The standard form of the rocket equation ÃŽâ€V= 9.81 x Isp x in( (M+F)/(M)) is useful for predicting what a rocket can do, but we rarely need to know that. What would be truly useful would be an equation to tell you exactly *how much* rocket you need to do a given job. Knowing this ahead of time helps efficiency by avoiding over-engineering your stages (thus making the entire rocket bigger and heavier than it needs to be) or under- engineering (thus wasting time with failed missions or needless math). This form of the equation assumes that you know: -How much payload /assorted crap you need to move (in metric tons) -How much delta-vee you need to generate (in m/sec) -what kind of rockets you intend to use (mass in metric tons and Isp in seconds) and how many (N) and -the ratio of tank mass to fuel in the tanks you'll be using. This ratio is generally constant from one size tank to another for the same type and manufacturer. The equation will spit out the mass of fuel you need to accomplish the goal and (by extension) the mass of tankage needed to carry it. I will break it down here into smaller chunks to keep it manageable and because the entire equation looks like crap in text. First step is to add up all the weight you will be lifting that's not directly related to holding your fuel or spitting it out. This would be your payload, engines, ladders, decouplers, science, etc. It does *not* include tanks or fuel (because you don't know that yet) M= P+Sr+E where P = payload and E=total mass of your engines and Sr = random stuff (in metric tons) and Rwd= e^( ÃŽâ€V/9.81x Isp) where e=the natural logarithm base (2.718) ÃŽâ€V= your desired change in velocity in M/Sec and Isp is the specific impulse of your chosen engine type in seconds. With these established, we can express the entire equation F=M(Rwd-1)/(1+Rtf) where F= the required mass of fuel and oxidizer (in metric tons) M= defined above (in metric tons) Rwd= defined above (ratio) and Rtf= the ratio of the mass of your chosen tank type to the mass of the fuel it holds. (ratio) Having defined F, we can figure out how much mass our tanks will cost us using the equation Mt= F*Rtf where Mt = tank mass in metric tons. And so our stage mass is known. Ms=F+E+Sr Add this to the payload, and you know how much mass the preceding stage will have to accelerate.
The standard form of the rocket equation ÃŽâ€V= 9.81 x Isp x in( (M+F)/(M)) is useful for predicting what a rocket can do, but we rarely need to know that. What would be truly useful would be an equation to tell you exactly *how much* rocket you need to do a given job. Knowing this ahead of time helps efficiency by avoiding over-engineering your stages (thus making the entire rocket bigger and heavier than it needs to be) or under- engineering (thus wasting time with failed missions or needless math). This form of the equation assumes that you know: -How much payload /assorted crap you need to move (in metric tons) -How much delta-vee you need to generate (in m/sec) -what kind of rockets you intend to use (mass in metric tons and Isp in seconds) and how many (N) and -the ratio of tank mass to fuel in the tanks you'll be using. This ratio is generally constant from one size tank to another for the same type and manufacturer. The equation will spit out the mass of fuel you need to accomplish the goal and (by extension) the mass of tankage needed to carry it. I will break it down here into smaller chunks to keep it manageable and because the entire equation looks like crap in text. First step is to add up all the weight you will be lifting that's not directly related to holding your fuel or spitting it out. This would be your payload, engines, ladders, decouplers, science, etc. It does *not* include tanks or fuel (because you don't know that yet) M= P+Sr+E where P = payload and E=total mass of your engines and Sr = random stuff (in metric tons) and Rwd= e^( ÃŽâ€V/9.81x Isp) where e=the natural logarithm base (2.718) ÃŽâ€V= your desired change in velocity in M/Sec and Isp is the specific impulse of your chosen engine type in seconds. With these established, we can express the entire equation F=M(Rwd-1)/(1+Rtf) where F= the required mass of fuel and oxidizer (in metric tons) M= defined above (in metric tons) Rwd= defined above (ratio) and Rtf= the ratio of the mass of your chosen tank type to the mass of the fuel it holds. (ratio) Having defined F, we can figure out how much mass our tanks will cost us using the equation Mt= F*Rtf where Mt = tank mass in metric tons. And so our stage mass is known. Ms=F+E+Sr Add this to the payload, and you know how much mass the preceding stage will have to accelerate.
