The Rocket Equation and why it doesn't always work.

The rocket equation is a relationship between the mass of the rocket, the mass of the fuel, the speed of the exhaust and the change in velocity of the rocket.

Here is a derivation of the rocket equation along with a better version.

[rachelkimbrough]

"YOU aren't a constant, you matter, but..." so wholesome, and very well and clearly communicated besides. Thank you for this.

[ManishKumarMishra]

Here are a couple of things that I would like to point out, so usually the mass of propellant is roughly 10 times the 'rocket' but the issue is you can eject all of it at such high speed. And the large number of small masses 'dm' captures it fairly well. Secondly, you mentioned that it is impossible to achieve constant exhaust vel with respect to rocket, if I haven't misunderstood, but that is actually possible. Constant chamber pressure can give you that condition.

[DrJeffSpirkoTAMUCC]

At 3:03, m represents the rocket mass but dm represents a bit of fuel. These should be different variables, such as m_r and dm_f. Then it would be clear that the integral on the right side at 5:00 should be negative of what it is. That's what flips the fraction upside down at 5:35.

[Eigenbros]

Very nice video with a clear explanation

[simondwilkinson]

Perhaps it is worth considering the force on the rocket itself. This idea of instant pellet ejection would require an enormous force and a huge acceleration which would be very impractical. This is evident in the step like velocity vs time graph. For each step the acceleration of the rocket is infinite. If instead you try to just eject your fuel very quickly, then you are back to the continuous fuel ejection case, and you haven’t gained anything. After all, the normal rocket equation doesn’t make any assumptions about how fast (in the sense of kg of fuel per second) the fuel is ejected.

Also the step where dmdv is considered small is completely justified by rigorous calculus, it isn’t an approximation used to simplify the maths.

It is an interesting video, but overall I think I am still a fan of the rocket equation 😉

[beachboardfan]

Gotta sort out your audio. Maybe its on my end, but the audio is super quiet.

[eliasniewerth]

Okay this only works if you know the equasion. I came here from reddit as a chemist thinking: shit I like rockets, what is this?
And get hit by this. With no knowlege on the topic. I understand the words but I am completely lost with the valueables...

What level is this? Who is supposed to understand / what do I need to do first to understand this?

Edit: after finishing the video, I understand the problem but have no idea what was calculated still lol