As soon as Vincent informed his women about his intention to construct a hot air balloon and also explaining to them how it worked, he proceeded to do a few preparatory calculations.
What should the volume of the balloon be so as to lift the weight of the gondola and its three occupants? There was also the weight of their supplies and the two heaters to consider. They would need to lift with them an good reserve of water, food and of course theirs few precious possessions, even if there were little of those.
It knew that it was very important that he should have an idea of the approximate total weight to be lifted so as to figure how big the volume of the balloon should be. But first, he had to find out the extent of the buoyancy of the hot air that the heater was going to provide.
Of course the lifting capacity of the air craft would depend on the difference in temperature between the air inside the sphere and the air outside of it as well as the volume of air in the sphere itself. For this reason he needed to have a general idea as to how much weight could be lifted by a unit volume of hot air.
On that first day on which he worked on his balloon project -- as he liked to think of it -- they cut strips of material to construct a much smaller trial balloon. The strips were cut in such a way that the middle of each section were wider than their ends so that once these were stitched together it would result with a volume that would have the general shape of a sphere.
They also had to find out, using the method of trials and errors, what would be the best shape of each strip so that once they were assembled the resulting test-sphere would be able to hold about a thousand cubic feet of hot air. A thousand cubic feet of air being his unit of measurement.
Vincent had to searched in his memory so as to recall from his school days the exact formula to calculate the volume of a sphere (4/3 x pi x cube of radius and pi being the constant 3.14) and thus using an approximate radius of a little over 6 feet, he arrived at the conclusion that a test-sphere of that radius would hold just about a 1000 cubic feet of air.
But once they had cut a number of strips of the green tarp material by mean of the small laser cutter hanging above each of the long tables, they were faced with the problem of sewing them together.
None of the numerous tarps covering the hundreds pieces of machinery had any stitches on them, it therefore suggested to Vincent that there had to be some kind of device that could fuse the material together. Furthermore the chances were that this gadget was somewhere in the room where the many rolls of material were stored and where the cutting tables were. It was logical to assume that the tarps were cut and also fitted in the same room.
After long minutes of looking around, they did find the fusing apparatus that would allow them to stitch or weld the many strips together. As best as he could tell, when he tried to test it on two small pieces, it seemed to send an electric current through the two adjacent samples which had been placed in-between the two plates of the machine. When the two sample came out at one end, there was a single and wider strip and it was impossible to tell that once there had been two of them.
It took them two and a half days to construct the eleven-foot diameter test-balloon. But it was time well spent since after performing a couple of tests on the balloon using increasing weights as a load and different air temperature inside the sphere, he was able to calculate how large the big balloon should be for their purpose. It turn out that the diameter of the larger balloon should not be less than forty feet.
Vincent was very satisfied with the performance of the small test-balloon; he did his many tests in one of the large rooms with a high ceiling and long strips of material as ropes. He didn't dare test it outside in case he should loose it and thus risk having it being detected by Kwola's friends or even by Valdo himself. As soon as all the tests he wanted to perform were done, they then proceeded with the construction of the larger balloon that would carry them all.
Fifty-foot long sections, of the green and beige synthetic material were cut to construct the huge sphere. These wide strips had to be longer than the diameter of the sphere since their length had to be as long as half of the circumference of the sphere. Each strip tapered off gradually at both ends thus being smaller there than at the center so as to create the shape of a sphere. Then the strips were trimmed and fused together alternately, a green one then a beige one and so on. In all, there were twenty strips, ten of each color.
From Vincent's calculation, the circumference of the balloon was to be 126 feet since the diameter was forty feet. Dividing that number by twenty he got 6.28 feet per trip at the center. They were then alternately welded or fused together from top to bottom and once the assembly process was over, a circular opening of three feet in diameter was cut at the bottom of the sphere so as to allow the hot air from the blower to enter. Next, they welded a tube-like flexible connection - made also of the same tarp-material - to the bottom hole, this tube was later going to be connected to one of the blower in the gondola.
Finally to give the sphere-shape more strength, two circular patches of ten feet diameter each were fused on the top and on the bottom of the sphere.
Once the balloon was completed, it was neatly folded then they got to work on the many ropes that would fix the gondola to the inflated sphere itself.
They looked everywhere in the complex but they couldn't find any ropes.
Vincent solved that problem by folding many times over and then fusing them together, long strips of the tough material, thus obtaining the long ropes he needed.
Once this task was done, they dragged the deflated balloon into one of the larger room and it was partially inflated using one of the hot air blower. It thus made it much more easy to install the crisscrossing of the many ropes around the sphere. Each rope was then spot-fused in a dozen places so that it would stay in place once the balloon would be inflated.
Now all that needed to be done, was the construction of the gondola and to attached it to the loose ends of the many ropes. It had taken them two long weeks so far but Vincent knew that the time spent was well worth it since they were going to travel much faster than walking if his air ship idea did work.
They took a day off from work so as to go hunting since their food supply was almost exhausted by then. But the smaller game that so far had been plentiful everywhere on the planet, was now scarce, as for the big game there was none to be seen. Vincent figured that they were still too close to the radioactive zones and these must have been keeping the animal life away.
All that they managed to catch were half a dozen rabbits and other small animals that he had never seen before. They cooked half of their catch and they smoked the rest so that the meat would keep for a while.