# John F. N. Salik

## Part 1: Design and Implementation of a Simple Rocket Motor

In Chemical Propulsion on December 22, 2012 at 1:00 pm

This article is the first 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.  While simplistic, it contains all of the key components found in a typical rocket system.  In this first part, the mission requirements are described and the rocket motor’s construction is discussed.
In the second part, the system will be 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.

### I. Introduction

Using commonly available components, a very basic oxyhydrogen (HHO) rocket motor is designed and implemented to propel a standard ping-pong ball for an arbitrarily long distance which is the loosely given mission requirement. The propellant is obtained from the collection and filtering of gases produced from the water electrolysis process within a hydrogen fuel cell that was designed specifically for this work (see [1]). The launch conditions were unspecified, but constrained for this work. The objective of this work is to show that a basic hot gas rocket design can implemented to launch a projectile, and to demonstrate that video analysis of the launch can yield basic telemetry data that can be used to characterize the system.

A. Mission Requirements

The mission requirements were informally stated avoiding specific design constraints in favour of promoting unique design propositions for a competitive bid. As stated, the requirement was to design and produce a propulsion system that would “move a ping-pong ball at least one meter from an initial position”. Clearly, certain assumptions were required in order to produce a feasible design.

It was assumed that the ping-pong ball was a standard ITTF unit with specifications listed in Table II. Furthermore, it was assumed that the unit was to be propelled at approximately 57m above sea-level at an incline of $15^\circ$ from vertical. The air pressure was assumed to have minor fluctuations about $1017.4\ mbar$ which is normal for the launch site in Dorval, Quebec (Canada) during the month of September. It was also assumed that wind conditions would be variable, but always under $5\ km/hr$ at launch time. A summary of these requirements is listed in Table I.

 Launch Altitude $57\ m$ Launch Incline $15^\circ$ Location $\mathrm{Dorval,\ Quebec\ (Canada)}$ Air-Pressure $1017.4\ mbar$ Wind $\leq 5 km/hr$

Table I
A summary of the launch specifications considered in the rocket motor design.

B. Design Overview

The design that was settled upon was a oxyhydrogen gas propellant system with a very short burn time. The propellant mixture was obtained from a fuel cell which relies on the electrolysis of water to obtain the gas components. The combustion chamber is partially closed was designed to accept a both gaseous hydrogen and gaseous oxygen in a 2:1 ratio respectively displacing approximately $1.25 \;\mathrm{cm^3}$ of air normally present before rocket operation. The ignition source produces an electric field strength above the $3\times 10^6 \mathrm{\;\frac{V}{m}}$ air dielectric breakdown. The resulting spark is an energetic catalyst that results in hot gas expansion within the chamber as propellant molecules recombine to form gaseous water vapour  The velocity of the hot gas flow as it escapes the chamber is increased through a narrow exhaust throat. The resulting high velocity gas flow passes through a rudimentary nozzle where a momentum transfer occurs between the hot gas and the ping-pong which is placed within the nozzle to move it alignment with mission requirements as stated in Section I-A.

### II. Principal of Operation

A. Injector & Ignition Source

The injector serves to introduce propellant into the combustion chamber at a pressure that is nominally constant. This pressure invariance is primarily due to the constant current draw which is a feature of the fuel cell [1].   By timing fuel-cell operation, the approximate propellant volume introduced into the combustion chamber can be established. The flow profile of the propellant at the injector nozzle is consistent with that of a low-pressure exit from a small-diameter cylindrical opening which is adequate for the mission requirements stated in Section I-A.

The ignition source provides an electric field which exceeds the dielectric breakdown voltage between the metallic contacts of a spark gap. The resulting temperature in the vicinity of the spark is far above the $570^\circ$ autoignition temperature of oxyhydrogen. The minimum energy to ignite an oxyhydrogen mixture is approximately 20 microjoules [2] and this is easily achieved by the spark thereby producing a sudden release of energy due to the recombination of hydrogen and oxygen [1]. This small explosion results in hot gas expansion within the combustion chamber.

B. Combustion Chamber

The combustion chamber is an open cavity that contains the explosive release of hot gas once autoignition has occurred. Because the system was designed for very short duration combustion, heat transfer to the combustion chamber walls can be assumed to be negligible, therefore heat loss for the given burn time is minimal. The hot gas expansion produces a flow which is channelled from the combustion chamber to an narrowed throat and eventually to the nozzle.

C. Throat & Nozzle

The throat is a narrow opening in the combustion chamber through which hot gas travels at subsonic speed. Because the throat cross-section is contracted relative to the rest of the chamber, the gas is forced to accelerate at it exits towards the nozzle.

For an ideal system, as the combustion gas enters the rocket nozzle from the combustion chamber it is travelling at subsonic velocities. As the cross-sectional area of the chamber decreases the hot gas is forced to accelerate until the linear velocity becomes sonic at the nozzle throat where the cross-section is minimum. From the nozzle throat the cross-sectional area then increases, and the gas expands and the linear velocity becomes progressively more supersonic [3]. The system designed is not ideal although the same principles apply, this is to say that the throat area provides an accelerating area for the hot gas as it is generated within the combustion chamber. While the pressure is reduced as the gas enters the nozzle area after the throat, pressure is reduced although the exit gas velocity is quite high.

The nozzle is placed after the throat following the hot gas flow from the combustion chamber and its purpose is to control the exit fluid flow characteristics. In the general sense, nozzles can be used to control rate of flow, speed, direction, mass, or the pressure of the stream that emerges from them [4]. In this context the nozzle is primarily used to control the direction and pressure of the escaping gas. This is done by varying the cross-sectional area of the section following the throat appropriately to transfer gas particle momentum to a ping-pong ball.

