Archimedes’ Principle 

Archimedes’ principle states that: “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.” This concept is well understood by many and easily applied to our context. 

In order to find the upthrust generated by a volume of helium, the weights of the immersing fluid, air, was required. Given that the density of air, reflective of its weight per unit volume, was well documented under various conditions, we were able to use it to determine the amount of upthrust required. 

Given the relative densities of air and helium at sea level, 1 liter of helium is expected to generate enough upthrust to lift an additional 1 gram of mass in addition to its own. Our estimated 50 gram envelope plus 50 gram would thus need to have a capacity of 100 liters of helium to float.  

Neutral buoyancy can be achieved by balancing the upthrust due to buoyancy and the weight of the HoverFish. At neutral buoyancy, the HoverFish will be idling in the air. Any slight changes to the balance of forces will cause the HoverFish to float up or sink down.

 

Centre of Buoyancy vs Centre of Gravity vs Line of action of the tail 

Central to the lifting and movement of the HoverFish are the forces acting on it and where they act. Due to the symmetries of the balloon used, centre of buoyancy was simply identified as the geometrical centre of the balloon. The centre of gravity was identified by modelling where each component was to be placed as well as their masses. 

As discussed before, balancing the magnitude of the buoyant forces about centre of buoyancy (CoB) and the weight of the HoverFish about the centre of gravity (CoG) is crucial. Moreover, making sure that the imaginary line connecting the CoB and CoG is perpendicular to the line of the action of the tail ensure that the HoverFish will stay upright and only move forward.

Changing the position of the CoG relative to the fixed position of the CoB will cause the entire HoverFish to tilt downward or upward. The forward thrust provided by the tail causes the HoverFish to gain or lose altitude as it is tilted upward or downward respectively. Simply shifting the CoG allows us to manipulate the altitude HoverFish can manoeuvre to.

Aerodynamic Drag 

Yet another significant force on which acts on the HoverFish is the aerodynamic drag, experienced as it moves through the air. 

Due to the speed of the HoverFish, the bulk of the drag arises from pressure drag as it pushes against the air in front of it as it moves forward. Skin friction drag also accounts for a fraction of the resistive forces as friction between the moving air and the envelope results in drag. 

Due to the choice of propulsion, aerodynamic drag plays a crucial role in stopping the Hoverfish, yet there is still a need to reduce drag to allow the Hoverfish to swim easier. The choice in envelope shape reflects this design, having a large yet pointed frontal area.