This booklet is written as an introduction to the essential concepts of water rocketry.
iii) Water rocket launchers, release mechanisms
iv) Nozzles
iv) Aerodynamic stability, fins, nose weights
vii) Measuring altitude
viii) Crash-worthiness, parachute recovery systems
x) Internet www sites, e-mail list
xi) Examples of water rockets, construction techniques
xii) History
xiii) Activities for schools
xiv) Appendix 1: Why does thrust = 2PA?
xv) Appendix 2: The Barrowman Equations xvi) Acknowledgements
xvii) Further reading
xviii) Glossary
* Only use bottles that are made to contain carbonated ("fizzy") drinks, other bottles are not made to withstand the pressures used with water rockets, the rectangular shapes in many non-carbonated drink bottles are deformed by pressure.
* Assume if it can go wrong it will go wrong. Bottles may explode. Poorly designed or incorrectly used launchers may tip over. Release mechanisms may fail, causing launches to occur spontaneously, or for the pressurised rocket to remain stuck on the launcher. An abort procedure should be rehearsed. Disconnecting the pump from a long air-hose extending from the launcher will allow the rocket to depressurise, provided the launcher and air-hose do not have valves prohibiting air escaping.
* In the US, Science Olympiad events do not use more than 75 psi or 500kPa pressure in 2 litre bottles. Smaller diameter bottles will withstand greater pressure, so are safer than 2 litre bottles at the same pressure. Damaged bottles may explode more readily than others. Nobody should be within a few metres of a pressurised bottle, this calls for a remote (eg. string operated) release mechanism. Exploding bottles are a rare occurrence if the above precautions are followed.
* Falling rockets may descend at great speed, possibly causing serious injury. Rockets should be fired away from observers. In Japanese distance competitions, launches are angled 60 degrees from horizontal. Everyone in the vicinity should be observing and be aware of what is about to occur, launches should be announced. If observers are made to wear bicycle helmets they will not only be safer but will see that the potential danger is a matter taken seriously.
* Cutting bottles can be dangerous. It is safest to make a small cut with a knife, allowing a scissor blade to be inserted, then use short-bladed blunt-nosed scissors to continue the cutting where desired. Adults may use knives for most cutting, but with children it is best to provide them with a bottle which already has a small knife-made cut, so they may continue with scissors.
Thrust:
Rocket thrust depends on both the nozzle size and the air pressure in the rocket. While water is being expelled, thrust is approximately equal to twice the product of the pressure and nozzle cross-sectional area. While on the launching tube, thrust is only half this (neglecting water expulsion between the sides of the tube and the bottle neck). (See Appendix 1 for an explanation generously provided by Bruce Berggren).
ie., during water expulsion phase:
Thrust = 2PA (twice the pressure multiplied by the nozzle cross-sectional area)
= 2*Pressure* pi *(nozzle radius)^2
= 2*P*pi*(0.5*nozzle diameter)^2
= 2*P*pi*0.25*(nozzle diameter)^2
= pi/2 * P D^2 (D = nozzle diameter)
= 1.57 * P * D^2
Units are newtons (N) for thrust, pascals (Pa) for pressure and metres (m) for diameter.
For example, consider an open-mouth rocket pressurised to 500kPa.
Pressure = 500,000 Pa, nozzle diameter = 0.022m
Thrust = 1.57 * 500,000 * 0.022 * 0.022 = 380 N
It should be noted that the above formula calculates the thrust provided at a certain instant, for a certain pressure. As water is expelled, the pressurised air inside the bottle expands, resulting is lowered pressure. Some people, including myself, may at first make the incorrect assumption that the air temperature remains constant, allowing for the next assumption of the product of pressure and volume to also remain constant, then reasoning that a 20% expansion in the volume of the air results in air pressure falling to 83% of the original, ie. 1 / 1.2 = 0.8333, or that doubling air volume will halve air pressure. However, rapidly reducing the air-pressure inside the rocket leads to a temperature reduction. Rockets may be seen to expel a fog of cold air at the end of their thrust phase (this is best observed with a slow-moving, restricted nozzle rocket). After landing fog is also often seen inside the bottle. The bottle is depressurised very rapidly, so it is more valid to make an assumption of adiabatic expansion, where Pressure * ( Volume ^ 1.4 ) = a constant, prediciting air-cooling during expansion. By this equation, a 20% increase in volume results in pressure falling to 77% of the original, ie. 1/ ( 1.2 ^1.4 ) = 0.7747. (Conversely, rapid pressurisation may heat the air in the bottle, possibly causing a rupture).
As water is expelled, thrust decreases due to the decreasing air pressure. This reduction in thrust may be compensated for by a reduction in mass due to the rocket carrying less water, so the acceleration may be greater with less thrust because the thrust acts on a lower mass.
Thrust duration:
Thrust duration depends on nozzle size, water volume, air pressure and air volume. Longer duration thrust can be achieved with a narrower nozzle, more water and/or lower pressure.
