Water Rocket Notes

Section 1: What is a water rocket?

• A water rocket is essentially an upside-down fizzy drink bottle with a nose cone and fins.

  • Nose cone: Makes the bottle more aerodynamic and usually holds any payload (like sensors) or a parachute.

  • Fins: Help make the rocket stable and steer it during flight.

• How it works:

  • You add water to the bottle and connect it to a special launch mechanism.

  • Air is pumped into the rocket, building pressure above the water.

  • When triggered, the pressurized air forces the water rapidly out through a nozzle, propelling the rocket upwards.

  • Typically, the bottle is filled about one-quarter to one-third full of water.

• Performance:

  • Launch speeds can reach around $30\ \mathrm{m\,s^{-1}}$ (about $60\ \mathrm{mph}$).

  • Heights of more than $30\ \mathrm{m}$ are achievable.

• Safety note: Launching straight up can be dangerous, so angled launches are often safer.

• Extra: Parachutes are discussed as a safety option to slow descent.

Section 2: How to make a basic water rocket

• What you will need:

  • A two-liter fizzy drinks bottle (PET plastic is strong enough for pressure).

  • A tennis ball (about $60\ \mathrm{g}$) for the nose cone.

  • Corrugated cardboard or plastic (like Corriflute™) for fins.

  • Strong tape (e.g., duck tape) and scissors/knife.

  • About $30\text{ to }40\ \text{minutes}$ to assemble.

  • Optional: Decorations and a fun name.

• First steps:

  • Empty, remove labels, and rinse the fizzy drink bottle.

  • Attach the nose cone and fins.

• Nose cone:

  • Tape the tennis ball securely to one end of the bottle.

  • Weight at the front (like the tennis ball) helps with stability.

• Fins:

  • Cut three identical fins from corrugated plastic/cardboard.

  • Tape them firmly to the side of the rocket, towards the back.

  • Arrange them symmetrically, $120^{\circ}$ apart.

  • Fins should be thin when viewed from the front.

• Basic Design Critique: This rocket is a good starting point and flies stably, but it can be improved for better performance (Section 4 covers this).

• Example Rocket Details:

  • Volume: $2\ \text{L}$, Empty Mass: $171\ \text{g}$, Length: $0.45\ \text{m}$.

Section 4: Optimising Rocket Design

• Goal: To make each part of the rocket as good as possible for the best flight.

• Key Design Ideas:

  • Size (Volume):

    • More volume means more stored energy ($E \propto P V$ ).

    • Safe pressure is limited (around $5\ \text{atmospheres}$ or $75\ \text{psi}$).

    • Use larger bottles or join multiple bottles to increase volume and energy.

  • Weight:

    • Lighter rockets fly better. Avoid adding unnecessary weight.

    • Weight distribution is key for stability: The rocket is stable if its balance point (Centre of Mass, CoM) is ahead of where air pushes on it (Centre of Pressure, CoP). This helps it fly straight.

    • Estimating CoM: Balance the empty rocket on a string; the point where it balances is the CoM.

  • Fins:

    • Provide aerodynamic stability.

    • They help correct the rocket's direction if it starts to tilt.

  • Aerodynamic Stability Explained:

    • If CoM is forward of CoP, air forces help straighten the rocket (stable).

    • If CoM is behind CoP, air forces make it more unstable, causing it to tumble.

  • Estimating CoP: A rough way is to find the balance point of a paper cut-out (silhouette) of the rocket.

  • Drag:

    • Air resistance that slows the rocket, becoming important above $10\ \mathrm{m\,s^{-1}}$.

    • To reduce drag: Use a cone-shaped nose, a smooth and long/thin body, and thin fins placed at the very back.

  • Fairings:

    • Streamlined covers that reduce drag, especially where bottles are joined.

    • Can also strengthen the rocket or extend its length to improve stability.

  • Nozzle:

    • Converts the gas energy into the water's outward momentum.

    • Good nozzle design minimizes energy lost to friction or water spraying sideways.

    • Flow Impedance: The nozzle's opening size affects how fast water exits. Too small, and water might get trapped.

  • Multibottle Rockets (Joining Bottles):

    • Involves mechanically connecting bottles with pressure-tight connectors, washers, and sealant.

    • A fairing can be added over the joint for strength and aerodynamics.

  • Safety: Large multi-bottle rockets need strict pressure safety (see Section 8).

Section 5: Testing your Rocket

• Purpose of Testing: To collect information, analyze it, and improve your rocket's design (like engineers do!).

• What to Measure (Rocket Properties):

  • Empty rocket weight (kitchen scale).