D. Momentum Transfer to Payload and Pressure Release

There are two mechanisms that allow for mission objectives to be achieved by this system: Momentum transfer, and pressure release. Momentum transfer from the escaping gas to the ping-pong ball occurs within the nozzle. For this to happen, the ping-pong ball is placed within the nozzle, and is actually considered as the system payload. This is an atypical payload delivery compared to normal rocket operations where propulsive components remain with the payload until release. Here, momentum from escaping particles within the nozzle are transferred to the ping-pong ball providing movement necessary for payload delivery (Newton’s third law). In addition to this, there is a gas pressure build-up behind the ball which partially obstructs gas flow. For the system to return to a state of environmental equilibrium, pressure release is required and is achieved by expulsion of the ping-pong ball from the nozzle area thereby providing the second payload delivery mechanism.

### III. Implementation

The rocket system consists of two fundamental parts. The rocket motor: combustion chamber, ignition system, and nozzle. The pressurized fuel delivery system: electrolyzer, check valve, bubbler, and power source. Only the rocket motor implementation is outlined here. For information about the fuel delivery system, the reader is directed to [1].

The rocket motor was built primarily out of standard household ABS plastic piping. The catalyst for hot-gas expansion is an electric ignition system that provides energy for the propellant and oxidizer to react. The nozzle is designed to maximize momentum transfer from the hot gas to the ping-pong ball which is placed within the nozzle (optimal nozzle design was not a consideration). The assembled rocket motor is shown in Figure 1.

FIGURE 1 – Shown here is the assembled rocket motor after the initial test. The ignition system, nozzle, and fuel lines are clearly visible.

Here, we can see the the motor itself with its nozzle, part of the ignition system, as well as the pressurized fuel line going into the combustion chamber. The following sections attempt at providing more details about each.

A. Ignition System

The ignition system consists of two fundamental parts: a potential energy source and a spark gap. The potential energy source is provided from a crystalline material. Certain crystalline materials demonstrate piezoelectric behaviour which is the releasing of an accumulated charge in response to mechanical strain [8]. Piezoelectricity is the direct result of the piezoelectric effect. The spark gap consists of two conducting electrodes separated by a small distance for the purpose of allowing a small electric spark to pass between them. This occurs when the voltage difference between them exceeds the air dielectric’s breakdown voltage allowing for current to flow between them through ionized gas the spark).

Figure 2 shows the crystal assembly which has an integrated spring that is used to provide kinetic energy to a striker which hits the crystal. The resulting charges move down the wires to the spark plug which has as its primary feature, a spark gap (also in Figure 2). When manually actuated, the striker generates enough current to travel down a long set of wires to the spark plug which is inserted into the combustion chamber where a spark is produced. In the presence of the hydrogen and oxygen propellant, this serves as a reaction catalyst to produce the hot propulsive gas from a safe distance.

FIGURE 2 – The ignition subsystem components. (a) shows the spark plug with the spark gap clearly visible with one electrode over the other which is surrounded by a ceramic dielectric. (b) shows the piezoelectric crystal housing and assembly which contains a spring loaded striker providing current through the visible wire and larger metallic electrode. In (c), all components of the ignition system are shown in their disassembled state. Finally, we can see the assembled ignition system with the spark plug installed in the combustion chamber in (d).

B. Fuel Source

Propellant is provided under pressure by a hydrogen fuel cell designed specifically for the rocket motor described here. Figure 3 shows the fuel cell filled with deionized water and a small amount of sodium bicarbonate ($\mathrm{NaHCO_3}$, an electrolyte).

FIGURE 3 – The hydrogen fuel cell designed for this rocket motor. It provides the oxyhydrogen propellant under pressure to the combustion chamber where it is ignited.

The plates are interleaved anodes and cathodes that are required for the electrolysis process. Visible in the photo are the two wires that provide current for the process, and the pressurized fuel line that transports the oxyhydrogen to the rocket combustion chamber. The reader is encouraged to read [1] to obtain more details on this component.

C. Throat & Nozzle

The nozzle is not designed with optimal gas expansion in mind. It is designed to act as a mechanical guide for the ping-pong ball so that it could be expelled in a non-random direction in operation. The shape of the nozzle is essentially cylindrical and the diameter is slightly larger than that of the ball. A loose wadding placed around the ball while it is placed in the nozzle provides a seal that allows for a pressure build-up. The sudden gas-expansion from the violent oxyhydrogen explosion provides high pressure that is only relieved from the expulsion of the ball and the wadding from the nozzle. Momentum thrust is also provided from the combustion chamber throat which is quite small and requires an acceleration of escaping gas for the hot gas flow.

Figure 4 shows a photo of the throat which is responsible for providing momentum thrust, as is the nozzle. As can be seen in the photo, the payload diameter is very close to that if the nozzle.

FIGURE 4 – This figure shows the rocket motor under construction where the nozzle and throat area are clearly visible. Once assembled with the nozzle shown on the left, the throat (pointed out in the centre) is not directly visible in the finished module. The combustion chamber is visible on the right and ping-pong ball payload is visible on the top.

It is the paper wadding put around the ball that allows for pressure build-up downstream from the hot gas flow (shown in Figure 5). The nozzle material was PVC plastic and was bonded to the ABS pressure chamber using a high strength epoxy-based glue.

FIGURE 5 – A figure depicting the author holding the assembled engine with the payload inserted into the nozzle. The wadding is clearly visible as the red material around the ball.

Part 2 of this series describes how the system was tested and characterized using basic image processing techniques on video data obtained from the experiment.

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