Understanding Kinetic Energy and Trauma

With every trauma call we run, there are two things that are almost absolute certainties. And I don’t mean that in the tongue-in-cheek sense, like, “We are certain that the elderly fall victim will live on the third floor and the elevator will be broken or nonexistent.” or, “We are certain that the nursing home C.N.A. will call for that extended inter-facility transfer 12 minutes before the end of our shift.” type of certainty. I mean…even more certain than that.


When people call us for trauma, these two things are certain.

1.) Two objects collided with each other.

2.) Someone called 911.

When we put these two certainties together, we can make some fair assumptions about trauma calls. Objects colliding with each other aren’t such a big deal. It happens all the time. If my fingers weren’t colliding with the keys on my computer keyboard, you wouldn’t be reading this right now. But nobody’s running off to call 911.

It’s the second certainty that gives us pause. You see, people don’t start activating 911 until things collide in uncontrolled ways. Trauma calls happen when things collide together in unexpected ways and with unexpected velocity. It’s as simple as that. Now that I’ve said that, it sounds so profound that I want to write it down again and put my name under it. Here:

“Trauma calls happen when things collide together in unexpected ways and with unexpected velocity.”

– Steve Whitehead

Doesn’t it sound more profound in quotes? I agree. …Lets move on.

As obvious as it sounds, it bears repeating for one simple reason. If all of our trauma calls originate with two or more objects colliding with each other, doesn’t it make sense to spend a little time learning the nature of how objects in our universe behave when they collide with each other? Regardless of what two objects collide, whether it be Grandma Smiths hip and her linoleum floor or a minivan and an SUV, there are some elements that are always true about the way things collide. When we understand them, we can better predict the potential for damage.

Warning: Math Equations Ahead

No…wait, where are you going? Come back. You can do this. You’ll thank me later.

So what do we mean when we say kinetic energy? We toss that phrase around a lot when we talk about trauma. When we talk about kinetic energy, we are referring to the amount of energy a moving body is carrying around with it.

If something is standing still, it requires energy to get it moving. that energy is carried by the moving object until it stops. To stop, that energy needs to go somewhere else. It needs to be transferred to another body or converted to another type of energy. (Like heat for instance.)

All of this happens because of four basic laws of motion.

1) Newton’s first law of motion. A body in motion or at rest will remain in that state until it is acted upon by an outside force. So if something is still, it stays still until something moves it. If something is moving, it will keep moving until something stops it. Gravity and friction count as somethings. So does an 18 wheeler.

2) The law of conservation of energy. Energy is never created or destroyed, it only changes form. So once something is carrying around all that kinetic energy in the form of mechanical energy, that energy has to go somewhere before the thing can stop. Primarily, it’s going to be transferred to another object or become heat, also known as thermal energy. (Think about vehicle brake pads.)

3) Newton’s second law of motion. Force (f) equals mass (m) multiplied by acceleration (A) or deceleration (D). That looks like this:

f = m X A    or    f = m X D

Lets look at one last law and then talk about what all these equations mean to us when we’re trying to predict the potential for damage or injury.

4) The law of kinetic energy. Kinetic energy (KE) always equals one half the mass (m) multiplied by velocity squared. For you visual folks, this one looks like this:

KE = 1/2m X v^2

If we want to figure out how much energy is moving around with an object, we need to find out how much it weighs and divide that weight by two. Then we need to figure out how fast the thing is moving and multiply the speed by itself. Then we need to multiply those two numbers together. It’s easy. You can do it with a hand calculator.

What we see when we start playing with the numbers is that, when we’re talking about moving energy, speed means way more than weight. Speed has a dramatic and exponential affect on the energy carried by moving bodies.Here’s an example.

Let’s say you’re driving around at 30 MPH in a Toyota Sienna. Strait off the dealers floor, it’s going to weigh about 5,600 pounds. (A quick apology to the entire metric-using world…this is an American blog.) Our kinetic energy equation is going to look like this:

KE= 2/5,600 X (30 X 30)  or  KE = 2800 X 900  or  KE = 2,520,000

So our Toyota is carrying around some energy for sure. 2,520,000 units of kinetic energy is about 84,000 foot pounds of force that all need to go somewhere when our Toyota hits a tree or a parked school bus. Now let’s try the equation two more times. First let’s double the vehicles weight, then let’s double its speed.

