Aim

• To measure the magnitude of the thrust produced by CD (Convergent Divergent) nozzles.
• To compare the results to straight through nozzles.

Experiment Setup

The thrust curve data shown below was for a rocket with the following parameters:

Because we were going to do quite a few experiments, we didn't want all that foam going into the garden so we collected the water and in a large plastic tray under the test rocket. We used up almost an entire bottle of bubble bath for these tests.

Nozzle design

We manufactured two CD nozzles: one with a 7mm throat and the other with a 9mm throat. In both instances the expanding section was 4 degrees from the centerline. The expanding shape was conical since that is much easier to manufacture. See diagram at left. We didn't want to design an optimal nozzle shape, we just wanted to see how much of difference an expanding nozzle makes, if at all, and only then would we attempt to optimise it.

7mm and 9mm Nozzle Profiles (click to enlarge)

The shape of the divergent section was based on video footage of previous tests where we measured the expansion rate of the foam. We made the slope of the divergent section less than the average slope in order for the expanding foam to have some sort of an "effect" on the nozzle.

We made sure that the baseline straight through nozzles had exactly the same hole as the minimum diameter (throat) in the CD nozzles. This turned out to be 7.1mm and 9.2mm respectively. This way we eliminated the bias due to different sized holes.

	The 9mm and 7mm CD nozzles tested.
	All the straight through and CD nozzles tested on the day.
	The foamy water is collected in a large tray

Results

We ran three tests with the 7mm nozzle in order to establish a baseline for the test. The first test looks quite out of place compared to the other two tests, and this we traced back to forgetting to put in the locking pin that prevents the dampner container from moving. We believe the fluctuations were due to this.

7mm straight through nozzle thrust curves (click to enlarge)

When we performed the 7mm CD nozzle tests we again repeated it 3 times in order to reduce experimental errors and get a sense of repeatability of the experiment.

7mm CD nozzle thrust curves (click to enlarge)

Now we average the two sets of data (ignoring test 1) we get the following graph:

7mm straight through and CD nozzle thrust curves
averaged and compared (click to enlarge)

We did not include test 1 in the average because the measurements weren't reliable.

When we compare the straight through nozzle performance to the CD nozzle performance we see that with the 7mm CD nozzle the total impulse is only 83% of the straight through nozzle.

We then switched to the 9mm straight through nozzle and ran another 3 tests. All three tests showed similar results which helped confirm that the test was reproducible fairly accurately.

9mm straight through nozzle thrust curves (click to enlarge)

Following that we performed another 3 tests with the 9mm CD nozzle. Again the results were fairly similar to each other.

9mm CD nozzle thrust curves (click to enlarge)

When we average the above results for the straight through nozzles and CD nozzles we get the following graph:

9mm straight through and CD nozzle thrust curves
averaged and compared (click to enlarge)

The thrust curve shapes were almost identical for the straight through nozzles
as well as the CD nozzles, however, it is quite evident that the total impulse is lower for the CD nozzles. In fact the 9mm CD nozzle produced only 92.6% of the total impulse of a straight through nozzle.

The results for both nozzles were disappointing as we were hoping to see some sort of improvement, however, the result was not unexpected.

We must stress that these tests were done at only 100psi and the results may be quite different at much higher pressures. Currently we do not have the technology to make these tests at the high pressures we think it is likely to make a difference (1000psi+) Antigravity used their CD nozzles with pressures over 1000psi.

The following graph shows the averaged results for 7mm and 9mm nozzles. You can see that the 9mm nozzles produced more total impulse than the 7mm nozzles and would therefore be better to reach higher altitude.

7mm and 9mm nozzles averaged and compared (click to enlarge)

Should others want to do further analysis of the data, the data for both nozzles is available in spreadsheet format here: Thrust_Curves_140407.zip

Conclusions / Analysis

• It may be that because the foaming agent affects the water's surface tension it is causing the foam to "stick" to the surface of the nozzle causing greater friction. Different nozzle materials may have a different effect on friction. Perhaps the length of the expanding section has an effect on the loss of efficiency?
• It may be that the foam also isn't an ideal foam and that a lot of loss of impulse is due to normal water being ejected. CD nozzles have a negative effect when only water is used.
• It may also be possible that the shape of the nozzle has to be quite different compared to what was tested here.
• One thing that is not evident from these results is that the total thrust does not end with the end of the thrust curve. In fact, a decaying amount of thrust usually continued for another at least another whole second. But the thrust was less than the weight of the rocket and so is not shown on the graph. In real life the rocket would actually decelerate less slowly during this time due to drag and gravity then if the thrust had ended completely.
• Some of the variance in the results is also due to how the water was distributed between the lower and upper bottles for the Jet foaming to be effective. It is difficult to accurately control the ratio of the water in the two bottles.
• Because both the 7mm and 9mm CD nozzles gave a lower performance than the straight through nozzles, we will put further testing and development of CD nozzles on the back burner until we can reach much higher pressures and then test again.

Test Record