Sounding Rocket Trajectories | Rocket Trajectories 2

This video covers all the equations of motion necessary to simulate a sounding rocket trajectory, which is a nearly vertical flight. The motion is 1 dimensional, but even one dimensional motion of rocket trajectories can be very interesting to simulate and analyze and is a baseline to build up to more complex simulations like gravity turn trajectories.
Link to video covering Newton's universal law of gravitation and the two body problem: • The Two Body Problem (...
The three forces we will model are are gravity, thrust and aerodynamics drag. The sum of the forces on the rocket is equal to the thrust plus the force due to gravity and that is equal to the change in momentum of the rocket with respect to time (From Newton’s 2nd law). In the propagation, we can use F = ma, since the differential equation only considers a single moment in time at each propagation time step. So from that we get the acceleration of the rocket is equal to the rocket’s thrust divided by its mass (at that specific time) plus the acceleration due to gravity.
For the acceleration due to gravity, we use Newton’s universal law of gravitation which states that the force due to gravity on the rocket is equal to the gravitational constant * the mass of the Earth * the mass of the rocket divided by the distance between them squared (the distance from the center of mass of the earth to the rocket, not the earth surface). Since the gravitational constant is constant in our universe, and the mass of the earth is constant, we put those numbers together to define a mu value for the Earth.
Again using Newton’s second law, we divide both sides of the equation by the rocket’s mass to get that the magnitude of the gravitational acceleration onto the rocket is equal to mu of earth over r squared, where r in this case is the radius of the earth plus the altitude of the rocket.
Links to the Space Engineering Podcast (RUclips, Spotify, Google Podcasts, SimpleCast):
• Space Engineering Podc...
open.spotify.com/show/01Gcgly...
space-engineering-podcast.sim...
podcasts.google.com/feed/aHR0...
Link to Orbital Mechanics with Python video series:
• Orbital Mechanics with...
Link to Spacecraft Attitude Control with Python video series:
• Spacecraft Attitude Co...
Link a Mecánica Orbital con Python (videos en Español):
• Mecánica Orbital con P...
Link to Numerical Methods with Python video series:
• Numerical Methods with...
#rockettrajectories #soundingrockettrajectories #rocketscience

[@catsonair9432]

100% underrated channel, keep up the great work :)

[@alfonsogonzalez-astrodynam2207]

Thank you! Will do. The best way to help the channel grow is to share it with anyone who you think would benefit from / enjoy watching the videos

[@kellanfeng]

You deserve more recognition, nice work man

[@alfonsogonzalez-astrodynam2207]

Thank you! The best way to support the channel is to share with others so slowly but surely people will find out about the videos

[@haikalxy]

A very thorough explanation! Thank you!

[@gaganaut06]

Thanks

[@Nammaooruscience]

Great video

[@alfonsogonzalez-astrodynam2207]

Glad you enjoyed it!

[@tekslice]

Great video. Can't wait for one dealing with gravity turn using the non-flat earth model.

[@alfonsogonzalez-astrodynam2207]

Me too! It will be very interesting reading more about it and implementing it into the simulations. The Rocket class I have now is set up to do an arbitrary amount of phases for sounding or gravity turn ODEs but I haven't implemented a non-flat model yet

[@karteektavarageri5140]

Nice video. I have a problem I'm working on similar to this. It's for a sounding rocket and we need to calculate the acceleration, with respect to time which I've done, but I'm having trouble figuring out the velocity and position of the aircraft during and after burn time. Is there any way I could reach out to you like through email about it? Thanks.

[@alfonsogonzalez-astrodynam2207]

I think you're looking for methods of how to solve 2nd order ordinary differential equations numerically. This is because acceleration is the first derivative of velocity and second derivative of position. Check out this playlist with 4 videos (currently), where I walk through all the fundamentals of ordinary differential equations, ODE solvers, and then how to create an RK4 solver yourself to propagate a spacecraft trajectory, which will be a similar process to this rocket trajectory, just slightly different equations of motion.
ruclips.net/p/PLOIRBaljOV8hBJS4m6brpmUrncqkyXBjB
Also, there is a GitHub repo where I post all the software for the videos: github.com/alfonsogonzalez/AWP

[@karteektavarageri5140]

@@alfonsogonzalez-astrodynam2207 Thank you Alfonso, I'll be sure to check those out. The equation for acceleration of the sounding rocket is given as :
du/dt = ((c*zeta/burntime)/(1-zeta*t/burntime)) - g - ((0.5*Cd*row*u^2*A/mass_initial)/(1-zeta*t/burntime))
From here we're asked to find velocity graph as a function of time, and position as a function of time. I'm not sure exactly how to approach it. But I'll check out your videos as well thank you.

[@alfonsogonzalez-astrodynam2207]

Yes those videos go through that process of solving the 2nd order ordinary differential equation, and specifically its implementation in Python. Definitely feel free to ask questions in the comments of those videos as well if anything is confusing

[@karteektavarageri5140]

@@alfonsogonzalez-astrodynam2207 Ok I'll be sure to do that then. Thank you!

[@kareemsalessi]

ONLY THEORIES::: Rockets do NOT launch on theories, but on facts!!!