A very important design constraint was the inflation limit of the combustion chamber, which dictates the volume of water that it can displace and thus the force generated and its potential velocity. Therefore, we tested its resistance and found a fracture point at approximately 15 N, which suffices for our purposes.
The equation for the number of moles of gas in the balloon as a function of r is given in the equation above where n is the number of moles of gas, C01 is a material constant of Ecoflex 10 Silicone given as 11.75 kPa, Vb is the initial material volume, R is the universal gas constant, T is the temperature of the gas, and r is the current radius.
Treating the Ecoflex 10 Silicone as a hyper-elastic material, a model for a balloon's volume and pressure was developed. Basic manipulation of the above equation using material properties of the silicone, electrolysis ideal energy cost, experimentally determined fuel cell efficiencies, external pressure at STP, and the displaced water volume produces a model of Buoyant Force vs Energy. Assuming a spherical elastomer with thickness of 5mm and initial radius of 5cm that weighs 0.1854Kg, the buoyant force per electrolysis energy input is as shown in the figure.
This model assumes atmospheric pressure and that energy input will increase as external pressure increases. The red circle indicates the fracture point of the material at approximately 15N.