VK=Pb g0 Ln [(GT+GJ)/GJ]
Where: VK-terminal velocity of rocket; Pb- 1 specific thrust (specific impulse); G0- ground gravity acceleration; GT—— Propellant mass when the rocket takes off; Structural quality of GJ- rocket, including payload.
The so-called ideal speed is that many factors are ignored in this formula, such as the loss caused by aerodynamic drag and gravity, and the change of g0 with the decrease of altitude. The speed calculated by this formula is greater than the actual value, so it is called ideal speed. Nevertheless, the formula is still sufficient to explain the relationship between speed and specific thrust and mass ratio. With the gradual entry of human beings into deep space exploration, the functions of spacecraft are increasing, which requires rockets to have greater carrying capacity, so multi-stage rockets appear. Simply put, multistage rockets are formed by connecting several single-stage rockets together. One rocket works first, then separates from other rockets, then the second rocket continues to work, and so on. Rockets composed of several rockets are called multistage rockets, such as two-stage rockets and three-stage rockets. It should be pointed out that if more than one rocket works at the same time, it can only be counted as level one. The advantage of multi-stage rocket is that it abandons useless structure every once in a while and does not need to consume propellant to fly with it and payload. Therefore, as long as the propellant quality is increased and the rocket is properly divided into several stages, the rocket can finally reach a large enough carrying capacity. It should be noted that the more stages a rocket has under a certain takeoff mass (GT+GJ), the better, because each stage of the rocket must at least have a power system, a control system, a servo mechanism and a connecting structure connecting rockets at all levels except tanks. These components are added with each additional level. Too many stages not only increase the cost and reduce the reliability, but also deteriorate the rocket performance due to the increase of structural quality. Because on the premise of the same take-off mass, increasing the structural mass will inevitably reduce the propellant, and from the principle of energy conservation, its carrying capacity will inevitably decrease. In a word, in order to improve the carrying capacity of rockets, it is a good idea to adopt multi-stage rockets, but the more stages, the better. It has a certain correspondence with the take-off quality.