Air-pulse:
After the water has been expelled, the remaining pressurised air provides a brief but significant final thrust to the rocket. Clifford Heath's rocket simulation www page treats the air-pulse as an instantaneous acceleration occurring immediately after all the water has been expelled.
Rubber stopper:
A rubber stopper, with a ball inflation needle passing through, is placed in a bottle and air pumped into the bottle. At a certain pressure the stopper is forced out and the water inside the bottle is able to escape. The main weaknesses of this launching method is that the exact time of release cannot be determined and it is less efficient and does not provide the directional guidance of a launching tube (see below).
Garden hose fitting:
Quick connecting plastic household hose fittings may be used, acting both as a release mechanism and a nozzle. In Japan a commercially produced fitting is available, one end fits a PET bottle neck, the other a hose fitting, a similar nozzle can be home-made from a bottle cap and a part from a garden hose fitting. This release method enables the launch time to be controlled, but does not allow for an open mouth rocket, ie. the nozzle is restricted to the diameter of the hose fitting. A restricted nozzle produces more modest thrust but for a longer duration than an open mouth rocket. In Japan, these releases are often remotely operated with a bicycle hand-brake lever and cable.
Open neck launching tube launchers:
A launching tube launcher is made from a length of pipe (the launch tube) that passes up and into the bottle. The pipe should be as large a diameter as possible that will allow the bottle neck to slide along the pipe with little friction. When the rocket is released, the launching tube acts like a piston inside a cylinder, enabling the rocket to accelerate without expelling much water until it reaches the end of the launching tube, this increases the performance of the rocket when compared to a crude rubber-stopper style launcher. Use of a launching tube placed into the rocket as far as possible, results in the expelled mass, when the launching tube is still in the bottle, effectively being the entire earth. Because the rocket's mass is negligible compared with the earth, the rocket velocity alters greatly and the earth is unmoved. As the rocket accelerates the optimum fluid density decreases, due to the optimum exhaust velocity being equal in magnitude to the rocket's velocity (less dense fluids result in greater exhaust velocity). For maximum efficiency a magically decreasing-in-density fluid could be used instead of water, but this would only make a marginal difference. Using a launch tube provides a high density initial expulsion object, followed by less dense water and then followed by still less dense air. The launch tube also provides guidance to ensure the rocket commences travelling in the intended direction. This style of launcher requires the rocket to have an open mouth nozzle, producing greater thrust but for a briefer duration than a restricted nozzle rocket. A launching tube conserves water to provide additional thrust, effectively the rocket is launched at the end of the launching tube, by which time it may already be travelling at 15 m/s or more. The development, in 1997, of the T-nozzle by Scott Chestnut, enables an open mouth to be transformed into a restricted nozzle after leaving the launching tube. For this reason, I feel the launching tube style of launcher is the best option, allowing both open-mouth or restricted nozzles.
Following are some schematic diagrams for various release mechanisms used with launching tubes.
Following are some schematic diagrams for the construction of a launching-tube style rocket launcher.
A open-mouth nozzle, where water may easily escape, produces rapid, but brief, acceleration, at times lasting only a few hundredths of a second.
Restricted nozzles may be used to provide lower thrust for a longer duration, when compared with an open-neck nozzle. A restricted nozzle may provide more modest thrust and acceleration, but for up to several seconds duration. Restricted nozzles may be advantageous due to the rocket encountering lower drag at the lower speeds encountered (drag is proportional to the square of the speed), but this must be balanced against the greater work done in carrying water further aloft. For a certain rocket at a certain pressure and fill-ratio, there is an optimum nozzle diameter. As restricted nozzle rockets take longer to expel their water than open-mouthed rockets, much mass (water) is towards the rear of the rocket for a longer time, often enough time to create instability problems. A restricted nozzle rocket should be designed to be aerodynamically stable while still bearing water, ie. before the much of the water has been expelled. A cylindrical fin is ideal for use with a restricted nozzle, as the fin is positioned far back and has a large surface area, conventional fins used with a restricted nozzle also need to be larger and swept backwards more than with an open-mouth nozzle.
T-nozzle construction:
Scott Chestnut was the first person to build a T-nozzle. Below is my own approach to this concept, using alternate materials to those used by Scott. Also see the illustrations of my approach.
A nozzle from a caulking gun tube has its base adjacent to the screw fitting filed down so it only just fits through the neck of a PET bottle. Some nozzles can just be squeezed through without modification. The nozzle tip is cut in the appropriate position to obtain the desired nozzle diameter.
Around 4 or 5cm of PVC tubing, such as launching tube, is required so the nozzle will fit well-aligned in the bottle, directing the exhaust in the correct direction. The outer circumference of this tube should be a tight fit with the inner sides of the PET bottle neck, but allow easy insertion, the inner sides of the PVC tube should fit tightly with the caulking gun nozzle. Adhesive tape may be wound around the PVC tube and/or the caulking gun nozzle to reduce any gaps that occur between surfaces. One end of this tube should have a bevelled edge to prevent any difficulty in the T-nozzle entering the bottle neck.
