# John F. N. Salik

## Part 2: Design and Implementation of a Simple Rocket Motor

In Chemical Propulsion on March 22, 2013 at 1:07 am

This article is the second of a two-part series describing the design of a rudimentary rocket motor implemented using standard, off the shelf components with the goal of demonstrating its propulsive ability. In the first part, mission requirements and motor construction were discussed. In this part, the system is tested and characterized using basic image processing techniques on empirical data obtained from video analysis experimentation.  This series of articles is intended for those with an involved, but not advanced technical knowledge of rocketry.  Readers should not attempt to repeat this experiment without a safe, working knowledge of the risks involved with combustible gases.

### IV. System Deployment

A. Experimentation

Oxyhydrogen fuel required for testing was provided by the set-up described in [1]. An open urban area was chosen with observance of reasonable safety precautions. Data collection was performed from the use of high speed video. The rocket was fired twice: first for testing the set-up and then for final deployment and concurrent data collection.

The test firing was performed without incident propelling the ping-pong ball in compliance with all stated mission requirements (Section I-A). Final deployment also complied with all mission requirements as depicted in Figure 6, which shows the last of several frames that capture the successful ping-pong deployment.

FIGURE 6 – Shown here is the final video frame depicting the ping-pong ball deployment. The frame shows complete ball displacement during a single frame captured at 1/60 s. The blur produced by the moving ball captures the movement in this time frame from which distance and therefore velocity can be estimated.

While successful, this deployment was not without incident.  The bubbler described in [1], is one of two a safety mechanism (along with a check valve) that prevents hot gas to enter the fuel cell which would pose many significant risks from the thermal and pressure build-up.  During the final deployment, this safety mechanism was used because of a back-firing of fuel through the fuel lines.  Figure 7 shows the incident in three cropped video frames in chronological sequence from left to right.

FIGURE 7 – Left to right. Three consecutive cropped frames extracted from the video taken of the rocket in operation of the bubbler safety mechanism being used. Immediately after gas ignition the bubbler is intact (first image). With a short delay, we observe combustion within the bubbler chamber in the next frame. In the last frame, we see the destruction of the safety apparatus due to hot gas expansion within the effectively closed volume.

The safety mechanism was completely destroyed from the blast but there was no damage to personnel or property present.  Future attempts to deploy in this manner will require more careful consideration of the quality of the check valve which is suspected to not have worked for the relatively low gas pressured required for this project as well as the volume of gas contained in the fuel lines.  Occurring concurrently with this incident, the addition of too much electrolyte into the water reduced its conductivity and increased current flow through the system.  While gas production and pressure increased, the current load was too great for the wires causing the insulation covering them to melt (Figure 8).

FIGURE 8 – Shown here is one of the wires that melted during the second attempt at payload development. This was caused by reduced conductivity of the water in the electrolysis process which demanded greater current flow to the anodes and cathodes. The wires were unable to carry this current.

Fire was prevented by disconnecting the battery but the threat of explosion was very real (attempt at your own risk). Future deployments will have larger diameter wire to accommodate more current as the additional electrolyte was deemed desirable.

B. Data Collection & Image Processing

While both times the rocket was used video was taken, emphasis on the second event is used for analysis here as the first was primarily to assure proper set-up and serve as an analysis tool in case anything were to go seriously wrong. The complete video sequence consists of several hundred frames at high resolution. Six frames out of these provided the data that was required for rocket engine characterization.

To extract the data from these six frames, they were initially extracted from the video sequence. Using an iterative process, frames were paired and superimposed to produce a difference map after a rectangular HSV filter was applied to enhance colour in the wavelength of the yellow ping-pong ball. Filtering was done to emphasize the ping-pong ball and differencing was done to correctly align the images to compensate for camera movement. The frames were then layered and pair-wise differenced to produce a global difference map. To enhance small differences between the images, a histogram equalization was performed. The final difference map was then desaturated in the HSV colour space to produce the image seen in Figure 9.

FIGURE 9 – Six frames were extracted from the video sequence of the final deployment of the system. In each frame, an HSV colour filter was used to enhance the solid yellow ping-pong ball. An image difference was computed between frames, and superimposed, followed by a histogram equalization of difference intensity values. Finally a variance filter was used to perform noise suppression and line detection.

After color thresholding in the wavelength of the ping-pong ball, pixel scaling was established from the payload dimensions (Table II, Figure 10).

FIGURE 10 – The payload used in this experiment: An ITTF regulation-compliant ping-pong ball.

Given the ball was 13 pixels in diameter, we determine the image scaling was $0.325 \mathrm{\frac{px}{mm}}$.  Using this scaling, a single video frame that captured motion data covering $\frac{1}{60}$ of a second, we observe a center of mass displacement of $11.8 \mathrm{cm}$.  The data obtained from video and image analysis is summarized in Table III.

 Diameter $40\ mm$ Coefficient of Restitution $0.89\ \mathrm{to}\ 0.92$ Mass $2.4\ g$ Material $\mathrm{Air-filled\ celluloid.}$ Colour $\mathrm{Yellow.}$

Table II
Specifications for the International Table Tennis Federation (ITTF) compliant ping-pong ball used in this experiment.

