paper helicopter experiment hypothesis

Paper Helicopter Experiment

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A paper helicopter experiment is a fantastic hands-on, and low-budget way for students to explore cause and effect relationships in experimental design. These models offer teachers easy STEM activities with paper and generate authentic data in the classroom. In fact, there are so many paper helicopter materials, lessons, and instructions online, it’s hard to know where to start!

Simple quantifiable scenarios can be examined and several criteria for success can be defined and explored. Paper helicopters provide educators with easy-to-do experiments to help students learn the scientific method.

The ASTC Science World Society concisely explains the many levels of inquiry teachers can offer students when conducting paper helicopter experiments. These levels of investigation range from more structured to less structured which suits various grade levels and abilities.

Paper helicopter lessons with more structure would generally target lower grade levels. More open assignments are suitable for independent students at the higher grade levels where the teacher acts as a facilitator. Teachers of all experience levels can take advantage of the learning opportunities provided by experimenting with paper helicopters.

Paper Helicopter Lesson Outline

The specific paper helicopter lesson outlined in this blog post targets students in upper elementary and middle school. It can be extended above and below these grade levels as well. This lesson covers methods of data gathering and provides teachers with easy-to-use activity resources.

This paper helicopter experiment is a simple introduction to experimental design and will target this testable science question:

Does changing the blade length of a paper helicopter affect how long it stays in the air? (Keep reading, however, this question needs a bit of clarification.)

The NGSS Standards do apply! Examples:

• 3-5-ETS1-3 Engineering Design – Plan and conduct an investigation collaboratively to produce data to serve as the basis for evidence, using fair tests in which variables are controlled and the number of trials considered.
• MS-ETS1-2 Engineering Design – Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

How Does a Helicopter Work?

In basic terms, an actual helicopter is a type of aircraft that creates lift (an upward force of air) with horizontally spinning rotor blades. These rotor blades are sometimes referred to as simply rotors or blades.

The physics of paper helicopters are different from real helicopters. Traditional paper helicopters do not use a power source to spin their blades and create lift. These models are typically created with two blades and dropped from a fixed height and spin as they descend.

Paper helicopters spin because of the earth’s gravity, lift, and configuration of the rotors. When dropped, the helicopter’s mass experiences gravity, and it naturally falls to the floor which causes paper blades to bend slightly upward due to lift. The lift force of the air pushes on each of the blades equally but in opposite directions, horizontally and vertically. As a result of the horizontal equal, opposite, and offset forces, the helicopter spins around as it descends.

The helicopter descends due to unbalanced forces: The weight of the helicopters is greater than the lift force of air.

2BrokeScientists studied the airflow around a helicopter and found that there were high-pressure areas under the blades. This high pressure results in equal and opposite opposing forces that cause the spin.

Framing the analysis in terms of Newton’s Third Law of Motion , a pair of equal and opposite forces acting horizontally under each blade and on the body of the paper helicopter cause rotation.

Simple Paper Helicopter

A simple paper helicopter can be made easily at home or school. Multipurpose U.S. letter-size printer paper (8.5 x 11 inches, 21.6 x 27.9 cm) works well for the model. The design is simple to make with only a few cuts and folds, and its parts can be easily adjusted to examine changes regarding flight behavior. To conduct the paper helicopter experiment, we should know the parts first!

Paper Helicopter Parts

The paper helicopter parts are similar to a real helicopter’s parts. The common paper helicopter with two blades has four major parts:

Blades – These two parts are identical rectangles arranged vertically at the top of the helicopter. These parts are sometimes called rotors , blades , rotor blades , wings , or even propellers . The blades provide the lift and are factors that cause the helicopter to spin. The width of the two blades together equals the width of the paper template used to make the helicopter. The thickness of the blades is one layer of paper.

Body – The top of the body of the paper helicopter connects to the blades. The body shape is a rectangle and is perpendicular to the blades. It is located between the blades and the tail. It is as wide as the paper template used to make the helicopter. The thickness of the body is one layer of paper.

Tail – The top of the tail connects to the bottom of the body. The thickness of the tail is three layers of paper. The width of the paper helicopter tail is one-third the width of the template. The tail provides the paper helicopter flight stability.

Stabilizer – The stabilizer is essentially the bottom tip of the tail. A horizontal fold in the tail creates the stabilizer. This fold also provides the paper helicopter flight stability by shifting the model’s center of mass downward.

Independent, Dependent, and Controlled Variables

The paper helicopter experiment requires that you control some variables, change others, and look for cause and effect. A variable is a characteristic or quantity that can be measured or counted in an experiment. Most experiments for this age group account for three kinds of variables: independent, dependent, and controlled.

Independent variables are manipulated by the researcher. These variables are changed and studied to determine if they are the cause in a cause-and-effect relationship. Independent variables are not influenced by other variables. Sometimes independent variables are not manipulated by the researcher but monitored to see how their changes may affect other variables. For example, time (seconds, days, years) is an independent variable that can be tracked to see how it may affect other variables (e.g., the growth of a plant).

Dependent variables are what researchers observe, measure, or count in an experiment. Changes in dependent variables depend on various influences. Independent variables are factors that may change a dependent variable.

Why are Variables Important in an Experiment?

That’s the point of an experiment: To find out what may or may not influence a dependent variable! These types of variables are the “effect” in a cause-and-effect relationship.

Controlled variables are variables that the researcher does not allow to change. The variables are maintained to be constant so that they do not influence any of the dependent variables. Variables that are kept the same for every measurement and test in an experiment, ensure that the dependent variables produce data that are as accurate as possible.

Knowing variables’ roles helps researchers be systematic with their observations, accurately collect relevant data, and be logical with their scientific thinking.

How Do You Make a Paper Helicopter Fall Slower?

