Rocket Fundamentals (Ideal Rocket Equation Derivation, Specific Impulse) | Rocket Trajectories 1

Alfonso Gonzalez - Astrodynamics & SE Podcast

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This video covers the fundamental equations needed to simulate rocket trajectories, such as the Tsiolkovsky / ideal rocket equation and specific impulse. Note that the equations for the position over time of rocket trajectories have no analytical solution, and thus must be solved numerically.
In its most abstract sense, a rocket is a vehicle which expels mass to accelerate. This can apply to something as simple as a balloon, which when is opened, air goes out in one direction, and the balloon accelerates in the opposite direction.
In order to understand the derivation of the Tsiolkovsky / ideal rocket equation, we must make sure we understand Newton’s second law, which states that the rate of change of momentum is directionally proportional to the force applied, in the direction of the force. And note that a lot of times we’re used to seeing Newton’s second law as F = ma. But this is only true when the mass of the system is constant. In this case, mass is factored out of the derivative, leaving us with this equation. B for rockets, mass is constantly changing, so we cannot make this assumption.
This video goes on to cover the derivation of the Tsiolkovsky / ideal rocket equation, which begins from the conservation of linear momentum and arrives at its final form after an integration.
CORRECTION: It was pointed out in the comments that the largest deviations from the ideal rocket equation come from gravity losses, which I did not mention in the video. That will be a whole video of its own in this series.
Links to the Space Engineering Podcast (RU-vid, 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 #rocketscience #idealrocketequation

Опубликовано:

23 июл 2024

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Комментарии : 26

@denissopichev5986 3 года назад

Great lecture! Regarding the ideal scenario: gravitational losses are the greatest losses (\int g dt) in comparison with aerodynamics and control losses. Looking forward to seeing explanations about launch trajectories (pitch program), how to find them in both ways: direct and indirect approaches.

@alfonsogonzalez-astrodynam2207 3 года назад

Yes you're right thank you for adding this! I should have put more thought into how I presented that, I'll be sure to correct it in the future videos in this series. The book Orbital Mechanics for Engineering Students by Howard D. Curtis has a chapter on rocket trajectories (chapter 11) and MATLAB functions for a gravity turn trajectory that I'll be referencing

@crazytextstories4u 2 года назад

hay im just starting rocket science do you think you could help

@DestroyerDunnski Год назад

That's the best rocket equation and specific impulse explanation I have found yet. Your derivation of the rocket equation was much much cleaner than I have seen in other derivations. Clean and simple way of implication specific impulse directly into the equation. Your caveats of SI in the case of sea level vs. vacuum, etc. was also very helpful.

@alfonsogonzalez-astrodynam2207 3 года назад

Let me know what topics you'd like me to cover! I have a list of topics in mind that I show at the end of the video (I forgot to put maximum dynamic pressure in there), so let me know what you think / if you have other ideas

@amonzi8646 2 года назад

Can you please do a calculation of the Saturn V's specific impulse? I can't find anything on it anywhere, just the value.

@kareemsalessi Месяц назад

@@amonzi8646 Saturns, SpaceX, etc, are all Fake-Rockets which take over 10 seconds to go up 100 meters, while real rockets are up several miles in 10 seconds.

@harvek4158 6 месяцев назад

I had such a troubling time understanding specific impulse, thank you!

@premyaragarla3600 2 года назад

Really well made and clear, and it was exactly what I was looking for to understand these concepts for my project!

@mrlucmorin Год назад

Great job!

@bencornforth1500 3 года назад

Thank you Alfonso for this video, I’m a student and one of the equations helped me with my launch vehicle plots. Definitely subscribing you have a bunch of useful videos.

@alfonsogonzalez-astrodynam2207 3 года назад

I'm glad to hear it! Which ones have you found to be most useful? I'm currently thinking about which series I want to be prioritizing, since there is 4 of them

@matthewlomeo6550 3 года назад

Another great video!

@alfonsogonzalez-astrodynam2207 3 года назад

Thanks again!

