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I made a model rocket.

Specifications:

Total weight - 1.635 N (wet).

It has a custom solid rocket motor with black powder producing 5 N for 15 sec.

So how can I calculate how high will it travel?

Some equations would be helpful....

My rocket is guided , works on thrust vector control , i could've just flown it to find the awnsere of my question but in future , i have plans of propulsive landing so i might need to have these precise calculations.

i did some research and found out Thrust - (mass x 9.8)/mass is my acceleration , and this will apply for all the cases , also during descent?? Why doesn't the acceleration of 9.8 need to be deducted from my final acceleration?

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  • $\begingroup$ Hello Shitka. How much powder does the rocket store prior to ignition? $\endgroup$ – joseph h Oct 2 '20 at 4:42
  • $\begingroup$ sorry , i am new to this field i did not understand what you just asked? $\endgroup$ – SHikha Mittal Oct 2 '20 at 4:44
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    $\begingroup$ Your rocket weighs about 16 N, which is greater than the thrust you've provided for your motor. By these figures, your rocket shouldn't lift off the ground. Are you sure the thrust force is correct? $\endgroup$ – DanDan0101 Oct 2 '20 at 4:49
  • $\begingroup$ OK. So your question states that (when ignited) the rocket burns the black powder (or the "fuel") such that a force of 5N acts for 15 seconds. To determine its maximum height you would need to know how much of this fuel it can store. $\endgroup$ – joseph h Oct 2 '20 at 4:53
  • $\begingroup$ If you're looking for a practical and accurate result and aren't as interested in learning the equations yourself, I'd recommending checking out openrocket.info $\endgroup$ – Leo Adberg Oct 2 '20 at 4:54
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So first you need to calculate the resultant force and this is $F_R = F_{Thrust} - F_{Weight} = (5 - 1.635)N$.

Next you should calculate the net acceleration. This would be the resultant force divided by the mass and your mass will be $1.635/g$. Let's call this $a$. Now you know that the rocket increases its velocity by $a$ every second so over the time interval you specify, which is 15 seconds the velocity will be $a \times 15$.

  • I have not factored in loss of mass as the rocket climbs, since the OP did not provide this information. The OP must be either looking for approximate values or the mass lost is relatively negligible.
  • Noting this is not a homework question so that it's OK to provide this much detail.
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  • $\begingroup$ so according to your equation , the acceleration should be 21 m/s . $\endgroup$ – SHikha Mittal Oct 2 '20 at 6:14
  • $\begingroup$ here how can i compensate for drag and aerodynamic forces? Is there a way to determine that or the theoretical acceleration will be the actual acceleration $\endgroup$ – SHikha Mittal Oct 2 '20 at 6:15
  • $\begingroup$ That should be about right for $a=21m/s^2$. And acceleration has units of $m/s^2$ not $m/s$. Drag and aerodynamic forces are complicated and are determined by the shape of the rocket, air pressure and density. $\endgroup$ – joseph h Oct 2 '20 at 6:35
  • $\begingroup$ is there a rough way to estimate a range of possible acceleration after considering aerodynamic forces and drag? $\endgroup$ – SHikha Mittal Oct 2 '20 at 10:27

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