Mathematical basis for the claim that gaining girth hinders length gains

[eow. Member of the Month April 2013 Find all posts View Profile Close eow.]

I am going to show you guys, using math/physics, why gaining girth makes it necessary to use more force to achieve the same elongation. I hope this will settle the score on the subject of girth hindering length gains. I'd like to have some people chime in and have a good discussion about this.

No LaTeX support on these forums so this will look a little messy.

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Average thickness of tunica albuginea = 1 mm

Penis #1 circumference = 101.6 mm (4")
cross-sectional area of tunica albuginea (assuming inner circumference of 100.6 mm) = 16.090564746 mm^2

Penis #2 circumference = 127 mm (5")
cross-sectional area of tunica albuginea (assuming inner circumference of 126 mm) = 20.133100289 mm^2

Penis #3 circumference = 152.4 mm (6")
cross-sectional area of tunica albuginea (assuming inner circumference of 151.4 mm) = 24.175635842 mm^2

Penis #1 length = 177.8 mm (7")
Penis #2 length = 177.8 mm (7")
Penis #3 length = 177.8 mm (7")

They have same length, but different circumference.

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elastic modulus of tunica albuginea = 12 N/mm^2
(source = Expansion of the tunica albuginea during penile inflation in the nine-banded armadillo (Dasypus novemcinctus)

NOTE: You could pick any random value for the elastic modulus and the relationship between girth/force will still be linear. There are multiple sources which quote 12 MPa as the elastic modulus for the tunica albuginea, so I will be using that value just for fun.

elastic modulus = stress/strain

Stress = F/A where F = force applied (N) and A = cross-sectional area of material (mm^2)
Strain = E/L where E = desired elongation (mm) and L = original length (mm)

Using these definitions, it follows that
12 = (F/A) / (E/L)

Let's assume we want to elastically stretch the tunica 25.4 mm (1") more than it's starting length. All three penises have the same starting length.

12 = (F/A) / (25.4/177.8)
12 = (F/A) / 0.142857143
12 = F / (A*0.142857143)

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Now let's calculate this for the three penises, plugging in the cross-sectional areas listed above:

Penis #1:
12 = F / (16.090564746 * 0.142857143)
12 = F / 2.298652109
F = 12*2.298652109

F = 27.583825308 N
This is equivalent to hanging 6.201 lbs

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Penis #2:
12 = F / (20.133100289 * 0.142857143)
12 = F / 2.876157187
F = 12*2.876157187

F = 34.513886244 N
This is equivalent to hanging 7.75903 lbs

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Penis #3:
12 = F / (24.175635842 * 0.142857143)
12 = F / 3.453662267
F = 12*3.453662267

F = 41.443947204 N
This is equivalent to hanging 9.317 lbs

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Keep in mind that the hanging values I listed are only for fun in this hypothetical post and should not be used in real life to determine how much to hang, lol.

Here is a graph showing the force required (measured in N) to elastically elongate all 3 penises (from 0mm elongation to 100mm elongation). 100mm elongation won't actually happen in real life, I just let the values go that high so that it more clearly shows the difference between the forces required.

Left side = N (newtons)
Bottom = elongation in mm
Blue = 4" girth
Red = 5" girth
Green = 6" girth
girthlengthcorrelation-1.jpg

As you can see, there is only a slight difference initially, but as you elongate further, the gaps become wider.

[namsokiek Banned Find all posts View Profile Close namsokiek]

I'm totally geeking out over the data. Great job!

Can you point me to the references on the tunica strain?

[eow. Member of the Month April 2013 Find all posts View Profile Close eow.]

Sent you a PM.

[billybrown Senior Member Find all posts View Profile Close billybrown]

I don't understand any of it, but basically you arrived to the conclusion that people with larger tunicas need more force to stretch it? Did I get that part right?

[eow. Member of the Month April 2013 Find all posts View Profile Close eow.]

Lol, yeah sorry if it is a bit complex at first glance. After a little bit of googling the concepts should be much easier to understand, though.

Yes, the larger your circumference is, the more force that is required to stretch it.

[billybrown Senior Member Find all posts View Profile Close billybrown]

Ok got ya. Is there a way you could estimate the time required or at least can you tell from this data if more force used allows less time spent with the same result?

[eow. Member of the Month April 2013 Find all posts View Profile Close eow.]

My calculations only deal with the elastic section and does not take viscoelastic creep into account. Creep is what pulls time/temperature into the equation. The physics knowledge required for calculating creep is beyond me right now, so I need more time before I can say anything about that.

Creep says that even if you apply a force to a material that is below the material's tensile strength, given enough time the material WILL fail. Technically, you can deform a material by immediately bringing it to its yield strength, OR you can deform a material by placing a sub-yield load on it and waiting for it to creep to the deformation. In my opinion, the latter strategy is safer for biological tissues because there is often a thin line between plastic deformation and absolute failure. Using creep allows things to happen slowly and safely.

My post is merely a simple physics calculation showing the relationship between cross-sectional area and the tensile force required to stretch something elastically. Of course, if it requires more force to stretch something elastically, it will require either more force or more time to reach deformation.

[rbi99 Retired Moderator Member of the Month Nov 2017PEGym Hero Find all posts View Profile Close rbi99]

I hit 6" meg very quickly when I started PE, and also had later success. However, length gains were so minimal that I quit trying early on. Just curious since I will never hang or extend, let's say that the 9 lbs is accurate (being over 6" might mean even more than 9 lbs), can one manually stretch equal to that, and how long would you have to hold the stretch?

[Padawan787 Moderator ReservePEGym Hero Find all posts View Profile Close Padawan787]

can one manually stretch equal to that, and how long would you have to hold the stretch?

You can yes, but the problem with manual stretching is that you don't know your force output, so progression and consistency are basically impossible.

Also, it's practically impossible to hold a uniform manual stretch over time due to fatigue (of the arm/hand).

This is why hanging is great, you can precisely control the weight/force while also precisely controlling how long that force is applied. Manual stretching is very hit and miss.

[billybrown Senior Member Find all posts View Profile Close billybrown]

"I hit 6" meg very quickly when I started PE, and also had later success. However, length gains were so minimal that I quit trying early on"

Man, Im your exact opposite. Length comes in no time and girth avoids me like fuckin' Plague! We should trade tips.

[camaro Senior Member Member of the month June 2013 Find all posts View Profile Close camaro]

RBI 99 is the MAN for tips...

[rbi99 Retired Moderator Member of the Month Nov 2017PEGym Hero Find all posts View Profile Close rbi99]

"I hit 6" meg very quickly when I started PE, and also had later success. However, length gains were so minimal that I quit trying early on"

Man, Im your exact opposite. Length comes in no time and girth avoids me like fuckin' Plague! We should trade tips.

Maybe we should just blend out two peckers together and create a monster!!! But I digress.

[billybrown Senior Member Find all posts View Profile Close billybrown]

Haha... I'd skip that one too! Nevertheless it is a brilliant idea!

[Jm123 Senior Member Find all posts View Profile Close Jm123]

This would assume that length gains come from tunica expansion/growth as opposed to ligament stretching. In which case I believe girth may be beneficial to length gains as it evens out the distribution of force on the ligaments. Other than that it is pretty much right on.

Side note, personally I have not researched the way the tunica fibers are laid/run. This would be the best info possible, to make a working theory from. If someone had a tensile tester and some spare phalluses that were constructed similar to humans; a better theory could be deduced.

[MrHammer Senior Member Find all posts View Profile Close MrHammer]

Good read!
Looks like I should be happy that my length came faster then the girth, since I am now doing a routine mostly for girth.