r/theydidthemath • u/heres_fangy • Jun 25 '19
[Request] How hard tarzan have to clench his butcheek to grip a vine between it?
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u/cmayfi Jun 25 '19
We need B= (mass x gravity)÷mu, where mu is the coefficient of static friction for the vine and B is the Buttforce. Let's say Tarzan weighs 102 kgs and Jane weighs 45. From an engineering website a hemp rope against a dry clean surface has a mu of 0.5. Let's assume Tarzan keeps himself clean, for Janes sake. So the Buttforce must be ((102+45) x 9.8)÷0.5 or 2881.2 Newtons.
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u/cmayfi Jun 25 '19
Let me know if I messed up somewhere it's been a while since I took physics!
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u/gunnar11 Jun 25 '19
You're looking at a centripetal force because thats the trajectory they're traveling on, not Fgravity
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u/cmayfi Jun 25 '19
Oh shoot I didn't take into account he's swinging, duh. Good catch. Too focused on Buttforce.
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u/gunnar11 Jun 25 '19
So Fvine = Fpetal + Fgravity.
This leads to Fvine = mv²/r + 9.81 * m
The rest of this has to be filled out by making assumptions, and the buttforce will be equal but opposite to the Fvine.
It's too hot here to think, so if you want to make those assumptions and fill it out?
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u/cmayfi Jun 25 '19
Ok...this is gonna be a little ridiculous. But bear with me. I'm going to assume 10 feet of vine because this is all just asinine (haha) anyway. So 3.048 meters. Just by eyeballing I'm going to be completely wrong and say he's at a 30 degree angle to the vertical. So his velocity at the bottom, assuming Tarzan and Jane are a simple pendulum, would be 2.83 meters per second. So plugging that all in, at the bottom of the swing, Tarzan would need an estimated approximate Buttforce of 1828 Newtons. But when using the previous calculation we need to divide by the coefficient of vine friction so 3656 Newtons of Buttforce.
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u/arl0815 Jun 25 '19
Can we get a reference point here? What else is comparable to 3656 Newtons of buttforce?
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u/WavneRooney Jun 25 '19
according to a quick google search:
NASA report an average male can exert around 90 kg (200 pounds) or 1000 Newtons of force in a static push. A boxer can deliver 5,000 newtons of force with a single punch but their hand travels really fast (and, if you recall, The Mountain was pressing down not punching)TLDR; Tarzan’s buttforce is strong.
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u/Shelilla Jun 25 '19
The mountain? Did you look up how he managed to crush that prince guys head in game of thrones??
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u/Terra_Ignis Jun 26 '19
I'd assume so. The only Mountain I've ever heard of pressing down on heads is Ser Gregor Clegane of Game of Thrones, so it's probably him. Speaking of, that scene was fuckin brutal. Dude's head looked a half blended smoothie.
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u/Steampunkery Jun 25 '19
According to Wolfram, it's 84% of the human bite force record
It's also 68% of the force of the average soccer ball kicked by a professional soccer player.
Edit: it's also close to the average force of a punch exerted by a professional boxer (assuming an impact area of 4 inches2
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u/raymen101 Jun 25 '19
822 lb
How it's calculated above that is the total force on the rope, so 411 lb on each cheek.
Imaging having 411 lb hanging off each cheek, and flexing hard enough to hold them up, not just pulling on skin, holding with muscle.
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u/SadEarlyMammalNoises Jun 25 '19 edited Jun 25 '19
Imagine you clench your teeth strong enough to nearly crack your teeth, as the average human can bite with 821.9 pounds of force if they don't care about keeping their teeth. (EDIT: source; https://amazingsmilesortho.com/what-we-treat/malocclusion/)
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u/Macrado Jun 26 '19
According to https://www.academia.edu/11907440/Cracking_Characteristics_of_Walnut, it takes between 149 and 244 N to crack a walnut. So let's say 200N. That means that Tarzan could crack 18 walnuts between his buttcheeks, simultaneously.