A rubber washer is also required, the inner diameter should be slightly smaller than the widest part of the parallel sides of the caulking gun nozzle, the outer diameter should be substantially larger than the diameter of a PET bottle neck. The washer should be at least several millimetres thick. A rubber washer I have used successfully was obtained from the plastic screw fitting that attaches to a brass garden water tap, the washer sits between the brass tap and the plastic fitting. This washer has an outer diameter of 26mm, inner diameter 16mm and is 3.5mm thick.
To construct:
Push the caulking gun nozzle inside the bottle. Push the rubber washer inside the bottle, holding on to it with one finger so that the caulking gun nozzle can be shaken into a position enabling its narrow end to pass through the rubber washer. Now insert a length of launching tube into the bottle so that it may be used to push the rubber washer all the way up to the widest part of the caulking gun nozzle, pushing the nozzle against the inside base of the bottle. Now withdraw the launch tube and insert the small length of PVC tube and again use the launching tube to push the small length, unbevelled end first, onto the caulking gun nozzle so it abuts the rubber washer. The T-nozzle is complete and should fall in and out of position in the bottle neck, but be unable to exit the bottle.
One problem with a water rocket is that the water (usually the major component of mass) lies towards the rear of the rocket, so the empty front of the rocket tends to be dragged around to the side (like throwing a dart backwards) as the rocket moves through the air. Rapid disposal of this water, via an open-mouth nozzle may overcome this problem, not allowing enough time for the rocket to change course. Alternatively, with a more restricted nozzle, larger fins towards the rear of the rocket are required to counteract the turning forces created at the front. One solution to restricted nozzle stability is a cylindrical fin, consisting of an open cylindrical section from a bottle, trailing behind the rocket, connected by struts.
In order for stable flight to occur, these two properties, centre of gravity and centre of pressure (exterior pressure) are required to be arranged so that the centre of gravity (CG) is ahead of the centre of pressure (CP). An open-nozzle rocket may briefly have the CP ahead of CG, but due to the rapid expulsion of water the rocket does not have time to commence unstable flight, this is at least true for smaller PET bottles, larger bottles require larger fins even with an open nozzle, though not as large as with a restricted nozzle.
The aerodynamic stability of a rocket, or lack of stability, may be investigated in several ways. The CG can be found at a point on a bottle where it balances horizontally, like a balanced see-saw. Finding the centre of pressure (a point where the rocket would be balanced vertically if held in a strong wind) is less simple, but with practice, predictions can be reliably made by looking at the appearance of the rocket. A good example of an object with CG ahead of CP is a dart. Objects with CG ahead of CP will naturally fall so that CG leads CP towards the ground. A rocketry rule of thumb is that rockets should ideally have CG one or two rocket diameters (calibres) ahead of CP. To test a water rocket's stability (when empty), a swing-test may be performed, a string is attached to a point on the circumference closest to the CG (CG is in fact located in thin air inside the bottle), and the rocket swung around in circles (larger circles are better). If the rocket consistently travels nose-first then it is aerodynamically stable. However, the swing-test is conservative, some stable rockets will fail this test. A windows-based computer simulation, CYBERROC, may also be used to test a rocket's stability, this can be downloaded from:
http://sunsite.unc.edu/pub/archives/rec.models.rockets/CYBERROC/vcp164.zip
Fins:
Conventional fins: These may be constructed in many ways. The most important thing is to minimise the drag they create, by keeping them small and also thin, so they present a small frontal area to the direction of motion. The further towards the rear fins are placed, the more effective they are. Small fins far back may be as effective as larger fins further forward. A screw-on fin platform may be made from the threaded screw section of a plastic PET bottle top and a plastic 35mm film canister. The top of the bottle cap may be removed with a hack-saw, leaving only a cylindrical threaded section. This threaded section is inserted into a modified 35mm film canister. The circular base of a film canister may be removed by cutting a circle slightly smaller in diameter than the inner diameter of the canister, this leaves a small lip which prevents the canister passing over the inserted bottle cap. This screw-on platform should be used in conjunction with the small ring on the bottle which originally proved the bottle had never been opened, this ring prevents the canister moving forward on impact, leave it in place when using this fin platform. Fins can be constructed by folding PET bottle material taken from the cylindrically curved sides of bottles, folding the material so that the faces originally inside the bottle become the outer surfaces of the fin. The fins can be cut using scissors and held together with glue, staples or electrical tape. Electrical tape is also useful for attaching fins to the film canister, some adhesive gum on either side of each fin may help hold them perpendicular to the canister. Removable fins are convenient because they may be readily moved between different bottles.
