# How to calculate force of a fall w/increased gravity

#### Duquin

This isn't homework persay and has nothing to do with school, but since it's a hypothetical question for personal intrest if it belongs in the homework section or anywhere else please let me know. I apologize if it's in the wrong place.

Hello everyone I participate on an online role playing forum where people make characters and interact socially, go on adventures, and fight, these kinds of things. I've had the blessings to gain a character with rather powerful abilities, the power over gravity among other things. Basically what I want to do is take an opponent and send them flying into the air with my wind powers and then increase the gravitational pull on their bodies to send them falling to the ground at increased speeds causing a greater force of impact.

So this is a hypothetical and theoretical question, but say I were to take gravities force and multiply it by 2x with the effects localized on a single target. If possible I'd like to take a 70kg person(average human mass google tells me) and figure out how to calculate how much force they would hit the ground with from say 30ft up. With no wind resistence as my character has the power to negate such a factor, if there is any other variables or factors I need please let me know.

I'll be taking things to extreme numbers such as 50 time earths gravity and up to 100 feet high, but for the sake of simplicity I'd like to start by learning how to do this on a smaller scale. The only reason I bring this up is if anyone thinks such an act would have adverse effects such as drawing myself towards the target dangerously or anything of the sort please do speak up. While it's all fantasy I would like to be as accurate as possible

Also I know this might be out of the knowledge range of physics but if anyone happens to have knowledge of how much force from a fall is required to break bones or shatter them, and other varying levels of damage to the human body, I would appreciate it if you could enlighten me. Whether here in this topic or through a pm if it would be considered off-topic.

This all isn't horribly important as it's merely for recreational use in a text based fantasy, but it would help me show accurately how much damage I am doing in a world where people like to underestimate the strength of other peoples attacks. It would be nice to give a scientifically exact description of just how hard a character is hitting the ground.

Big please and thankyou's all around to any whom respond *bows* If this is too childish or doesnt seem serious enough to solicite a response I assure you I am completely serious however, I completely understand. Feel free to delete this topic and if that is the case, please send me a pm letting me know what was wrong.

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#### redargon

Ok, just using Newton's third law, F=ma (force = mass x acceleration). If you ignore wind resistance affects (and consider your body inelastic, so that it doesn't bounce off the ground or absorb any impact), the force that you would hit the ground with, from any height will be F=mg (where g is the acceleration due to gravity). You can make g whatever you like. At the moment, on earth, it's about 9.81m/s². So, for a 70kg person, the force would be 686.7N. At three times normal gravity the force would be 70*9.8.1*3=2060.1N etc. Wind resistance will decrease this reaction force by generating a "slowing" force in the opposite direction to your falling force (ie. upwards). This isn't so hard to work out. It would be the drag force of the falling body. I'm pretty sure there is a terminal velocity or at least an approximate of the drag force on a human in different positions at terminal velocity (the maximum velocity acheived by a falling object when the wind resistance prevents the object from falling any faster).

The damage to be done to a falling object will be more to do with the amount of energy that is imparted when it suddenly stops (ie, when it hits the ground). Assuming all this energy is converted into bodily damage, then this can be easily calculated as the kinetic energy of the object just before impact. Energy is always conserved, so the potential energy that the object has in the air before it falls, is the same as the kinetic energy it will have when it hits the ground. Simply speaking, the potential energy of an object can be calculated using PE=m*g*h (Potential Energy = mass x gravity x height above the ground). This would be converted into Kinetic energy as the object falls and gathers speed, becoming a maximum at impact. KE=1/2*m*v² (Kinetic energy = 1/2 x mass x the velocity of the object squared). As I said this kinetic energy (at impact) will be the same as the potential energy (before falling), so impact energy would be the mass (take 70kg) * gravity (9.81m/s) * height (take 30m) = 20 601 Joules (the unit of energy). For an idea, 1 ton (1000kg) of TNT yields about 4.184 GJ (4 184 000 000 Joules), an atomic bomb (hiroshima) about 50TJ (50 000 000 000 000 joules). For interest, you could put your energy into your kinetic energy equation to calculate the speed at impact.

What energy you require to do damge to a human, no idea, but i'm sure it's documented somewhere.

Please note, this is a bit of a ramble and is based on very simplified ideas and physics.

PS, if your character can negate wind resistance, then it could most probably create a vacuum. Why not kill your opponent by generating a vacuum around him and sufficating him. Or generate gravitational forces in all directions around the opponent and tear him into pieces. Just my 2 cents for more carnage :)

#### Duquin

Firstly allow me to say, in the most humble way to express my thanks I can remember from my old japanese class, Doumo Arigatou Gozaimasu *bows* This will help boat loads. Now onto my question and comment o.o

For interest, you could put your energy into your kinetic energy equation to calculate the speed at impact.
Which energy? The potential energy? Sorry I dont follow on that bit.

