Rocket Propulsion: Question About Relationship of V and M0/M(t)

[aaaa202]

Did a question about this a few weeks ago, but I thought I might do another, as I don't quite get, what is going on.
The relationship:
v=vex * log(m0/m(t))
tells us that a rocket will attain greater and greater acceleration as time goes. However, when I try to simulate this in Matlab I get the curve attached (time versus velocity). Anyone got an idea, what could be wrong? It looks similar to that of a ln-curve, but shouldn't it look differently. If someone is into Matlab programming, can they please look at what I've failed in my (short!) script (attached).

 

[Filip Larsen]

If you want something to compare with you can look at plot of the normalized rocket equation on WolframAlpha: http://www.wolframalpha.com/input/?i=plot+-ln(1-x)+from+0+to+1 where x-axis is the mass ratio (relative to initial mass) spend as fuel and y-axis is the change in velocity relative in unit of the exhaust speed.

 

[D H]

aaaa202: Typically the independent variable (time in this case) is on the horizontal axis and the dependent variable (velocity in this case) is on the vertical axis. You are plotting time on the vertical axis, velocity on the horizontal.

Switch the arguments to the plot function and all will be well.

 

[aaaa202]

OMG! I can't believe that solved it! Thank you so much!

 

[PJC01]

Hello,

Thank you for your question about the relationship between velocity and the ratio of initial mass to current mass in rocket propulsion. I can offer some insights and suggestions to help clarify the issue.

Firstly, the equation you provided (v=vex * log(m0/m(t))) is known as the Tsiolkovsky rocket equation. It describes the relationship between the velocity of a rocket (v), the exhaust velocity (vex), and the ratio of the initial mass (m0) to the current mass (m(t)) of the rocket. This equation is derived from the principle of conservation of momentum and assumes that the rocket is being propelled by a constant exhaust velocity.

Based on this equation, we can see that as the ratio of initial mass to current mass decreases (meaning the rocket is burning fuel and getting lighter), the velocity of the rocket increases. This is because the rocket is experiencing a decrease in mass, but the exhaust velocity remains constant, resulting in a higher acceleration.

Now, in terms of your simulation in Matlab, there could be a few reasons why the curve you obtained does not match the expected logarithmic shape. One possibility is that your simulation is not taking into account the changing mass of the rocket as it burns fuel. This would result in a constant velocity, rather than an increasing one.

Another possibility is that there may be errors in your script or in the input values you are using. I would suggest double-checking your equations and input values to ensure they are accurate. It may also be helpful to consult with other experts in Matlab programming to review your script and offer suggestions for improvement.

In conclusion, the Tsiolkovsky rocket equation is a fundamental principle in rocket propulsion and describes the relationship between velocity and the ratio of initial mass to current mass. It is important to ensure accurate calculations and simulations in order to understand and predict the behavior of rockets. I hope this response has been helpful and I wish you success in your future simulations and experiments.