OK, let’s switch out of the Toyota and try a Dodge Ram 3500. This baby comes off the showroom floor at a whopping 11,000+ pounds. Now our equation looks like this:

KE = 2/11,000 X  (30 X 30)  or  KE = 5,500 X 900  or  KE = 4,950,000

Good to know. We almost doubled our vehicle weight and we also almost doubled our amount of kinetic energy. So vehicle weight has a constant effect on kinetic energy. Twice as much weight means twice as much energy to absorb or disburse.

Now let’s get back in our Toyota and double the speed. Our equation is going to look like this:

KE = 2/5,600 X (60 X 60)  or  KE = 2800 X 3600  or KE = 10,080,000

Wow. For the record, that is exactly four times the kinetic energy. So, for every time we double an objects weight, we get a proportional doubling of the kinetic energy moving around. For every time we double the same objects speed we get four times the amount of kinetic energy moving around.

For the record, our Dodge Ram traveling at 60 MPH would be carrying 20,160,000 units of kinetic energy or 673,000 foot pounds of force. That’s 8 times more energy than the Toyota Sienna had at 30 miles per hour.

What does all this mean to us? It means that weight is important, but speed really is king. Consider how much the moving object weighs, but really pay attention to how fast it was traveling. The same is true for falling people or objects that fall on people. How much the falling object weighs is important. How far it fell is very important.

This also applies to people. A 180 pound man who strikes his steering wheel at 30 miles per hour will have to absorb 81,000 units of kinetic energy with his body. The same man traveling 60 miles per hour will need to absorb 324,000 of those units. That could make for two very different calls.

This is definitely something worth keeping in mind as we consider the three collision rule. What is the three collision rule you ask? We’ll talk about that next.

(Author Addendum: In this post, “units of kinetic energy” is an arbitrary quantity used to demonstrate the relationship between the several examples offered. To calculate true kinetic energy in a usable form like joules, you would need to do several conversions prior to calculating.)

What do you think?: Does an understanding of kinetic energy help you evaluate your trauma patient? How much attention do you pay to the forces involved in a traumatic incident?

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  1. Your physics has left me a bit confused. Let’s just tackle the first equation. To begin with, I can’t say I’ve seen someone use units of mph in the kinetic energy equation, so I converted to SI. 5600 lbs is 2540kg (you can’t use pounds anyway due to it being a measure of weight, not mass, you’d convert to slugs I guess). 30mph is about 13.4 meters/second. Doing the math, you arrive at 228041 joules of energy, which is actually 168194 foot-pounds. Foot pounds is not a measure of force however, it is a measure of energy or torque. Pounds is a measure of force, as is Newtons. To discover the force of impact would require calculating rate of acceleration. Also, going from 2520000 to 10080000 is a 3 fold increase by my calculations: 2520000 to 5040000 is two fold, double it again is 1008000, which is a “third fold” (just how 2^2 is 4, and 2^3 is 8, not 6). Not trying to be terribly critical, but I have some engineering background, if you want to emphasize the physics, then I feel it should be accurate.

    As far as the question you asked at the end, is it really useful to estimate energy absorption prehospitally? The trauma team and surgeon may want to know the size of the vehicles to decide likelihood of brain trauma, etc., but prehospitally I think we should be more concerned with doing a good physical assessment and provide appropriate care. Afterall, we don’t hyperventilate a patient because we estimate his head received 300000 joules of energy, we do it because of clinical signs of increased ICP.

  2. Steve Whitehead says:

    @ER, no need to apologize for your criticism. The moment I picked up a calculator I knew that you’d be coming. Thanks for showing up so soon.

    I’ll start with some of the big picture questions and then hit a few small ones as well.

    “Is it useful to estimate energy absorption prehospitally?” – By grossly estimating weight and speed and applying it to the visible damage and considering it during patient assessment? Yes. By performing complex calculations? No. Absolutely not.

    I really hope none of my readers get the impression that I think people should be doing complex math in their heads and calculating approximate energy for various speeds in the middle of a trauma scene. That would be patently ridiculous. I brought out the calculator to demonstrate a few ideas that are useful when considering mechanism. Mainly, the idea that vehicle weight and mass is important, but speed is far more important.