@DhruvSondhi05 3 года назад

awesome video :)

@alfonsogonzalez-astrodynam2207 3 года назад

I'm glad you enjoyed it! I'm excited about this series

@ElArmanGee Год назад

I am a little unsure of what the specific impulse is if a spacecraft/rocket is in a vacuum and in deep space (out of Earth's gravitational field, or any other). Does the equation still hold given that the gravitational constant would be negligible?

@senaysew8231 2 года назад

Mn, I love your teaching method

@alfonsogonzalez-astrodynam2207 2 года назад

Thank you for the kind words!

@catsonair9432 2 года назад

Quick Question when it comes to specific impulse, wouldnt the equation have to be rewritten for now Vfuel aka Isp1 is no longer a constant value?

@alfonsogonzalez-astrodynam2207 2 года назад

It all depends on how you want to model the engine thrust. In real life, the thrust and specific impulse are changing throughout flight, because of engine throttling and atmospheric pressure. However you can still do decent 1st order analysis assuming constant thrust and isp for the first stage, and then changing it for the second stage. Later in this series I'll be going over throttling for max-q, so I'll be sure to cover this concept.

@engchoontan8483 Год назад

I feel the math while downhill petrol-scooter 125cc...

@gustavomorales2055 3 года назад

Do you have the code for the graph.

@alfonsogonzalez-astrodynam2207 3 года назад

I'm not going to be posting any of the rocket trajectory simulation software unfortunately. But I do have a bunch of orbital mechanics simulation software posted in the GitHub repository for this channel! github.com/alfonsogonzalez/AWP And here is a video explaining the whole Spacecraft class in that repository line by line: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yMJ_VU3jt7c.html And here is the Python script for the ideal rocket equation plot: ''' Ideal Rocket Equation plot ''' import numpy as np import matplotlib.pyplot as plt plt.style.use( 'dark_background' ) g0 = 9.81e-3 def dv( psi, isp ): return -isp * g0 * np.log( 1 - psi ) if __name__ == '__main__': psi = np.arange( 90, 100, 0.1 ) / 100.0 dvs0 = dv( psi, 200 ) dvs1 = dv( psi, 300 ) dvs2 = dv( psi, 400 ) psi *= 100 plt.figure( figsize = ( 12, 8 ) ) plt.plot( psi, dvs2, 'w', label = r'$I_{sp} = 400 s$' ) plt.plot( psi, dvs1, 'c', label = r'$I_{sp} = 300 s$' ) plt.plot( psi, dvs0, 'm', label = r'$I_{sp} = 200 s$' ) plt.hlines( 13.3, psi[ 0 ], psi[ -1 ], color = 'r', linestyle = '--', label = 'Mars Transfer' ) plt.hlines( 11.9, psi[ 0 ], psi[ -1 ], color = 'g', linestyle = '--', label = 'GTO' ) plt.hlines( 9.4 , psi[ 0 ], psi[ -1 ], color = 'b', linestyle = '--', label = 'LEO' ) plt.xlim( [ 90, 100 ] ) plt.ylim( [ 0, 16 ] ) plt.xticks( np.arange( 90, 100.5, 0.5 ) ) plt.yticks( range( 0, 16, 2 ) ) plt.grid( linestyle = 'dotted' ) plt.ylabel( r'$\Delta$V ( km / s )', size = 15 ) plt.xlabel( '% Fuel Mass', size = 15 ) plt.title( r'$\Delta$V vs. % Fuel Mass', size = 20 ) legend = plt.legend( bbox_to_anchor = ( 1, 1 ), prop = { 'size': 15 } ) plt.savefig( '/mnt/c/Users/alfon/RTWP/v1_fundamentals/ideal_eq.png', bbox_extra_artists = ( legend, ), bbox_inches = 'tight', dpi = 300 )

@DestroyerDunnski Год назад

You can code it yourself for the Isp graph with simply: y= -400*9.8*ln(1-x) where 0

@boptah7489 10 месяцев назад

No. Newtons second law does not talk about momentum at all. This is N2 from Principia " The alteration of motion is ever proportional to the motive force impressed ; and is made in the direction of the right line in. which that force is impressed." momentum is not a force.