Water rocket

Water rocket launch

A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water is forced out by a pressurized gas, typically compressed air. Like all rocket engines, it operates on the principle of Newton's third law of motion.

Operation

Simplified animation of how a water rocket works. 1) A bubble of compressed air is added and pressurizes the contents of the bottle. 2) The bottle is released from the pump. 3) The water is pushed out through the nozzle by the compressed air. 4) The bottle moves away from the water because it follows Newton's Third Law.

The bottle is partly filled with water and sealed. The bottle is then pressurized with a gas, usually air compressed from a bicycle pump, air compressor, or cylinder up to 125 psi, but sometimes CO₂ or nitrogen from a cylinder.

Water and gas are used in combination, with the gas providing a means to store potential energy, as it is compressible, and the water increasing the propellant mass fraction and providing greater force when ejected from the rocket's nozzle. Sometimes additives are combined with the water to enhance performance in different ways. For example: salt can be added to increase the density of the reaction mass resulting in a higher specific impulse. Soap is also sometimes used to create a dense foam in the rocket which lowers the density of the expelled reaction mass but increases the duration of thrust. It is speculated that foam acts as a compressible fluid and enhances the thrust when used with De Laval nozzles.

Launching a water rocket. The rocket is in its peak with no water inside it.

The seal on the nozzle of the rocket is then released and rapid expulsion of water occurs at high speeds until the propellant has been used up and the air pressure inside the rocket drops to atmospheric pressure. There is a net force created on the rocket in accordance with Newton's third law. The expulsion of the water thus can cause the rocket to leap a considerable distance into the air.

In addition to aerodynamic considerations, altitude and flight duration are dependent upon the volume of water, the initial pressure, the rocket nozzle's size, and the unloaded weight of the rocket. The relationship between these factors is complex and several simulators have been written to explore these and other factors.^[1][2][3]

Often the pressure vessel is built from one or more used plastic soft drink bottles, but polycarbonate fluorescent tube covers, plastic pipes, and other light-weight pressure-resistant cylindrical vessels have also been used.

Elements

Bottle

Two multi-bottle rockets with a cat for scale.

A larger multi bottle rocket with cylindrical fins.

The standard bottle used is a single polyethylene terephthalate two-liter bottle as used for carbonated soft drinks.

Multi-bottle rockets are created by joining two or more bottles in any of several different ways; bottles can be connected via their nozzles, by cutting them apart and sliding the sections over each other, or by connecting them opening to bottom, making a chain to increase volume. This adds complexity and the increased volume leads to increased weight - but this should be offset by an increase in the duration of the thrust of the rocket.

Multi-stage rockets are much more complicated. They involve two or more rockets stacked on top of each other, designed to launch while in the air, much like the multi-stage rockets that are used to send payloads into space. Techniques to time the launches in correct order and at the right time vary, but include the "crushing-sleeve" method.^[4]

Gas

Several methods for pressurizing a water rocket are used including:

• A standard bicycle/car tire pump, capable of reaching at least 75 psi (520 kPa).
• Water pressure forcing all the air in an empty water hose into the rocket. Pressure is the same as the water main.
• An air compressor, like those used in workshops to power pneumatic equipment and tools. Modifying a high pressure (greater than 15 bar / 1500 kPa / 200 psi) compressor to work as a water rocket power source can be dangerous, as can using high-pressure gases from cylinders.
• Compressed gases in bottles, like carbon dioxide (CO₂), air, and nitrogen gas (N₂). Examples include CO₂ in paintball cylinders and air in industrial and SCUBA cylinders. Care must be taken with bottled gases: as the compressed gas expands, it cools (see gas laws) and rocket components cool as well. Some materials, such as PVC and ABS, can become brittle and weak when severely cooled. Long air hoses are used to maintain a safe distance, and pressure gauges (known as manometers) and safety valves are typically utilized on launcher installations to avoid over-pressurizing rockets and having them explode before they can be launched. Highly pressurized gases such as those in diving cylinders or vessels from industrial gas suppliers should only be used by trained operators, and the gas should be delivered to the rocket via a regulator device (e.g. a SCUBA first-stage). All compressed gas containers are subject to local, state and national laws in most countries and must be safety tested periodically by a certified test centre.
• Sublimating carbon dioxide gas from dry ice. Dry ice expands 800 times in volume upon sublimation. A #3 rubber stopper is forcefully inserted into the neck of a two-liter plastic bottle partially filled with water. The pressure builds up enough to pop the stopper out.
• Ignition of a mixture of explosive gases above the water in the bottle; the explosion creates the pressure to launch the rocket into the air.^[5]

