Ok, so i finally finished my personal project, BUT it will be used for my senior paper since its interesting results.
Here is the background; I took sensor data that was given to me from various members here on the forums. I then used excel in 2 different ways to find the Drag Coefficient (Cd) of the rocket.
A little about Cd for beginners, this number usually has been calculated from HUNDREDS and THOUSANDS of tests in a windtunnel. IE, they take the rocket, put it in the wind tunnel and find the FORCE the wind pushes on the rocket at low, medium and HIGH speeds. Using the Drag Force equation
You then massage the above equation a little bit to solve for Cd. Since you have the force of drag(Fd), area, velocity, and air density. you can calculate the Cd quickly with wind tunnel data.
But what if you didnt have a wind tunnel? This is where i come in, i kind of made a "virtual" wind tunnel in a way, but not really. I used excel to calculate theoretical (modeled) velocity values based off of total force the rocket is feeling and acceleration as in the next set of equations: Frr is for friction of a car, not a rocket. its not needed for rockets
This gave me a list of MODELED aka calculated velocities. I then had excel compute the difference between my calculated velocities and the ACTUAL velocities then squared that value for my error. I gave excel an initial guess for Cd, because you ALWAYS have to have an initial guess to work with, even if its WAY off. Then using the excel add-in called solver, i let it adjust the Cd until my error was close to 0. Once it found this Cd value, i graphed the modeled velocities to the actual and they were right on top of each other, meaning, that i found the Cd of that rocket for that particular set of data.
To verify this even more, i calculated the Cd from a first order diff eq for EACH velocity, so about 389 different entries, using the following equations:
I then solved for B
Once i got a value back, such as 0.00647 for B, i then back substituted it back into the B=(Cd)(A)(rho)(0.5) and solved for Cd yielding 0.67 and open rocket says its 0.63.. so i am pretty close. Here is the graph of beta (y axis) and velocity (x axis) you can see how around 200m/s, this is where the Cd doesnt change much
SUPER grateful for the sensor data and ALL the help i received on this from the physics forums. I hope you enjoy. This was an excellent learning project for me.
Here is the background; I took sensor data that was given to me from various members here on the forums. I then used excel in 2 different ways to find the Drag Coefficient (Cd) of the rocket.
A little about Cd for beginners, this number usually has been calculated from HUNDREDS and THOUSANDS of tests in a windtunnel. IE, they take the rocket, put it in the wind tunnel and find the FORCE the wind pushes on the rocket at low, medium and HIGH speeds. Using the Drag Force equation
You then massage the above equation a little bit to solve for Cd. Since you have the force of drag(Fd), area, velocity, and air density. you can calculate the Cd quickly with wind tunnel data.
But what if you didnt have a wind tunnel? This is where i come in, i kind of made a "virtual" wind tunnel in a way, but not really. I used excel to calculate theoretical (modeled) velocity values based off of total force the rocket is feeling and acceleration as in the next set of equations: Frr is for friction of a car, not a rocket. its not needed for rockets
This gave me a list of MODELED aka calculated velocities. I then had excel compute the difference between my calculated velocities and the ACTUAL velocities then squared that value for my error. I gave excel an initial guess for Cd, because you ALWAYS have to have an initial guess to work with, even if its WAY off. Then using the excel add-in called solver, i let it adjust the Cd until my error was close to 0. Once it found this Cd value, i graphed the modeled velocities to the actual and they were right on top of each other, meaning, that i found the Cd of that rocket for that particular set of data.
To verify this even more, i calculated the Cd from a first order diff eq for EACH velocity, so about 389 different entries, using the following equations:
I then solved for B
Once i got a value back, such as 0.00647 for B, i then back substituted it back into the B=(Cd)(A)(rho)(0.5) and solved for Cd yielding 0.67 and open rocket says its 0.63.. so i am pretty close. Here is the graph of beta (y axis) and velocity (x axis) you can see how around 200m/s, this is where the Cd doesnt change much
SUPER grateful for the sensor data and ALL the help i received on this from the physics forums. I hope you enjoy. This was an excellent learning project for me.
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