## Soda Bottle Rocket

posted on 15 Sep 2013 by guy
last changed 23 May 2017

 3.8 Average: 3.8 (10 votes) Select ratinghated itdidn't like itliked itreally liked itloved itCancel rating Your vote (click to rate)ages: 12 to 99 yrs budget: $0.00 to$25.00prep time: 0 to 60 min class time: 10 to 60 min This lesson gives instructions for a simple rocket that can be constructed out of a soda bottle and some alcohol in a matter of seconds. I also explain the basic principles of rocket propulsion (Newton's 3rd law) and offer some suggested design refinements, including a remote ignition system.
required equipment: plastic soda bottle, alcohol
optional equipment: rocket fins
subjects: Engineering, Physics
keywords: rocket, bottle, alcohol

Video showing Steve Spangler fire his ethanol rocket on Denver Channel 9 News.

## principles of rocket propulsion

Liquid fuel rockets have been around since the 1920's when the first one was built by Robert H. Goddard and his team (Figure 1), using a gasoline-oxygen mixture for fuel. The V2 rocket, developed by Werner von Braun and his team in the 1930's, used an alcohol-oxygen mixture for fuel. In this lesson, we construct a simple homemade version of an alcohol-fueled rocket from a plastic soda bottle, as Steve Spangler demonstrates in the video above.

All rockets operate off of the same basic principle, Newton's 3rd law, which states "for every action, there is an equal and opposite reaction". In the case of a rocket, a gas is heated to high temperature, and directed out the back of the rocket. As Newton's third law explains, while the rocket is pushing the gas out the back, the gas exerts an opposite recoil force on the rocket, pushing it forward. This force on the rocket is known as the "thrust".

It may seem counterintuitive to think that something as light as a gas can propel a Saturn V rocket (3000 metric tons) into outer space. However, the key is that a large rocket uses a large amount of gas released at very high velocity (typically several thousand meters per second — far in excess of the speed of sound in air).

For a rocket in outer space, the increase in rocket velocity for a given amount of emitted gas is determined by the conservation of momentum (which can be derived from Newton's 3rd law): $$m_{rocket}\Delta v_{rocket} = m_{gas}v_{gas}$$ where $m_{rocket}$ is the mass of the rocket, $\Delta v_{rocket}$ is the increase in its velocity, $m_{gas}$ is the total mass of the ejected gas, and $v_{gas}$ is its velocity. In the case of our little soda bottle rocket below, we would expect a 1-liter soda bottle (about 35 grams when empty) burning 8 g of alcohol with an exhaust velocity of 20 m/s (typical for a 1/4-inch nozzle — see under nozzle modification below) to accelerate to a velocity of about 4.5 m/s.

## details for geeks

There are two issues that complicate the calculation when applying the conservation of momentum to rocket propulsion. First of all, as the rocket uses up fuel, its mass decreases, so the expression for the mass of the rocket in the equation above ($m_{rocket}$) is not constant throughout the flight. The rocket is slower to accelerate right after the launch, when it is carrying all of its fuel, than it is later in the flight after it has shed some of its fuel weight. Secondly, even if the engine emits the gas at a constant velocity relative to the engine, the engine is speeding up with the rocket during the flight, so the velocity of the gas relative to the fixed stars ($v_{gas}$) is not constant either. In 1897, the Russian rocket scientist Konstantin Tsiolkovsky took account of these issues to derive1 the increase in velocity of a rocket, based on the exhaust velocity of the gas (relative to the engine) and how much fuel is consumed: $$\Delta v_{rocket} = v_{exhaust}\ln\left({M_{initial}\over M_{final}}\right)$$ In this equation, $M_{initial}$ is the total initial mass of the rocket, including fuel, and $M_{final}$ is the final mass of the rocket after the fuel has been used up. In the case of our 1-liter soda bottle, this predicts a final velocity of about 4.1 m/s.