A common problem to examine is how to make a paper helicopter fall slower. In other words, many paper helicopter designers want to know how to make a paper helicopter that stays in the air the longest. A simple two-rotor paper helicopter is a good design choice to study this common problem.

The researcher can manipulate any of the four helicopter parts to determine what factors affect the flight time of a paper helicopter. By adjusting a part of the helicopter, researchers are manipulating the independent variable to determine if this change affects the time the helicopter stays in the air (time in the air is the dependent variable). Parts of the helicopter that do not change from a standard model to an adjusted model, are considered control variables.

Paper Helicopter Variables

To ensure that testing is fair so that cause-and-effect data are a reliable source of information, the three types of paper helicopter variables need to be defined. For our paper helicopter experiment example, the independent, dependent, and controlled variables are identified as follows.

I ndependent Variables :

• blade length (which changes the body height)
• body height (which changes when the rotor blade length is adjusted)

Dependent Variable :

Controlled Variables (Helicopter Parts):

• rotor blade width and thickness
• body width and thickness
• tail length, width, and thickness
• stabilizer length, width and thickness

Controlled Variables (Materials and Conditions):

• paper size and mass
• drop height
• drop start time

From a persnickety perspective, there are more variables to control like the angle between the blades and the body. This should be 90 degrees by the way. How deep you go as far as what variables are controlled–what you look at–depends on the students’ age group and experience.

By taking into account the types of variables in an experiment, our actually scientific inquiry question for the paper helicopter experiment is:

Does changing the blade-length-to-body-height ratio of a paper helicopter affect how long it stays in the air?

It’s important to note that since paper helicopters easily offer many cause-and-effect relationships to explore, students may eagerly start changing parts of the helicopter to see what happens–how flight changes. Once students get their hands on a template, without focused guidance, teachers may see many different configurations, and helicopters being thrown up into the air.

The time to be creative with designs to more freely explore flight dynamics is after a procedural scientific experiment is conducted.

Paper Helicopter Experiment Considerations

If you are conducting the paper helicopter experiment in a classroom, you will need to set up a testing area. Two paper helicopter models are needed as well to explore how to make a paper helicopter fall slower. It may be easiest to refer to each model by their blade lengths: shorter-blade model and longer-blade model.

The student tester usually holds the completed helicopters away from their body and just above their head while standing on a chair. This drop distance is sufficient for comparing two different helicopters. Make sure there is enough clearance between the tester and any objects or observers to not interfere with the paper helicopters’ descent (i.e., to avoid introducing unwanted variables).

Having multiple students drop the two different helicopter types from the same height and at the same time can provide a simple and solid experimental design.

Here’s an example from NASUWT showing three students testing paper helicopters at once:

How Many Trials Should a Good Experiment Have?

What is a trial in a science experiment? A trial is one of many tests that make up the experiment itself. For example, each time you drop the paper helicopter from a fixed height to see if increasing the blade length increases how slowly a paper helicopter falls, you are conducting a trial.

We want a good experiment–one that offers fair testing and produces not only accurate data but lots of accurate data. The more trials we have, the more evidence we have that random factors are not influencing the outcome.

Other ways to think about the role of trials are: How many trials in an experiment should you conduct to get valid results? How many trials are required to validate a hypothesis? We want the results to truly represent what we are investigating.

So, how many trials should a good experiment have? As many as possible. Three trials minimum seems to be a consensus. With easy-to-test paper helicopters, students can conduct many trials in a short period of time. Multiple helicopters can be tested at once as well. With a design such as the aluminum foil boat investigation , fewer trials are possible because it takes more time to prepare and test.

How to Collect Data in a Science Experiment

If you can gather as much good data as possible without too much logistic fuss, do it! For example, provide half of your class with the shorter-blade paper helicopter template. The other half of the class would be given the longer-blade helicopter template.

When ready, the two helicopter groups could be separated, face each other, hold up their models at the same height, and then drop them simultaneously. Repeat as needed. Students should keep their hands and arms as far away from the helicopters as possible, holding the tips of the blades before release.

Videos of the experiment offer easily reviewable data that would offer a more sound determination to see if longer or shorter rotor blades cause a paper helicopter to stay in the air the longest. Each model type should be clearly identified especially if relying on videos for data analysis.

Other Ways to Collect Data

There are other ways to collect data while ensuring a fair test. Establishing a fixed height from the floor (i.e., controlling the distance-flown variable) can be done by hanging a small mass from the classroom ceiling with thread.

One successful set-up I have used has a paper clip on one end of a thread with a piece of blue painter’s tape on the other end. The top end with the paper clip is tucked into the metal drop ceiling frame grid, and the piece of blue paper tape has enough mass to hang down properly and be easily visible. I prefer not to have a paper clip hanging on the lower end because if hit or smacked for “fun” it could hurt someone’s hand, stick in the ceiling, etc.

A distance of 200 cm from the tape to the floor is a good distance to establish as a controlled variable for dropping and observing paper helicopters. Place six to eight of these paperclip-thread systems around the classroom to create testing spaces for groups of two to four students.

Paper Helicopter Flight Times

The easiest and quickest way to determine which paper helicopter model falls more slowly may be the aforementioned multi-copter drop method with or without a video recording. So, if you need a quick and easy STEM activity, go this route.

Another way to perform a fair test requires a stopwatch. After setting up the six to eight test stations around the classroom with the paperclip, thread, and blue painter’s tape, each group of students can perform the 200 cm drop and time the helicopter models multiple times.

