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Tsiolkovsky's rocket equation question 
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#1
Nov2612, 06:20 PM

P: 22

How would the equation look if instead of knowing the effective exhaust velocity we knew the force the exhaust was exerting on the rocket.
The equation is: [tex] \Delta V = v_e * ln(\dfrac{m_0}{m_1}) [/tex] would [tex] \Delta V [/tex] still be proportional to the log of the initial mass over the final mass? http://en.wikipedia.org/wiki/Tsiolko...ocket_equation 


#2
Nov2612, 07:06 PM

Sci Advisor
P: 2,470

[itex]\Delta v[/itex] does not depend on thrust. Only on I_{sp} of the propellant. As long as I_{sp} is some constant, the [itex]\Delta v[/itex] will always be proportional to natural log of the mass ratio.



#3
Nov2612, 07:22 PM

P: 22

ah k. i followed the link to specific impulse and it helped me understand.
http://en.wikipedia.org/wiki/Specific_impulse 


#4
Nov2712, 02:34 PM

P: 1,008

Tsiolkovsky's rocket equation question



#5
Nov2712, 04:50 PM

Sci Advisor
P: 2,470

Depending on definition. For impulse per weight, v = I_{sp}*g. For impulse per mass, v = I_{sp}. Both conventions are used, mostly, depending on application. For rocket taking off from Earth's surface, I_{sp} per weight is a more directly useful quantity. For rocket accelerating in deep space, you just want the exhaust velocity, so I_{sp} per mass.



#6
Nov2712, 07:54 PM

P: 1,008

(Note that I use g_{0} rather than g  this is because no matter where you are in the solar system (or elsewhere), g_{0} = 9.8 m/s^{2}, and since it is a conversion factor rather than a variable, it is independent of the local gravity field) 


#7
Nov2712, 08:56 PM

Sci Advisor
P: 2,470

1) I_{sp} = dp/dw = (dp/dm)/g 2) I_{sp} = dp/dm = v_{e} Both are used in the literature and you differentiate by the units. First definition gives you units of inverse seconds. Second definition gives you units of m/s and is identical to exhaust velocity for a conventional rocket. 


#8
Nov2712, 09:10 PM

P: 1,008

I've never seen the second one called I_{sp}  everywhere I've seen it used, it was called effective exhaust velocity. If it is called I_{sp} anywhere, it is at least a somewhat nonstandard usage. Also, just because I'm in a somewhat nitpicky mood at the moment, it's not necessarily identical to exhaust velocity. It's identical to exhaust velocity if and only if the nozzle is perfectly expanded (and thus the pressure thrust is zero). Otherwise, there will be a difference between effective exhaust velocity and actual exhaust velocity.



#9
Nov2712, 09:18 PM

Mentor
P: 15,066




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