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Assuming a parabolic motion, from the data values of variable acceleration, and assuming horizontal thrust is constant we can:

1. Calculate the maximum acceleration and at which point this occurs based on the data values

2.  Process data to find the total time of flight, using the inital velocity and angle of projection, using formula        T = (U sinθ) / g https://courses.lumenlearning.com/boundless-physics/chapter/projectile-motion

3. If assuming the angle is 90 degrees (vertical motion), we can calculate the max height when velocity is equal to 0, (by integrating acceleration to find velocity), and the total time of flight as the time taken for displacement to reach 0.

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From the Pressure sensor, we can calculate the maximum/minimum pressure recorded and when this occured.  Other calculations include comparing with the normal atmospheric pressure, and how pressure varies during the time of flight.

Potentially also using the Barometric Formula, we could calculate the maximum altitide of the rockect using the fromula P = P₀ e(-Mgh/RT)  where h is the change in altitude

https://www.math24.net/barometric-formula

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The data values from the various sensors in the payload circuit include

1. Atmospheric Pressure whilst in flight,  measured by the analogue pressure sensor

2.  Variable acceleration from the accelerometer

This data will be stored into the SD card as a textfile, which can be used for further calculations

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4.6305e-4 m^3 (5sf)

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Pinmode() lets you change the behavoiour of a pin, for example setting an analogue pin as an OUTPUT allows is to act as and pin that can supply voltage to other components. This has drawbacks however such as electrical noise when in close proximity to other analog pins in use. https://www.arduino.cc/en/Tutorial/Foundations/AnalogInputPins

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https://create.arduino.cc/projecthub/SURYATEJA/use-a-buzzer-module-piezo-speaker-using-arduino-uno-89df45
Arduino has its own library for controlling buzzers.
"tone(buzzer, 1000) sends a 1KHz sound signal to pin 9, delay(1000) pause the program for one second and noTone(buzzer) stops it." furthermore tone(pin, frequency, duration) allows you to specifiy a duration in ms.

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Seriel.print() can be used to print and plot variables to a monitor in the programming window which can be used to check the equipment is functioning correctly.

serial monitor

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https://www.adafruit.com/product/254
SD card board uses  the digital pins on the arduino. When refering which pin to write to for the SD card we use the pin number corresponding to the the pin the CS on the board.

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https://arduinotogo.com/wp-content/uploads/2016/07/ch3-schematic-arduino-compare-01.png

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"Divide an object into independent parts." The circuit is already split into multiple different components. We should take advantage of this during assembly to make sure the circuit is designed efficiently and compact to minimise size.

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"Make a part or object perform multiple functions; eliminate the need for other parts." This could be shown by how all the sensors and other components can be powered through the arduino board which means its acting as a microcontroller and a connection point to distribute power.

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"Allow (or design) the characteristics of an object, external environment, or process to change to be optimal or to find an optimal operating condition."
This could be linked to the mass distribution in the rocket. The payload needs to be designed to be as light as possible and placed in an optimal position in the rocket for maximum height.

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"Prepare emergency means beforehand to compensate for the relatively low reliability of an object."  This could be shown by how all the sensors and other components can be powered through the arduino board which means its acting as a microcontroller and a connection point to distribute power.

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http://www.triz40.com/aff_Principles_TRIZ.php

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This payload circuit should fit inside the model rocket approx 60mm diameter x 120 mm length, with an engine containing a ESTES D12-5 motor.

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Home / Engines / C11, D & E (24mm) / 001567 - D12-5 Engines

$11.99

ENGINES FOR MODEL ROCKETS

2 - D12-5 Engines
2 - Starters
4 - Plugs

PLEASE NOTE: This item will ship by US Postal Service only. You MUST HAVE a physical mailbox or post office box for delivery.

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Description

The Estes D12-5 engine is a single stage engine designed for model rocket flight. This engine is a 24mm diameter engine designed for rockets with a maximum lift weight of less than 10 ounces. Each package includes 2 engines, 2 starters and 4 starter plugs.

ATTENTION: Residents of California, New Jersey, Rhode Island and North Dakota please review the Terms of Sale for state specific restrictions or Click Here for State Specific Restrictions.

WARNING

This warning applies to all Estes products containing wood

Warning

Drilling, sawing, sanding or machining wood products can expose you to wood dust, a substance known to the State of California to cause cancer. Avoid inhaling wood dust or use a dust mask or other safeguards for personal protection.