If students do, say, ten trials for each model they should have sufficient data to minimize random factors. Each group’s ability to time the drops accurately will factor into the integrity of the results. Measuring the paper helicopters’ times over a fixed distance will also produce data that can be analyzed mathematically. Some examples of mathematical analyses are:

• represent and interpret data in a chart or graph
• measures of center (e.g., average time for each model)
• measures of variability (e.g., differences in trial times for each model)

Other Simple Paper Helicopter Launcher Ideas

There are other ways to launch paper helicopters rather than dropping them from your hand. For example, two meter sticks, side-by-side, can launch two to four helicopters at once. Two people are needed to hold the ends of the meter sticks. A bit of practice helps to keep the sticks level at a prescribed height and to separate them at the same time for launching.

With the two-stick method, you can launch even more helicopters at once using longer pieces of wood. Consider using two 1 in. x 2 in. x 8 ft. furring strip boards for launching seven to ten paper helicopters at once with just two people.

Paper Helicopter Experiment Lesson Plan

The focus of this paper helicopter investigation explores how the independent variables of blade length and body height together affect time aloft. Remember that, the blade length cannot be changed without changing the body height (unless we change the mass, which is a variable we are controlling). This means for both types of helicopters:

Blade length (shorter) with body height (taller) = equals = Blade length (longer) with body height (shorter)

And, as a reminder, our paper helicopter scientific inquiry question is:

Lesson Plan Parts and Documents

Paper Helicopter Template – There are four free printable pdf templates (8.5 x 11 inches, 21.6 x 27.9 cm). Each helicopter template is one page with the two types of helicopters:

• paper helicopter template with instructions and labels
• paper helicopter template with instructions (no labels)
• paper helicopter template with minimal instructions
• paper helicopter template no instruction (just cutting and folding lines)

Choose the template that makes the most sense for your students. Generally, the lower the grade level, the more instruction, and guidance are needed to make a paper helicopter.

Teacher Lesson Plan Outline

Grade Levels 4 – 7 (8 – 10 works too!)

Time How deep do you want to go? What is the grade level? Are you looking for a quick STEM activity or a long-term stem project ? Consider 45 minutes (one class) to 90 minutes (two classes), and keep in mind any extension activities.

Scientific Inquiry Question Does changing the blade-length-to-body-height ratio of a paper helicopter affect how long it stays in the air?

If you’re working with lower grade levels, or want to simplify the question, pose it like this: Does changing the blade length of a paper helicopter affect how long it stays in the air?

Standards Connections Common Core Next Generation Science Standards (NGSS)

Elementary School

• 3-5.Engineering Design
• 3-PS2-1 Motion and Stability: Forces and Interactions

Middle School

• MS.Engineering Design
• MS-PS2-2 Motion and Stability: Forces and Interactions

Materials and Set-Up (for the multi-test station method)

• Stopwatch (can be an online version )
• 8.5 x 11.5-inch paper helicopter template – one per group
• Group of two to four students students
• Six to eight helicopter test stations spaced about the classroom. A testing station consists of a thread hanging from the ceiling vertically that ends with a piece of tape 200 cm above the floor.

Paper Helicopter Experiment Lesson Documents

If you would like additional instructional activities to extend the paper helicopter activity and go deeper into learning, check out the Paper Helicopter Experiment (purchase link) resources at TPT !

You’ll find all the resources shared in this blog post, plus :

• teacher lesson presentation with custom graphics
• paper helicopter experiment report template
• pre/post test
• reading comprehension activity
• thinking routines writing activity
• group member role definitions
• vocabulary definitions for the paper helicopter experiment
• vocabulary definitions for the scientific method

Books about Paper Helicopters and Flight

Check out this captivating collection of books (paid links) that explore the fascinating world of flight. From exploring the mechanics of flight and the similarities between living creatures and machines to unraveling the story of the Wright Brothers, these books provide an immersive experience of the wonders of aviation.

Planes, Jets and Helicopters: Great Paper Airplanes Make your own fantastic flying paper aircraft! Instructions to fold paper, fly, and troubleshoot paper planes and helicopters from standard 8.5 by 11-inch paper. No glue, scissors, or tape required! Two dozen fold and fly designs with fold-by-fold illustrated instructions.

Science Comics: Flying Machines: How the Wright Brothers Soared A National Science Teachers Association Best STEM Book Winner in 2017! A delightfully illustrated comic about the history of the Wright brothers told by Katharine Wright Haskell, the younger sister of American aviation pioneers Wilbur and Orville Wright.

Planes, Gliders and Paper Rockets: Simple Flying Things Anyone Can Make–Kites and Copters, Too! A STEM-oriented book for older students who have access to tools and want to go beyond paper designs. Great for going deep into making hands-on, DIY flying crafts with everyday materials!

Paper Helicopter Experiment Summary

Teachers, are you searching for an engaging and cost-effective STEM activity to foster scientific thinking among your upper elementary and middle school students? High school students as well can benefit from the paper helicopter experiment!

This exciting low-budget DIY activity encourages students to develop essential scientific thinking skills by creating hypotheses, gathering relevant data, and interpreting results to draw conclusions. As a result, they will gain invaluable skills that will serve them well in future studies.

But the benefits don’t stop there! The paper helicopter experiment also allows students to explore various scientific concepts such as gravity, lift, and air resistance. Students will better understand these essential scientific principles by testing different blade sizes.

The paper helicopter experiment’s simplicity and low-cost nature make it an excellent starting point for Year 1 students to learn the MYP Design Cycle . Students can better understand the design process by identifying a problem related to helicopter design, creating a prototype, testing and evaluating their design, and communicating their findings.

To get started, check out the free resources in this blog post and on TPT ! They offer step-by-step instructions for building a paper helicopter and comprehensive tips for conducting the experiment and analyzing results. So what are you waiting for? Get started on this exciting hands-on STEM activity today!

