STEP 1: CALCULATE THE BOUYANT STRENGTH OF THE FOAM

The next few steps describe how to calculate the neutral buoyancy of an object in sea-water when buoyed by a measured piece of foam. The first step is to weigh the object, or in this case, the camera housing, while it's underwater, so you know exactly how much weight you need to support. I explain one way to do this here.

You also need to know how many pounds per cubic-foot your chosen foam weighs. Foam is sold in defferent denities, often in lbs per cubic foot. For example, you may choose to work with PVC foam that is 6 lbs per cubic-foot. With this information you can move on to the next step.

The diagram below illustrates Archimedes' Principle. Using this principle you can figure out exactly how much foam it will take to make any object perfectly neutrally buoyant in water.

SOLUTION:

In this example our foam is 6 lbs / per 1 cubic ft. The average density of sea water is 64.1 lbs / per 1 cubic foot. Since these are both measured in the same units (lbs / per cu. ft) they can easily be compared. (If you decide to use a foam of different density, like 4 lbs/ per cu. ft, then you will need to adjust the calculation below accordingly.)

To visualize this calculation, imagine dropping a 6 lb block of foam that is exactly 1 cubic foot, into a 64.1 lb container of sea water that is also exactly 1 cubic foot.

The foam, weighing 6 lbs, will push aside and displace exactly 6 lbs of water from the 64.1 lb container. The remaining water in the container weighs 58.1 lbs. This water at the bottom of the container supports (buoys) the much lighter cube of foam and therefore the foam floats.

Therefore the weight of the remaining liquid in the container is exactly the amount of weight that the 1 square foot foam cube can support! In this example, 1 cubic foot of 6 lb foam can support exactly 58.1 lbs.

Ultimately, to achieve neutral buoyancy, we want the volume of foam and the volume of water to weigh exactly the same. That is, neither one should sink or float in the other; they should be exactly the same weight per volume.

Now you just need to convert the units to a smaller scale.


STEP 2: CONVERT THE UNITS TO SMALL SCALE

Now all there is left to do is scale down the cubic feet into cubic inches and convert pounds into ounces.

UNIT:
CONVERSION:
1 cubic foot = 1728 cu. in
1 lb = 16 ounces

Example: 1 cubic-foot of foam can support 58.1 lbs (as calculated above). Divided that by 1728 cubic-inches:

58.1 divided by 1728 = 0.0336 lbs per cubic-inch.

This means that each square-inch of foam will support 0.0336 lbs.

Finally, multiply 0.0336 lbs x 16 ounces:

0.0336 x 16 = 0.538 oz per cubic inch.

This means that each square-inch of foam will support 0.538 ounces. The results are shown in this table:

UNIT OF FOAM
FORCE OF BUOYANCY IN POUNDS
FORCE OF BUOYANCY IN OUNCES
1 cubic foot
= 58.1 lbs
= 929.6 oz.
1 cubic inch
= 0.0336 lbs
= 0.538 oz.

In the example above, the camera rig weighs 2.4 lbs (38.4 oz) when it's underwater. So in order to achieve neutral buoyancy there needs to be an equal 38.4 ounces of lift provided by the foam.

Knowing the buoyant force of the foam in ounces per cubic-inch, it's easy to calculate the total amount of foam needed:

38.4 oz = negative weight of camera rig underwater.
0.538 oz = lift provided per cubic inch of foam.
71.38 cu. in = number of cubic inches of foam needed to provide 38.4 ounces of lift.

(38.4 divided by 0.538 = 71.38).

This means that 71.38 cubic-inches of foam is needed to neutralize 38.4 ounces of dead-weight underwater.


STEP 3: CALCULATE AMOUNT OF FOAM NEEDED

LIFT NEEDED (in ounces) divided by LIFT PROVIDED (in ounces per square inch of foam) = TOTAL CUBIC INCHES OF FOAM NEEDED.

N / P = Cubic Inches of foam you need.

Where N = Lift Needed (underwater weight of camera), and P = Lift Provided (lift potential per 1 cubic inch of foam)

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