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You have
made a rocket from a 2 litre pop
bottle and it is aerodynamically
stable. You have pressure tested it
for safe launches at 100 psi. You are
using a circular parachute but not
using a launch tube. You want to find
the optimum weights of the empty
rocket and water for (1) the highest
flight and (2) the longest duration
flight. |
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Measurements |
Results |
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Weigh the rocket
empty. This is your absolute minimum
weight so, even if the model says you
should use less weight for the
rocket, you are stuck with this one.
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90g |
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Capacity - Either:
fill the rocket with water, weigh it,
empty it and weigh it again - the
difference in weight represents the
capacity of the rocket assuming 1g =
1cm3; or fill the rocket
with water and measure it into a jug
or other volumetric measuring device.
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2050cm3 |
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Rocket diameter. Get
a tape measure and measure the
circumference, divide the result by
3.142 which will give you the rocket
diameter.
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9.5cm |
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Measure the internal
nozzle diameter. Unless you have a
set of callipers for measuring
internal diameters, the best you can
do is put a ruler up to the end and
estimate it. Most open necks are
around 21.5mm so you could skip this
and just put 21.5 in the model
instead.
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21.5mm |
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Lay the parachute
out flat on the floor and measure its
diameter. The distance it takes to
open will usually be between 2 and 10
metres. There are a lot of factors
that can affect the actual value but,
if you feel so inclined, you can
measure the distance that you run
down your path with it whilst it
deploys.
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1.2m dia
5m opening |
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Optimisations(1)
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Put the
above results into the model in
addition to the pressure of 100 psi
and a launcher height of 1.5 feet.
For the water, assume that a fill of
around 30% (600cm3) will
give reasonable results for a
starting point for the model. Leave
everything else at the default
settings including the angle of 88º
and the temperature of 10 unless it
is exceptionally hot where you are.
As you are testing for height and not
total time, uncheck the Parachute
in use check box so as to
make the model calculate faster. Put
the Model Time on 10ms and press Calculate.
The initial result should be close to
180 feet (178.8). Press the 3D
Graphs button. Make sure
that the Mass of Rocket Empty
and Mass of Water
option buttons in the Variables
(X and Y) frame and Maximum
Height in the Results
(Z) frame. Click on the Number
of Steps combo box and press
 . Repeat for the other
axis. This should make the number of
steps in each axis 31, ie maximum.
Press the View
button.
Press  and the cursor will be
taken along to the right hand side of
the grid to the maximum on the grid.
Rocket Empty weight of 157g with 750g
of water.
Press  and, without moving the
mouse from the square that the search
function left it in, click the mouse.
This will put the new weights into
the appropriate forms and take you
back to the 3D Graphs form. If you
are using the simulator in a Windows
95 DOS box and went into the graphs
full-screen, the mouse should still
be over the View button. Press it.
Press and the mouse will be
taken to the new maximum - Rocket
Empty weight 164.3g with 598.0g
water.
Again, press , click the mouse and the
new values will be copied to the
forms and you will be returned to the
3D graphs form. These were performed
with a 10ms Model Time and if you
really want to reduce that
integration error and re-search for
the maximum at 1ms, you can click on
the 1ms option button and repeat the
process. With zooming in, this will
give you 159.5g rocket weight and
585.5g water, a difference of 5g in
rocket weight and 13g of water.
Considering that, unless you work in
a laboratory, you will not be able to
measure your rocket to this accuracy
and in the field, you will not be
able to measure in your water this
accurately, combined with the fact
that the model says that they should
both get to 200.1 feet, there is
little point in spending this extra
time on going to 1ms.
Press Return and
then Calculate to
see the statistics and graphs for
your flight.
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Results(1)
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The
model predicts a height of 200.1 feet
with an optimised rocket weight of
159.5g and 585.5g of water. In real
terms this translates to
approximately 200 feet with a rocket
weight of 160g, carrying 580g of
water (to the nearest 20g or 575g to
the nearest 25g). We should therefore
add a further 70g of weight to the
nose of the rocket to bring it up to
160g. There are many factors that
influence the performance of the
rocket, many of which you can only
guess at (such as coefficient of
drag) so, if you use this as a
starting point, you won't be too far
out. If you suspect that there may be
a significant area of error in a
particular variable such as
coefficient of drag, you can try
putting in different values and
optimising on them, seeing what
effect it has. This is the beauty of
having a model to play with - you can
have some idea of what to
expect before you go out with your
rocket.
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Optimisations(2)
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Put in
the results as in the first part of
this example but, as you are
testing for total time, check the Parachute
in use check box so as to
make the model calculate faster. Put
the Model Time on 10ms and press Calculate.