• Quality Improvement
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Learning Design of Experiments with Paper Helicopters and Minitab

Topics: Design of Experiments - DOE , Minitab Statistical Software , Articles

This article was written by g uest blogger Matthew Barsalou , Statistical Problem Resolution Master Black Belt and Engineering Quality Expert at BorgWarner Turbo Systems Engineering GmbH with over 15 years of experience in quality. 

The late statistician George E. P. Box, along with Soren Bisgaard and Conrad Fung, used a paper helicopter to teach statistics. The idea originated with Kip Rogers of Digital Equipment and is useful for demonstrating factorial designs. Decades after Box, Bisgaard and Fung’s publication, the DOE helicopter has become a useful staple of DOE training.

The paper helicopter provides a way to quickly explain basic DOE concepts. It also offers an easy-to-do experiment you can analyze using Minitab.

We can’t just declare we want a high-quality helicopter. Quality must be clearly defined.

To perform a DOE with a paper helicopter we need to identify the desired output, which would be our response variable.

A good helicopter is one which stays in the air for a longer time, so the response variable would be flight time as measured from the time the helicopter is dropped from a height of 2 meters until the time it hits the floor. Without defining the test conditions it could be possible that sample helicopters would be dropped from different heights, in which case our DOE results would be not be valid.

Test factors that influence flight time must also be identified. For the helicopter experiment, the factors could be paper type, rotor length, leg length, leg width and paper clip. The helicopter experiment levels are varied by using two different types of paper, using longer or shorter leg and rotor lengths and adding or removing a paper clip.

Here’s how to make the paper helicopters.

• Step 1: Cut the paper to a width of 5cm.
• Step 2: Cut the paper the length of paper rotor length plus leg length, and add 2 cm for the body.
• Step 3: Cut dotted lines at Leg A and Leg C. The length of each cut is 5 cm minus leg width divided by 2.
• Step 4: Fold leg A onto leg B.
• Step 5: Fold leg C onto leg B.
• Step 6: Fold rotor A and rotor B in opposite directions. They should form 90° to the body and be 180° away from each other.
• Step 7: For the paper clip version: Add a paper clip to the bottom of the leg

Table 1: Helicopter factors

Designing the Experiment

Statisticians and Six Sigma black belts should know how to set up and perform the calculations in a designed experiment by hand. However, computer programs make DOE a much simpler task, particularly for people who need to perform experiments only occasionally.

To create a fractional factorial design in Minitab Statistical Software, go to Stat > DOE > Factorial > Create Factorial Design where we can select the desired design.

Resolution is the degree to which effects are aliased with other effects. In other words, aliased effects are mixed and can’t be estimated separately. This can also be referred to as confounding, and it results from not testing every possible combination of factors.

This is a disadvantage of a fractional factorial design. However, not testing every possible combination can be a significant advantage in time and expense over a full factorial design. If you’re not sure what resolution you should use, click on Display Available Designs… to see a list of designs and resolutions.

We typically use three levels of resolution: Resolution III, IV and V. There is no confounding of main effects with each other in these three resolution types; however, in a Resolution III design, main effects will be confounded with 2-factor interactions. This is a problem because 2-factor interactions are quite common in practice. Resolution IV designs do not have 2-factor confounding with main effects, but 2-factor interactions are aliased with other 2-factor interactions, and main effects are confounded with 3-factor interactions.

We try to use Resolution IV designs instead of Resolution III designs when possible because they have less aliasing, but still require fewer experimental runs than higher resolution experiments.

Resolution V designs have the added advantage that no 2-factor effects are confounded with other 2-factor effects; however, 2-factor effects are aliased with 3-factor effects, and main effects are aliased with 4-factor effects. This is a good thing, as 3-factor and above interactions are rarely significant in practice.

The confounding problem can be eliminated by performing a full factorial design. However, this requires more experimental runs, which might be prohibitive in terms of both time and money.

Looking at the Display Available Designs… option in Minitab, we can conduct a fractional factorial experiment using either a Resolution III or a Resolution V design for the 5-factor helicopter experiment. A Resolution III design would only need 8 runs, but because of the extreme confounding, the Resolution V design that requires 16 test runs is the better option. Click on Designs… and select the desired design.

As you set up the experiment, Minitab also asks for the number of blocks. Blocks are simply homogenous groupings of measurements that can be used to account for variation. The default value is one because, ideally, everything is homogenous.

The helicopter experiment will be set up so that there is only one experimental block. Each type of paper will come from the same source. The helicopters will all be built by the same person using the same scissors and ruler. If we used paper clips from two manufacturers or had some other potential causes for variation, then we would need separate blocks. Fortunately, this is not the case.

After you select your design, click Factors to enter the names and levels of the variables in your experiment. To change the name of a factor, type the name of the factor over the letter in the name field. The factor settings can also be renamed by replacing the default values of -1 and 1 with the actual factor levels.

When you’ve completed the dialog box, Minitab creates the experimental design and displays it in a Minitab worksheet. The Session Window above the worksheet provides a description of the selected design with the resulting alias structure.

In the resulting Minitab worksheet, the experimental results are entered into column C10. We can name the column “Flight time” because that is our experimental response variable.

A randomized run order is provided in the “RunOrder” column. Without randomization there is a risk that the experimental results will reflect unknown changes in the test system over time – such as if the scissors grow dull, resulting in slightly different cuts.

Minitab’s default setting for a designed experiment is one replicate. If you observe a lot of variation in the process or the resulting measurements, you can use Stat > DOE > Modify Design to add replicates to your design. Suppose the person making the helicopters had difficulty cutting a straight line so all edges are not uniform; the differences in results may reflect this variation. Replicating runs minimizes the effects of this kind of unanticipated variation.

