STEP 1:
I'll start by using Luffy running southbound at full speed along the coastline of Jaya(lower half/mouthpiece) from Mont Blanc Crickets house to Mocktown and back to ultimately find the size of the Lower half/Mouthpiece of Jaya which we will then use to find the size of the Upperyard/Top half of Jaya.
"Distance=Speed×Time" so to begin I'm going to need to outline the speed Luffy ran and the timeframe.
Speed
For this I could just use the speed of an athlete and be done with it but it would be pretty disingenuous to Luffy who is already operating at superhuman levels of speed and strength at the earliest arcs so instead I'll be using a statement from the Kuro arc to obtain a travel speed for Luffy.
Luffy says it would take him 20 seconds to cover the same distance it would take Ussop 3 minutes to cover.
With assumed athlete level speed for Ussop(no one in his village could catch him while he was sprinting so it's a safe assumption) which is 6.7m/s, I got Luffy's travel speed to 60.3m/s.
You can as well say that Luffy is throwing a random number into the air but there is no reason to believe so given the direness of the situation they were facing at the time(plus he manages to tag Kuro who could move FTE so his travel speed wouldn't scale that far off anyways) but if you're still indecisive about it you can assume a slightly higher speed value than 6.7m/s for Luffy since bare minimum those scans would translate to Luffy being faster than Ussop and it's not like he isn't to begin with.
Timeframe
Nami gives Luffy an ultimatum of 3 hours to go to Mocktown, defeat Bellamy, retrieve the gold stolen from Cricket and return back to which Luffy returns 46 minutes later than the intended time so the total time taken is 3 hours and 46 minutes(note: Nami does not state it takes 3 hours to make the journey but is the time Luffy had to do what he needed to do and return).
Now we can remove 46 minutes from the total timeframe to account for the time it takes for him to fight Bellamy, get the gold and find a stag bettle(a minor gag that was suppose to make light of Luffy coming late). Removing that amount time is more than generous as if you would read chapters 232 and 233 of OP, you would see for yourself that Luffy's ordeal with Bellamy and his crew takes 5-10 mins at most.
So after subtracting that time, the final timeframe(or the timeframe to run to and from Mocktown and Cricket's house respectively) is 3 hours. You can remove an additional 1 or 2 hours if you please but that would likely reduce the very end result to mid-high 2 digit kilometers or island sized.
STEP 2:
Now that I have both speed(60.3m/s) and time(3 hours or 10,800 seconds), I got 651.2km as the distance Luffy covered going to and from. To get the singular distance, I divide 651.2km by 2 which is 325.6km.
Using a nifty geometry software I was able to do this:
So to get the diameter of that circle/diameter of the island/size(width) of the island, I use the distance between Cricket's house and Mocktown like an arc on a circle and with a geometry software, I was able to get the angle of that arc to be 206° meaning the opposite angle is 154°. And so:
206°=325.6km(Length of arc DE)
154°=Unknown(Length of arc ED)
Using direct proportions, Unknown=243.4km
Now to find the radius which will ultimately lead to finding the diameter, we have to get the circumference:
So Circumference(C)=Length of arc DE+Length of arc ED=325.6km+243.4km=569km
r(radius)=(C/2.pie)=569/(2×3.142)=90.56km
D(Diameter)=2r=2×90.56=181.12km.
So we have that the length of the mouth part of the skull shaped Island Jaya is 181.12km. Comparing it to it's top half or the upperyard, it's visibly smaller.
Just by looking I can estimate that the upperyard is at least 200km wide(Using pixel scaling I got it to be 253.52km). For reference, Israel which is a small country is about 205km.
So what are your thoughts on this?
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