The initial result (600cm3
water, 90g rocket) should be close to
45 seconds (46.9). Press the 3D
Graphs button. Make sure
that the Mass of Rocket Empty
and Mass of Water
option buttons in the Variables
(X and Y) frame and Flight
Time in the Results
(Z) frame. If they are not
already on 31, click on the Number
of Steps combo boxes and
press .
Note
that the lower limit for rocket
weight has been set by the program to
22g. As our rocket already weighs 90g
and we cannot make it lighter (the
optimum weight is 58g) we should make
this value read 90g instead of 22g.
Press the View
button.
Press and the cursor will be
taken to the maximum on the grid.
Rocket Empty weight of 90g with 450g
of water.
Press and, without moving the
mouse from the square that the search
function left it in, click the mouse
and you will be returned to the 3D
graphs form.
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Results(2)
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The
model predicts a time of 47.9 seconds
with a Rocket Empty weight of 90g
with 450g of water. In real life,
this us just under 50 seconds with a
90g rocket and 450g of water.
As a matter of interest, the
results for an optimum weighted
bottle are 58g (60g) bottle weight,
420g water giving 48.5 seconds flight
time so, around 1 second less is not
too bad.
One consideration that should be
made is that the coefficient of drag
of the parachute is important as it
is so big and, perhaps more
importantly, updraughts and
downdraughts can make a significant
difference. I have seen a rocket
hover 10 feet in the air and then
fall to the ground in a fraction of a
second just due to air currents.
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You have
a 1 litre black currant bottle that
you have used heat treatment on to
make the nose almost spherical and
the diameter at the front end
smaller. Again, it has fins and is
aerodynamically stable. You have
pressure tested it for safe launches
at 140 psi. You want to find the
optimum rocket weight, water and
angle for the furthest downrange
distance.
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Measurements
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Results |
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Weigh the rocket
empty. This is your absolute minimum
weight so, even if the model says you
should use less weight for the
rocket, you are stuck with this one.
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100g |
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Capacity - you
determined the capacity of the rocket
by weighing the rocket full of water
and empty.
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900cm3 |
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Rocket diameter. Get
a tape measure and measure the
circumference, divide the result by
3.142 which will give you the rocket
diameter.
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6.5cm |
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The coefficient of
drag is substantially lower as the
rocket is almost elliptical. The rear
half is elliptical and the front has
a reduced diameter and a spherical
nose. The coefficient is therefore
somewhere between 0.56 and 0.35.
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0.42 |
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The internal nozzle
diameter is the same as in the above
example (they are mostly the same
even though this bottle was never a
pressure vessel, it was cast from the
same blanks and has the same nozzle
and top as the other pop bottles).
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21.5mm |
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The Constant K for
the nozzle is different as it is
almost conical with a short, small
step. K for a conical section is 0.05
and for a D/d=1.5 step is 0.28 The
step is smaller than that so an
estimate should be made.
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0.2 |
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Optimisations
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Put the
above results into the model in
addition to the pressure of 140 psi
and a launcher height of 1.5 feet.
For the water, assume that a fill of
around 30% (say 300cm3)
will give reasonable results for a
starting point for the model. Leave
everything else at the default
settings except the angle which you
could set to 45º. Put the Model Time
on 10ms and press Calculate.
The initial result should be close to
120 metres (123.3). Press the 3D
Graphs button. You now
have three variables to optimise for:
Mass of Rocket Empty,
Mass of Water and Angle
of Elevation. For the Variables
(X and Y), select the one
that you think will vary the least
once it is established (Angle
of Elevation possibly
:-) and one of the others - Mass
of Water. Click on Distance
Downrange in the Results
(Z) frame. If not already
set, click on the Number of
Steps combo box and press . Repeat for the other
axis. This should make the number of
steps in each axis 31, ie maximum.
Press the View
button.
Press and the cursor is taken
to 38º and 285g water. Press and the values are
adopted by the model.
Select Mass of Water and Mass of
Rocket and press the View button
again.
Press as before and the cursor
is taken to 284.5g water and 100g
weight of rocket. Press to adopt the values. If
you repeat this procedure with any
combination of the three variables,
you will get the same results. It is
worth trying with the first variable
that you used (angle in this case) to
check that that has not changed. It
has not in this case. If your
variables do interact significantly
(ie optimise on 1 and 2, then 2 and
3, then 1 and 2 again and you find
that 1 has changed) you can go
through several cycles of this before
you reach a steady, 3 variable point.
Press Return and
then Calculate to
see the statistics and graphs for
your flight.
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Results
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The
results are a rocket with a mass of
100g (no need to add anything to the
real rocket), carrying 284.5g of
water (in reality this would
approximate to 285 or even 300g) and
launched at an angle of 38º. With
these settings, the rocket should
travel approximately 125 metres
downrange. |