Does anyone know the calculations to workout a rocket trajectory? And does it work in simplerockets2?
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Mod sflanker+2 4.4 years ago
There are a couple of special cases of trajectory:
- In the atmosphere
- Under power
- Not under power
- Not in the atmosphere
- Not under power
- Under power
In the atmosphere under power is the most complicated. In order to solve this you have to account for all of the changing variables: velocity is changing, therefore atmospheric drag is changing (even if we assume your angle of attack is constant so that your drag coefficient stays constant); mass is changing, therefore acceleration due to thrust is changing; gravity is changing, assuming your altitude is changing, although this change will be relatively small in the range of altitudes in the atmosphere; the direction of thrust is probably changing. I recently made an attempt to solve for displacement over time of a missile fired more or less horizontally, ignoring many factors, and I found out the math is really hard and I had to watch 12 hours of youtube videos about differential equations in order to figure it out. In the end I dropped most of the math and used a simple formula that approximated the flight path (but it would not be generalizable to any other missiles).
The simplest case-- not in the atmosphere, not under power-- is much easier. It is basically orbital mechanics plug and chug. Given your current position and velocity (a.k.a. cartesian state vectors), assuming only one planetary body is going to affect your path, you should be able to plot you trajectory and find your position and velocity at any given time. Here is a list of resources:
- In the atmosphere
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Also here is the missile I was talking about. It plots the ballistic re-entry of a target ignoring drag, and does a ham handed job of projecting and guiding the trajectory of the missile that is fired at it.