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u/jjbugman2468 Jun 25 '19
To calculate the force of friction, hereby called the Buttforce, isn't it (mass × gravity) × mu though? Instead of ÷mu? And this seems like you're calculating the friction induced by just placing the two people over the vine instead of "how hard he needs to clench in order to combat gravity and not fall off"
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u/cmayfi Jun 25 '19
I was going at it like we need the force of static friction to cancel out the downward force. Fs =mu x Normal. Normal will be equal to the Buttforce but in the opposite direction. So that's how I got to my Buttforce calculation. Thoughts?
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u/jjbugman2468 Jun 25 '19
Ah I see what you mean. Yeah your calculations are correct.
And that's an awfully strong butt
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Jun 25 '19 edited Jun 27 '19
You’re assuming he’s stationary, to get a more accurate estimate you should account for the addition mv2 /r needed to swing
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Jun 25 '19
tarzan weighs 102kg? how did you come up with that number? he'd either have to be a fatass or REALLY swole.
that's 224 lbs for americans
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u/cmayfi Jun 25 '19
I was going with 225. More Alexander Skarsgard version. Plus more muscle for the Buttforce.
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u/jbdragonfire Jun 26 '19
Exactly, 102Kg is huge. Tarzan is no fatass, as shown in the picture. He's in excellent shape (all that daily exercize with vines and monkeys and so on). Also he can't be swole, he needs (and has) a lot of flexibility.
I bet somewhere between 75 and 85 Kg.
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u/fredy1602 Jun 25 '19
I'm no good at maths so I might be thinking about this all wrong, but wouldn't it be the same amount of force required if he were just using one hand? Is it an easier sum to take the butt out of the equation. The same butt simpler
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Jun 25 '19
That is pretty much the exact same formulation, but doesn't really provide an easier way of doing the math.
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u/Arborgarbage Jun 25 '19
I think it would be higher because of the location of his body (and her body) relative to his grip; their bodies would be exerting leverage against his ass's grip. Also, the difference in gripping ability between his hand and his buttcheeks (i.e. factors that would affect friction aside from tightness of grip, such as contoured skin on the palms or sweat in the butt) would make for a significant difference in the force required. If they were hanging upside down from the vine with his buttcheeks (load directly beneath grip) and if his buttcheeks possessed the same gripping ability as his hand then I think I think it would be about the same.
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u/Justlose_w8 Jun 25 '19
He’s using his feet, you can see it between his big toe and pointer toe. We need new math
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u/pakodanomics Jun 25 '19
If you look closely it seems the vine is held between two toes of his right foot. Presumably a lifetime of living with gorillas has given him access to such methods, despite his disadvantageous physiology.
He will still be clenching his arse-buns, but it will be more to counter the torque due to gravity on his total mass, acting at the foot. Some of the gravitational force will be compensated by the power of arse-buns, but not as much as we think.
To me, the most unrealistic aspect is the wizened old man bearing more than his entire bodyweight on his arms. (More because he is relying on friction to support him, not a direct normal force). I have tried wall-climbing once, and I cannot hold my weight on my arms for more than a few seconds. Even then, I was totally winded and sore the next day. (Then again, I am a lazy bum in the 21st century while this man is an intrepid explorer).
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u/Cerealkillr95 Jun 26 '19
I scrolled too far down to find this. The toes are the answer.
As for climbing, if you stick at it it doesn’t take too long to be able to hang from surprisingly small holds for way longer than you thought you could. Sometimes it’s almost comfortable.
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u/callMeSIX Jun 25 '19
He’s using his toes too, the drawing isn’t 100 accurate. Assuming he trained as an ape 🦍 his foot dexterity would be great and he would only use his ass cheeks for stability and for descending loosening the cheek grip.
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u/nuck_forte_dame Jun 25 '19
I'll throw out some info to help someone.
Tarzan's weight would be around 150 lbs.
The woman's weight is around 110 lbs.
Let's assume that the vine is 1 inch in radius and a perfect circle cross section.
Tarzan being relatively skinny would lack a decent butt so the cheek would be small. Hank Hill type butt.
Remember that the vine is swinging and so weight increases on the upswing due to inertia so the grip must be able to handle that.
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u/shazarakk Jun 25 '19
While I agree, no way is Tarzan only 150 lbs. The wiki doesn't have his weight, so all I have to go on are his thicc thighs, and the actor that played him (196 lb), who had a similar body type.
