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
Tnozzle.
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 postthrust 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 

cm^{3} 
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] TNozzle in use 
Used 


TNozzle 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/m^{3} 
Density of Liquid in Rocket 
998 

kg/m^{3} 
Acceleration due to Gravity 
9.80267 

m/s^{2} 
Atmospheric Pressure 
1013 

mBar 
Density of Air at STP 
1.293 

kg/m^{3} 
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.