When the rocket is traveling inside the atmosphere, there are two more complications to consider. First of all, there is air drag, which depends on the speed and cross-sectional area, as well as the precise shape and texture of the rocket2. Secondly, the thrust derives not only from recoiling against the emitted gas as Newton's law describes, but also from any pressure difference between the interior of the rocket (at the exhaust) and the external atmosphere. The usual expression for the thrust is: $$f_{thrust} = v_{gas}{dM\over dt} + (P_e-P_a)A_e$$ where ${dM\over dt}$ is the rate at which gas flows out the exhaust (in mass per time), $P_e$ is the gas pressure at the exhaust, $P_a$ is the atmospheric pressure, and $A_e$ is the cross-sectional area of the exhaust. The first term on the right side describes the recoil force from pushing the gas out the back, while the second term describes any additional push (or pull) from pressure differences between the exhaust and the atmosphere.

## the soda bottle rocket

All you really need for a homemade rocket is a soda bottle, some alcohol and a match. A true soda bottle is preferred, rather than a water bottle. Soda bottles are made of heavier plastic and are designed to hold up to carbonated pressure, which is convenient if you plan to use them for combustion chambers. The bigger the soda bottle the better. For fuel I prefer isopropyl alcohol, which is readily available at any drug store, although ethanol (ethyl alcohol) is also fine. A solution of 70% isopropyl will work, but 90% or more is better.

Pour a small amount of alcohol (1 or 2 teaspoons) into the soda bottle, cap and shake for one minute. The goal is to vaporize as much liquid as possible. The alcohol vapor is the explosive fuel that will be used; liquid alcohol burns too slowly for our purposes. When the alcohol has vaporized as much as possible, pour out the excess liquid. Any liquid alcohol that remains in the bottle may spew out during ignition, leaving a somewhat hazardous blazing trail behind ... but maybe this is something you want?

Remove the bottle cap, lay the bottle on its side on a smooth table, put on your safety glasses, and hold a match up to the mouth of the bottle. The alcohol vapor should ignite and come rushing out of the bottle as it heats and expands. As the gas rushes out the back, the bottle should recoil forward.

WARNING! As you ignite the rocket, keep your hand to the side of the bottle, clear of the mouth. A long neck barbecue lighter works better than a match for this purpose.

### bottle size

If you're using a 1-liter bottle or smaller, you may discover that even though the gas ignites and rushes out the back with an audible whooshing sound, the rocket does not move forward. The thrust is not big enough to overcome friction with the table. Rather than look for a smoother table, try using a larger bottle. Changing from a 1-liter bottle to a 2-liter bottle doubles the fuel volume, and increases the pressure in the combustion chamber, with only a modest increase in rocket mass (from about 35 grams to about 50 grams), thereby improving the thrust-to-weight ratio.

### nozzle modification

For bigger thrust and a faster rocket, we want to increase the pressure in the combustion chamber so that the gas comes out the nozzle at higher velocity, and the rocket recoils faster. For the bottle rocket, this means narrowing the exhaust opening so that the gas has a harder time getting out, and the pressure inside the bottle rises. When the gas does come out, it will be traveling at a faster speed3 (more than making up for the smaller opening through which the gas must travel), and the corresponding thrust will be bigger.

To accomplish this feat, drill a hole in the center of the bottle cap, 1/4 inch to 3/8 inch diameter, and screw the cap on tight. Don't use a hole smaller than 1/4 inch; the pressure may build high enough to make the bottle explode.

Even a bottle that barely moved without the modified cap will now take off like ... well, a rocket.

### nose cone

The bottom end of a soda bottle is pretty blunt, and it causes a fair amount of air drag when used as the nose of a bottle rocket. To get something a little more aerodynamic, try cutting off the top of another identical bottle and fit it over the nose of your rocket. A paper nose cone glued or taped to the bottle has also been known to work.

So you'd like send a rocket up vertically rather than horizontally. A ring stand works very well for a launch pad (Figure 2).

