Abstract

What does it take to launch a robot to Mars or for a satellite to explore our outer solar system? In this project you will explore the physics of a rocket as you predict its performance, launch it, and measure the actual results. This is rocket science!

Objective

Launch a model rocket with different engines, predict its performance, and measure how high it actually goes.

Introduction

Model rockets come in a variety of shapes and sizes (Figure 1). A basic model rocket consists of the rocket's body, the nose cone, a recovery system (like a parachute), the fins, and the engine (also called the motor or propellant), along with some additional components, as shown in Figure 2. You can safely launch low-power model rockets from a field using a launch system like the one shown in Figure 3. If you are new to model rocketry, you should review the "New to Model Rocketry?" guide by Apogee Components in the Bibliography before you proceed. The rest of this introduction will explain the physics of model rocket flight and how you can take measurements of a rocket's flight for your science project.

Model rocket flight is broken up into three phases (Figure 4). During the boost phase, the rocket's engine burns propellant, which generates thrust and pushes the rocket upward. During the coast phase, the engine has burned out, but the rocket continues to fly upward due to the high velocity it achieved during the boost phase. The highest point of the rocket's flight is called the apogee. Finally, during the recovery phase, the rocket slowly falls back to the ground. The descent is typically slowed by something like a parachute or streamers, although some rockets may be designed to tumble or glide back to the ground.

Electronic sensors can help you measure different aspects of your rocket's flight. An accelerometer is an electronic sensor that measures acceleration. An altimeter is an electronic sensor that measures the rocket's altitude by measuring barometric pressure. If your rocket has a payload bay (Figure 5), you can mount a sensor inside your rocket and it will record information about the flight. Altimeters require static ports, small holes that are drilled in the payload bay so air pressure inside the bay will equal the outside air pressure (Figure 6).

Different electronic sensors record different information. For example, some sensors record certain values that characterize a flight, like the apogee, along with maximum and/or average accelerations, the flight duration, or the amount of time between different points in the flight, like the burn time (how long the engine burns before running out of propellant) (Figure 7). Other sensors may continuously log data throughout the entire flight, producing graphs of altitude and acceleration vs. time when the data is downloaded to a computer or displayed on a smartphone (Figure 8). Either type of sensor should work for measuring the maximum altitude in this project.

We have briefly covered how you can measure rocket flight, but how can you predict a rocket's motion? You are probably familiar with Newton's second law of motion, which is commonly expressed in equation form as:

Equation 1:   $F \:=\: ma$

where

• F is force, in newtons (N)
• m is mass, in kilograms (kg)
• a is acceleration, in meters per second squared (m/s²)

In high school physics problems, Newton's second law is usually applied to objects with constant mass (for instance, the classic example of a force pushing a block on an inclined plane). However, that presents a problem when applied to rockets: their mass is not constant! Rockets expel high-velocity exhaust in one direction, which pushes the rocket in the other direction due to conservation of momentum. As the engine burns and expels fuel, its mass decreases; therefore, rocket motion is modeled mathematically with the Tsiolkovsky rocket equation (see Bibliography), which takes the rocket's changing mass into account. This equation is extremely important for real rockets that fly into space. Reaching orbit requires so much fuel that the majority—nearly or sometimes exceeding 90%—of a rocket's mass at launch is fuel (this ratio is called the propellant mass fraction).

However, the propellant mass fraction is much lower for model rockets. For example, the model rocket at the bottom of Figure 1 (the Apogee Apprentice) has a mass of 60.8 g when loaded with a new A8-3 model rocket engine, and a mass of 54.9 g with a used engine (we will discuss model rocket engines and what the letters and numbers mean below), a difference of 5.9 g. Less than 10% of the rocket's weight at launch is propellant. This means that you can roughly predict a rocket's maximum height using a simplified equation that assumes the rocket's mass is constant. This height is the sum of the height the rocket reaches at the end of its boost phase plus the additional height it gains during the coast phase.

Equation 2:   $h_{max} \:=\: \frac{1}{2}a_{boost}t_{boost}^2 \:+\: \frac{v_{max}^2}{2g}$

where

• h_max is the rocket's maximum height, in meters (m).
• a_boost is the rocket's acceleration during the boost phase, in meters per second squared (m/s²).
• v_max is the rocket's maximum velocity, which is achieved at the end of the boost phase, in meters per second (m/s).
• g is acceleration due to gravity, which is 9.81 meters per second squared (m/s²). Note: Do not plug negative 9.81 into the equation, the minus sign is already accounted for.

To solve for the maximum height in this equation, first you need to find the boost phase acceleration, a_boost, and the maximum velocity, v_max. The average acceleration during the boost phase can be calculated using Newton's second law (see technical note):

Equation 3:   $a_{boost} \:=\: \frac{T_{avg}}{m_{avg}}-g$

where

• a_boost is the rocket's acceleration during the boost phase in meters per second squared (m/s²)
• T_avg is the engine's average thrust in newtons (N)
• m_avg is the rocket's average mass in kilograms (kg)
• g is acceleration due to gravity, which is 9.81 meters per second squared (m/s²). Note: do not plug negative 9.81 into the equation, the minus sign is already accounted for.