Cylindrical fins:
A cylindrical fin may be the easiest way to achieve stability with a restricted nozzle rocket. This is a cylindrical section from a PET bottle, trailing behind the rocket, attached by two struts made from timber strips, integrated circuit anti-static containers, windscreen wiper blade inserts, rulers, or whatever is available. This cylindrical fin is open at both ends so that air may pass freely through it, but has a large surface area when placed side on, so the rocket's course is self-correcting and continues in a straight path.
As far as I know Clifford Heath was the first person to make a cylindrical fin for a water rocket, after I suggested it to him as a possible means of obtaining stability. Cliff attached his cylindrical fin with thin strips of timber and packing tape. Since then Scott Chestnut has used integrated circuit containers (long plastic square tubes) as struts. I have also used stainless steel inserts from car wiper blades, though they were probably too flexible and also often became bent on impact. A cylindrical fin is obviously impractical for a rocket which obtains thrust from burning gases, the fin would be incinerated. Fuel-burning rockets do not have the "water toward the rear" instability problem of water rockets. Cylindrical fins are useful because they are easy to make and, particularly with restricted nozzle rockets, they help to move the CP far towards the rear, even behind the nozzle if the fin is far enough back. More recently I have seen a World War 2 television documentary, showing cylindrical fin equiped bombs dropped from aircraft in training exercises in Australia. Obviously the cylindrical fin idea is not new.
Mass addition: Addition of nose mass is another way to move the CG ahead of the CP. Surprisingly (to me anyway, at first) heavier rockets will often reach higher altitudes due to their slower decceleration after the thrust has finished. This is similar to what occurs when a thrown foam ball is compared with a thrown tennis ball: similar drag acts on different masses, the heavier ball travels further.
Drag = 1/2 * Cd * A * air-density * Velocity^2
where drag is measured in newtons (N), Cd (coefficient of drag, a constant for a given object in a certain orientation) is a measure of "dragginess", A is the frontal area of the rocket, square metres, (m^2), air-density is measured in kilograms per cubic metre (kg/m^3) (air density is typically around 1.2kg/m^3) and velocity is measured in metres per second (m/s).
The above formula indicates that doubling velocity will quadruple drag, if we triple the velocity then nine times as much drag results. This is why it is difficult to go very fast through air.
A streamlined shape (reduced Cd) and/or low frontal area and/or lower velocities and/or lower air density will result in reduced drag.
Lowering Cd by streamlining: A nose cone made from the top section of a PET bottle may be connected to the base of a rocket, often just by pushing it into place. As well as improving aerodynamics, this also protects the base of the bottle from impact damage. A semi-elliptical nose shape is desirable, similar to the nose of a passenger jet.
A tennis ball, partly enclosed by a PET nose cone, may provide some crash protection for the rocket, aid stability by moving CG further forward and also be moderately well streamlined.
Adding adhesive putty may help further smooth the nose shape while also adding mass, in some cases further improving stability and maximum altitude.
A tear-drop shaped rocket, tapered towards the rear, like the rear of a passenger jet, will reduce Cd further. Clifford Heath has developed a method of altering the shape of PET bottles, his Guppy rocket may have a Cd as low as 0.15, similar to a passenger jet. Cliff's original method has now been modified, bottles may be thermoformed by pressurising them using a screw cap with a tyre valve inserted and pumping air into the bottle, hot hair blown onto the bottle will allow the heated parts to be stretched by the internal air pressure. With practice, bottles may be re-shaped into more aerodynamic forms. Compressed air stores much energy, an over-heated bottle may burst. Pressures should be kept as low as possible and the bottle should be secured firmly to an object to prevent it becoming airborne in the event of a rupture during thermoforming. This procedure is experimental and potentially dangerous.
Reducing frontal area: This requires using narrower bottles, so longer skinnier bottles are desirable for a given volume.
Reducing velocity: A restricted nozzle will result in lower thrust of greater duration, more modest acceleration, lower speeds and less drag, but also increases the weight of the rocket due to water being carried higher. An optimum nozzle size may exist for a certain rocket.
Lowering air-density: For most purposes, this cannot be achieved, though it is possible that the lower air pressure at high altitudes may have some effect. Certainly, a water-rocket launched in a vacuum, as on the moon or in space, would experience no drag at all.
While it is desirable to reduce drag, many of the actions taken to achieve this may have detrimental effects on other factors affecting rocket performance. Reducing volume will result in less overall thrust. Lengthening thrust duration with a restricted nozzle will lead to slower acceleration, but greater weight carried to a higher altitude. Optimal rocket design requires many design compromises to be made.
