propellant mass ratio

[r1pper]

i was hoping somone can help explain something to me. i'm a student and have been working on an assignment. basically we are supposed to optimize a multistaged rocket, try and minimize the initial mass. <br /><br />now from what i gather is there are two ways to approach this problem; one you can assume that the propellant mass ratio is constant and solve for the initial mass. The second involves splitting up the total delta velocity required into the seperate delta velocities of each stage. <br /><br />so the first way is easy, book type stuff. but the second approach seems to be more of the plug and chug sort. i decide what the velocity is of each stage then calculate the initial mass based on what i decide.<br /><br />we're restricted (given) the Isp and the step mass fraction. <br /><br />the part i really dont understand is what are you physically doing when you "choose the delta v of each stage". Are you changing the propellant mass of each stage?<br /><br />and by doing so (because of the fixed step mass fraction) also varying the structural mass used?<br /><br />any help is greatly appreciated.<br />rip

 

[barrykirk]

If the ISP is a fixed constant that you were given.<br /><br />Than the Delta V of each stage depends solely on the <br />initial mass and the final mass of that stage. Please <br />remember that you have to add the mass of all of upper<br />stages to the initial and final masses.<br /><br />Example<br /><br />Delta V = ISP * ln ( m0 / m1 )<br /><br />where ln is the natural log, m0 is the initial total mass,<br />and m1 is the final total mass.<br /><br />So for the first stage of a three stage rocket.<br /><br />m0 = starting mass of first stage + mass of second stage + mass of third stage.<br /><br />m1 = final mass of first stage + mass of second stage +<br />mass of third stage.<br /><br />Note that this equation does NOT take into account <br />gravity losses or aerodynamic losses.<br /><br />The gravity losses are simpler, I didn't see anything<br />in your statement about thrust to weight ratio of the <br />engines.<br /><br />As an example, if your first stage engine develops <br />10,000 Lbs force and your entire vehicle initial weight<br />is 9,000 Lbs. Your initial acceleration is going to be<br />very slow. Most of your Delta V is going to be used up<br />by fighting gravity.<br /><br />Aero losses are much harder to calculate and depend on<br />a whole lot of factors.<br /><br />There is a theoretical velocity for the earth called the<br />escape velocity, it's about 25,000 MPH.<br /><br />However, any real practical rocket will need a much<br />higher Delta V to acheive Escape Velocity.<br /><br />This is needed to overcome those gravity and aero<br />losses.<br /><br />Hope this helps.

 

[josh_simonson]

I've heard that the optimal ratio of first to second stage is in the vicinity of 5:1. That'd be a good starting point. <br /><br />How is the dry weight of the stage calculated? If it's just something like 15% of the weight of the fuel it holds, an infinity stage rocket would be optimal. <img src="/images/icons/wink.gif" /> How this is calculated will determine the optimal number of stages.<br /><br />I had a simlar multi-variable problem in grad school and I just wrote a C program to successively optimize each of the parameters I had while holding the others fixed until it came to a satisfactory solution. No need to make a multi-dimentional table if you can just try a point, find the slope and work your way uphill.