The maximum velocity can be calculated using the equations of motion for constant acceleration (see Technical Note):

Equation 4:   $v_{max} \:=\: a_{boost} t_{burn}$

where

• v_max is the rocket's maximum velocity, in meters per second (m/s).
• a_boost is the rocket's acceleration during the boost phase, in meters per second squared (m/s²).
• t_burn is the engine's burn time, in seconds (s).

You can measure the mass of your rocket yourself, but where do you find out the engine thrust and burn time? You will need to look up that information from the manufacturer (note: information from the manufacturer may not always be 100% reliable, but it is a good place to start. See the Technical Note about rocket engines for more details). For example, look at this page for the popular Estes A8-3 engine and click on "Technical Specifications." You will see that it lists a "Total Impulse" of 2.50 N-sec and a "Thrust Duration" of 0.50 sec (thrust duration is another way of saying "burn time"). An impulse is a force that is applied for a certain amount of time. If you know the total impulse and amount of time, you can calculate the average force using this equation:

Equation 5:   $J \:=\: F_{avg} \Delta t$

where

• J is impulse, in newton-seconds (N-s).
• F_avg is average force, in newtons (N).
• Δt is change in time, in seconds (s).

See the Technical Note for the full derivation of these equations. Even if you do not understand all the physics to derive the equations yourself, you should understand that it relies on a few assumptions:

• As discussed above, the physics assumes the rocket's mass is constant. It ignores the change in mass due to the engine burning propellant.
• It ignores air resistance.
• It assumes the rocket moves straight up in a vertical line. It ignores any horizontal motion due to wind or launching the rocket at an angle.

That is a lot of information to absorb! Take your time to review this introduction, the references in the Bibliography, and the terms and questions before you proceed. Once you have done so, you should be prepared to do a science project with independent and dependent variables involving a model rocket. For example, you can test different rocket engines with different total impulses. You can predict your rocket's maximum height using Equation 2, measure its maximum height using an altimeter, then compare your theoretical and experimental results. For other ideas, see the Variations section. Now, get ready to do some rocket science!

Terms and Concepts

• Nose cone
• Recovery system
• Fins
• Engine
• Boost
• Thrust
• Coast
• Apogee
• Recovery
• Accelerometer
• Altimeter
• Payload bay
• Static ports
• Burn time
• Newton's second law of motion
• Conservation of momentum
• Tsiolkovsky rocket equation
• Propellent mass fraction
• Impulse
• Constant acceleration equations
• Delay time
• Ejection charge

Questions

• Which forces act on a model rocket during flight?
• What factors influence the maximum height that a rocket will reach?
• How can you use math and physics to predict a rocket's maximum height?
• How can you measure a rocket's maximum height?
• What do the letter-and-number labels on a model rocket engine mean?

Materials and Equipment

You will need to decide exactly what to purchase for this project based on your budget, how many trials you want to do, etc. There are multiple options, so we did not write the instructions for a specific model of rocket or altimeter. Model rocket supplies are available at many hobby stores. Supplies are also available from Estes Rockets and Apogee Components . Remember to review the "What All Do I Need For a Model Rocket Launch?" section on the New to Model Rocketry? page if you are new to model rocketry and not sure what supplies you need, but here is an overview:

• Model rocket with payload bay
• Altimeter
  • You will need mounting hardware or tape to attach the altimeter inside your rocket's payload bay (check manufacturer recommendations).
  • Make sure you buy an altimeter that is intended for use with model rockets and will fit in your rocket's payload bay. Such altimeters are typically only a few centimeters long and may only weigh a few grams.
  • Most model rocket altimeters will record maximum altitude. Some will record additional data. Make sure you understand what data your altimeter will record and how you will access it. For example, does the altimeter display the data on a built-in screen, connect to your phone, or do you need to download the data to a computer?
• Launch controller and launch pad
• Engines (at least 3 of each type you plan to test). A-sized engines are best if this is your first model rocket project. Your rocket will not go as high, but it will be easier to recover. For example, you could compare Estes 1/2A6-2 engines to Estes A8-3 engines. B-sized engines and above are best for students who already have some experience with model rockets and access to a larger launch site.
• Recovery wadding
• Tools and supplies for assembling your rocket. You will need to read the manufacturer's instructions for your rocket, but these typically include a hobby knife, ruler, pencil, wood glue, and plastic cement or superglue.
• Materials to finish, paint, and/or decorate your rocket, such as sandpaper, spray paint, and stickers
• Kitchen scale to weigh your rocket, with at least 0.1 g sensitivity
• Large, open field free of obstructions like trees and power lines in which to launch your rocket. Refer to the Model Rocket Safety Code for required launch site dimensions.
• Helpers can be useful when launching the rocket, such as a spotter to carefully watch where the rocket lands or to take photos/video from a distance while you operate the launch controller
• Lab notebook

Experimental Procedure

Global Connections

The United Nations Sustainable Development Goals (UNSDGs) are a blueprint to achieve a better and more sustainable future for all.

Variations

Careers

If you like this project, you might enjoy exploring these related careers:

Related Links

• Science Fair Project Guide
• Other Ideas Like This
• Physics Project Ideas
• Space Exploration Project Ideas
• My Favorites

Cite This Page

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

MLA Style

APA Style