Storyline

Standards

Teacher Background

### Grade 6-8 | 10 (45 min) Classes

In this unit students will answer the question: **How is slope represented in a model rocket launch?**

Students will learn about the different types of slope and practice calculation methods to find slope from a graph. Students will then analyze launch data to identify and calculate where a rocket has a positive, negative and/or neutral slope on its flight path.

For their final assessment students will be creating a visual of the four types of slope that shows how slope is seen on a model rocket’s flight path.

## Standards

## Targeted Performance Expectation(s):

## Common Core Standards - Math

## GRADE 7

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

## GRADE 8

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

## High School

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

## Vocabulary

### APOGEE

**T****he peak altitude or highest point of a rocket’s flight**

### HORIZONTAL

**Goes left to right, parallel to the horizon**

### VERTICAL

**Goes up and down, perpendicular to the horizon **

### PAYLOAD

**The object being carried by an aircraft or launch vehicle**

### RATIO

**A comparison of two or more numbers or measurements**

### SLOPE

**Shows the rate of change, steepness, and direction of a line**

### X-AXIS

**Horizontal axis, on a graph it shows the dependent variable**

### Y-AXIS

**Vertical axis, on a graph it shows the independent variable**

## Teacher Background

### Slope

Slope measures the steepness of a line. A line that is steep will have a bigger slope than a line that is flatter. Slope is calculated as the ratio of the amount of vertical change to horizontal change. Basically, it shows a rate of change. This is often referred to as “rise over run.” The rise is the y-axis and the run is the x-axis.

### There are four types of slope.

1. Positive

- The line goes
**up**from left to right. - The y-axis values are
**increasing**as the x-axis values are**increasing.** - Example: The funnier the cat videos are that I post on Facebook, the number of likes goes up.

- The line goes
**down**from left to right. - The y-axis values are
**decreasing**as the x-axis values are**increasing.** - Example: If I increase my time watching Netflix, the time I have left to study will decrease

- The line is
**horizontal.** - The y-axis values
**do not**change as the x-axis values are**increasing.** - Example: If I stand in one place and don’t move, time will continue to increase but my distance travelled will not.

- The line is
**vertical.** - The x-axis values
**do**change as the y-axis values are**increasing.** - Example: An elevator can go up and down, but does not move horizontally.

### How does a Rocket Fly?

Students should be familiar with how a model rocket launches and all safety procedures that should be followed. The safety requirements can be found in the Model Rocket Safety Code of the National Association of Rocketry (NAR).

### A Typical Model Rocket Flight

**Thrust** is the upward force that makes a rocket move off the launch pad. This is a demonstration of **Newton’s Third Law of Motion:** “For every action there is an equal and opposite reaction.” The action of the gas escaping through the engine nozzle leads to the reaction of the rocket moving in the opposite direction. The casing of a model rocket engine contains the propellant. At the base of the engine is the nozzle which is made of a heat-resistant, rigid material. The igniter in the rocket engine nozzle is heated by an electric current supplied by a battery-powered launch controller.

The hot igniter ignites the solid rocket propellant inside the engine which produces gas while it is being consumed. This gas causes pressure inside the rocket engine, which must escape through the nozzle. The gas escapes at a high speed and produces thrust. Located above the propellant is the smoke-tracking and delay element. Once the propellant is used up, the engine’s time delay is activated.

The engine’s time delay produces a visible smoke trail used in tracking, but no thrust. The fast-moving rocket now begins to decelerate (slow down) as it coasts upward toward peak altitude **(apogee)**. The rocket slows down due to the pull of **gravity** and the friction created as it moves through the atmosphere. The effect of this atmospheric friction is called **drag**. When the rocket has slowed enough, it will stop going up and begin to arc over and head downward. This high point or peak altitude is the apogee. At this point the engine’s time delay is used up and the ejection charge is activated. The ejection charge is above the delay element. It produces hot gases that expand and blow away the cap at the top of the engine. The ejection charge generates a large volume of gas that expands forward and pushes the recovery system (parachute, streamer, helicopter blades) out of the top of the rocket. The recovery system is activated and provides a slow, gentle and soft landing. The rocket can now be prepared for another launch.

**To summarize, the steps of the Flight Sequence of a Model Rocket are:**

- Electrically ignited model rocket engines provide rocket liftoff.
- Model rocket accelerates and gains altitude.
- Engine burns out and the rocket continues to climb during the coast phase.
- Engine generates tracking smoke during the delay/coast phase.
- Rocket reaches peak altitude (apogee). Model rocket ejection charge activates the recovery system.
- Recovery systems are deployed. Parachutes and streamers are the most popular recovery systems used.
- Rocket returns to Earth.
- Rocket touchdown! Replace the engine, igniter, igniter plug and recovery wadding. Rocket is ready to launch again!

### Engine Types

Rocket engines are governed by the National Association of Rocketry (NAR) and follow the same alphanumeric coding:

**Letters**: Each successive letter has TWICE as much power as the previous letter (a B engine would have twice as much impulse power as an A engine).**First number**: Average Thrust: This is a measure of how slowly or quickly the engine delivers its total energy. Engines with low numbers will have a weak thrust for a long duration. Engines with high numbers will have a high thrust over a short duration (high numbers are good for heavy rockets).**Second number**: This number tells you the delay (in seconds). In other words, the time between the end of thrust and the ejection charge. The ejection charge is activated after the delay. It produces a quick puff of gas that pressurizes the inside of the body tube to push out the recovery system.**Color**- Green: Single stage engine
- Purple: High performance single stage/final stage multistage engine
- Red: Booster-stage engine
- Blue: Special use engine

## Materials

### Each Student Needs:

### The Class Needs:

Ruler

Sandpaper

Camera (optional)

## Unit Plan

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## Student Portfolio

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