For more information go to www.P65Warnings.ca.gov/wood.

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This product can expose you to chemicals including crystalline silica, which is known to the State of California to cause cancer, and birth defects or other reproductive harm. For more information go to www.P65Warnings.ca.gov.

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Home / Engines / C11, D & E (24mm) / 001567 - D12-5 Engines $11.99 ENGINES FOR MODEL ROCKETS 2 - D12-5 Engines 2 - Starters 4 - Plugs PLEASE NOTE: This item will ship by US Postal Service only. You MUST HAVE a physical mailbox or post office box for delivery.

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How does the acceleration of a model rocket compare to the Space Shuttle? By using the resultant force and mass, acceleration can be calculated.

Forces acting

The two forces acting on rockets at the moment of launch are the thrust upwards and the weight downwards. Weight is the force due to gravity and is calculated (at the Earth's surface) by multiplying the mass (kilograms) by 9.8.

The resultant force on each rocket is calculated using the equation resultant force = thrust - weight.

Calculating the acceleration of a model rocket

Acceleration is a measure of how much the speed increases each second. It can be calculated using the equation
acceleration = resultant force (newtons, N) divided by mass (kilograms, kg).

One model rocket has a mass of 50 grams and a rocket engine that produces a thrust of 5 N for 1 second.

To find the weight, 50 g needs to be changed into kilograms by dividing by 1000. This gives a mass of 0.050 kg. Weight is mass (in kg) x 9.8, which gives 0.050 x 9.8 = 0.49 N.

The resultant force is the thrust - weight = 5 - 0.49 = 4.51 N (unrounded).

Acceleration = resultant force divided by mass = 4.51 ÷ 0.050 = 90 metres per second squared (90 m/s ²). This means that, every second, the speed of the rocket increases by 90 m/s.

This is nine times the normal acceleration due to gravity.

The same method can be used for a full-sized rocket such as the Space Shuttle.

Calculating the acceleration of the Space Shuttle

The Space Shuttle mission that launched on 24 February 2011 was called STS-133. It had a lift-off mass of 2 million kilograms (2000 tonnes). This means the total weight at lift-off is 2 million x 9.8, which is approximately 20 million newtons (20 mega newtons).

The thrust of each of the big white solid rocket boosters on the side was 12.5 million newtons, and the three main engines at the tail end of the bit that looks like a plane (the Space Shuttle orbiter) had a combined thrust of 5.5 million newtons. This gives a massive total thrust of 30.5 million newtons!

Resultant force = thrust - weight = 30.5 million - 20 million = 10.5 million newtons.

Acceleration = resultant force ÷ mass = 10.5 million ÷ 2 million = 5.25 m/s ².

Comparing accelerations

The acceleration of the model rocket at 90 m/s ² is far greater than the Space Shuttle at 5.25 m/s ², but there is a significant difference in the motion after launch.

Firstly, the model rocket only had enough propellant for 1 second of thrust. After 1 second, it reaches a maximum speed of 90 m/s (ignoring drag and mass change), but after that 1 second of thrust, the model rocket starts to lose speed due to the weight and drag forces both acting in the opposite direction to its motion.

For the Space Shuttle, the solid rocket boosters (SRBs) have enough propellant to provide thrust for 124 s. This means that the space shuttle accelerates for more than 2 minutes before the solid rocket boosters separate. (As the shuttle uses its propellant, it also becomes much lighter, which increases acceleration.)

After 124 seconds, the shuttle has already reached an altitude of 45 km and is travelling at 1,380 m/s (4,973 km/h). At this time (once all of the fuel is consumed), the SRBs separate away from the external tank (the big orange part). Fuel continues to be pumped to the three main engines for another 6 minutes. Acceleration continues until the Space Shuttle orbiter eventually reaches a speed of 28,000 km/h and an altitude over 300 km. This allows it to orbit around the Earth.

Related content

Useful link

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How does the acceleration of a model rocket compare to the Space Shuttle? By using the resultant force and mass, acceleration can be calculated. The two forces acting on rockets at the moment of launch are the thrust upwards and the weight downwards.