As mentioned in the stability section, a PC program, CYBERROC, may be used to test stability for various rocket designs. Cyberroc may be downloaded from:
http://sunsite.unc.edu/pub/archives/rec.models.rockets/CYBERROC/vcp164.zip
Timing the entire flight or just the descent tells you something, but drag makes things more complicated than they might appear. 4.9 * (descent time, seconds)^2 will give the upper possibility for altitude (in metres), this is how far something falls neglecting drag. I don't think it is too far out for heavy, low altitude rockets. For comparing similar rockets, the descent time will say which fill ratio or which launch went highest, but may not allow accurate measurement of apogee. Comparing flight times for different rockets may not be helpful in determining which reaches greater altitude, it is possible than the shorter flight time was at a greater average speed, a rapid ascent and descent may take a rocket higher than a flight of longer duration undertaken by a lighter, "draggier" and slower rocket.
Impact-resistant nose: A tennis ball nose provides protection to the bottle. See the streamlining section for an explanation of the tennis ball nose. A children's buoyancy aid, or other material, may be cut into a desired shape and will also provide impact protection. In Japan, a commercially manufactured foam nose-cone is available.
Parachute descents: Various means of deploying parachutes at or near apogee have been devised.
Nose falls off at apogee: Noses can be arranged so that they will stay in place during near vertical flight, but fall off when the rocket turns to commence descent. This method was developed in Japan by Dr. Michio Orii. An example of this method of parachute deployment, seen in Japan by Dave Johnson, can be seen at Dave's www page, the third picture down at:
http://www.geocities.com/CapeCanaveral/Lab/5403/tripreport.html
Balloon: Gary Ensmenger has used a small inflated balloon inside the nose cone, the balloon is squashed down during high-speed flight, as the drag force on the front of the rocket decreases the balloon expands, pushing the nose open and allowing the parachute to be released.
Air-speed flap: In February 1997, Dave Johnson first successfully used a self-designed air-speed flap system to release a parachute when rockets slow down near apogee. An air-speed flap is held down by the force of high-speed air currents, but springs open at apogee when a rubber band is able to overcome the then negligible wind force. The air-speed flap allows the rocket's nose-cone to swing open, releasing a parachute or payload with an attached parachute. Even without a parachute, but with an open nose-cone, a rocket may be unstable during descent, thereby having a much lower impact speed that otherwise. While on the launch-pad an air-speed activated trigger holds the air-speed flap down, the trigger is released once the rocket has attained a certain speed. Herve Bregent has also held the air-speed flap down with a paper-clip, pulled away after launch by a string attached to the launcher. See Dave Johnson's or Herve Bregent's www pages.
Clockwork timer: Bruce Berggren has used a clockwork mechanism from a toy to provide a time release for a parachute. After launch the clockwork device unwinds, a string wound around a rotating rod is released after a certain number of turns.
Bruce Berggren - crushing sleeve staging mechanism, construction tips, propped lever release, 1000ft Millennium rocket: http://www.geocities.com/CapeCanaveral/Lab/5402
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My favourite, and simplest rocket is made using a 660ml PET bottle. This rocket has removable fins and nose cone, allowing for easy interchange if the bottle becomes damaged. I have only ever retired these 660ml bottles as a precaution, they are very tough, surviving impacts on to sun-dried grass.
Part of a similar bottle is used as a nose. The nose cone is simply pushed into place, no glue or tape is required, a gum-nut (Eucalyptus seed capsule) is pushed into the neck to act as a nose weight and to improve the aerodynamics, a table tennis ball or rubber ball may serve the same function. This rocket comes down fast, so the nose cone must withstand large impact forces.
The fins can be made from any material that is easy to cut into shape, not too fragile, not too flexible and not too thick. The fins are attached to a cylindrical section from a 35mm film canister, as described in the conventional fin section.
Simulations indicate that this rocket, with an open mouth nozzle, should have considerable mass added to achieve maximum altitude, depending on air pressure and the drag coefficient (Cd). Higher air-pressure or higher Cd rockets will benefit most if mass is added.
2 litre rocket with cylindrical fin:
This rocket has a cylindrical fin cut from a similar bottle. The fin is attached with packing tape to the rocket body by two struts. Integrated circuit containers, light timber, plastic rulers or other materials may be suitable for use as struts. A tennis ball inside the nose-cone helps with both stability and crash-worthiness. With an open-mouth nozzle, screw-on fins similar to those on the 660ml rocket may be adequate, but with the cylindrical fin a T-nozzle may be used to investigate the flight characteristics of restricted nozzle rockets.
Fins:
Making fins: Many people use flat-sided sections from PET bottles, folding the material so that the concave surfaces are outermost, making a rigid and flat fin from two layers of PET (previously curved in opposite directions). Fins such as these can be attached to a screw-on film canister mount, the rocket body itself, or a cylindrical section joined at the sides of the rocket. See below:
Bruce Berggren, has expressed a preference for " 1/16 basswood fins attached with E6000 adhesive. Not interchangeable, but very thin and light, and just about impossible to destroy."
Attaching fins: Fins can be placed on a screw-on mount, the rocket body itself or a cylindrical section joined at the sides of the rocket.
