Leicontis Posted December 15, 2011 Share Posted December 15, 2011 So, I decided it was time to actually try mathing some of this stuff out. I was able to work out how to calculate delta-v for a rocket under continuous thrust in 0G vacuum, but when I tried to actually start working in gravity to figure total altitude, I hit a dependency loop that I\'m too rusty at this to resolve. Anybody know how to solve this and/or where I could find a solution?What I\'ve got so far:Assumptions:[li]Constant thrust[/li][li]Start at t=0 and y=0[/li][li]No jettisoned parts[/li][li]No atmospheric drag[/li] Link to comment Share on other sites More sharing options...
Hypocee Posted December 15, 2011 Share Posted December 15, 2011 Not too much help, but if you\'re trying to extract 'altitude' you\'re probably best going through kinetic and potential energy-style equations rather than translating things into velocity; presumably the mass and time units will fall out in the end. I also notice that if I\'m reading your equations right, your altitude result is going to be altitude at burnout rather than maximum altitude reached. I suspect you\'re more interested in the latter, and they\'d only be equal by massive coincidence.Also, because I\'m an Internet Cheater...it\'s been too long since I worked with logarithms and I wasn\'t great anyway, but are you sure your fundamental equation is a correct transform of the Tsiolkovsky Equation? Link to comment Share on other sites More sharing options...
Saaur Posted December 15, 2011 Share Posted December 15, 2011 All the equations you\'ll ever need, right here.http://www.thespaceshop.com/itonroscash.htmlI have it on a coffee mug here at my desk, too. Link to comment Share on other sites More sharing options...
Leicontis Posted December 16, 2011 Author Share Posted December 16, 2011 All the equations you\'ll ever need, right here.http://www.thespaceshop.com/itonroscash.htmlI have it on a coffee mug here at my desk, too. Looks useful, but I\'m not entirely clear on the meanings of all of the variables/symbols. If I can translate that, it\'ll probably help immensely. Link to comment Share on other sites More sharing options...
Ivan Ivanovich Posted December 16, 2011 Share Posted December 16, 2011 Also, because I\'m an Internet Cheater...it\'s been too long since I worked with logarithms and I wasn\'t great anyway, but are you sure your fundamental equation is a correct transform of the Tsiolkovsky Equation?I\'d say it looks like he turned the full/empty masses around, which cancels each other out in the end, though.delta-v=veq*ln(m0/m1)=veq*(ln(m0)-ln(m1)Isp=Veq/g and F=Isp*mdot*g -> F/mdot=Isp*g -> F/mdot=Veq -> mdot=m0-m1/t -> F*t/(m0-m1)=veqYup, looks correct. But the result just doesn\'t make sense... Link to comment Share on other sites More sharing options...
Guest ThatCrazyPilot Posted December 18, 2011 Share Posted December 18, 2011 I am 14, what is this? =P Link to comment Share on other sites More sharing options...
Ivan Ivanovich Posted December 18, 2011 Share Posted December 18, 2011 The stuff you\'ll learn at college, if you go into engineering. Link to comment Share on other sites More sharing options...
Leicontis Posted December 18, 2011 Author Share Posted December 18, 2011 I\'d say it looks like he turned the full/empty masses around, which cancels each other out in the end, though.delta-v=veq*ln(m0/m1)=veq*(ln(m0)-ln(m1)Isp=Veq/g and F=Isp*mdot*g -> F/mdot=Isp*g -> F/mdot=Veq -> mdot=m0-m1/t -> F*t/(m0-m1)=veqYup, looks correct. But the result just doesn\'t make sense...Want me to show my work? Link to comment Share on other sites More sharing options...
Guest ThatCrazyPilot Posted December 18, 2011 Share Posted December 18, 2011 The stuff you\'ll learn at college, if you go into engineering. I feel pain in my soul :\'( Link to comment Share on other sites More sharing options...
WX_Echo Posted December 20, 2011 Share Posted December 20, 2011 You\'ve done a decent job so far. A couple of recommendations.- Express the difference between the natural logs of the dry and full masses as a ratio [i.e. ln(mass_dry) - ln(mass_full) = ln(mass_dry/mass_full)]- the variables in front of this natural logarithm actually work out to be the effective exhaust velocity of the rocket engine. Finally, this analysis has one fatal flaw: without accounting for drag within the atmosphere (which transfers your equation into a non-linear ODE), you\'re restricting yourself to orbital maneuvers. If your burn is applied at a constant orbital altitude, then the work done by gravity on your rocket is zero and your gravity-loss term is meaningless. In this case, your delta-v is simply a function of the mass ratio and exhaust velocity.For the assumptions you provided, the solution to your equation will also require you to solve a non-linear ODE. This will require numerical integration methods that are probably beyond the scope of your analysis. If you would like to try your hand at the constant gravity field version, however, you can do so knowing there is a convenient analytically solution waiting for you at the end.delta-v = c * ln(mass_full/mass_dry) - g * t (note: c = exhaust velocity)Enjoy! Link to comment Share on other sites More sharing options...
Leicontis Posted December 20, 2011 Author Share Posted December 20, 2011 I had basically planned on trying to implement gravity first, then once I had that worked out, try to account for drag. If I\'m going to have to resort to numerical integration, that takes this from a curiosity project in Excel to a more challenging proposition in Python, which I\'m not certain I feel like tackling at the moment... Link to comment Share on other sites More sharing options...
mincespy Posted December 20, 2011 Share Posted December 20, 2011 *Reads All Responses**Mind Explodes* Link to comment Share on other sites More sharing options...
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