Nozzles

Water rocket nozzles differ from conventional combustion rocket nozzles in that they do not have a divergent section such as in a De Laval nozzle. Because water is essentially incompressible the divergent section does not contribute to efficiency and actually can make performance worse.

There are two main classes of water rocket nozzles:

• Open also sometimes referred to as "standard" or "full-bore" having an inside diameter of ~22mm which is the standard soda bottle neck opening.
• Restricted which is anything smaller than the "standard". A popular restricted nozzle has an inside diameter of 9mm and is known as a "Gardena nozzle" named after a common garden hose quick connector used to make them.

The size of the nozzle affects the thrust produced by the rocket. Larger diameter nozzles provide faster acceleration with a shorter thrust phase, while smaller nozzles provide lower acceleration with a longer thrust phase.

It can be shown that the equation for the instantaneous thrust of a nozzle is simply:^[6]

$F = 2 P A_t$

where $F$ is the thrust, $P$ is the pressure and $A_{t}$ is area of the nozzle.

Fins

As the propellant level in the rocket goes down, the centre of mass initially moves downwards before finally moving upwards again as the propellant is depleted. This initial movement reduces stability and can cause water rockets to start tumbling end over end, greatly decreasing the maximum speed and thus the length of glide (time that the rocket is flying under its own momentum).

To lower the centre of pressure and add stability, fins or other stabilizers can be added which bring the centre of drag further back, well behind the centre of mass at all times. Stabilizers of any sort are normally placed near the back of the bottle where the center of mass is found. The increase in stability which well-designed fins give is worth the extra drag, and helps to maximize the height to which the rocket will fly.^[7]

Landing systems

Stabilizing fins cause the rocket to fly nose-first which will give significantly higher speed, but they will also cause it to fall with a significantly higher velocity than it would if it tumbled to the ground, and this may damage the rocket or whomever or whatever it strikes upon landing.

Some water rockets have parachute or other recovery system to help prevent problems. However these systems can suffer from malfunctions. This is often taken into account when designing rockets. Rubber bumpers, Crumple zones, and safe launch practices can be utilized to minimize damage or injury caused by a falling rocket.

Another possible recovery system involves simply using the rocket's fins to slow its descent and is sometimes called backward sliding. By increasing fin size, more drag is generated. If the centre of mass is placed forward of the fins, the rocket will nose dive. In the case of super-roc or back-gliding rockets, the rocket is designed such that the relationship between centre of gravity and the centre of pressure of the empty rocket causes the fin-induced tendency of the rocket to tip nose down to be counteracted by the air resistance of the long body which would cause it to fall tail down, and resulting in the rocket falling sideways, slowly.^[8]

Launch tubes

Some water rocket launchers use launch tubes. A launch tube fits inside the nozzle of the rocket and extends upward toward the nose. The launch tube is anchored to the ground. As the rocket begins accelerating upward, the launch tube blocks the nozzle, and very little water is ejected until the rocket leaves the launch tube. This allows almost perfectly efficient conversion of the potential energy in the compressed air to kinetic energy and gravitational potential energy of the rocket and water. The high efficiency during the initial phase of the launch is important, because rocket engines are least efficient at low speeds. A launch tube therefore significantly increases the speed and height attained by the rocket. Launch tubes are most effective when used with long rockets, which can accommodate long launch tubes.

