Water Rocket Computer Model Problems

Here is the fifth Water Rocket Computer Model Problem.

The screen shot below is from the 3D optimisation of a 2 litre water rocket with a T-nozzle.

As always, I have included the file details so that you can reproduce it yourself to investigate the peculiar nature of the maximum displayed in the screen shot on the right.

It is a plot of Distance Downrange as the output variable with Angle of Elevation (39° to 89°) on the Y axis and Mass of Water (100g to 600g) on the X axis with a post-thrust integration interval of 10ms.

The graph shows a the maximum as it runs upwards and to the right on the display. The greater the angle, the greater the mass of water needed for the maximum.

 Variables Water Rocket Computer Model Problem 05 Rocket Mass of Rocket Empty 64.6 g Capacity of Pressure Vessel 2200 cm3 Rocket Diameter 9.5 cm Rocket Coeff of Drag 0.52 Nozzle Diameter 21.5 mm Constant K for nozzle 0.16 [X] Launch Tube in use Used Duration of air impulse 16748.3 ms [ ] Parachute in use Not Used Launch Tube Length 20 cm External Diameter 21.3 mm [X] Hollow Launch Tube Used Wall Thickness 2 mm Length of Tube Empty 10 cm Distance of Vent from End 0 cm [X] T-Nozzle in use Used T-Nozzle Diameter 1.8 mm Parachute Diameter opened out flat 0.25 m Parachute Coeff of Drag 0.9 Deploy () Apogee.( ) Timer 4 s Delay in opening 3 m Initial Mass of Water 462.7 g Pressure in Vessel 140.0 psi Height 1.3 feet Angle of Elevation 87 ° Speed at Angle of Elevation 0 m/s Temperature 20 C Environmental Gamma of Gas in Rocket 1.402 Density of Gas in Rocket 1.293 kg/m3 Density of Liquid in Rocket 998 kg/m3 Acceleration due to Gravity 9.80267 m/s2 Atmospheric Pressure 1013 mBar Density of Air at STP 1.293 kg/m3

 The problem here is . . . 1. to find an explanation for the fact that the amount of water required for a maximum increases with angle of elevation; 2. to find an explanation for the fact that even at an angle of elevation of 89°, the downrange distance is over 93 metres; and, 3. to find an explanation for the fact that the maximum downrange distance is not at an angle of 38° (as in a golf ball) or 45° (as in an artilary shell) or somewhere near that angle.

The variables are in the table on the left...

If you give up or you think you know what is going on, look at the answers.