Gathering the Experimental Data

Variability can have a major impact on experimental results, so take steps to reduce the variability. Have the same person make all helicopters and have them use the same pair of scissors and ruler. Drop the helicopters from a height of 2 meters, and identify the drop point clearly to ensure consistency. A higher or lower starting point would affect flight time, and this could throw off the results. The helicopters must also be held and released the same way, or variation in our data might be the effect of the release method and not the design of the helicopter.

The Minitab worksheet below contains the experimental results listed under “Flight time” in column C10.

Analyzing the Data

After running the experiment and entering the collected data in the Minitab worksheet, select DOE > Factorial > Analyze Factorial Design…

Significant factors are those that influence the response as they changed from one setting to another. When you click OK, Minitab provides an ANOVA table as well as a Pareto chart of effects, which make it very easy to identify significant factors.

With all our factors included in the model, we have no degrees of freedom left for Error, and you need at least 1 degree of freedom to calculate p-values. But while we can’t accept this model based on the ANOVA results, we can use the normal plot or Pareto chart to identify factors and interactions that are not significant.

At this point, the experimenter would typically begin eliminating these factors, rerunning the analysis until only significant factors and interactions are left. This is usually referred to as “reducing the model.” As factors are removed from the model, additional degrees of freedom become available for the calculation of p-values. The number of models you need to evaluate depends on the number of factors in your analysis.

Reducing the model takes only one step with Minitab’s stepwise DOE tool. To use this feature, return to Analyze Factorial Design… (or hit Ctrl+E to open your most previous dialog box). Select C10 “Flight time” as the response, then click Stepwise…

The stepwise regression feature makes it simple and fast to select the optimal model for your data by automatically removing factors to find the model that best fits your data. You can choose from four stepwise analysis methods: Stepwise, Forward selection, and Backward elimination, and Forward Information Criteria. In Backward elimination, all factors are included in the initial analysis, and then non-significant factors are removed one by one. In Forward selection, we start with an empty model and search for significant terms. This can be a useful tool when you have a situation like we currently have: Too many terms with too few runs.

Regardless of the stepwise method you use, the model Minitab selects contains the same significant factors shown below:

To help you interpret your results, Minitab can also provide main effects and interaction plots. Select DOE > Factorial > Factorial Plots… Because we have already analyzed the results, Minitab automatically selects the factors used in our model:

Clicking OK gives us plots of the significant main effects and interactions. The main effects plot shows the results of changing from one setting to another for each factor. Be cautious with these. You can only directly interpret main effects that are *not* involved in a significant interaction. This is why we only select B and E, because the A*C interaction overrides the main effects.

The main effects plot shows we have longer flight times with the paper clip off, and longer rotor length. The interaction plot shows the interactions between the factors.

This interaction tells us about these two factors. With heavy paper, leg length DOEs not matter much. With light paper, leg length has a much larger impact. Here it shows us our longest flight is with light paper and short leg length.

Finally, we can use the Response Optimizer to find the combination of factor settings that will give us the longest flight time. Select Stat > DOE > Factorial > Response Optimizer… Our goal is to maximize the flight length.

The optimizer produces the following graph showing the optimal factor settings in red, and the predicted response for helicopters made with those settings in blue. Take note that factor D DOEs not appear, as our analysis did not flag it as significant. Because it has no statistically significant impact on flight time, we can choose the setting for Factor D based on other considerations, such as cost:

For the data we collected, our analysis with Minitab indicates the optimal helicopter settings are lighter paper, longer rotor length, shorter leg length, and no paperclip on the leg.

To design an even better helicopter, we could repeat the entire DOE using even lighter paper and longer helicopter blades. A 50 cm wing may be bigger, but that does not mean it will be better. You may be able to predict the ideal settings based on a DOE result, but you should always be cautious when extrapolating beyond the data set, or the result may be a crashing helicopter.

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Out for a spin — paper helicopters.

Grade Levels

Grades K-4, Grades 5-8

Physical Science, Flight and Aeronautics

Play and Learn

By building and test flying two different paper helicopters, you will learn how the size of the Mars helicopter, Ingenuity’s, rotor blades are important for it to be able to fly in the thin atmosphere of Mars.

Out for a Spin

The Learning Hypothesis

How Helicopters Work: A STEM Challenge

Elementary · Middle School · Physical Science

The focus is on lessons that are accessible and adaptable for multiple ages. When possible, I try to provide hands-on experiments. If that isn’t possible or the process is difficult to visualize, my goal is to create a hands-on activity that will illustrate the concept and reinforce the learning.  Make sure to check out our other great physical science explorations.

Don’t forget to grab the template for today’s lesson.

Our Physics and Engineering Journey

We are focusing on physics and engineering this semester after studying human anatomy in the fall. We have been using a book to work through several physics and engineering lessons this semester. The book has been a little disappointing.  The directions are often lacking and so many of the links don’t work that it becomes a bit of an issue to try to get through the lessons.

One of these frustrating lessons was on a paper helicopter experiment. We basically got the topic and then had to start from scratch. The good news is that there is lots of great information about helicopters out there and we had a great time. We actually were able to do more than anticipated by allowing our imaginations and curiosity to drive innovation.

How Helicopters Work

Helicopters work based on changes in air pressure that result in lift. As the blades rotate it causes a pressure shift that results in build up of pressure under the blades and a decrease in pressure above that moves the air and the helicopter.

You can see the example of lift using this toy.  This toy is based on an ancient Japanese design known as a taketombo.   You spin the toy and release.  The spin is fast enough to create the pressure changes resulting in lift.  As the blades slow down, the toy falls.

What We Did

We couldn’t really make a helicopter (not yet) so in order to illustrate how helicopters work, we designed our own in this paper helicopter experiment.  These are known as roto-copters.  These float down because it isn’t rotating quickly enough to cause lift, but it is rotating enough to cause a slight change and create drag. This results in slowing down the speed of descent.

