Will The Boarding Ladder Float?

I’ve been thinking about making a boarding ladder for quite some time. Some friends on Facebook showed me photos of theirs. It has helped us decide on a final design. I found some scrap pieces that I’d like to use. Here are some of the calculations to determine if it would float if dropped overboard. I know what you thinking…there is nothing more exciting than buoyancy calculations! Yay!

An object will float if it displaces more water than it weighs.

The center rail material is 1.375 inches in outside diameter. It appears to be 6061-T6 tube. According to the Alro Steel metals guide, that tube weighs .577 lbs/linear foot. The weight per inch is determined to be .577lbs/12inches=.048lbs/linear inch. The length is 46 inches. The total weight is 2.2lbs.

The rung material is 1.315 inches in outside diameter. It appears to be 6061-T6 sch. 40 pipe. According to the Alro Steel metals guide, that pipe weighs .581 lbs/linear foot. The weight per inch is determined to be .581lbs/12inches=.048lbs/linear inch. The length is 72 inches. The total weight is .048 x 72=3.456lbs.

1 cubic foot of freshwater weighs 62.5lbs. That works out to be 12x12x12inches=1728 cubic inches. 62.5lbs/1728cubic inches=.036lbs per cubic inch (one cubic inch of water weighs .036lbs).

The center rail material displaces how much water? We’ll let’s see! So the formula for volume of a cylinder isV=πr2h. The outside diameter is 1.375inches. The height is 46 inches. So the radius is R=1.375/2=.6875. To work the formula then it is 3.14 x (.6875)^2 x 46= 68.3. So the volume or displacement of the rail material is 68.3 cubic inches. 68.3 cubic inches x .036lbs per cubic inch=2.458lbs.

The rung material displaces this much water: Radius=1.315/2=.6575. Height 72inches. 3.14 x (.6575)^2 x 72 inches=97.7. The volume or displacement of the rung material is 97.7 cubic inches x .036lbs per cubic inch=3.51lbs.

Now we compare the weight of the materials to how much they displace. The center rail material weighs 2.2 lbs and displaces 2.4lbs. It has 0.2lbs of positive buoyancy. The rung material weighs 3.456lbs and displaces 3.51lbs. It has .05lbs of positive buoyancy.

So in total there is .25 lbs of positive buoyancy. In actual practice, that means it might float, but probably not. Since the rungs are to be inserted through the rail, we would lose several cubic inches of critical buoyancy there. Also, there needs to be plugs on the ends of the pipe, welds, gussets, and a single piece of stainless hardware. All of which have negative buoyancy. So without doing any more calculations on this blog post, it’ll probably come out neutrally buoyant or slightly negative. Since the calculations were based on the Alro Steel metals guide, they would need to be personally tested in order to be absolutely sure of the data. So there is the possibility that all of the calculations are fundamentally wrong anyway.

Basically all this mean that if we drop it overboard it will be gone! Time to redesign and recalculate! Yay!

6/30/2022 Update: We used a commercial telescoping boarding ladder along with a custom install to make the boarding ladder work. It hinges on the starboard side when the railing gate is opened. This way it is captured and can’t be lost by falling in the water. I found it very difficult to get just the right idea for this to work. A thanks to internet friends who showed me their boarding ladders.