Need Help ... Pitch Angle Calculation

[Nang Ha]

Assumptions:

1. Point mass model or 3DOF
2. Target is located to the west of launch point (270 degrees launch azimuth)
3. Trajectory: pitch rate is known; roll and yaw are equal to zeros.
4. Two stage rocket: first stage has the positive pitch rate; second stage has the negative pitch rate. There is the gravity turn at the end of the first stage and second stage pitch rates.

Problem:
Pitch angle: theta = -arcsin(MBToNED(3,1)) [-90 to 90 degrees]

When the pitch rate is negative for both stages, there is no issue since the rocket flies toward the target from launch.

When the first stage pitch rate is positive and the second stage pitch rate is negative, the equation above is no longer valid. In the first stage, the rocket flies in the opposite direction of the intended target due to the positive pitch rate (fly to the east) and then, in the second stage, the rocket flies toward back to the target (fly to the west) due to the negative pitch rate.
Pitch angle in the first stage and part of the second stage will be greater than 90 degrees. Hence, the equation above cannot be used.

Pitch angle is measured between the rocket body direction and the local horizontal direction toward to the target.

What is the algorithm that I can use to calculate the pitch angle through out the flight?

Greatly appreciate your help ... Thanks in advance.

Nang Ha

 

[ADSWNJ]

Not quite sure what you are trying to achieve, but generally when you want an angle that can work in all quadrants around the circle, you should consider using the function atan2.

 

[Col_Klonk]

With pitch angle i take it you mean from the vertical as your vehicle ascends into the heavens.

It depends on vehicle's 'lift coefficient' (for want of a term) as the shuttle has wings so it has a 'shallower' path, whereas a pure rocket has a more vertical path profile.

The pitch profile would be controlled via computer to optimise the fuel/weight expenditure of the vehicle.

For my 'toys' I find that 'rocket' pitch control of 1 degree per 1000m is optimal.. but this is on simulation games, and not reality.
This profile gives me a near 'G-Turn' in the lower-medium atmosphere which reduces drag/Q effects, and minimises off-vector thrust losses in the upper atmosphere/space.

It also helps minimise G loads to just under 5 for end of stage 1... I haven't bothered yet to play with other G options but I'm sure i can reduce the loads with different stage configs.



Works pretty well.
:thumbup: