Figure 5-12. A graph of the rocket equation (Wikipedia)
mass to be much larger than the final mass. What does that mean? Your rocket is mostly made of propellant. There is very little mass left for the body of the rocket, and more importantly, the payload that you want to send into space. This is a true fact about rockets. The need for huge amounts of propellant in missions with a large delta v sparks research into propellant efficiency, since the cost of the propellant is a major factor in the cost of rocketry with chemical reaction engines. There are alternative ways to express the ideal rocket equation which then let you look at the propellant consumption. The rocket equation can be written in terms of the propellant mass ratio as mi mf
Δv
= e ve
the mass ratio increases for different ratios of Δv compared to ve. It illustrates how rapidly the mass ratio increases with respect to delta v. The rocket equation can also be written in terms of the amount of propellant mass: Δm = mi − mf = mf (e ve − 1). Δv
From this equation you can see that when Δv is Δv
very small compared to ve, e ve becomes a small number and little propellant mass is needed. When Δv is equal to ve, then using e 1 = 2.7128, you get that you need nearly twice as much as the rocket’s dry mass to be propellant. Finally, when Δv is large compared to ve, the growth is exponential and you need a lot of propellant mass relative to the dry mass. This is generally the case for rockets launching from Earth into space, as you’ll see in the next chapter.
where e is the e-function, the inverse function of the natural logarithm. Figure 5-12 shows you how 111