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.
|
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