The simulation of the flight on the spreadsheet

If we apply the theory previously explained to a virtual water propulsion rocket using the spreadsheet and we then compare the maximum reached heights resulting by the simulation to the experimental values, we can validate the theoretical model.
It has been verified that the motion of the rocket is strongly affected by the nozzle diameter. Even with a little variation such as 0.2 mm, the calculated maximum height nearly doubles.
Same sensitivity has been noticed for the following parameters: initial air pressure, filling water mass and viscosity coefficient, which has been chosen quite empirically.
Future studies, even thanks to the laboratory measurement of the thrust developed during the water discharge phase, will surely provide new data, allowing reviews and improvements of the model.
Two spreadsheet simulations have been inserted in the tables 2 and 2.bis.

• Table 2 shows a simulation with an initial air pressure of 1. 5 atm and a nozzle diameter equal to 22.0 mm.
• The other simulation (Table 2.bis) has been carried out giving as input values 2.0 atm for initial air pressure and 22.2 mm for the nozzle diameter.
• Graphs (Graph 2 and Graph 3) show the elevations reached in the two cases.
• Graph 2.bis shows the air pressure into the bottle and the air pressure exerted on the water versus time for a rocket with an inital pressure of 1. 5 atm and a nozzel diameter equal to 22.0 mm.
  

Maximum height, as already said, results to be very sensitive to light variations, even of tenths of millimetre, of the nozzle diameter.
For sure it will be necessary to increase the number of measurements to be recorded on field during practical experiences and to improve their accuracy.
Another factor to investigate consists in carrying out some launches varying the internal pressure of the air as well as the nozzle diameter.
As can be noticed comparing the experimental data in Table 1 with the elevation graphs (Graph 2 and Graph 3) resulting from the simulation, the theoretical model provides data consistent with the experimental values.