# Crash Test Dummies

 Author: Kevin Tucker Unit Title: Crash Test Dummies Grade: 12 Subject: AP-Calculus Estimated Duration: 5 Days Unit Activities: Activity 1: Big idea  Activity 2: Acceleration of CO2 Car Activity 3: Crash Test Materials Activity 4: Redesign Background Knowledge:  Students will know that the derivative of position is velocity and that the derivative of velocity is acceleration.  We will extend this thinking in reverse with the introduction of integration. Date: July 2014
##### The Big Idea (including global relevance)

Safety in frontal crash test.

##### The Essential Question

How can we measure the safety of a car in a frontal crash?

##### Justification for Selection of Content

This unit will incorporate area under the curve (integration) as it relates to velocity and average value.  Students will use accelerometers to see the real world application of integrals.  In the past students have difficulty going from the rate of change back to the initial value using integration.  This will give them a realistic application for area under the curve.

##### The Challenge

Students will create a CO2 car that will have the lowest HIC (Head Injury Criterion) as measured byâ€¦

, this is the formula used by the National Highway Traffic Safety Administration (NHTSA) and the Insurance Institute for Highway Safety (IIHS).  Students will used different materials and processes to lower the HIC of a Balsa wood Car crashed at a distance of 80 feet (the length of the track we have, also all of the CO2 should be expelled at this time.)

##### The Hook

Video compilation of Crash Tests.

Videos Used for my Compilation

2014 Toyota Corolla | Frontal Crash Test | CrashNet1

Nissan Altima | 2013 | Frontal Crash Test | NHTSA High Speed Camera | CrashNet1

1959 Chevrolet Bel Air vs. 2009 Chevrolet Malibu IIHS crash test

Crash test results for midsize family cars - IIHS news

##### Teacher's Guiding Questions
1. How can we make a car safer in a frontal crash?
2. What is the best design and materials to reduce the possibility of a head injury?
3. What are the important parameters in a frontal car crash?
4. What types of injuries seem to be the most devastating?
5. What area of the body is the most important to protect?

##### ACS (Real world applications; career connections; societal impact)

A â€“ (Real World Application):  Safety in automobile construction to save lives in a crash.

C â€“ (Career Connections): Automotive Engineer, Biomechanics, Materials Engineer

S â€“ (Societal Impact):  Automobiles are tested and rated to ensure that they are as safe as possible.

As a result we can lower insurance costs, and increase quality of life.

##### Engineering Design Process (EDP)

Students will design a car with the lowest Head Injury Criterion.  The HIC will be measured using an accelerometer to measure the deceleration of a CO2 powered car that is crashed 80 feet from the start.

The students will use the Engineering Design Process to develop and test their cars.  Students will use calculus and integration to evaluate their design.  Students will refine their design to develop the safest car possible.

Topics from the AP Calculus course guide.

• Definite integral as a limit of Riemann sums.
• Definite integral as the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval

• Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations.
##### Unit Activities

Lesson 1: Acceleration

Lesson 1 will focus on the math needed to describe the motion of a car accelerating.  For this project we will introduce the relationship between acceleration and velocity as the area under the curve (introduction to integration and Riemann sums).  Students will develop a graph of velocity based on data collected from an accelerometer.

Activity 1: Big idea (essential and guiding questions)

Activity 2: Acceleration of CO2 Car.

Lesson 2: Crash Test:

Lesson 2 will focus on the crash testing of the cars.  The students will use calculus to evaluate their design.

Activity 3: Crash Test Materials

Activity 4: Redesign

Activity 5: Video Presentations

##### Where the CBL and EDP appear in the Unit

On the first day the students will be presented with the challenge.  This will start the engineering design process.  The groups are tasked with developing a car that will be crash tested.  The students will investigate integration as the area under a curve.  Students will evaluate the effectiveness of their design using

The groups will use Google Docs to document their steps though the engineering design process.

Lesson 1 Activity 1 and 2

• Identify Problem:

The students will identify the problem.  How can we design a safer car The students will have to define the constraints of the problem.

Lesson 2 Activity 3 and 4

• Brainstorm ideas:

At this stage the students will have to think about how they are going to make the car safer in a frontal crash.  In activity 3 each group will test a different material or construction method to lower the HIC.

• Design:

Groups will develop their initial design during class time as well as outside of class over the course of 5 days.

• Test:

Students will test their design by attaching an accelerometer to their car and launching it down the track into a wall 80 ft. away.  Students will use the data to evaluate the effectiveness of their device.

Each group will present their findings.

• Redesign:

Students will have 5 days to refine their design and retest.

Lesson 2 Activity 5

• Communication:

The students will create a video presentation to the class on their process though the engineering design process high lighting key components of their process with pictures, sketches, tables, graphs and equations.

##### Misconceptions

Students take the derivative of a function when they really want to integrate it.

Videos Used for my Compilation

2014 Toyota Corolla | Frontal Crash Test | CrashNet1

Nissan Altima | 2013 | Frontal Crash Test | NHTSA High Speed Camera | CrashNet1

1959 Chevrolet Bel Air vs. 2009 Chevrolet Malibu IIHS crash test

Crash test results for midsize family cars - IIHS news

Pre Assessment

Post Assessment

##### Results: Evidence of Growth in Student Learning
After analyzing the Pre-Assessment and the Post-Assessment data I noticed that the grades improved dramatically.  The Assessment was 10 questions each worth 5 point per question. The average score on the Pre-Assessment was a 13% and the average score on the post assessment was a 70%.  This was a 438% increase.  The pre and post-test was designed as the chapter test that covers integration as the major concept for the project was integration, area under the curve, and average value.
##### How to Make This a Hierarchical Unit

For a middle school unit the students could go through the design process to build the fastest car and do a bracket and have students race to find a winner.  You could also use the Vernier sensors to talk about acceleration and velocity without introducing derivatives.  You can graph the data and talk about non-linear relationships

##### Reflection

The success of the lesson is that the students had the opportunity to apply advanced mathematical concepts in a real world situation.  This was the fifth unit I taught from the CEEMS project.  This time around I felt that working through the essential and guiding questions went very well.  Similar to the last 2 project I gave the students about 8 minutes to come up with their list of questions and had each group share 2 or 3 of their questions.  As a class we decided if it is an essential or a guiding question.  After each group shared I asked if there were any other questions they would like to add.  This worked better because each group was forced to contribute something to the conversation and by allowing the students to add at the end everyone could have their ideas heard.  For many of my students in this class this was their fourth time going through the Engineering Design Process and Challenge based learning.  The transitions from day to day and topic to topic seemed to be very smooth as they knew what to expect.

Another success of the lesson was how well the technology worked, specifically the Vernier LabQuest2 and the wireless accelerometers.  For the portion of the project when the students launched the cars and used the area under the acceleration curve most groups got a number very close to zero, which makes sense.  The total velocity from start to finish should be zero since the car came to a stop.  When using the HIC formula the numbers were very realistic in comparison to actual values obtained by the groups in their research.

A short coming of the lesson was just the learning curve associated with new technology.  This was my first experience with the Vernier LabQuest2 and the wireless accelerometers.  The instructions for set up were easy to follow but I found that setting up the accelerometers to get the readings we wanted took a little bit of trial and error.  I would definitely recommend that a teacher trying this for the first time spend some time after school getting things dialed in.  I also had to consult the internet to find out how to export data from the LabQuest to excel so the students could estimate the area under the curve.

Below is the video I used.  It walked me through step by step.