Check out this Video to Make Your Own.

Grab this project and so much more

After you make the primary design and get them to “fly”.  Experiment with aspects of the design: fold the blades differently; add more weight; add additional blades; keep it open ended.  Challenge teams to see whose copter can stay in the air the longest.

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Articles and Reports by George E.P. Box

• Bill Hunter
• George Box Articles
• Statistics for Experimenters

williamghunter.net > George Box reports > Teaching Engineers Experimental Design with a Paper Helicopter

Teaching Engineers Experimental Design with a Paper Helicopter

Copyright © 1991 by George E. P. Box. Used by permission.

How a paper "helicopter" made in a minute or so from 8 1/2" x 11" sheet of paper can be used to teach principles of experimental design including - conditions for validity of experimentation, randomization, blocking, the use of factorial and fractional factorial designs, and the management of experimentation.

Keywords: Randomization, blocking, factorial, fractional factorial, and experimental design

How a paper "helicopter" made in a minute or so from a 8 1/2" x 11" sheet of paper can be used to teach principles of experimental design including- conditions for validity of experimentation, randomization, blocking, the use of factorial and fractional factorial designs, and the management of experimentation.

The scenario I'll describe requires three people whom I'll call Tom, Dick, and Harry. To make an experimental run Tom stands on a ladder and drops the helicopter from a height of twelve feet or so while Dick times its fall with a stopwatch. We explain to the class that we would like to find an improved helicopter design which has a longer flight time. The helicopter can then be used to illustrate a number of important ideas.

We start by Tom dropping a helicopter made from blue paper. He drops it four times and we see that the results vary somewhat. This leads to a discussion of variation and to the introduction of the range and the standard deviation as measures of spread, and of the average as a measure of central tendency.

Comparing Mean Flight Times

At this point Dick says "I don't think much of this helicopter design, I made this red helicopter yesterday and dropped it four times and I got an average flight time which was considerably longer than what we just got with the blue helicopter. So we put up the two sets of data, for the four runs made with the blue helicopter and the four runs made with the red helicopter, on the overhead projector and we show the two sets of averages and standard deviations. Eventually we demonstrate a simple test that shows that there is indeed a statistically significant difference in means, in favor of the runs made with die red helicopter.

Validity of the Experiment

At this point Harry says "So the difference is statically significant. So what? It doesn't necessarily mean it's because of the different helicopter design. The runs with the red helicopter were made yesterday when it was cold and wet, the runs with the blue helicopter were made today when it's warm and dry. Perhaps its the temperature or the humidity that made the difference. What about the paper? Was it the same kind of paper used to make the red helicopter as was used to make the blue one? Also, the blue helicopter was dropped by Tom and the red one by Dick. Perhaps they don't drop them the same way. And where did Dick drop his helicopter? I bet it was in the conference room, and I've noticed that in that particular room there is a draft which tends to make them fall towards the door. That could increase the flight time. Anyway, are you sure they dropped them from the same height?" So we ask the class if they think these criticisms have merit and they mostly agree that they have, and they add a few more criticisms of their own. They may even tell us about the many uncomfortable hours they have spout sitting around a table with a number of (possibly highly prejudiced) persons arguing about the meaning of the results from a badly designed experiment.

We tell the class how Fisher once said of data like this that "nothing much can be gained from statistical analysis about all you can do is to carry out a postmortem and decide what such an experiment died of." And how, some seventy years ago, this led him to the ideas of randomization and blocking which can provide data leading to unambiguous conclusions instead of an argument. We then discuss how these ideas can be used to compare the blue and the red helicopter by making a series of paired comparisons. Each pair (block) of experiments involves the dropping of the blue and the red helicopter by the same person at the same location. you can decide which helicopter should be dropped first by, for example, tossing a penny. The conclusions are based on the differences in flight time within the pairs of runs made under identical conditions. We go on to explain however that different people and different locations could be used from pair to pair and how, if this were done "it would widen the inductive basis" as Fisher (1935) said, for choosing one helicopter design over the other. If the red helicopter design appeared to be better, one would, for example, like to be able to say that it seemed to be consistently better no matter who dropped it or where it was dropped. As we might put it today we would like the helicopter design to be "robust with respect to environmental factors such as the 'operator' dropping it and the location where it was dropped." This links up very nicely with later discussion of some of the ideas of Taguchi.

A Fractional Factorial Design

Later on in the class we use the paper helicopter to illustrate the running of a fractional factorial(orthogonal array) design. We suppose that a brainstorming session by an engineering design team on ways of improving the helicopter flight time has resulted in the selection of eight factors to be studied in a designed experiment. These selected factors are listed at the top of Figure 2 together with the two conditions (indicated by minus and plus signs) at which each will be tested. It is thought likely that only a few of these factors will have important large effects. We are thus in the familiar "Pareto" situation where, as Dr. Juran says we want to screen out the vital few from the trivial many." The design, shown in Figure 2, is a fractional factorial design. Bisgaard (1988) provides a very useful table of this and other eight and sixteen-run designs with a succinct description of their properties and analysis. Such designs which were developed in England during and just after World War II, are particularly useful for this purpose of screening, and this one which is a 1/16th fraction of the full 2 8 (256 run) design has two very valuable properties (see for example Box, Hunter & Hunter (BH 2 , 1978 ).

• if there are interactions between pairs of factors they will not bias any of the eight main effects Of the factors;
• if only up to three factors are of importance, the design will produce a complete 2 3   factorial design replicated twice in those three factors no matter which ones they are.

This latter property is particularly remarkable when we consider that there are fifty-six different ways of choosing three factors from eight. You can check it for yourself by picking any three columns in the design of Figure 2 and verifying that whichever three you pick you have every combination of (±,±,±) in those factors repeated twice over.