If you don't have access to a ring stand, two parallel rails tilted up at an angle of about 20o can serve as a good launch ramp. Most any smooth pipe or rod will work, or try a piece of rain gutter. I like to use two broomsticks because it's even more spectacular when the straw catches fire during launch.

### remote ignition

Mike at The Geek Pub has developed an ingenious design for a remote starter using a piezoelectric barbecue igniter and some PVC pipe. If you're going to be supervising many launches, you should definitely check out his instructions.

## trouble shooting

Your rocket doesn't ignite, or is very hard to ignite. This is likely an issue of poor vaporization. Try shaking the alcohol in the bottle for a longer period before trying to light it. Temperature may also be an issue. Ignition should be pretty easy at 15oC (60oF), but at 4oC (40oF) there are often problems with the alcohol condensing too much in the bottle. If you have previously launched the same bottle, you may have little oxygen left in the bottle. Be sure to store the bottle upside down with the cap removed for at least an hour so that any carbon dioxide (which is heavier than air) flows out of the bottle and fresh air flows in.

Your rocket ignites but doesn't go anywhere. You need more thrust. Try a larger bottle, and especially try the nozzle modification suggested above.

Your rocket blows to smithereens on the launch pad. The exhaust hole was probably restricted or blocked. I told you not to use anything smaller than a 1/4 inch opening.

Your rocket flies, but erratically, and never in a straight line. If you used the modified nozzle above, the drill hole may be off center. It has to be dead center for a straight flight. Attaching some fins to the side of the bottle may help stabilize it. Nice foam fins can be found for water bottle rockets that work well. The fins on the rocket in figure 2 came from a water rocket kit. See the link under "optional equipment" at the top of the page for suggested manufacturers.

## question to ponder

• Even if I pour out all the excess alcohol before ignition, afterwards there is still some liquid in the bottle. What is it?

The liquid left in the bottle after ignition is most likely water, maybe mixed with some unburnt alcohol. During combustion, isopropyl alcohol ($C_3H_7OH$) will combine with oxygen in the air to produce carbon dioxide and water according to the chemical equation $$2C_3H_7OH + 9O_2 \rightarrow 6CO_2 + 8H_2O + heat$$

## teaching notes

Any lesson based on rockets almost always comes with some misconceptions in students' minds.

One common confusion is that rockets need something solid to push against. (In fact, they push against the exhaust gas, which supplies the necessary thrust.) Start by asking your students what a rocket pushes against when it takes off. Odds are, some of them will say the launch pad. (Even undergraduate engineering majors make this mistake.) Next, ask them what a rocket pushes against when it is in outer space. That question will slow them down and give you a 'teaching moment'.

Another common misconception is that rockets are inherently unstable in response to small disturbances. Many folks imagine that a rocket taking off is like a pencil with a finger underneath pushing it upward. If the pencil tilts even a tiny bit, the upward thrust of the finger will cause the pencil to flip over. In the 1920's, prior to modern rocket development, a number of scientists who should have known better were thinking a rocket behaves the same way. In fact, when a rocket tilts the thrust is no longer upward like it is with the finger, but instead tilts with the rocket. When a rocket tilts, the engine tilts with it. The rocket will no longer be headed upward — it will fly off in the new direction — but it will not be inclined to flip over. A rocket will only flip if the engine is misaligned and the direction of thrust does not line up with the center of the rocket.

• 1. Robert A. Braeunig offers a clear and concise derivation of Tsiolkovky's equation at http://www.braeunig.us/space/propuls.htm (equ. 1.17).
• 2. A generic but lucid discussion of air drag can be found in The Physics Hypertextbook at http://physics.info/drag/ .
• 3. The exhaust speed is determined not by the absolute pressure in the combustion chamber, but by the pressure difference between the combustion chamber and the external atmosphere. If the initial pressure difference is small, a modest increase in combustion chamber pressure can lead to a large fractional increase in the pressure difference.