spl2 - Trajectory Calculation Lab 2 Lecture Notes...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
V Trajectory Calculation Lab 2 Lecture Notes Nomenclature t time ρ air density h altitude g gravitational acceleration V velocity, positive upwards m mass F total force, positive upwards C D drag coefficient D aerodynamic drag A drag reference area ˙ ( ) time derivative ( = d ( ) /dt ) i time index Trajectory equations The vertical trajectory of a rocket is described by the altitude and velocity, h ( t ), V ( t ), which are functions of time. These are called state variables of the rocket. Figure 1 shows plots of these functions for a typical ballistic trajectory. In this case, the initial values for the two state variables h 0 and V 0 are prescribed. h 0 h t V 0 t V h Figure 1: Time traces of altitude and velocity for a ballistic rocket trajectory. The trajectories are governed by Ordinary Differential Equations (ODEs) which give the time rate of change of each state variable. These are obtained from the definition of velocity, and from Newton’s 2nd Law. h ˙ = V (1) V ˙ = F/m (2) Here, F is the total force on the rocket. For the ballistic case with no thrust, F consists only of the gravity force and the aerodynamic drag force. mg D , if V > 0 F = (3) mg + D , if V < 0 The two cases in (3) are required because F is defined positive up, so the drag D can subtract or add to F depending in the sign of V . In contrast, the gravity force contribution mg is always negative.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern