where:
P
is the pressure of the compressed air
Pa
is the atmospheric pressure
AN
is the area of the nozzle
This extra credit exercise requires that a participating et181 Rocket team collaberates with a Junior Lab team in order to compare the rocket thrust vs time with experiment. This quarter a number of junior lab teams have expressed ibterest in developing an experiment to measure and record the thrust force of the water rocket vs time. Recall from the rocket analysis that as long as the water is being expelled through the nozzle, the thrust force is given by the following equation:
where:
P is the pressure of the compressed air
Pa is the atmospheric pressure
AN is the area of the nozzle
Since the pressure P varies with time as the air expands to expel the water the thrust force varies in unison. In this extra credit exercise we wish to plot the thrust force vs time, and compare the results with those measured by the Junior Lab team.
The Computer Program "rockthrust"The program rockthrust is a modification of the last exercise rockplot in that we wish to plot the thrust force vs time,
and save the thrust force array together with the time, velocity
and height arrays on a data file rocket.out to allow off-line plotting using MATLAB. We first
get the rocket data from a data file in order to construct a rocket
, and subsequently invoke the method findvelht to evaluate
the thrust. As before we show a typical example of a datafile
as follows:
43.0 591.0 0.4 0.3 4.0 0.3 8.0 ################################################ The small urieli root beer water rocket -10/8/05 The above data items are (in sequence): ms [gm] - solid mass (rocket + payload) vtot [cc] - total volume (water + air) dnoz [cm] - diameter of nozzle fill - fill ratio (water/total volume) pgage [atm] - charge gage pressure [atmospheres] cdrag - Coefficient of drag dbottle [cm] - outside diameter of bottle ################################################ |
The method findvelht is modified such that the local variable thrust becomes an argument passed by reference, as shown in the schematic below. The prototype of the modified method findvelht can be seen in the header file rockthrust.h
A typical execution is shown below together with the output data file rocket.out. As in program rockplot, the input data defining the rocket is read from the input data file. All data items that are input by the user are shown in italics.
enter the filename containing the rocket data: urieli.data
get rocket data from the "urieli.data" file
data read:
43, 591, 0.4, 0.3
4, 0.3, 8
################################################
The small urieli root beer water rocket -10/16/06
The above data items are (in sequence):
ms [gm] - solid mass (rocket + payload)
vtot [cc] - total volume (water + air)
dnoz [cm] - diameter of nozzle
fill - fill ratio (water/total volume)
pgage [atm] - charge gage pressure [atmospheres]
cdrag - Coefficient of drag
dbottle [cm] - outside diameter of bottle
################################################
Water rocket initialized as follows:
Solid mass[gm]: 43, total volume[liters]: 0.591
absolute charge pressure[kPa]: 500
initial air charge volume[liters]: 0.4137
Nozzle free flow area [sq.cm]: 0.125664
Bottle cross sect. area [sq.cm]: 50.2655
Density - water: 1000kg/m^3, outside air: 1.2kg/m^3
Ratio of specific heat capacities for air (k): 1.4
Drag coefficient: 0.3
gravity acceleration: 9.807m/s^2
enter the max time to test (sec)
1
value entered is 1(s)
enter the number of points to evaluate
21
number of points is 21
plot width is 61 characters
rocket thrust (N) vs time(s):
0 I *
0.05 I *
0.1 I *
0.15 I *
0.2 I *
0.25 I *
0.3 I *
0.35 I *
0.4 I *
0.45 I *
0.5 I *
0.55 I *
0.6 *
0.65 *
0.7 *
0.75 *
0.8 *
0.85 *
0.9 *
0.95 *
1 *
minimum value: 0, maximum value: 10.0531
rocket upward velocity(m/s) vs time(s):
0 *
0.05 I *
0.1 I *
0.15 I *
0.2 I *
0.25 I *
0.3 I *
0.35 I *
0.4 I *
0.45 I *
0.5 I *
0.55 I *
0.6 I *
0.65 I *
0.7 I *
0.75 I *
0.8 I *
0.85 I *
0.9 I *
0.95 I *
1 I *
minimum value: 0, maximum value: 29.5986
enter the filename: rocket.out
21 rows of data written to "rocket.out" file
|
The plot of thrust vs time should be compared to the measured data obtained by the Junior Lab team using your rocket. In your report you should describe the experiment and discuss the results obtained. The rocket.out file is shown below - notice the fourth column that includes the thrust force in Newtons.
0.000 0.000 0.000 10.053
0.050 1.801 0.045 9.348
0.100 3.632 0.181 8.729
0.150 5.512 0.409 8.181
0.200 7.461 0.733 7.692
0.250 9.502 1.156 7.253
0.300 11.661 1.685 6.857
0.350 13.973 2.325 6.497
0.400 16.478 3.085 6.169
0.450 19.234 3.977 5.868
0.500 22.320 5.014 5.592
0.550 25.854 6.216 5.336
0.600 29.599 7.609 0.000
0.650 28.261 9.056 0.000
0.700 26.936 10.433 0.000
0.750 25.775 11.759 0.000
0.800 24.597 13.014 0.000
0.850 23.488 14.213 0.000
0.900 22.442 15.360 0.000
0.950 21.436 16.453 0.000
1.000 20.513 17.516 0.000
|
You can now use the data file in a similar
manner to the previous exercise rockfile in
which you used the FTP program
to fetch the file and save it on the local computer disk.
You should read the file into the MATLAB
application and plot the thrust vs elapsed time, as shown below.
Note the following: Even though your team will share the results of the rocket experiment data, the program, MATLAB plot, and report should be your individual work, done without colloboration or help from any source. The MATLAB plot should contain a box with your name printed (not handwritten) on the plot, including the basic data used to determine the plot as shown. Your program (named rockthrust.cpp) should be saved in your home directory together with the nielsen.data data file by 10:00am of the due date shown on the calendar, however the report can be submitted at any time before the final exam date.
Wow - teaming up
with the Junior Lab to compare our calculated thrust to actual
measurement - this is REAL engineering!