Rocket formula Δ V = VC× ln {(m+p)/m} According to the law of conservation of momentum, the relationship between oil load and speed of rocket propulsion system can be deduced. The formula is: δ v = VC× ln {(m+p)/m} or (m+p)/m = e (δ v/VC).
V => The change of rocket speed, the final velocity of a rocket with zero initial velocity is 0+Δ V =ΔV. VC = > Jet speed. Ln => natural logarithm. M => mass of rocket body. P => fuel quality. (M+P)/M = & gt； Mass ratio.
Where (M+P)/M is the ratio of the mass of rocket body plus fuel to the mass of rocket body, which is called mass ratio.
Its significance can be seen as the transportation efficiency of rockets. That is, the ratio of fuel consumed to payload that can be transported.
Because the P term is in the ln function, when the value of Δ V/VC is greater than 1, that is, the last stage speed is greater than the jet speed, the mass ratio of the rocket system will become very sensitive to any speed increase, and any slight increase in the last stage speed will increase the mass ratio exponentially.
law of conservation of momentum
Law of Conservation of Momentum: If the interacting object system is not affected by external forces or the sum of external forces is zero, the total momentum of the system remains unchanged.
First, the mathematical expression:
1, p=p' (total momentum p before system interaction is equal to total momentum p' after system interaction)
2.△p=0 (the total momentum increment of the system is zero)
3.△p 1=-△p2 (for a system composed of two interacting objects, the momentum increments of the two objects are equal in size and opposite in direction).
4. m1v1+m2v2 = m1v1'+m2v2' (two interacting objects form a system, and the sum of front momentum is equal to the sum of back momentum).
Second, the establishment conditions:
1, the system is not affected by external force or the resultant force of external force on the system is zero.
2. Although the resultant force of external force on the system is not zero, it is much smaller than the internal force of the system, such as friction in collision and gravity during explosion. The external force is far less than the internal force of interaction, which can be approximately considered as the conservation of the total momentum of the system.
3. Although the resultant force of external force on the system is not zero, but the component in a certain direction is zero, the component of the total momentum of the system in that direction remains unchanged.