  • Total volume (weigh empty, then full of water; $1\ \text{g}$ water = $1\ \text{cm}^{3}$).

  • Water volume (usually $20\%\text{–}30\%$ fill; mark this on the bottle).

  • Launch angle (often best around $45^{\circ}$ for farthest range).

  • Launch pressure (note pressure; stop at $5\ \text{atm}$ or $75\ \text{psi}$ if gains are only from drag reduction).

  • Fin configuration and other changes.

• What to Measure (Rocket Performance):

  • Ground Range (distance rocket travels horizontally).

  • Height (difficult; can use string method or data logger).

  • Time in air (use a stopwatch).

  • Launch Velocity (use frame-by-frame video analysis).

• Testing Guidance:

  • Safety first: Always read Section 8 before testing.

  • Bring plenty of water and tools.

  • Record everything you try and what happens.

  • Use a computer model (Section 7) to predict results.

  • Initial precision of $\sim5\%\text{–}10\%$ is usually fine.

• Experiment Ideas:

  • Repeat tests three times to check consistency.

  • Test with no water, then small amounts, to see the effect of water.

  • Launch in teams (e.g., Safety Marshal, timer).

  • Vary the launch angle and record range, expecting optimal range around $45^{\circ}$.

  • Use a simulator to visualize how different factors affect flight.

• Data Collection: A Water Rocket Test Sheet is available to help record results.

Section 6: Physics of a water rocket

• This section explains the launch physics using a vertical launch model for a 2-L rocket (empty mass $100\ \text{g}$, quarter-filled water).

• Example Parameters:

  • Empty rocket: $0.100\ \text{kg}$, Water: $0.500\ \text{kg}$, Total: $0.600\ \text{kg}$.

  • Initial pressure: About $4\ \text{bar}$.

  • Volume: $2\ \text{L}$.

• Launch Sequence (Simplified Timeline):

  • Start: Pressure reaches launch level (e.g., $4\ \text{atm}$ total).

  • $t \approx +0.01\ \text{s}$: Water starts leaving, rocket lifts, gas pressure and temperature drop.

  • After $0.1\ \text{s}$: Half the water gone, rocket height $\sim0.5\ \text{m}$, velocity $\sim10\ \mathrm{m\,s^{-1}}$, high acceleration ($\sim100\ \mathrm{m\,s^{2}}$ or $10\ \text{g}$).

  • After $0.22\ \text{s}$: All water gone, velocity $\sim26\ \mathrm{m\,s^{-1}}$, air cooled but still pressurized.

  • $0.25\ \text{s to } 5.4\ \text{s}$: Final gas pushes, maximum speed around $35\ \mathrm{m\,s^{-1}}$.

  • Cruise Phase: Only gravity and drag act; example height $\sim34\ \text{m}$ and impact speed $\sim20\ \mathrm{m\,s^{-1}}$.

• Flight Outcomes: Good design means stable flight; poor design can lead to tumbling.

• Key Physics Concepts:

  • Energy Storage: Energy in compressed gas is proportional to pressure and volume ($E \propto P V$).

  • Nozzle: Converts gas energy into water's momentum; efficiency matters.

  • Drag: Air resistance increases with speed and affects stability if the rocket is misaligned.

  • Centre of Mass (CoM) vs Centre of Pressure (CoP): CoM must be ahead of CoP for stability.

  • Silhouette Technique: A way to estimate CoP.

• Practical Notes: Drag is significant above $10\ \mathrm{m\,s^{-1}}$; nozzle and fairings are important for drag reduction and efficiency.

Section 8: Safety

• Water rockets are generally safe, but you must take precautions during building and launching.

• Sharp knives and blades:

  • Always cut away from your body/fingers.

  • Keep blades covered when not in use.

• Rocket design:

  • Avoid sharp points on the nose cone or fins.

  • Do not use external metal parts.

• Pressurized systems and pipes:

  • Launch systems are under high pressure and can create large forces.

  • Always wear safety spectacles and ear protection when the launcher is pressurized.

• Pressure limits and materials:

  • Only use PET bottles designed for fizzy drinks; other bottles are not strong enough.

  • The energy in large rockets is significant. Keep pressure below $5\ \text{bar}\ (75\ \text{psi})$ with new, undamaged bottles to avoid explosion risk.

  • Instead of increasing pressure, improve drag reduction for better performance.

• Launch procedure and environment:

  • Choose a safe launch site with plenty of clear space, away from people and animals.

  • Launch in teams with a Safety Marshal to watch the launch area.

  • Start with low pressures to get familiar with the