PS, if your character can negate wind resistance, then it could most probably create a vacuum. Why not kill your opponent by generating a vacuum around him and sufficating him. Or generate gravitational forces in all directions around the opponent and tear him into pieces. Just my 2 cents for more carnage :)
Well I try not to abuse my powers for instant kills as I love battles and enjoy to drag them out, the attack I'm asking about in this thread is only one part to a combo of attacks. Although I will keep those in mind for foes I wish to torture or give horrible deaths once the battle is over, thankyou ^^

I alread possess a move where I create a vaccum around all the targets open wounds in order to cause extreme pain and suffering, my character in question is my only "evil" one but he is very sadistic :D

#### redargon

Which energy? The potential energy? Sorry I dont follow on that bit.
Indeed. The PE at the top of the fall is the same as the KE at the point of impact, so you can put your initial PE into the KE equation to find the impact velocity. ie. mgh=1/2mv² therefore, v=sqrt(2gh)

#### Rasalhague

Ok, just using Newton's third law, F=ma (force = mass x acceleration). If you ignore wind resistance affects (and consider your body inelastic, so that it doesn't bounce off the ground or absorb any impact), the force that you would hit the ground with, from any height will be F=mg (where g is the acceleration due to gravity). You can make g whatever you like. At the moment, on earth, it's about 9.81m/s².
Mass times g is the force we experience normally due to gravity. To find the force of impact on falling from a height, we need to use a different acceleration, don't we? Namely the acceleration that reduces the speed of the falling body to zero.

30ft = 9.144m. In normal earth gravity, we'd have:

Potential energy = height * gravitational acceleration * mass = 9.144m * 9.8m/s^2 * 70kg = roughly 6 000 joules = kinetic energy at impact = 1/2 mass * speed squared. Therefore speed at impact would about 13 m/s or 30 mph. You can get the same answer from the equation:

h = 0.5 * a * t^2

where h is height, a is acceleration due to gravity, and t^2 is time squared. Solve for time (1.367 seconds, the duration of the fall), then differentiate to get the speed:

speed = a * t = 9.8 * 1.366 = about 13 m/s.

To double the gravity, just replace 9.8 with 9.8 * 2 = 19.6 in either equation. I get 19 m/s = 43 mph. This is ignoring atmospheric drag, as suggested.

"Most crash impacts have a duration of less than 250 milliseconds or one-quarter of a second, which is considered to be in the realm of abrupt acceleration."
ftp://ftp.rta.nato.int/PubFullText/RTO/EN/RTO-EN-HFM-113/EN-HFM-113-06.pdf[/URL]

Quarter of a second from 19 m/s to zero gives a mean acceleration of 76 m/s^2, which--over the sort of duration we're looking at--puts us somewhere in the "area of severe injury" of their graph. How would hitting the ground from a fall compare? I'm guessing the impact would be quicker, which means a higher acceleration. There must be statistics out there somewhere for the survivability of falls...

[quote="redargon, post: 2364671"]So, for a 70kg person, the force would be 686.7N. At three times normal gravity the force would be 70*9.8.1*3=2060.1N etc. Wind resistance will decrease this reaction force by generating a "slowing" force in the opposite direction to your falling force (ie. upwards). This isn't so hard to work out. It would be the drag force of the falling body. I'm pretty sure there is a terminal velocity or at least an approximate of the drag force on a human in different positions at terminal velocity (the maximum velocity acheived by a falling object when the wind resistance prevents the object from falling any faster).[/QUOTE]

Wikipedia gives "120 mph or 55 m/s" as the typical terminal velocity for a sky diver and says "a speed of 50% of terminal velocity is reached after only about 3 seconds".

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#### Molydood

Hi Duquin,

key factors effecting the survivability (in my non expert opinion only):
-the deceleration sustained by the victim
-the period of time that this deceleration is sustained for
-orientation of victim on impact (eg upright may give higher survival rate, but increased chances of broken legs)
-understanding of human tolerance to these two factors (statistical data provided in the link posted by Rasalhague looks like a pretty good start)
-and others… but lets keep it simple :-)

(Putting aside the more complicated case of broken bones and other non-mortal damage, unless you can find some statistics for the strength of bones and/or tolerance of other parts of the body etc)

I see the human body acting as a 'crumple zone' upon impact, ie the less critical parts of the body eg muscles/flesh acting as an absorber for the more critical parts eg bones and (even more so) head and internal organs
We need to make some assumptions about how the body is decelerated during impact, to determine the duration of the deceleration period, which will then give us the actual deceleration (in g) as well as time in seconds (assuming we know the impact speed)

Assuming the speed of the falling victim is 50 m/s, then I would guess that when the body hits the ground (assume landing on back) it is decelerating over quite a small distance, say 0.1m, depending on how much deformation occurs during impact (obviously this will change as the terminal velcoty increases!)

My numbers suggest incredibly high values of deceleration (about 2000g) occuring over 0.002 seconds, but that shows how sensitive the numbers are to the assumptions (hard impact surface, 50 m/s, all decel. occuring over 0.1m). I suspect that the deceleration period is longer than 0.002 seconds and hence possibly lower values of deceleration, but certainly if a human is falling out of the sky and being decelerated by a solid surface rather than by the fuselage of an aircraft or car, then I would expect to see some fairly crazy decelerations, hence why people die when their parachutes don't open!

In simper terms, it seems to me that anything more than a second or two of freefall would result in such high values of deceleration that it would be difficult to survive. Of course, this all changes if the victim lands feet first and hence massively changes the effectiveness of the crumple zone, thus protecting the heart, lungs, head etc etc… but then if you don’t make *some* assumptions then you will never be able to calculate anything.

Maybe you could go conservative, and give the victim the best odds of survival based on feet first approach, hence the crumple zone could then be 1 metre, and thus the deceleration is decreased by a factor of 10. It's still pretty high for a terminal velocity fall however!

#### Duquin

Thank you very much to everyone for the follow up replies, this will all help tremendously. Now my foes can taste the accurate wrath of my attacks, for that I am very thankful.

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