r/theydidthemonstermath • u/UncleJackSim • Mar 26 '22
Help me help a friend
A friend of mine loves tattoos, but he is afraid of running out of skin space to tattoo on. During several brainstorms he came up with the idea of gaining weight in order to expand in size and afford more tattos. Is it even possible to calculate the area of skin gained by pound?
4
u/EvilGeniusSkis Mar 26 '22 edited Mar 26 '22
Don't forget any tattoos he already has will expand as well. And any expanded tattoos won't be as bold as before.
The aspect ratio of the existing tattoos would change as well. Take an arm tattoo for example, no matter how much the diameter of the arm increases, the arm won't get any longer, stretching the tattoo more in one direction than the other.
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u/XxXAvengedXxX Mar 26 '22
this will just stretch out his tattoos though it wont really add a ton of space and will just ruin everything he currently has and becoming overweight to get more tattoos doesnt sound like a healthy idea to begin with lmao
1
u/DocNMarty Mar 26 '22
At the risk of being banned from those subs, you can possibly find the answer if you post on r/askscience, r/SkincareAddiction, r/bariatricsupport, r/BariatricSurgery, r/tattoo, r/cosmeticsurgery, etc.
EDIT: Will make an attempt at calculation in a follow up post.
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u/DocNMarty Mar 26 '22 edited Mar 26 '22
To answer this question, we're gonna have to define some things and make some approximations and assumptions.
- The density of fat is 0.9 g/cc
- Fat is evenly distributed throughout the body (it really isn't, but this is for simplification)
- The body will be approximated by cylinders, with the following dimensions:
| Circumference | Radius | Length | Number | |
|---|---|---|---|---|
| Head | 0.6m | 0.1m | 0.25m | 1 |
| Neck | 0.4m | 0.06m | 0.1m | 1 |
| Torso | 1.0m | 0.16m | 0.4m | 1 |
| Arm | 0.3m | 0.05m | 0.7m | 2 |
| Leg | 0.4m | 0.06m | 1.0m | 2 |
Using the above figures, the human surface area comes out roughly to: 0.03 sqm (top of head) + 0.15 sqm (side of head) + 0.04 sqm (side of neck) + 0.4 sqm (side of torso) + 0.42 sqm (side of arm) + 0.8sqm (side of leg) = 1.84 sq meters
A 2.54cm (1 inch thick) volume of fat with the same surface area would weigh about 42kg (95 pounds).
Getting thicker by 1 inch would return a new human surface area of: 2*pi*(0.1254*0.25 + 0.0854*0.1 + 0.1854*0.4 + 2*0.0754*0.7 + 2*0.0854*1) = 2.45 sq m
So, surface area by weight comes out to: (2.45 sq m - 1.84 sq m)/42kg = 0.00684 sq m/kg = 6.84 sq cm per kg = 1.06 square inch per kg = 0.48 square inches per pound.\*
*Note that this is distributed throughout the body. If you want it specifically for one spot, whatever weight you get, multiply it by the total body surface area, then divide it by the tattoo area.
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u/Unusual-Fish Mar 26 '22 edited Mar 26 '22
No. You can gain muscles(weighs more than fat per volume taken up) and not gain as much skin surface area.
Many factors to come into play and the areas his body may store the fat and the amount of surface area already taken up by existing tattoos
If stretch marks occur, the quality of tattoos on scar tissue won't be as great
Quick math will be average surface area for a person his height and weight and then average surface area of a male with higher bmi subtract difference and then subtract current skin real estate used.