# Needing information on calculating surface area in regards to moving an object thru a medium.

• June 8th, 2017, 12:32 PM
flysketcher
Needing information on calculating surface area in regards to moving an object thru a medium.
Hello. I am stupid. But I am writing a book and trying to at least sound smart. What I am trying to figure out is if the part that I have written below is correct.

"That said, once the track is built, it is cheaper to move people over a larger train with a greater cross section. Any moving object has to take into account any counter-forces that are trying to impede its movement. If there was no gravity and we were in space then the only counter force would be resistance to acceleration. But we are on a planet and we are on a planet with an atmosphere and that atmosphere is 14lb per cubic foot at sea level. You don't really notice it much when you are standing still but it will rip your clothes straight off of you at 160 mph. This train will have to contend with surface drag. Surface drag increases with the cube of velocity. The faster the train, or any object goes, the more resistance to movement there is and that resistance does not increase in a linear manner, it increases in an exponential manner, so whatever we can do to reduce that drag gives us a more efficiently moving train. Lets take a look at a simplified cross sectional analysis.

(This website is not allowing me to upload images so you'll just have to use your imagination. Its four separate boxes of the same size spaced apart in two rows of two columns and each side of each of the four boxes has a 1 next to it.)
Here we have four boxes. Each box has four surface units. One, two, three and four. There are four boxes (squares actually and not boxes, if we are looking at it in cross section.) with four surface units for a total of 16 surface units.
But now look what happens when we move those boxes together.

(Imagination time again. Now the boxes have been combined into one box and the 1 text has been removed from all of the sides of the boxes that are now touching each other and only the only "ones" that are left are the ones around the surface of the box.)
All of the surface units that were in the middle are now magically gone. And now we only have 8 surface units. Same amount of area inside of the larger box that was inside of the smaller boxes but now with only 8 surface units instead of 16.
In other words, from a standpoint of surface area, it is cheaper to run one 4 unit train than it is to run 4 one unit trains. This the reason why there are such things as gigantic container ships. Because its just cheaper to do it that way. It cost less in fuel to use a vessel with a lower surface area to usable volume ratio. Its cheaper to run one big ship than it is to run four smaller ships with the same total volume as the larger ship."

So, my question for this forum is, am I correct about this? From the standpoint of surface drag, does it make more sense to use a larger vessel to overcome it or is there something that I am missing here?