Water Rocket Computer Model Problems

Here is the sixth Water Rocket Computer Model Problem.

Someone wrote to the water rocket group saying that they knew of a steel tube rocket, powered with steam that had a capacity of 33 litres and weighing 40kg.

The water rocket computer model does not deal with the vapourisation of water so I wondered how the rocket would perform with just water and air at ambient temperatures. This is what happened. I guessed a rocket diameter of 20cm, a pressure of 300psi and an air impulse of 4 seconds.

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

It is a plot of Height as the output variable with Mass of water (1000g to 26000g) on the Y axis and Nozzle Diameter (10mm to 50mm) on the X axis with a post-thrust integration interval of 1ms (the picture is the same using 10ms as well).

The graph shows an area of viable flight and on the right is an area of short impulse and on the left is an area of low thrust. The maximum on the right of the viable flight area is echoed to the left and less obviously again (where the cursor is).

 Variables Water Rocket Computer Model Problem 06 Rocket Mass of Rocket Empty 40000 g Capacity of Pressure Vessel 33000 cm3 Rocket Diameter 20 cm Rocket Coeff of Drag 0.56 Nozzle Diameter 21 mm Constant K for nozzle 0.16 [ ] Launch Tube in use Not Used Duration of air impulse 4 ms [ ] Parachute in use Not Used Launch Tube Length 20 cm External Diameter 21 mm [X] Hollow Launch Tube Used Wall Thickness 2 mm Length of Tube Empty 25 cm Distance of Vent from End 0 cm [ ] T-Nozzle in use Not Used T-Nozzle Diameter 4.75 mm Parachute Diameter opened out flat 1.2 m Parachute Coeff of Drag 0.9 Deploy () Apogee.( ) Timer 4 s Delay in opening 5 m Initial Mass of Water 10000 g Pressure in Vessel 300 psi Height 1.5 feet Angle of Elevation 88 ° Speed at Angle of Elevation 0 m/s Temperature 10 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 9.81 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 maxima that occur.

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.