I have recently been studying basic rocket science and I have been trying to figure out by searching online for tutorials on this particular matter and I have not found anything. The problem I am having is I don't know how to calculate how much thrust power I need to reach a certain acceleration.

Let's say I have a rocket. This rocket has a mass of 2,5 kg. It's weight is 24,5 N, I want it to accelerate with a speed of 2 m/s^2.

How do I calculate that, formulas would be appreciated as I don't want cheats, only help.


closed as off-topic by ACuriousMind Dec 20 '17 at 13:22

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  • $\begingroup$ Pretty much anything useful you do with rockets requires you to consider what kind of fuel you are using. At a minimum, you need to know the specific impulse of the fuel. $\endgroup$ – Chris Dec 19 '17 at 23:07
  • $\begingroup$ Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. $\endgroup$ – ACuriousMind Dec 20 '17 at 13:22
  • $\begingroup$ @ACuriousMind Are you confident enough that this is a homework problem to drop the mod-hammer? To me it looks like a budding rocket scientist who is looking for the correct equations and has grasped the wrong ones. It seems certainly worth asking whether it is homework first. $\endgroup$ – Cort Ammon Dec 20 '17 at 16:25
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    $\begingroup$ @CortAmmon I'm not sure what you mean - our homework policy applies regardless of whether or not the question is actual homework, and just asking for the formulae needed to compute a particular quantity does clearly fall under the HW policy. $\endgroup$ – ACuriousMind Dec 20 '17 at 16:34
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    $\begingroup$ @CortAmmon He's basically asking for a formula to plug all this information into. He didn't really ask about the related concepts. I think you could also make a case for this being "too broad" or even "unclear what you're asking"; because we know nothing about this rocket besides it's "mass", which may or may not include a fuel estimate. $\endgroup$ – JMac Dec 20 '17 at 17:10

The answer to your question is really straightforward: F=MA. You have a mass of 2.5kg, and want a 2m/s^2 acceleration, so the force you need is straightforward to find.

However, in reality, that equation isn't all that useful. The acceleration is going to change as the mass of the rocket decreases (you're burning propellant!). Rocketeers aren't as worried about accelerations as they are about the total change in velocity that the rocket undergoes.

For that, you will want Tsiolkovsky's Rocket Equation.

$$\Delta V=v_e\ln\frac{m_0}{m_f}$$

Where $m_0$ is the starting mass (propellant and all), and $m_f$ is the final mass (which is just the dry mass, after all the propellant is gone). $v_e$ is the effective exhaust velocity, which is a property of your engine and your fuel. It is related to the specific impulse (Isp), $v_e=I_{sp}g_0$ where $g_0$ is the acceleration of gravity at sea level.


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