Screw-on mount: Screw a cap onto a bottle, hold the bottle and, with a hacksaw, saw the top off the bottle cap, so that a threaded section is left. This threaded section may be placed inside a cylinder, such as a 35mm film canister, so that it makes a screw-on fin mount. The hole in the base of the film canister can be cut to equal the inner diameter of the threaded section, leaving a small lip, this way the film canister will not come away from the threaded section during launch, otherwise glue may be used.
Cylindrical mount: A cylindrical section is positioned at the rear of the rocket, fins are attached with tape, staples or glue. The cylindrical mount itself can be taped to the rocket body.
Attaching to rocket body: The fins are further forward this way, so not as effective as similar sized fins positioned further back. The fins may be attached with tape or glue, beware of glues that may weaken the pressure-containing bottle. This form of attachment has the disadvantage of fins being difficult to remove and place on another bottle if the rocket is damaged.
Children find the collaborative design and decision making a powerful learning experience. Concepts such as streamlining and stability are grasped by hands-on learning. Fins, nozzles and nose cones may be made from various materials, using very different approaches. Parachute attached payloads may be delivered into the air, providing yet another design and construction challenge.
also:
1. Consider a few of the following plants and animals and describe how you think they may or may not be structured to move in air or water.
Dandelion seed, tumbleweed, coconut, wedge-tailed eagle, feather glider, fruit bat, wombat, jelly fish, dolphin, hippopotamus.
2. Build a paper plane. Find where the centre of gravity is. Try moving the centre of gravity by adding one or more paper clips to different parts of the plane. How does it fly when the centre of gravity (CG) is in the middle? CG far forward? CG towards the back? Can you make it fly backwards?
3. As part of a team, see if you can make a PET bottle more streamlined, and move the centre of gravity forward of the centre of surface area. You may use adhesive gum and parts of other bottles for weight and streamlining material, fins may also be added to give more surface area. Think about the shapes and structures that animals have to assist them moving through air or water.
Parachutes may be made from old plastic bags, the large surface area and consequent high drag may be compared to the shapes of plants and animals, eg. wind-dispersed seeds, feather gliders, flying birds and mammal, jellyfish.
Parachutes may be deployed to either slow the descent of the entire rocket or that of a payload, such as a plastic figurine. The differing masses of these objects demonstrate the advantages of reducing mass when attempting to stay air-borne. The light-weight bones of birds, with honey-combed internal structures could be compared to those of terrestrial or marine mammals, where weight reduction is not an evolutionary priority.
Water rockets can be related to function and structure of living organisms, perhaps mostly by making students consider the way motion through air or water may be accomplished, and what features are desirable or essential.
Multi-stage rockets may be constructed, simulating the method used to place objects in earth orbit, or even to travel to the moon, planets or beyond the solar system.
1. Why does thrust = 2 * pressure * nozzle area ?
The following explanation was generously provided by Bruce Berggren, after I expressed my opinion that this relationship was not obvious to me, thinking thrust might only be half this value.
Bruce's explanation:
Yes, not intuitive at all. For those of us that use internal launch tubes, it implies that the thrust doubles when the last of the tube passes out of the nozzle. I suspect Gary has observed this when he had to 'help' his Big Bertha off the pad (see his web page).
The exit velocity of the water is given by Bernoulli's law:
Pressure = (1/2)(density)(Velocity)^2
so Velocity = sqrt(2P/density) (eq. 1)
Rocket thrust is given by Newton's second principle
Thrust = Time rate of change of Momentum
= (Velocity)(Mass rate of change)
= (Velocity)[(Nozzle Area)(Velocity)(density)]
= (Velocity)^2 (Nozzle Area)(density) (eq. 2)
Substituting the definition of Velocity from eq. 1, the density cancels
and the thrust is
Thrust = 2PA
i) angle of attack less than 10°
ii) air-speed well below speed of sound
iii) smooth air flow over rocket body
iv) rocket body is thin and long
v) rocket nose comes smoothly to point
vi) rocket has radial symmetry
vii) rocket fins are thin, flat plates.
Brad Calvert 27 June 1998.
Barrowman, Jim. 1970 Centuri TIR-33. (Reprinted in the March, 1998 issue of High Power Rocketry ("Centuri TIR-33: Calculating the Center of Pressure of a Model Rocket," by Jim Barrowman, p. 74).
Kagan, D., Buchholtz, L. and Klein, L. 1995. Soda-Bottle Water Rockets, The Physics Teacher, pp. 150-157, Vol. 33.
National Aeronautics and Space Administration. 1996. ROCKETS: A Teacher's Guide with Activities in Science, Mathematics, and Technology
Stine, Harry G. Handbook of model rocketry .......