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The forces on a model rocket change dramatically in both magnitude and direction throughout a typical flight. This figure shows the acceleration on a rocket just following liftoff. The acceleration is produced in response to Newton's first law of motion. A net external force is being applied to the rocket. The only forces present are the thrust (T) and the weight (W).The weight is always directed toward the center of the earth; the direction of the thrust is along the rocket axis. For a vertical launch, the thrust is directly opposite the weight and the net vertical force (Fv) is the thrust minus the weight (Fv = T - W). There is no horizontal force present for a vertical launch. The acceleration of the rocket can be determined by Newton's Second Law of Motion. For a constant mass, this law can be written as force (F) equals mass (m) times acceleration (a); (F = m * a). We can solve for the acceleration using algebra ( a = F / m). Then the vertical acceleration (av) of the rocket is given by the equation ( av = [T - W] / m ).

Since the aerodynamic forces depend on the square of the velocity, and the velocity is low during liftoff, the magnitude of the aerodynamic forces is very small. That is why there is no horizontal component of the acceleration for this vertical launch configuration.

For a model rocket, the weight of the propellant is small relative to the weight of the entire vehicle. So, in determining the acceleration we can assume that the weight remains nearly constant. This is different from a full scale rocket in which the propellants represent a large portion of the weight of the vehicle. Changes in the weight (mass) of the propellant must then be included in any determination of velocity or acceleration during the flight. The equations shown on this slide would not be valid for a full scale rocket because of the change in mass. For a model rocket, the thrust changes greatly with time due to the design of the solid rocket engine. We can use the equations on this slide to determine how the acceleration changes with time for a model rocket.

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Beginner's Guide Home Page
byTom Benson
Please send suggestions/corrections to: benson@grc.nasa.gov

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The forces on a model rocket change dramatically in both magnitude and direction throughout a typical flight. This figure shows the acceleration on a rocket just following liftoff. The acceleration is produced in response to Newton's first law of motion. A net external force is being applied to the rocket.

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An accelerometer uses a monocrystalline silicon capacitive sensor, to measure the acceleration forces acting on the rocket at various time intervals. This data should help calculate maximum acceleration, maximum height attained and the total time of flight.

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Payload must be close to centre of mass so rocket remains upright and reaches the theoretical maxium height.

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Weight is the force generated by the gravitational attraction on the rocket. We are more familiar with weight than with the other forces acting on a rocket, because each of us have our own weight which we can measure every morning on the bathroom scale. We know when one thing is heavy and when another thing is light. But weight, the gravitational force, is fundamentally different from the other forces acting on a rocket in flight. The aerodynamic forces, lift and drag, and the thrust force are mechanical forces. The rocket must be in physical contact with the gases which generate these forces. The gravitational force is a field force and the rocket does not have to be in contact with the source of this force.

The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists. For an object the size of a rocket, the explanation given three hundred years ago by Sir Isaac Newton is sufficient to describe the motion of the object. Newton developed his theory of gravitation when he was only 23 years old and published the theories with his laws of motion some years later. As Newton observed, the gravitational force between two objects depends on the mass of the objects and the inverse of the the square of the distance between the objects. More massive objects create greater forces and the farther apart the objects are the weaker the attraction. Newton was able to express the relationship in a single weight equation. The gravitational force, F, between two particles equals a universal constant, G, times the product of the mass of the particles, m1 and m2, divided by the square of the distance, d, between the particles.

F = G * m1 * m2 / d^2

If you have a lot of particles acting on a single particle, you have to add up the contribution of all the individual particles. For objects near the Earth, the sum of the mass of all the particles is simply the mass of the Earth and the distance is then measured from the center of the Earth. On the surface of the Earth the distance is about 4000 miles. Scientists have combined the universal gravitational constant, the mass of the Earth, and the square of the radius of the Earth to form the Earth's gravitational acceleration, ge .

ge = G * m Earth / (d Earth)^2

ge = 9.8 m/sec^2 = 32.2 ft/sec^2

The weight W, or gravitational force, is then just the mass of an object times the gravitational acceleration.

