Flight control law clearance provides the conditions needed for the system to operate in the stability boundaries. One way to do so is to test all the parameters and variables in question. This method is time and resources wasteful, and not free of errors. A different approach, that has already been proven effective, is to use optimization tools. Instead of proving the system can endure every condition, the search can be narrowed to find only the critical conditions and determine a boundary of safety.
When it comes to rockets, there are various factors in the acceleration phase that affect its trajectory. A very important factor is side-winds that cause angles-of-sideslip that affect the rocket’s motion during the acceleration phase, and eventually the whole trajectory by shifting the ballistic plane.
The chosen optimization method for solving this problem is Neustadt’s. This is a simple method for finding the minimal effort required to bring a linear system from the initial condition to its ending condition with minimum control effort. This mathematical method was chosen since it yields a simple analytical solution as compare with other methods.
The critical side-wind was found using a simplified model of an accelerating rocket and tested on the full model. Since ballistic motion is always forward, it is a common analytical practice to express some of the equations using downrange distance instead of time as the independent variable. This way, some expressions become simpler and calculations are easier.
A sensitivity study will be presented, showing the critical side-wind that was found is indeed the critical boundary for a safe launch. Furthermore, it is shown that an aerodynamic controller can help widen the boundaries.