Whole Earth News
Japanese books:
ISBN 4-575-28729-6
ISBN 4-88493-258-7
ISBN 4-526-02942-4
ISBN 4-575-28568-4
ISBN 4-88493-261-7
ISBN 4-337-33025-9
some of the above, and perhaps others may be available from:
Pet Bottle Craft Association
c/o Sayama Shiyakusko
1-23-5 Irumagawa Sayama shi
Saitama pref. Japan #350-13
Phone 0429-69-1710
Fax 0429-69-1707
or:
Pet Bottle Craft Association (Canada branch)
contact details obsolete and requested to be removed May 2006, maybe they still exist somewhere.
or:
http://www.bookservice.co.jp/english.htm
Bookservice Co. is a Japanese bookstore which accepts international orders
.
Acceleration: the rate at which velocity is increasing. The acceleration (m/s2) of an object is equal to the resultant force (N) acting on that object divided by the object's mass (kg).
Adiabatic expansion: circumstances where a gas, eg. air, expands without external heat entering the system. In the case of a water rocket, the compressed air expands very rapidly, so that heat entering the bottle is negligible during the gas-expansion phase. During adiabatic expansion:
Pressure * (Volume ^ 1.4) = constant
Air-speed flap: a hinged flap which is held down by the force of passing air until that force is reduced and no longer able to hold the flap down, allowing it to flip open and release a parachute or payload.
Altitude: the vertical distance, at a certain time, between an object and some other level such as the ground or sea.
Angle-of-attack: the angle between the long axis of the rocket and the relative wind speed. Launching in a cross-wind will lead to a non-zero angle-of-attack. Apogee: the maximum altitude reached during an object's travel
Atmosphere: sometimes air pressure is measured in atmospheres. One atmosphere is approximately equal to 101kPa or 14.7 PSI.
Barrowman equations: A set of equations developed in 1966 by NASA aerospace engineer Jim Barrowman. Barrowman's equations allow the small-angle-of-attack CP to be estimated. First published in 1970 as a report, Centuri TIR-33, they have more recently been reprinted in the March, 1998 issue of High Power Rocketry ("Centuri TIR-33: Calculating the Center of Pressure of a Model Rocket," by Jim Barrowman, p. 74).
Booster: a water rocket used to launch a second pressurised bottle (the sustainer), providing the sustainer with greater altitude and initial velocity than without the booster. The booster and sustainer are temporarily coupled by a staging mechanism, such as the Berggren crushing sleeve.
Calibre: the cross-sectional diameter of a rocket.
Cd: coefficient of drag, a constant, a measure of an object's ability to pass easily through air at a given speed. Low Cd values are desirable for ease of motion through air.
Centre of gravity: The point where an object can be balanced horizontally, like a balance scale. This may be demonstrated with by holding an object at the point where it balances. The centre of gravity (CG) depends on how the mass of an object is distributed.
Centre of pressure (CP): If an object was held at its CP and able to swivel about this point, it could be balanced vertically if held in a strong horizontal wind.
Circumferential splice: A method of joining two bottles at their circumferences.
CG: see centre of gravity
Conventional fin: a flat surface with low frontal area presented to the direction of motion, but greater area presented if motion is in an unintended direction. A non-cylindrical fin.
CP: see centre of pressure
Crushing sleeve: part of a staging mechanism, a flexible semi-elastic tube. When the booster is depressurised, the greater internal pressure in the sustainer compared to the booster forces the crushing sleeve to expand, thereby releasing the sustainer nozzle housed in the crushing sleeve and allowing the sustainer to commence providing thrust unencumbered by the larger and "draggier" booster.
Cylindrical fin: a fin made from a cylindrical section of a PET bottle or other material. Such a fin is held by struts so that it travels behind a PET rocket in such a way that the open ends of the cylinder allow air to pass freely through the cylinder while the rocket is travelling in the intended direction. Usually only one cylindrical fin trails behind a water rocket, but it is possible to use several attached to the sides of the rocket.
Deceleration: negative acceleration, ie. the rate at which velocity is decreasing. (See acceleration).
Drag: the force acting on an object due to the object's motion through air. Drag resists an object's motion through air.
Elevation (angle of): i) the angle between the line of sight at which an object is observed and a horizontal line. ii) the angle between a rocket prior to launch and the horizontal, eg. a vertical launch has a 90 degree angle of elevation.
Feet: plural of foot, a unit often used to measure altitude. One hundred feet = 30.48 metres (exactly).
Fill ratio: the ratio between water and air in a bottle, eg. a bottle one-half filled with water may be said to have a fill ratio of one-half or 50%.
Fin: a structure, usually used several at a time, intended to result in an object being aerodynamically stable. Fins present a low frontal area when an object is travelling in the intended direction, but will present a large area if the object travels otherwise. Also see Cylindrical fin.
Foot: singlular of feet, see feet. FTC: Flourescent Tube Cover, a plastic tube that protects flourescent tubes, also used to construct water-rocket sustainers.
Force: an influence, measured in Newtons (N), which is required to alter the velocity of a mass.