Flight times for the sixteen helicopter types obtained from an experiment run in random order are shown in Figure 2. From these flight times, eight main effects and seven strings of two factorial interaction effects may be calculated.* These are plotted on probability paper in Figure 3 suggesting that real effects are associated with W (wing length) and, less Certainly, L (body length). On the basis that the remaining effects falling around the straight-line are mostly due to noise, we can summarize the data simply in terms of the inset diagram in Figure 3. Going back to the original data it will be seen, for example, that there are four runs with short wing length and short body length with flight times averaging 2.6 seconds and four runs with long wing length and that body length averaging 3.3 seconds and so on. These averages are set out at the corners of the square in the inset diagram.

A direction in which one might expect still Ionger flight times by using larger wings with a shorter body is indicated by the arrow. Thus the experiment immediately provides not only an improved helicopter design but also indicates the direction in which further experimentation should be carried out and so demonstrates the value of the sequential approach to experimentation -learning as you go.

Another aspect of this approach is highlighted by discussing with the class whether they are satisfied with flight time as the sole criterion. In earlier lectures we have emphasized to the class that what happens in each run of an experiment must be carefully documented - for example the fact that Helicopter #7 hit the table leg and that run had to be repealed. Such careful observation might suggest, for example, that an additional criterion that should be included in future experimentation was flight stability . This teaches the Lesson that the criteria to be used in assessing the results may need to be modified or totally changed during as investigation as we learn more of the phenomena under study. Appropriate and feasible objectives cannot always be determined in advance.

*It is supposed in this analysis that interactions between three or more factors can be ignored. A fuller discussion of such analyses can be found, for example, in BH 2 p. 402.

Management of Experimentation

In running an experiment as complex as this, the safest assumption is that, unless extraordinary precautions are taken, it will be run wrongly. Therefore the opportunity should be taken of getting the class involved in the careful organization of the experiment. In particular, members of the class should be assigned to systematically check, and recheck independently, that each one of the sixteen helicopter designs to be flown exactly corresponds to the specification set out in the appropriate row of Table 2. Our course for engineers lasts only a few days so we find it necessary to prepare the paper helicopters in advance. After the preliminary explanation and the careful checking, the actual running of the experiment takes less than six minutes.

No elaborate analysis is needed for two-level experiments of this kind and certainly no Analysis of Variance table, which at this stage and for this purpose serves only to waste time and confuse the class. In earlier discussions, members of the class have already satisfied themselves, by one or two had calculations, that factorial effects are just the differences between the average results at the plus and minus levels of a given factor. Also the rationale of Daniels normal plot has already been explained. So for the helicopter experiment we enter the data in the computer as it becomes available and use the SCA program to calculate the effects at once, and to produce the normal pics which is immediately projected onto the overhead screen.

We find that participatory demonstrations of this kind even with such a simple device 55 a paper helicopter seizes the imagination of the engineer and produces very rapid learning.

Acknowledgments

This research was sponsored by the National Science Foundation under Grant No. DDM-8808138.

Box. G.E.P.. Hunter. W.G., and Hunter. J.S., Statistics for Experimenters. New York: John Wiley. p. 398. 1978.

Bisgaard. S., A Practical Aid for Experimenters. Starlight Press, Madison, Wisconsin, 1988.

Fisher, RA., The Design of Experiments. Oliver and Boyd, Edinburgh and London. 1935.

Articles by George

Advertisement

Show your children how to make paper helicopters for home experiments

Most children can fold a paper plane, but Alom Shaha prefers paper helicopters – and they are better for experimenting with

By Alom Shaha

24 August 2022

Emily Robertson

THERE is a deep satisfaction to be had from making and throwing a paper plane. From the number I have had fly across my classrooms, I have been able to ascertain that most children over the age of 11 know how to make one, albeit of varying quality.

I wouldn’t be doing my job properly if I didn’t encourage further experiments. They might investigate the factors that contribute to a good flight, and find out for themselves the importance of precise folding and the exact position of the centre of mass. Apparently, real scientists also do this sort of thing and get their work …

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SCIENCE EXPERIMENTS FOR KIDS

Making paper helicopters.

Use up those extra office supplies while giving your kids a quick science lesson

This animal is not on exhibit in the habitats.  It is one of our Animal Ambassadors and is used in public and school programs.

Download a PDF of this experiment

“Falling with style” is how Woody famously described Buzz Lighyear’s flight in “Toy Story,” but he might have been describing these paper helicopters too.

Paper helicopters are a fun activity that demonstrates gravity, drag and thrust. Using paper, scissors, and a few paper clips to make helicopters, you too can design something to fall with style. Use the attached template for the design of the helicopters, or design your own! Even Woody and Buzz would be impressed.

GATHER THIS:

• Paper clips
• Color pencils

THEN DO THIS:

• Cut along all of the solid lines of the helicopter pattern.
• Fold the lower sections (C & D) toward each other along the dotted lines.
• Hold the folded sections and place a paper clip at the end.
• Fold the top blades (A & B) in opposite directions.
• Hold the helicopter high above your head. Release!
• Try shaping your blades or using different amounts of weight. You can also try uneven blades.
• Did the helicopter rotate clockwise or counter-clockwise?
• How can you make it rotate in the opposite direction?
• Does the height you drop it from affect its flight?
• How does the weight (paperclips) affect the flight?
• If you cut the blades unevenly how does it affect the helicopter’s travel? How?

WHAT IS HAPPENING?

When the helicopter falls, air pushes up against the blades and bends them up just a little. When air pushes upward on the slanted blade, some of that thrust becomes a sideways – or horizontal – push.

The helicopter doesn’t move sideways through the air because there are two blades, each getting the same push but in opposite directions. The two opposing thrusts work together to cause the toy to spin.

