I was working with one of my kids on math problems the other night. We were calculating the volumes of various geometric shapes: cubes, spheres, cylinders, etc. Then I got the idea to use the same math formulas to approximate the load carrying capacities of catarafts. I've always been perplexed by how different raft manufacturers can advertise vastly different "load capacity" numbers for tubes that are almost exactly the same shape, diameter, and length??? With watercraft of all types, load capacity is actually the "displacement" (volume) of the water supporting the "weight" of the vessel, and cataraft tubes are just about the simplest hull shape in the boating world.
Cataraft tubes are basically cylinders, with cones at each end. So I used the following formulas:
Volume of a cylinder = Pi (3.14) multiplied by the tube's radius squared (r2), multiplied by the length of the tube (h), or = 3.14 r2 h.
Volume of a cone = one-third of same formula for a cylinder, or = 1/3 (3.14) r2 h.
In order to keep all of the numbers managable, I converted all of the dimensions into feet (cubic feet),
and then multiplied the volumes by 62.4 lbs, which is the weight of one cubic foot (ft3) of fresh water.
I wanted to get an "apples-to-apples" comparison, so I used measurements provided by the same manufacturer, and since I'm thinking about buying a big Aire cataraft, I did calculations for all of their 18-foot models. I also had to use some standard for where the full sized tubes (cylinders) ended, and where the tapered ends (cones) began. I decided to use Aire's advertized "waterline lengths". I don't think Aire would favor any one of their own models over another, and so the comparisons should be useful. And I know that the tapered ends of catarafts kick up, instead of pointing straight back like on some sportboats. But, for comparisons of similar tubes, from the same manufacturer, the formulas should be pretty accurate.
All are the same 18 feet in length, and the dimensions used for each are:
Leopard: 10ft waterline / 1.1ft radius (26.5" tubes) / 4ft cones
Lion: 13ft waterline / 1.15ft radius (27.5" tubes) / 2.5ft cones
Cougar: 10.33ft waterline / 0.75ft radius (18" dual tubes) / 3.84ft cones
Super-Leopard / 10ft waterline / 1.1ft & 0.67ft radii (26.5" & 15" dual tubes / 4ft cones
Calulations accounted for both tubes of the Leopard & Lion and all four tubes of the Cougar and Super-Leopard.
Total volume displacement means how much "weight" it would take to fully submerge the whole cataraft under water:
Leopard = 6052 lbs / Lion = 7548 lbs / Cougar = 5682 lbs / Super-Leopard = 7992 lbs
Surprised? So, was I! Turns out that having twice as many small tubes (i.e. Cougar), does not give you more load capacity.
(Volume increases are "squared" with larger diameter/radius tubes, not just multiplied.)
But, having big single tubes that carry their full diameter for a longer part of their waterline (i.e. Lion) does!
And having a big and a small tube on each side (i.e. Super-Leopard) really displaces alot of water!
Now, nobody would load their cataraft until it literally sinks! But, reduced loads will still be proportional.
In other words, since all of these catarafts use the same round/cylindrical shaped tubes, and only vary in size (diameter/radius), if we load each cataraft until the tubes are only half submerged, the differences would remain the same:
Leopard = 3026 # / Lion = 3774 # / Cougar = 2841 # / Super-Leopard = 4870+#
Note that on the Super-Leopard, because the smaller (15") tube is attached to the larger (26.5") tube at the bottom, the smaller tube is nearly fully submerged (13.25") and providing almost all of it's total displacement, even when the Super-Leopard is only loaded until the big tube is half submerged. That is some real load carrying ability!
In fairness, the Cougar does have one real important load carrying advantage over the regular Leopard and Lion, and that is a much shallower draft. Because it's four tubes are arranged side-by-side on each side, when carrying it's load of 2841#, it will only be drafting 9" of water, while the regular Leopard will sink to 13.25" carrying only 185# more. In shallow water, 4.25" of deeper draft can mean a lot less work (and damage) trying to drag a ton-and-a-half over the rocks, if it can be done without portaging at all? Most folks already give the Cougar high marks for having a lower profile above the water, which makes better against the wind.
I'm not sure how the Cougar got such a reputation as a bigger load hauler than the single-tube boats?
If you've got deep enough water, it would seem that bigger tubes are better than multiple smaller tubes.
I'm also fully aware that my use of the published waterline length might have skewed some of the data?
I sure didn't set out to prove any pre-conceived agenda. I'm just a guy who is shopping for a cataraft, while helping my kid with some math homework!
Thanx for reading, Dave.