W = m * ge

An object's mass does not change from place to place, but an object's weight does change because the gravitational acceleration ge depends on the square of the distance from the center of the Earth. Let's do a calculation and determine the weight of the Space Shuttle in low Earth orbit. On the ground, the orbiter weighs about 250,000 pounds. In orbit, the Shuttle is about 200 miles above the surface of the Earth; the distance from the center of the Earth is 4200 miles. Then:

m = Ws / ge = Wo / go

Wo = Ws * go / ge

where Ws = surface weight (250,000 pounds), Wo is the orbital weight, and go is the orbital value of the gravitational acceleration. We can calculate the ratio of the orbital gravitational acceleration to the value at the surface of the Earth as the square of Earth radius divided by the square of the orbital radius.

go / ge = (d Earth)^2 / (d orbit)^2

go / ge = (4000/4200)^2 = .907

On orbit, the shuttle weighs 250,000 * .907 = 226,757 pounds. Notice: the weight is not zero. There is a large gravitational force acting on the Shuttle at a distance of 200 miles. The "weightlessness" experienced by astronauts on board the Shuttle is caused by the free-fall of all objects in orbit. The Shuttle is pulled towards the Earth because of gravity. But the high orbital speed, tangent to the surface of the Earth, causes the fall towards the surface to be exactly matched by the curvature of the Earth away from the shuttle. In essence, the shuttle is constantly falling all around the Earth.

Because the weight of an object depends on the mass of the object, the mass of the attracting object, and the square of the distance between them, the surface weight of an object varies from planet to planet. We have derived a gravitational acceleration for the surface of the Earth, ge = 9.8 m/sec^2, based on the mass of the Earth and the radius of the Earth. There are similar gravitational accelerations for every object in the solar system which depend on the mass of the object and the radius of the object. Of particular interest for the Vision for Space Exploration, the gravitational acceleration of the Moon gm is given by:

gm = G * m Moon / (d Moon)^2

gm = 1.61 m/sec^2 = 5.3 ft/sec^2

and the gravitational acceleration of Mars gmar is given by:

gmar = G * m Mars / (d Mars)^2

gmar = 3.68 m/sec^2 = 12.1 ft/sec^2

The mass of a rocket is the same on the surface of the Earth, the Moon and Mars. But on the surface of the Moon, the weight force is approximately 1/6 the weight on Earth, and on Mars, the weight is approximately 1/3 the weight on Earth. You don't need as much thrust to launch the same rocket from the Moon or Mars, because the weight is less on these planets.

All forces are vector quantities having both a magnitude and a direction. For a rocket, weight is a force which is always directed towards the center of the Earth. The magnitude of this force depends on the mass of all of the parts of the rocket itself, plus the amount of fuel, plus any payload on board. The weight is distributed throughout the rocket, but we can often think of it as collected and acting through a single point called the center of gravity. In flight, the rocket rotates about the center of gravity, but the direction of the weight force always remains toward the center of the Earth.

During launch the rocket burns up and exhausts its fuel, so the weight of the rocket constantly changes. For a model rocket, the change is a small percentage of the total weight and we can determine the rocket weight as the sum of the component weights. For a full scale rocket the change is large and must be included in the equations of motion. Engineers have established several mass ratios which help to characterize the performance of a rocket with changing mass. Full scale rockets are often staged or broken into smaller rockets which are discarded during flight to increase the rocket's performance.
Guided Tours

Rocket Weight:

Forces on a Rocket:

Activities:
Fundamental Terminology: Grade 10-12

Related Sites:
Rocket Index
Rocket Home
Beginner's Guide Home

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Weight is the force generated by the gravitational attraction on the rocket. We are more familiar with weight than with the other forces acting on a rocket, because each of us have our own weight which we can measure every morning on the bathroom scale.

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Lower mass = Higher efficiency

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We can now look at the role of specific impulse in setting the performance of a rocket. A large fraction (typically 90%) of the mass of a rocket is propellant, thus it is important to consider the change in mass of the vehicle as it accelerates.

There are several ways to do this through applying conservation of momentum. Here we will apply the momentum theorem differentially by considering a small mass, , expelled from the rocket during time , Figure 14.2.