Frontal area: the area an object presents facing its direction of motion.
FTC tube: Fluorescent tube container tube. A clear plastic tube manufactured to protect fluorescent lights, these have also been used to make long and narrow water rockets.
Guppy: A rocket that has been thermoformed to be a low-drag streamlined shape.
kg: kilogram, a unit of mass.
kPa: kilopascal, a unit of pressure, see Pascal.
Launching tube: a tube that passes through a PET bottle neck and inside the bottle. The launching tube provides both guidance and additional thrust to a water rocket.
Mass: often confused with weight, however a certain object will have the same mass even in different gravitational fields. On the moon objects have the same mass but one-sixth as much weight. Throwing a brick through a window on the moon will do just as much damage on earth, the brick has the same mass, it will take as much force to accelerate the brick, but only one-sixth as much force to lift it vertically.
N: Newton, a unit of force.
Nozzle: the opening through which water and air escapes from a PET bottle after it has been released.
Pa: see Pascal
Parallel staging: a sustainer commences thrust at the same time as a number of boosters attached at the side. The boosters fall away when exhausted, the sustainer continues for a longer thrust duration. The US Space Shuttle launch is an example of parallel staging. See also: series staging.
Pascal: a unit of pressure equal to one Newton per square metre. Standard atmospheric pressure is 101325 Pa.
PET bottle: a plastic bottle made from polyethylene-terephthalate. These bottles are commonly used to contain carbonated drinks.
Propulsion: the process of propelling or forcing an object to move in a direction.
PSI: pounds per square inch, a unit of pressure. One atmosphere is approximately equal to 14.7 PSI. Relative wind speed: the wind speed as measured by an imaginary rocket passenger, ideally this is the exact reverse of the rocket's speed relative to the ground, but crosswinds may alter this, leading to a non-zero angle-of-attack. In still conditions, a cyclist travelling at 30km/h feels a relative wind speed of 30km/h, but windy weather will alter this.
Resultant force: the sum total of all the forces acting on an object. A PET rocket may have thrust, drag and weight due to gravity all acting simultaneously. Drag and gravity both act downwards during ascent but drag acts upwards during descent. During ascent, if thrust is greater than the sum of drag and weight, the resultant force causes the rocket to accelerate.
Robinson coupling: method of joining two pressure-containing bottles, base-to-base, using a threaded lamp-rod connector (a threaded pipe with two nuts tightened from inside the bottles). Named after Bill Robinson, the first person to use such a joining method, in January 1997.
Series staging: the sustainer does not commence thrust until the booster is exhausted. The two or more stages are used sequentially. Most satelite launch vehicles use series staging. Also see: parallel staging.
Speed: the rate at which an objects position changes, may be measured in metres per second (m/s), kilometres per hour (km/h) or other units.
Stability: An aerodynamically stable object passes through the air (or water) in one direction without tumbling end over end in a chaotic way. A gliding bird or a dart is aerodynamically stable, a football is not. To be aerodynamically stable, an object must travel so that its centre of gravity is positioned towards the front of the object, ahead of the centre of pressure.
Staging mechanism: a device, such as the Berggren crushing sleeve, which allows two previously connected PET bottles to decouple after one (the booster) has become depressurised, the second bottle (the sustainer) then commences thrusting. See also: parallel staging, series staging.
Streamlined shape: A streamlined shape, when travelling in a certain direction, experiences less drag than a similar-sized non-streamlined shape. A dolphin is streamlined, it travels more freely through water than does a non-streamlined jellyfish. Birds are more streamlined than terrestrial animals. Many cars use streamlined shapes to reduce drag so they will consume less fuel by passing more easily through the air.
Surface area: Surface area contributes to drag. If a large surface area faces into the direction of motion or wind, much drag is encountered. If motion in a certain direction is wished to be reduced, orientating surface areas to face in that direction will increase drag and reduce the motion in that direction. A paper plane has a low frontal surface area to reduce drag that would otherwise inhibit forward motion, but when observed from below has a large surface area, resisting downward motion.
Sustainer: a water rocket which has been launched using a booster rocket. After the booster is depressurised the sustainer is released by a staging mechanism and then commences thrust. Called a sustainer because it sustains its pressure until after the booster has been exhausted.
Swing-test: a test of a rocket's aerodynamic stability, conducted by attaching a string near the rocket's CG and swinging the rocket around in a circle.
Terminal velocity: The maximum speed attained by a falling object, occurring when acceleration ceases due to the drag force being equal and opposite to the weight force acting on the object.
Thrust: the force acting upon an object due to that object's propulsion system.
VCP: Visual Centre of Pressure, a freeware Windows computer program enabling the CP of a rocket to be determined.
Velocity: a speed in a specified direction, velocity occurs in a straight line. An object travelling in circular motion may have a constant speed but has a continuously changing velocity due to the direction component changing continuously.