Like this experiment? Explore more flight science with the  CuriOdyssey Flight Science Kit  in the  CuriOdyssey Shop !

WHAT THIS TEACHES:

Skills:  Scientific process, fine motor skills, observation

Themes:  Gravity, drag, lift

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Science Fair Guide: Helicopter

In addition to the helicopter materials, you’ll need a tape measure.

Ask a Question

What shape and size of paper cutout causes the helicopter to fly the farthest?

Gather Information

The rubber band helicopter relies on the paper cutout to redirect the rubber band’s energy to the propeller. Without it, the energy would be wasted spinning the craft stick.

However, if the paper is too heavy, then excessive energy will be required to make the helicopter fly.

The total surface area of the paper has an effect on how much energy is diverted to the propeller. Additionally, whether the surface area is close to the center of rotation (the craft stick) or farther away also matters.

Make a Hypothesis

Using the information above, make an educated guess about which type of paper cutout will work the best. Your hypothesis should be a simple statement, such as: “A wide and narrow rectangle will help redirect the most of the rubber band’s energy to the propeller” (This is not necessarily the best hypothesis; it’s just an example).

Conduct an Experiment

Create 3-7 different paper cutouts of varying shapes and sizes. Try making: a 2x2" square, a 2" circle, a 2x6" rectangle, a 2x6"-wide bowtie shape, and a 2x6"-wide diamond shape.

One at a time, attach the paper cutout to the helicopter.

Fly the helicopters sideways instead of straight up. This way, you can measure the effectiveness of the paper cutout by using a tape measure to measure the distance the helicopter flies.

Fly each paper cutout three times. This will ensure that no single test skews your results.

If you accidentally mess up one of the tests, then redo the test and record in your notes why you chose to not include the results of one test. For example, "The propeller bumped into my sleeve during launch."

Setup the Controls

Controls are measures put in place to prevent unintended things from affecting your results.

Follow these procedures to ensure your data is accurate:

Test a helicopter without any paper 3 times and record the results to ensure that the paper cutout has an effect at all.

Wind up the helicopters the same number of turns each test. Your goal is to test the paper cutouts, not how much energy is put into the rubber bands.

Each time you test a new paper cutout, put fresh rubber bands on the helicopter. The rubber bands can stretch out and loosen over time, which would make each subsequent flight slightly less powerful.

Fly the helicopters when it’s not windy.

Collect Data

Record the distance of each test for each paper cutout. When finished, add up the results for each paper cutout, then divide by 3 to get an average distance. For example, if one paper cutout flew 12', 10', and 14', then 11+12+13 divided by 3 is an average of 12'.

Your data might look something like this (this is not real data; don’t use in your conclusion):

In addition to the helicopter materials , you’ll need a tape measure.

View the Helicopter project

Make Observations

Describe any additional observations you made during the experiment. Be sure to include things might have affected your results such as flying errors, wind during some tests, or anything else unexpected.

Draw Conclusions

Look at your data and conclude which paper flap works the best.

Present Findings

Present your main conclusion in a visual form, such as writing the average distance flown onto each paper cutout, and creating a graph that shows the distance the each one travelled.

Summarize your hypothesis, experiment method, the controls you put in place, and your raw data.

Write your conclusion, and explain why you think the results are the way they are.

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• how-to-make-a-paper-helicopter

How To Make A Paper Helicopter

Paper aeroplanes are great and a great way to learn about science but they've got nothing on paper helicopters, that's for sure!  All you'll need is some paper, scissors and maybe a paperclip!

What Do I Need?

• A piece of paper
• Some scissors
• A paperclip

How Do I Do It?

STEP1  - The perfect size to make your helicopter is 1/8th of a piece of paper. Great news as you can make 8 of them out of one sheet of paper! Fold your paper into eights and cut one out ready.

STEP2   - I've marked on the image how to make it! Just make a cut where you see a solid line and make a fold where you see a dashed line!

STEP3   - Make the two small cuts and fold the paper over and use a paperclip to hold it in place, as shown.

STEP4   - To make the wings simply make the cut down the middle of the unused side and fold the wings down so you've got something that looks like our final helicopter!

STEP5   - No pre-flight checks needed! Simply hold the helicopter up high and drop it! Watch how it spins! If you're feeling brave you can try throwing it but pretty soon you might need to make another helicopter!

What’s Going On?

As you helicopter starts to fall the air pushes past the wings. 

Most of this air pushes upwards against the falling helicopter (which is why it falls slowly) but each wing causes some of that air to push to the side. 

There's an equal sideways push on each of the wings but in opposite directions and that's what causes the helicopter to spin!

More Fun Please! - Experiment Like A Real Scientist!

• What happens if you add more weight? Blue Tac is great for this!
• What are the perfect proportions to make your helicopter spin as fast as possible?
• How big a helicopter can you make?

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We help students to generate custom paper helicopter templates for their experimental planning lab...

...and lecturers - to incorporate a variation of the paper helicopter experiment project in their design of experiments course. we also ensure that students have all the necessary educational material to engage with the project independently..

For the students

For the teachers.

A paper helicopter experiment project is an excellent assistant in teaching two-level fractional factorial designs. You are invited to integrate the paper helicopter experiment project into your own syllabus - simply create a unique variation of the project by following instructions on our website. And if you find this website useful, help others to discover our printable paper helicopter pdf templates by adding a link to the paper helicopter experiment website on your course homepage. Your support matters!

Explore more

Check the project task in the PROJECT section, explore the paper helicopter design and assembly guidelines in the DESIGN & ASSEMBLY section, and make sure to generate ready-to-print PDF TEMPLATES that will not only save you hours of your time but also ensure that your paper helicopters align perfectly with the specified dimensions. Finally, learn more about this website in the ABOUT section.

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