The initial momentum of the mass in the control volume (the vehicle) is . The final momentum of mass in the control volume (the vehicle and the mass expelled, ) is

The change in momentum during the interval is
since is a higher order term. Now consider the forces acting on the system which is composed of the masses (the rocket), and (the small amount of propellant expelled from the rocket during time ):
Applying conservation of momentum, the resulting impulse, , must balance the change in momentum of the system:
Then since
where is the propellant mass flow rate, we have
or, for ,

(14..1)

Equation 14.1 is known as The Rocket Equation. It can be integrated as a function of time to determine the velocity of the rocket.
If we set , assume that at , , neglect drag, and set , then we can simplify the rocket equation to

which can be integrated to give
where is the initial mass of the rocket. We can also write this result as
We can view this equation as being similar to the Breguet Range Equation for aircraft. It presents the overall dependence of the principal performance parameter for a rocket (velocity, ), on the efficiency of the propulsion system (Isp), and the structural design (ratio of total mass to structural mass, since the initial mass is the fuel mass plus the structural mass and the final mass is only the structural mass).
Assuming the rate of fuel consumption is constant, the mass of the rocket varies over time as

where is the time at which all of the propellant is used. This expression can be substituted into the equation for velocity and then integrated to find the height at the end of burnout:
which for a single stage sounding rocket with no drag and constant gravity yields
The final height of the rocket can then be determined by equating the kinetic energy of the vehicle at burnout with its change in potential energy between that point and the maximum height. This is left as an exercise for the reader.
To conclude this section, Figure 14.3 shows the most powerful rocket built, the NASA Saturn V rocket, which was used during the Apollo program to reach the Moon.

UnifiedTP

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We can now look at the role of specific impulse in setting the performance of a rocket. A large fraction (typically 90%) of the mass of a rocket is propellant, thus it is important to consider the change in mass of the vehicle as it accelerates.

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This is when the rocket experiences maximum aerodynamic pressure.

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These are sensors that are used to measure the amount of pressure applied, and can be added to the circuit to detect atmospheric pressure changes as the rocket ascends

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A single-chip microcontroller wich will be used to process the data taken from the sensors

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How to read SD cards using Arduino - Roshan

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How to read SD cards using Arduino - Roshan

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Using a formatted SD Card with an Ethernet shield, which has an onboard SD slot. Using the functions setup(), we can create a new file with SD.open() which enables to read and write access to the file, starting at the end. Once opened, use myFile.println() to write a string to the card, which could store the information obtained from the sensors. An examle of the code would look like this:

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https://www.arduino.cc/reference/en/

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control structures and comparison operators

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control structures and comparison operators

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If statements and comparison operators can be used to excecute code when a certain condition is met. This could be used for finding a maximum value by comparing it to a previously recorded value and if it is larger storing it in a variable.

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There are many math functions and operators that could be used on the data gathered from the sensors. In particular max() returns a maximum value from a list, Sqrt(), Sq() root and square values, map() can be used to map values to a new range which is useful since arduino maps the analog voltages it reads between 0 and 1023 and simple operators like +,-,/,*.

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We are using analog sensors so they will be plugged into the analog in pins on the arduino board. When the sensors are taking readings they send a voltage to the analog pin between 0 and 5 volts. This voltage corresponds to the physical quantity the sensor measured e.g for an accelerometer which can measure accelerations between +-3g, an aceleration of 0 (half way between +-3g) would correspond to a voltage value of 1.65V (half way between 0 and 5V) at the analogue pin. Link about accelerometers:
https://www.sparkfun.com/pages/accel_gyro_guide

The analogRead() Function can be used to record the voltage at the analog pins where the sensor is connnected. Ardunio maps the read voltage to a value between 0 and 1023. we can use this to find the voltage at the pin and the corresponding physical quantity from the sensor. On the arduino it takes abaout 100 microseconds to read an analogue signal so the maximum reading rate is 10,000 times a second
In the example below, the variable sensorPin is created to storing the number of the analog pin, A0. This makes the code easier to  read and understand. the value from analogRead(sensorPin) is then stored in the variable sensor value.

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Programming structure - Setup() and loop() functions

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Programming structure - Setup() and loop() functions

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The programming language is structured around 2 functions for which we write code in. Code written in the void setup() section will only be ran once when the board is powered on or the reset button is pressed. This should be used to up set up any initial variables, libraries and pin codes.
The second section where we write code is the void loop(). This runs after the setup() fucntion has run and repeats indefinitely. This is where the main part of the code controlling the board should be written.
The example below shows the pin corresponding to the LED being set up as an output which allows us to control how it behaves. This only needs to be ran once so it goes in the setup function. In the loop function the code makes the LED constantly swictch on and off with a delay.

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Sketches in Arduino refers to program used to write code.  The code is based on C++ and can be uploaded onto the board.

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- Kwasi