Safety

Water rockets employ considerable amounts of energy and can be dangerous if handled improperly or in cases of faulty construction or material failure. Certain safety procedures are observed by experienced water rocket enthusiasts:

• When a rocket is built, it is pressure tested. This is done by filling the rocket completely with water, and then pressurizing it to at least 50% greater than anticipated pressures. If the bottle ruptures, the amount of compressed air inside it (and thus the potential energy) will be very small, and the bottle will not explode.
• Using metal parts on the pressurized portion of the rocket is strongly discouraged because in the event of a rupture, they can become harmful projectiles. Metal parts can also short out power lines.
• While pressurizing and launching the rocket, bystanders are kept at a safe distance. Typically, mechanisms for releasing the rocket at a distance (with a piece of string, for example) are used. This ensures that if the rocket veers off in an unexpected direction, it is less likely to hit the operator or bystanders.
• Water rockets should only be launched in large open areas, away from structures or other people, in order to prevent damage to property and people.
• As water rockets are capable of breaking bones upon impact, they should never be fired at people, property, or animals.
• Safety goggles or a face shield are typically used.
• A typical two-litre soda bottle can generally reach the pressure of 100 psi (690 kPa) safely, but preparations must be made for the possibility that a bottle unexpectedly ruptures.
• Glue used to put together parts of water rockets must be suitable, to avoid the chance that it will chemically weaken the bottle, which may then fail catastrophically.

Predicting peak height

If aerodynamic drag and transient changes in pressure are neglected, a closed-form approximation for the peak height of a rocket fired vertically can be expressed as follows:

$h=\left({M_i \over M_R}\right)^2 \left({P_i \over \rho g}\right)$^[9]

($h$ = peak height reached, $M_{i}$ = Initial mass of water only, $M_R$ = Rocket mass with water, $P_{i}$ = Initial gauge pressure inside rocket, $\rho$ = density of water, $g$ = acceleration due to gravity) Assumptions for the above equation: (1) water is incompressible, (2) flow through the nozzle is uniform, (3) velocities are rectilinear, (4) density of water is much greater than density of air, (5) no viscosity effects, (6) steady flow, (7) velocity of the free surface of water is very small compared to the velocity of the nozzle, (8) air pressure remains constant until water runs out, (9) nozzle velocity remains constant until water runs out, and (10) there are no viscous-friction effects from the nozzle (see Moody chart).

An independent variable that influences peak height is weight/mass. Depending on the thrust of the rocket propulsion system, a rocket requires a minimum mass to overcome the deleterious effects of drag. For example, the greater the thrust/the less the original weight of the rocket, the more weight or mass must be added to the rocket to insure maximum apogee. The mass is generally referred to as ballast. This principle is demonstrated by having a student throw a straw with and without a piece of clay attached to the 'nose' of the straw. The straw with the greater mass will travel further, provided that there is sufficient thrust to overcome the ballast or extra mass.

Competitions

The Water Rocket Achievement World Record Association^[10] is a worldwide association which administrates competitions for altitude records involving single-stage and multiple-stage water rockets, a flight duration competition, and speed or distance competitions for water rocket–powered cars.

Many local competitions of various sorts are held, including:

• In Scotland, the The Oscar Swigelhoffer Trophy is an Aquajet (Water Rocket) competition held at the Annual International Rocket Week^[11] in Largs or nearby Paisley, and organized by STAAR Research^[12] through John Bonsor. The competition goes back to the mid-1980s, organized by the Paisley Rocketeers who have been active in amateur rocketry since the 1930s. The trophy is named after the late founder of ASTRA,^[13] Oscar Swiglehoffer, who was also a personal friend and student of Hermann Oberth, one of the founding fathers of rocketry. The competition involves team distance flying of water rockets under an agreed pressure and angle of flight. Each team consists of six rockets, which are flown in two flights. The greater distance for each rocket over the two flights is recorded, and the final team distances are collated, with the winning team having the greatest distance. The winner in 2007 was ASTRA.
• In the United Kingdom, the largest water rocket competition is currently the National Physical Laboratory's annual Water Rocket Challenge.^[14][15] The competition was first opened to the public in 2001 and is limited to around 60 teams. It has schools and open categories, and is attended by a variety of "works" and private teams, some travelling from abroad. The rules and goals of the competition vary from year to year.
• In Germany, the oldest and most popular water rocket competition is the Freestyle-Physics Water Rocket Competition.^[16] (^[17]) The competition is one part of a larger part of a student physics competition, where students are tasked to construct various machines and enter them in competitive contests.
• In the United States, the Science Olympiad also runs water rocket event for elementary school age contestants.^[18]
• In Pakistan a water rocket competition is held every year in World Space Week by Suparco Institute Of Technical Training (SITT) in which different schools from all over the Pakistan take part.^[19]
• In Ukraine, a Water Rocket Competition^[20] is held every year in the Center for Innovative Technology in Education^[21] (CITE). and schools from all over the Ukraine take part. The design of the rockets is standardized.^[22] The competition promotes the selective collection of solid dry waste in schools.^[23]
• In Russia, Water Rocket.^[24]

