The velocity formula of the first stage rocket is usually based on the basic principles in physics, especially Newton's second law (F=ma) and kinematics formula. Suppose we have an ideal first-class rocket that runs without gravity and air resistance.
1, Newton's second law: This law shows that the force on an object is equal to its mass times its acceleration. Expressed as F = ma by mathematical formula.
2. Kinematics formula: Kinematics is a discipline that studies the laws of motion of objects. The basic kinematics formula is v = u+at, where v is the velocity of the object after time t, u is the initial velocity and a is the acceleration.
Combined with these two principles, the first-stage rocket speed formula model can be established.
Let the initial velocity of the rocket at launch be u(0), the thrust acting on the rocket be F, and the mass of the rocket be M. After time t, the velocity of the rocket is v(t).
According to Newton's second law, we have F = ma, where a = v/t is the acceleration of the rocket. Substituting this formula into v = u+at, we get v = u+ft/m.
This model shows how the speed of the rocket changes under the conditions of given thrust f, time and mass m. It should be noted that this model simplifies many real-world conditions, such as gravity, air resistance, fuel consumption and so on. , will have an impact on the actual speed of the rocket.
Rocket velocity formula
According to the law of conservation of momentum, the formula of rocket speed is derived, which expresses the relationship between fuel carrying capacity and speed of rocket propulsion system. The formula is: Δ V = Vc× ln {(M+P)/M}, where Δ V is the velocity variation of the rocket, VC is the jet velocity, and (m+p)/m is the mass ratio (where m is the mass of the rocket and p is the mass of the fuel).
The formula is mainly used in the aerospace field, which can help scientists better understand the performance and motion law of rockets. In practical application, besides the injection speed and fuel carrying capacity of the rocket, the influence of gravity, air resistance and fuel consumption on the rocket speed should also be considered.