Ships and Sea Level

Date: 03/23/2002 at 00:56:00
From: Mark
Subject: Physics

How would removing all ships from the ocean affect sea level? How 
would someone calculate or estimate a mass for all ships in the 
world? A rough estimate would suffice, as this would help settle a 
longtime debate.

Date: 03/24/2002 at 15:40:40
From: Doctor Ian
Subject: Re: Physics

Hi Mark,

I once went to a job interview where one of the things I was asked was 
to estimate how many barbers there are in the United States. This 
reminds me a little of that. 

Let's use 6350 km as the radius of the earth.  (It's within 1% of the 
true value.)  That makes the surface area of the earth about 500 
million square kilometers.  

If 4/5 of that is covered by water, then we're talking about 400 
million square kilometers of ocean. 

Now, suppose we want to change the level of the ocean by 1 centimeter.  
That's 1/100,000 of a kilometer, so we're talking about a volume of 

                        1
  400,000,000 km^2 * ------- km = 4000 km^3 
                     100,000

So, in order to change the level of the ocean by 1 cm, you'd have to 
have 4000 km^3 of displacement. 

How much weight are we talking about? The density of water is about 
1 g/cm^3:

    1 g      1 lb    1 ton     (100 cm)^3   (1000 m)^3
  -------- * ----- * ------- * ---------- * ----------
  (1 cm)^3   454 g   2000 lb   (1 m)^3      (1 km^3)


    100^3 * 1000^3
  = -------------- ton/km^3
      454 * 2000

  = about 1 billion tons/km^3

According to the U.S. Department of Transportation's Maritime 
Administration:

  Top 20 World Merchant Fleets by Country of Owner
  Self-Propelled Oceangoing Vessels of 1,000 Gross Tons and Over
  http://www.marad.dot.gov/Marad_Statistics/MFW-10-01-01-C.htm   

the top 20 merchant fleets have a combined displacement of about 800 
million tons. So if you removed them from the ocean, the level would 
drop by a little less than a centimeter. (Of course, this ignores 
military ships and non-commercial vessels, as well as the fleets of 
smaller countries, but it's not clear that those would change the 
result by all that much.) 

Thanks for asking such an interesting question.  

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/