    “I think we should be more concerned with doing a good physical assessment and provide appropriate care.” – Agreed. Solid assessment and appropriate care are hallmark themes on this blog. Their priority isn’t an excuse to ignore the physics involved in mechanism of injury.

    “if you want to emphasize the physics, then I feel it should be accurate.” – I agree that the physics should be accurate to the degree that they remain helpful to the reader. Round numbers and commonly understood rates of speed can give us a feel for how weight, speed and height can affect the potential for damage in trauma. Converting these commonly understood measures to their SI equivalents and recalculating them to the ones place is a degree of accuracy that doesn’t seem helpful to me. I don’t think anyone read your calculations and left with a better understanding of the concept than I already gave them.

    Your calculations are, hands down, far more accurate. Yet, I don’t feel they are a bit more useful in demonstrating the concept.

    “I can’t say I’ve seen someone use units of mph in the kinetic energy equation” – And I’ve never once had a patient tell me that they were driving at 13.4 meters per second. I’ve also never estimated my patients weight in slugs. So these examples would be entirely worthless to most of my readers.

    “Also, going from 2520000 to 10080000 is a 3 fold increase by my calculations” – You’re absolutely right. While I stand by my calculation, my grammatical description was inaccurate. I’ve made the correction above. I now describe it as four times the kinetic energy.

    “We don’t hyperventilate a patient because we estimate his head received 300000 joules of energy, we do it because of clinical signs of increased ICP.” – Actually, I don’t hyperventilate head injuries at all, but I don’t want to get nit-picky.

    “Foot pounds is not a measure of force however, it is a measure of energy or torque.” – Good point. I’m going to have to think about whether or not changing this wording in the post would be more useful to the reader or if it is clearer as stated.

    ER you seem to have to conflicting points of view that are confusing to me. In the first half of your comment you argue for an unhelpful degree of accuracy. You’re proposing that these equations be presented to an absurdly accurate degree. Then you argue that these concepts wouldn’t be helpful during emergency care. Should the expectation of the readers understanding of the physics of motion be greater or less?

    Understanding the basic physics involved in our mechanisms of injury is extreemly helpful when a slightly intoxicated driver involved in a motor vehicle accident wants to refuse our care. Calculating meters per second and joules of energy is not.

    Thanks for getting the comments kicked off ER.

  3. I think you may have missed the point I was trying to emphasize. I was not trying to be precise, but accurate, and there is of course, a difference. Maybe I should have rounded to the thousands place to de-emphasize precision and emphasize understanding. Your calculation, by definition, must be wrong because you are using incorrect units for energy. You can’t use pounds, it must be converted to mass, regardless of whether it’s the SI or imperial system. This is likely why your calculation for joules and then foot-lbs is wrong. And it’s wrong, not just inaccurate due to rounding. Finally, calling foot-lbs a “force” is wrong and could lead novices reading to future confusion. Off the top of my head, if you’re looking to make the amount of energy absorbed in an impact more easily understood, you could possibly make a comparison to a light bulb. For instance, 30,600 joules would be capable of powering a 100 watt bulb for an hour. 

    My point, is that if you are choosing to discuss a physics concept with people, there is a certain responsibility to do so correctly. I’m not saying that things can’t be simplified, but calling foot-lbs a force and using weight in the calculation of kinetic energy is error not simplification. Again, I’m not trying to attack, but to educate and be sure your readers (which obviously are numerous) receive correct information. I’ve read your blog for a while and have enjoyed it.

  4. Oh, and regarding SI vs Imperial. As an American, I’m capable of recognizing that the SI system is far superior, and feel it would be silly to utilize English units out of some misguided patriotism, hopefully you were being sarcastic. I converted your units because it makes the equation more natural to deal with, I know that may not be immediately obvious, but using English units resulted in your calculation being wrong. I forgot to mention you also can’t use mph in kinetic energy because it won’t convert properly to joules, it has to be in the form feet/second if you’re choosing english units.

  5. I see both your points equally. Both are valid arguments. As a new member to the EMS community (just under 5 months certified, 2 years in field) I think i have a perspective here.