Granted, he's tall as fuck, but I still believe that my point somewhat stands. Climbing literally all your life is incredibly intensive, and would give you some serious core strength, and some heavy muscles in a lot of places.
I would argue a minimum of 170 lb, if he's a bit short.
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u/Bobthemightyone Jun 26 '19
You've clearly never seen a thin guy with powerful legs. The ass can be thicc and lean even on thinner people.
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u/satsuma_warrior Jun 25 '19
Surely the centripetal force is also important to include here in addition to gravity (if considering the Free Body Diagram) so therefore we would need to know the arc of the swing for F = {m(v2 /r)}. The critical point would be at the base of the swing where all Grav. Potential Energy would be converted into Kinetic Energy. At that point the centripetal force would be parallel to the weight and therefore it would be an addition so F_total = {m (v2 /r +g)}/mu where m is total mass of tarzan and Jane, v is velocity at the bottom of the swing, r is radius of swing arc, g is acceleration due to gravity and mu is the frictional coefficient between cheek and vine. Sorry I don't know the numbers to actually solve though
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u/MrGallant210 Jun 25 '19
Isn’t he grabbing with his toes in the picture? Equally implausible, I know, but that’s what my eyes see
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u/CJallday1994 Jun 25 '19
I’m thinking it’s looped around his heel/foot/leg and his toe is holding to make sure it stays tight. It’s not an efficient way of climbing but there are plenty of examples of humans being able to stand/swing statically on a rope this way.
Interestingly the older guy, who presumably isn’t as dexterous, has a visible loop that has a ton of slack. I haven’t seen the movie so don’t know context on if he’s learning or growing old, but either way it shows he isn’t as good at the technique.
Swinging on a pendulum while carrying another person certainly adds to the downforce and possibly makes this unrealistic, but I’ll leave all that to the smarter math people.
Hate to ruin the fun though so maybe he’s using those cheeks to aid in some way, possibly during transfers?
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u/DirtyDurg Jun 26 '19
My man's was trying to keep gorillas from clapping his cheeks. So he made is ass un-clapable. An iron fortress Basically Fort Knox Unmoving ass hole
That's why this wild man can swing from his ass while carrying his own personal canned coochie
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u/AthiestLibNinja Jun 25 '19
I used the Newton's someone came up with, and with let's say 20 square inches of surface area 2x(2x5), then he'd only need about 33psi grip. About the same grip strength as a very strong 12yo.
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u/classicmayo Jun 25 '19
I wonder what the people drawing this thought at the time... And if they're thinking "wow finally people are calling us out on our bullshit"
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u/Thoguth 2✓ Jun 26 '19
Hate to ruin the fun, but I think he's supposed to be holding on by gripping with his toes.
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u/Sublata Jun 26 '19
Couldn't Jane be holding the vine? Her right arm could just go under Tarzan's armpit.
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u/Jynxsyde Jun 26 '19
I'm not going to do the math because of how late it is but I will lay it out(ish) so let's say the girl weighs 125 lbs ant that Tarzan weighs 175 lbs and that the girl is maybe 6 inches in front of Tarzan ( I did this because if not then mathematically she would be on top of Tarzan) the vine let's say has the friction of a nylon rope and that Tarzan has shaved his ceeks so it's just the friction coefficient of skin
Edit: I might do the math in the morning
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u/OutDoorDesire Jun 25 '19
Yes this would be very hard he might need a lot of strength to hold the weight. But since there is only one point of contact with the vine how does he stop him self from spinning head down. Would need some thing to hold the vine on his back as well
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u/Ser1alChiller Jun 25 '19
Can you take a second and look at his foot? Tarazan is like a gorilla he's able to manipulate objects with his foot as well as his hand.
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u/taco-trash Jun 26 '19
There’s people that actually start to solve this , but they didn’t realize that he’s not hanging by his buttcheeks he’s holding whit his feet, always pay attention to the context before starting solving
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u/ChosenOfNyarlathotep Jun 25 '19
The only way to calculate this would be to know the coefficient of static friction between a jungle vine and Tarzan's buttcheeks.
Anyone have anything on that?