I am making a script for kerbal space program, which will calculate the height where a "hover slam" should be started when the rocket is full.
I have worked out that the velocity after a certain amount of time is:
$Δv=\int^t_{0}{\frac{T}{m_0*Bt}} dt$
where:
- T is the thrust of the engine in kN
- $m_0$ is the initial mass of the rocket in kg
- B is the burn rate of the engine in $kgs^{-1}$
Then the distance traveled is: $Δs = \int^t_{0}Δv$
I want to find t when the current height would be equal to Δs (i.e $Δs(t) = h$) But I couldn't find online if this can be done.
