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The Optimal Surface area to Volume Ratio for Wine Barrels

Note this section involves some basic math... Lets determine the ratio of surface area to volume for several sized oak wine barrels. For simplicity, lets assume that a wine barrel is a cylinder. (In reality, a wine barrel has some curvature along the length. To analyze this correctly, we would need to use calculus, but that would unnecessarily complicate our analysis.)



Calculations

From our high school geometry class, we know that the volume of a cylinder is expressed as:

Volume = PI * Radius * Radius * Height

Now, we should also recall that the area of a cylinder is expressed as:

Area = 2* PI * Radius* Height

Where:

  • The Radius refers to the radius of the barrel.
  • The Height refers to the height of the barrel
  • PI = 3.14159265...

    Now, taking the area to volume ratio of our wine barrel we get:

    Area / Volume = 2 * PI * Radius * Height / PI * Radius * Radius * Height

    Canceling terms, this yields the simple expression:

    Area / Volume = 2 / Radius

    So the surface area to volume relationship is simply two divided by the radius of our wine barrel.

    Now, lets compare this relationship for various size wine barrels:

    • A five gallon wine barrel has a radius of about 6 inches
    • A sixty gallon wine barrel has a radius of about 12 inches.

    Applying our formula shows that a sixty gallon wine barrel has an area to volume ratio of about half that of a five gallon oak barrel.





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