Four factors mainly affect airship sizing. These are: payload weight/size, range/endurance, max airspeed and operational altitude requirements. Also significant are considerations regarding means to accommodate variations in weather conditions that typically may change significantly over long distances, height and day/night conditions; where temperature and atmospheric pressure changes over 24 hours and from the artic to the tropics causes significant LTA-gas volume change.
What’s needed from these requirements to determine size is an estimate of the airship’s all-up-weight (AUW). Naturally, the payload weight is given, although there may be a need for a factor on this to cover for later customer needs and/or potential growth issues. The altitude required and expected temperature range set the proportion of total aerostat volume needed for air in ballonets to compensate for LTA-gas expansion and thus aerostat size. The airspeed requirement sets the power needed to push the airship underway against aerodynamic drag and thus the weight of the propulsion system. However, the range/endurance requirements then set the disposable load levels needed (fuel, oil, ballast, crew, food, and so forth).
One can make initial estimates based on proportions of similar successful airships before, such as 25% for payload weight alone (maybe optimistic, but probably good enough to start with and where later refinement may enable better), allowing the LTA-gas quantity needed to be first calculated. Knowing the expansion to accommodate then allows the aerostat’s size to be roughly determined; needed to calculate aerodynamic drag underway, which naturally is affected by form.
Form is an issue, where one must balance structural matters against aerodynamic aspects and the need to minimise surface area to minimise aerostat weight; where a sphere does this best but has a high coefficient of drag compared with elongated slender forms. However, slender longitudinal forms bend and buckle more easily. Non-rigid aerostats with a slenderness ratio of 4 to 1 (length to diameter) have been found to function acceptably.
Otherwise, instead of elongating the sphere (causing a unidirectional type that then needs tail fins for stability – adding weight) it may be squashed – leading to types retaining omni-directional characteristics with reduced drag in the horizontal plane, which may be better suited to the objectives for operation.
For airships that operate near as-light-as-air (ALAA) displaced (conventional), it’s necessary to establish a helium volume enabling sufficient buoyancy to support the AUW (including LTA-gas). As a rule of thumb, one can expect to achieve approximately 66 lb (30 kg) effective lift for each 1000 ft3 (28.32 m3) of helium in the aerostat’s envelope at sea level; where ‘effective lift’ equals the buoyancy applied less the true weight of helium contained. However, since airships are large (leading to rather big numbers for ft3, difficult to imagine), it’s better to calculate with metric values, where the effective lift is roughly 1 kg/m3, good enough for initial calculations.
It should be noted that, when calculating ballonet capacity needed, consideration for a factor of safety should be included. This is needed to allow for effects such as significant temperature and atmospheric pressure variations that can occur when the airship is ground captured at a location far from and topographically different to its initial launch location. An in-flight safety factor or safety limits also are needed to allow for updraft conditions that can be experienced from rising air (e.g., thermals) to avoid exceeding maximum pressure height. The higher an airship is required to fly, the smaller the proportion of LTA-gas put into its aerostat. Buoyancy experienced is proportional to the volume that the LTA-gas charge attains at atmospheric temperature and pressure. Airships are most efficient flying at altitudes below 10,000 ft (3050 m) where ballonet size needed isn’t so large as to excessively penalise payload capability. The heavier the payload and the higher the altitude to fly at, the larger the airship design becomes!