World record

Apogee photograph taken by the onboard video camera from U.S. Water Rockets' record breaking X-12 Water Rocket at an altitude of 2,068 feet (630 m).

The Guinness World Record of launching most water rockets is in hands of Kung Yik She Secondary School^[25] when on 7 December 2013, they launched 1056 of them at the same time, together with primary school students in Tin Shui Wai, Hong Kong.^[26]

The current record for greatest altitude achieved by a water and air propelled rocket^[27] is 2723 feet (830 meters), held by the University of Cape Town^[28] which achieved the feat on 26 August 2015, beating the previous record of 2044 feet (623 meters) held by US Water Rockets.^[29] The rocket also carried a video camera as payload as part of the verification required by the competition rules.

Hot water rockets

A steam rocket, or "hot water rocket", is a very different device - a rocket that uses water held in a pressure vessel at a high temperature, and which generates thrust through this being released as steam through a rocket nozzle.^[30]

Bibliography

• D. Kagan, L. Buchholtz, L. Klein, Soda-bottle water rockets, The Physics Teacher 33, 150-157 (1995)
• C. J. Gommes, A more thorough analysis of water rockets: moist adiabats, transient flows, and inertials forces in a soda bottle, American Journal of Physics 78, 236 (2010).

References

1. Water Rocket Computer Model from NASA
2. Sim Water Rocket from Dean's Benchtop
3. Water Rocket Simulation from Clifford Heath's website
4. "The 'Crushing Sleeve' Staging Mechanism ", stemharmony.com
5. Dean's benchtop: hydrogen powered water rocket
6. Hydroflite: Rocket Science
8. "Super Roc Rocket Gliders", 2002, LUNAR.org
9. Schultz, William W. "ME 495 Winter 2012 Lecture." University of Michigan, Ann Arbor. Mar.-Apr. 2012. Lecture.
10. Water Rocket Achievement World Record Association
11. Annual International Rocket Week
12. STAAR Research
13. ASTRA
14. National Physical Laboratory's annual Water Rocket Challenge
15. Playlist
16. Freestyle-Physics Water Rocket Competition
17. Rangliste Wasserraketen
18. https://www.soinc.org/sample_k6_events#water
20. Oleksandr, Zahoruiko. "Фестиваль "Еко-техно-Патріо" E". ueeu.in.ua.
21. Александр, Загоруйко. "Центр інноваційних технологій освіти". ueeu.in.ua.
22. Олександр, Загоруйко. "Робимо ракети, озброєного робота та ліс Еко-дерев". ueeu.in.ua.
23. Олександр, Загоруйко. "Програма "ТЕРИТОРІЯ ІННОВАЦІЙ"". ueeu.in.ua.
24. >Юные техники
25. http://www.guinnessworldrecords.com/world-records/7000/most-water-rockets-launched-simultaneously
26. http://www.sphrc.edu.hk/birthday.htm
27. Single stage water rocket altitude record competition rules
29. U.S. Water Rockets
30. tecaeromex- steam rockets

External links

• The Water Rocket Achievement World Record Association – International association dedicated to the construction and safe operation of water rockets and the governing body for all water rocket world records.
• The equations describing the water rocket trajectory and a water rocket calculator based on these equations.