    What Steve was doing was getting the person to understand the size of forces involved in traumas. Thinking about how speed affects more then weight is the point I believe to the article. An example I can think of using this article would be traveling to the scene thinking about the accident, hearing a small car hit a pole at 60mph gets me thinking more along the lines of internal bleeding, hidden dangers. Hearing a larger truck hit a pole at 30mph I would be thinking more along the lines of superficial injuries then internal ones.

    Or hearing a multivehicle accident where a large vehicle and a small vehicle collided at a high rate of speed, you get your brain turning on to different things and anticipating certain things.

    Not that the math has to be accurate for anything but knowing that speed is more important to MOI then actual weight helps me understand that certain things need to be anticipated and looked for depending on speeds involved.

    Grandma tripping over Fluffy and landing on the kitchen floor may or maynot break her hip but Grandma falling off the step stool reaching for Fluffy’s food would lead me to believe a broken hip is more likely.

    I dont know if thatw as such a great example but I hope my point gets across. As far as ERs points of what measures were used in the calculations he is correct from an engineering point of view that the measure were wrong to be put into those equations BUT Steve is also correct by using the laymans version with measures that would be easily understood by all. To me its like us (ems/ medical personel) saying STEMI but telling the family it was a heart attack. Yes there is no such thing as a “heart attack” but the family understands that better then us saying myocardial infarction or precisly ST-Segment Elevation Myocardial Infarction. Using MPH or KPH instead of FPS might be wrong from a professional standpoint but relates to the end reader easier. Being Steve wasnt doing IV Fluid math or building a bridge I dont see the harm in not using the precise units of measure to make the point.

    I guess in the end what I am trying to say is Steve thanks for the great article and getting me to realize speed is more of a factor then how heavy and object is and ER thanks for letting me know the correct units of measure to do accurate calculations if they should ever arise to be used.

  6. Just wanted to tell you that “Trauma calls happen when things collide together in unexpected ways and with unexpected velocity.” is going up on my personal Great Quotes board (properly attributed of course.

    Thanks for another great article.

    PS: Slight typo in point one…should be Two objects, not To objects…. 🙂

  7. Steve Whitehead says:

    @ER The great thing about blogging is the open door invitation for readers to contribute and expand upon the original piece. In this case, I think your input has made this piece much better.

    I work with engineers when I do consulting in the bio-tech industry and I’m always impressed with their command of the way things work. They measure things with their hands with amazing accuracy and do complex calculations in their heads without blinking. I’m well aware that arguing with an engineer about math equations is like arguing with Chuck Liddell about the best way to throw a right jab. Sooner or later, you’re libel to get knocked out.

    Based on your input, I made several revisions to the piece.

    I’ll continue to use mph and lbs. in the equations for a few reasons.

    First and foremost, because it’s the way most of my readers think. That’s what I meant when I said, “This is an American blog.” And that’s why I offered the statement as an apology. The metric system is vastly superior to English units in every way, but we insist on keeping English units anyway. So here, I’ll perpetuate the problem by using it in this analogy, simply so that the majority of my readers will understand what I’m talking about. I apologize to all my readers who drive their vehicles in Kilometers per hour and have the utmost respect for your metric system.

    Second, It’s also the way I learned it. I refer to Mosby’s Paramedic Textbook (Second Edition) By Mick Sanders chapter on Kinematics of trauma (pg 529) where kinetic energy is calculated using MPH and body weight in pounds to produce a value described as “units of kinetic energy” in the same way I have here.

    Where I got into trouble is when I tried to use this value to approximate foot-pounds and came up with a value that was incorrect. I have now removed the references to foot-pounds from the article. I think the article reads better without them.

    I have also noted for the reader that “Units of kinetic energy” is an arbitrary value used for comparison within the piece. I included a link to clarify how to calculate kinetic energy into a more useful value for folks that might like to carry the equation further. I know that this still makes you want to pull your engineering hair out…but it will have to suffice.

    Thanks again for your input ER and thanks for your help in making the piece far better. Come back soon.

  8. Steve Whitehead says:

    @Jude I like your STEMI analogy. I think you see the conflict clearly. Thanks for adding your voice.

  9. Steve Whitehead says:

    @Alex Thanks Alex. I kinda liked that one too. And thanks for the spell check heads-up. I made the correction.

  10. great read, im writing a paper on kinetic energy and your post will be great for some extra research, thanks



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