. You won't get quite that because of air resistance. But if you used a dense round shaped object, you could get reasonably close.

So, the real question is, would a five pound ball of metal in the shape of a baseball moving 50 meters per second and hitting you in the head kill you? It's interesting that energy releases can be calculated in kilograms of TNT. I think we can agree that one kilogram of TNT placed against your head would kill you.

The metal ball would deliver about 2/3 of a kilogram of TNT to a six centimeter area of your head. I am pretty much certain that you would die. If it hit your hand, it would rip your hand off. If it hit your shoulder, it would destroy your shoulder if not rip your arm off.

To be fair, I think you answered your own question early on - logically one would assume dropping a 5 pound weight from 400 feet up would be lethal. Assuming you pick a dense object with a small cross-sectional area, your assumption is reasonable. And a little disturbing.

 

[NascentOxygen]

I was thinking 18^th century warfare, and how fast would a cannonball need to be coming down...

I wonder if its surface were dimpled like a modern golf ball's, how much more damaging would a cannon ball's higher incoming velocity become?

 

[berkeman]

I was thinking 18^th century warfare, and how fast would a cannonball need to be coming down...

I wonder if its surface were dimpled like a modern golf ball's, how much more damaging would a cannon ball's higher incoming velocity become?

Ouch. A cannonball to the head would likely hurt...

 

[NascentOxygen]

Ouch. A cannonball to the head would likely hurt...

Undoubtedly it would be felt. But more likely any impact would be elsewhere on the body, the aiming of those old muzzle loaders must have been wild guesswork.

[emoji378] [emoji378]

 

[Tsu]

Basically, I have been trying to solve my own fictional equation of the amount of weight/mass needed to be dangerous or lethal from roughly 400 feet in the air. I have tried multiple equations and what not to come to no answer besides the answer to the amount of kinetic energy. This does not yield the stress value, or even tell me the amount of stress a human or animal could withstand. I understand it is an odd question, and logically I think 5 pounds dropped from 400 feet would be lethal, but the math would yield the proper answer.

You planning something?

 

[Jake Sparre]

Amazon prime air has projections of a maximum weight around 5 pounds, flying just under/around 400 feet

 

[Jake Sparre]

Might I add how awesome this forum is. I expected 0 responses for weeks

 

[Bystander]

Amazon prime air has projections of a maximum weight around 5 pounds, flying just under/around 400 feet

Odds are FAA/whoever will require "failsafe" delivery modes; no parachutes, and sufficient surface area that "terminal velocities" are loowww.

 

[berkeman]

Amazon prime air has projections of a maximum weight around 5 pounds, flying just under/around 400 feet

Ah, so you are developing a cellphone app to send out an alert to the local subscribers when an Amazon drone's power fails so they can seek shelter (or put on their hard hats). That's a very good idea. I will definitely download your app, and will buy stock in your company!

(You can use PulsePoint as a starting point for a local subscriber cellphone alert model -- I'm signed up there to provide bystander CPR when needed in public places...)

 

[1oldman2]

This explains a lot... http://www.bbc.com/news/technology-38458867

 

[rkolter]

If it's Amazon Prime and drones and five pound packages you are concerned with, the drones and their packages will have significantly more drag than a round metal ball. But, if the drone fails, you might have a more massive object - the drone AND the package.

I would be more concerned with Amazon's patent for floating warehouses 45,000 feet up. Drones would be airlifted to them, and would launch from them with five pound packages - dropping in a controlled manner to 400 feet before delivering their package. A drone or package that dropped uncontrolled from THAT height would definitely hit terminal velocity on the way down.

"I am so sorry for your loss. How did he die?"
"Car accident."
"Oh no. What happened?"
"Well, we ordered a radio controlled car from Amazon, and the drone accidentally let go..."

 

[gleem]

But his problem is more complex than is appreciated here. Assuming no skull penetration or fracture then acceleration of the head is the thing to look at. You not only need to know the mass of the object and height but the elastic properites of the object and the head and the area size of the impact area .

A 100 mph or less baseball (150 gms). can kill a person and that is about 148j of energy. A soccer ball (424gms) of that same energy travels at about 58 mph and there are no known deaths(?) due to head injuries in that sport and soccer ball can travel up to 70 mph. As for TBI's in soccer the jury is still out. The difference is that with the baseball more energy is transferred to the head while the soccer ball on the rebound carries off a great deal. On impact the soccer ball absorbs a great deal of energy when compressed while the baseball does not.

 

[Dr. Courtney]

A common head injury criterion for non-penetrating head injury is based more on the acceleration of the head than the energy of the impactor. But even the head injury criterion depends on the length of the interaction. A 1 ms smack requires more acceleration to kill you than a 100 ms smack.

Penetrating injuries to the head have a good chance of killing you.

The army long used 58 ft-lbs as the energy of a projectile (bullet or fragment) needed to cause a casualty, but that just assumed a hit and not necessarily a hit to the head.

http://history.amedd.army.mil/booksdocs/wwii/woundblstcs/chapter2.htm

More recent military models are more concerned with the probability of incapacitation given a hit with a certain energy.

See: https://www.ncbi.nlm.nih.gov/pubmed/291265

350 ft-lbs turns out to have a 50% chance of incapacitating a soldier on the battlefield.

Helmet design focuses on the conversion of impact velocity to maximum head acceleration and resulting injury potential.

 

[Mondayman]

A 100 mph or less baseball (150 gms). can kill a person and that is about 148j of energy. A soccer ball (424gms) of that same energy travels at about 58 mph and there are no known deaths(?) due to head injuries in that sport and soccer ball can travel up to 70 mph. As for TBI's in soccer the jury is still out. The difference is that with the baseball more energy is transferred to the head while the soccer ball on the rebound carries off a great deal. On impact the soccer ball absorbs a great deal of energy when compressed while the baseball does not.

I couldn't help but extend this to hockey: a puck is about 160 grams, and is solid. The hardest shooters in the NHL are capable of blasting slapshots over 100mph (108.8 is the all-star game record, set by Zdeno Chara). Seeing as how, with curved sticks and all, players shots can vary wildly from along to ice to head height, I find it incredible that no one has been seriously hurt (eg. resulting in career altering injuries or death). In fact some players have continued playing the game after taking a puck to the face!

 

[BillTre]

Here's another one:

About a year ago I was trying to film a 2" iron ball dropped from about 15 feet (from the top of my garage) onto a melon as model of an impact on Mars. (Mars has some truly giant craters.)
I wanted to film it in slow motion, but could not get anything with a faster frame rate than an iphone camera (240 fps) which only gave me a single frame of the impact.

Faster cameras are either expensive to buy or rent.
Some friends in a lab had a camera that could do 100,000 fps, but it was not portable, fragile, and very expensive. They had it mounted in a lab and linked to a fast computer with big cables.

I did not get the kind of impact I wanted. I needed more speed (longer drop), a larger ball, or a larger melon with less curvature so it would punch in rather than bouncing off. Accuracy was also a problem. The release method (hand release) was inconsistent. I'll probably try it again sometime with an electromagnetic release.