I'm currently writing a military science fiction story set in a post cyberpunk world I've been building. The story focuses on a tank crew, but it also prominently features an enormous airship that functions as a flying airfield or aircraft carrier. I'm trying to get a sense of scale such a ship would have. The nice thing about the square cube law is that it means that doubling the size of an airship octuples its volume.
- The airship needs to be large enough to carry at least 40 strike fighters with a maximum takeoff weight of roughly 20 tonnes each, and at least two helicopters with a maximum takeoff weight of 10 tonnes each. Plus extra fuel, munitions, and other expendables.
- The airship uses hydrogen as a lifting gas. I realize this is very flammable, but I think it can be made safe enough through the use of compartmentalization, blow off panels, and lightweight graphene armor to protect against stray shell fragments. I'm also considering helium, it would an even bigger airship, but the reduction in required safety features may make up for this.
- The airship is propelled using ducted electric fans powered by an onboard anuetronic fusion reactor (less than 1% of the reactor's output is in the form of high energy neutrons.)
- The airship needs to have 360 degree turret coverage for its point defense weapons systems. It's a big ship, so it will need at least a dozen of these turrets (let's use the Phalanx CIWS as a reference at 6.2 tonnes each)
- The airship's flight deck should ideally be long enough to land the above mentioned fighters without arresting cables. If they overshoot, they can just fall until they regain enough airspeed to try again. Likewise, there is no need for catapult launches. I'm thinking the flight deck will be suspended below the airship's envelope, with the hangers within the envelope.
- This airship is not designed to land on the ground. Instead it can be docked to a tower like traditional airships were and resupplied using its own cargo winches.
So, my question is: What would the length, width, and height of airship like this be for it to contain enough hydrogen (or helium) to lift its fully loaded weight of approximately 50,000 tonnes? Assume a prolate spheroid (typical cigar shape) for any volume calculations.
Edit: My sleep deprived brain took the name "square-cube law" too literally. Someone pointed out that burying the reactor and the ammunition magazines deep within the ship would provide adequate protection since if anything penetrates that far, the ship is doomed anyways. My initial reason for using hydrogen was that it is a better lifting gas and is currently far more abundant on Earth than helium. However, given the prevalence of fusion power in my world, helium may be readily available in large quantities. At this point, I'm preferring helium.
I am aware that 50,000 tonnes is half the displacement of a modern super carrier, but those are predominantly made from steel. My airship is made predominantly from woven graphene fiber which is a couple hundred times stronger than steel by weight. The lack of steam catapults, arresting cables, and dramatic reduction in the need for radiation shielding compared to a fission reactor also translates into significant weight savings.