Are Catamaran Blimps Feasible?

July 4, 2017

Concept art for a catamaran-style blimp

It’s not uncommon for a client to request the feasibility of building a catamaran blimp modeled after a pontoon boat. The concept is depicted in artist renditions that can easily be Googled for, and we occassionally see the idea pop up as part of a business plan for a startup. It would seem logical that this sort of design would result in a more stable aircraft in the same way that catamarans act as stable water boats.

Catamarans in the water don’t tip over or lean nearly as far to the side as a conventional sail boat. They seem to be more stable. And since blimps operate on similar principles of buoyancy to boats, it would seem only logical that a pontoon-style blimp would achieve greater stability in the air. But nothing could be further in the truth.

Buoyancy Differences Between Boats and Blimps

While blimps and boats are both designed with buoyancy as the foremost design principle, a huge difference still exists in their respective buoyant properties.

Boats, and catamarans in particular, reach equilibrium in the water by sitting expressly in between two layers of separate fluids - the denser fluid on the bottom being the water and the lighter fluid being the air immediately above. As the density of the pontoons are much heavier than the air but much lighter than the water, the pontoon is forced to float exactly on the surface of the water. It cannot sink below the surface, nor can it float in the air above the surface of the water. So when two pontoons are forced to float on the surface of the water and they’re connected by the structure of the boat in between, that boat is basically forced to stay level or parallel to the water. It takes an extreme force to tip that boat over; it must be great enough to either lift one of the pontoons completely out of the water and suspend that pontoon in the air, or the force must push one of the pontoons below the surface of the water and continue to counteract the buoyancy once submerged.

The buoyant forces associated with blimps operate on seriously different principles. The fluid surrounding the blimp is homogeneous, and therefore the difference in density above and below the blimp is virtually non-existent. While the density of air decreases with altitude, it’s not significant enough to provide a meaningful difference with a blimp of any reasonable size. Therefore, a pontoon boat does not provide an analagous comparison, and any conclusions that could be drawn from another watercraft would be more appropriate from a catamaran submarine, which is in no way a canonical design.

A balloon in the air that is sitting neutrally buoyant climbing or descending ten feet does not require a significant change in force. In other words, once a balloon is floating in the air, it can be lifted up or pushed down easily with just the force of a feather. You could blow on a balloon and it could be moved in any direction. You could drop water droplets on a balloon and it would sink. This is not true with a pontoon-style boat. You can’t blow air to make it rise or drip water on it to make it sink. A catamaran is forced to float at exactly one level while a balloon is not, and this fundamental difference is what must be considered in understanding the feasibility of a multi-balloon airship.

If you have two balloons in the air, and you connect them with a structure - whether it be a fuselage or wing or gondola or whatever else you might think of - there is absolutely no increased level of stability because there is no problem lifting or lowering either side. No inherent stability is achieved by spreading the buoyancy out across an airship made up of multiple structures.

Disadvantages of Catamaran Design

All said, there are in effect no benefits to a catamaran design. However, major disadvantages are maniphested instead.

The first disadvantage is a higher level of rotational inertia. If the mass of an aircraft is spread out to its edges, rotational inertia along the roll axis increases proportionally, thereby making it more difficult to hold the aircraft stable. So if any force is applied to the structure that causes a roll action, whether that be a small gust of wind or a change in buoyancy from a hot pocket of air, the aircraft must apply counteracting forces to stop the roll which consumes energy and therefore flight time in the process. Moreover, since it’s rotational inertia in particular that requires mitigation, the aircraft’s responsiveness will decrease, and counteracting forces would inevitably result in low frequency oscillation as the pilot continues to fight. Every time the pilot applies forces to stop the roll in one way or another, the final results of that force will not be maniphested until seconds later. Getting the aircraft back to level will require opposite forces at some point to dampen the counteracting rotational inertia, which becomes decreasingly intuitive with respect to an increase in inertia.

In addition to a decrease in stability from a pontoon style blimp, there’s also a significant decrease in efficiency. This is because an airship’s buoyancy is proportional to its volume. The payload that the airship has to carry in the air is affected by the weight of the airship itself. And that airship’s weight has a lot to do with the envelope of the corresponding buoyant structure. This envelope, the structure that holds the lifting gas - whether it be hydrogen, helium or hot air - inevitably requires a large surface area to envelope the gas. The cost of surface area is an increase in weight since surface is made up of material with mass. A pontoon style design - whether that be in the form of an airship or a boat - is composed of at least two separate structures that could have alternatively been created as one large structure. Given two or more structures with the same aggregate volume as a single structure, the set of multiple structures will have a higher surface area.

Surface area and volume differ in their proportionality to an object’s size. For the sake of simplicity, consider an example of a cube of arbitrary size. If we double the size of the cube in every dimension, the surface area will have increased by a factor of four. Meanwhile, the volume will have increased by a factor of eight. Volume is equal to width multiplied by height multiplied by depth. Surface area is a function of those same 3 components, but is not multiplicative. Rather, it is a summation that is proportional to the square of the length of a cube. Volume, meanwhile, is proportional by a cubic factor to an increase in size of identical proportions.

This is why blimps become increasingly efficient the bigger they are. Consider a mylar helium balloon you might purchase for a child: a non-zero minimum size exists that can feasibly float in the air (about ten inches in diameter). This is because a break-even point is reached as balloon size increases in which the buoyancy generated as a result of volume exceeds the weight produced by the surface area of the same balloon. In other words, the ratio of volume to surface area increases as balloon size is scaled up.

To provide another example, blimps are not even capable of carrying a single person until they reach around 100 feet in length. But a blimp of identical proportions that’s twice that length may have a payload capacity ten times greater!

To come full circle, a blimp design consisting of two or more pontoons is already disadvantaged by its surface area to volume ratio. Just to reach a point at which the aircraft’s weight is lighter than air requires a significantly larger design. As the design is scaled up, the surface area to volume ratio decreases, but not at any rate that’s close to that of any conventional dirigible design. And while larger and larger designs can eventually overcome the poor payload capacity, we are ultimately constrained by an efficient utilization of resources or, in more recognizable terms, money.

An efficient airship can only be built by using a single envelope. So if you find yourself allured by a startup advertising a “new” dirigible design - maybe under the false guise of increased stability or speed - go out of your way to tell that person to take a physics class. Conventional blimp designs have hardly changed in over a century and for good reason.

comments powered by Disqus