 Video Frame Rate $60\ fps$ Image Resolution $800 \times 600$ Scaling $0.325\ \frac{px}{mm}$ Single-Frame Ball Displacement $11.88\ cm$ Estimated Ball Velocity $7.128\ \frac{m}{s}$

Table III
Analysis data obtained from video and image processing of the rocket in operation.

C. Total Impulse & Thrust

Table III yields three physical parameters were obtained from test. The ping-pong distance $d= 11.88 \mathrm{cm}$ covered in a specific time $t=16.7 \mathrm{ms}$. From these parameters, we can determine the average velocity of the ball:

$\displaystyle\begin{array}{rcl} v_{avg} &=& \frac{d}{t}\\ &=& 7.128 \mathrm{\frac{m}{s}} \end{array}$

This value was assumed to be effectively constant over the initial blast. This is justified in that when velocities are computed from the initial position for each of the centre of masses shown in Figure 9, we find an error of 3%. This means that initial acceleration is small enough to be neglected for first approximation calculations. Since there was no initial ball velocity, we can analytically compute the work done on the ball from the difference in kinetic energy:

$\displaystyle W=\frac{1}{2} m \left( v_{avg} -v_o\right)^2$

Where $m$ is the mass of the ping-pong ball. Because the force required to move this ball is a function of the work done on it and distance, we can find the average thrust $F$ for the rocket motor:

$\begin{array}{rcl} F &=& \frac{1}{2} \frac{m}{d} \left( v_{avg} -v_o\right)^2\\ \nonumber &=& 0.5773679998 \times 10^{-3} \mathrm{N}\\ \nonumber &=& (0.5774) \times 10^{-3} \mathrm{N} \end{array}$

For our system, we find the thrust to be approximately $0.5774 \times 10^{-3} \mathrm{N}$. Which is clearly sufficient to move the ball significantly. For a short duration burn time of approximately $t_b=16.7 \mathrm{ms}$, the total impulse for this rocket motor can be found as well  ($I_t=F t_b$):

$\begin{array}{rcl} I_t &=& \frac{m\,t_b}{2 m} \left( v_{avg} -v_o\right)^2\\ \nonumber &=& 0.9622800000 \times 10^{-5} \mathrm{\frac{kg \cdot m}{s}}\\ \nonumber &=& (0.9623) \times 10^{-5} \mathrm{\frac{kg \cdot m}{s}} \end{array}$

The specific impulse is not known because the effective exhaust velocity could not be determined due to limitations in available instrumentation as well as the open-environment test conditions. Also, because testing was done in a practical (and not ideal) environment, we could not assume complete combustion of our propellant and therefore determination of mass flow rate by direct measure or inference would have yielded unreliable reliable results. All of this is complicated further because effects of ball friction within in the rocket’s nozzle and drag induced by air medium in which the ball travels.

### V. Conclusion

An oxyhydrogen (HHO) rocket system was designed, constructed and implemented with the purpose of propelling a standard ping-pong ball for an arbitrary distance greater than one meter. The propellant used for this system was obtained from a hydrogen fuel cell that was developed specifically for this rocket system. The system deployed its payload twice however, not without incident. While the rocket motor described in this work operated without any problems, this highlighted the need for better safety protocols and better construction methods for future endeavours concerning the fuel-cell. Specifically, we refer to the delivery of fuel to the combustion chamber and in the matching of wire thickness to the amount of electrolyte added to water in the electrolysis process.

Telemetry data for the deployment was obtained from video data from which image frames were extracted and analysed using various filtering filtering techniques and morphological operators in an appropriate colour space. With image scaling obtained, the basic specifications for the rocket were found using basic energy and kinematic equations and are summarized in Table IV.

 Total Impulse $0.9623 \times 10^{-5} \mathrm{\frac{kg \cdot m}{s}}$ Thrust $0.5774 \times 10^{-3} \mathrm{N}$ Burn Time $16.7\ ms\ \mathrm{(approx.)}$

Table IV
Specifications determined for the simple rocket motor.

Author’s Note – This author fully acknowledges the excellent work and contribution of Sarfraz Salik and Dany Khawam who constructed and characterized the HHO generator used in this work.  A video of their production is shown below that sumarizes the effort put into the entire project.  It was a fun an enjoyable little project that I will remember for some time.

References:

1. S. Salik and D. Khawam, “Gaseous hydrogen-oxygen propellant production from the electrolysis of water.” Concordia University, Tech. Rep.,2010.
2. “Oxyhydrogen,” November 2010. [Online]. Available: http://en.wikipedia.org/wiki/Oxyhydrogen
3. “Rocket engine nozzle,” November 2010. [Online]. Available: http://en.wikipedia.org/wiki/Rocket_engine_nozzle
4. “Nozzle,” November 2010. [Online]. Available: http://en.wikipedia.org/wiki/Nozzle
5. H. D. Ng, Course Notes, Concordia University – MECH 6521 (Space Flight Dynamics and Propulsion Systems), 2010.
6. G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 8th ed. John Wiley & Sons, 2010.
7. M. Tajmar, Advanced Space Propulsion Systems. Springer-Verlag/Wein, 2003.
8. “Piezoelectricity,” November 2010. [Online]. Available: http://en.wikipedia.org/wiki/Piezoelectricity