NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Cel nav in space
From: Derrick Young
Date: 2005 Jan 4, 18:00 -0500
From: Derrick Young
Date: 2005 Jan 4, 18:00 -0500
Gravity turn trajectory. I was hoping that someone would jump in and no one has - so here goes. First, sorry folks, this is not navigation - so delete and ignore if not interested. If you have ever watched a rocket launch (such as the space Shuttle), you will notice that as it just clears the gantry, the path that it follows starts to bend. The Shuttle does not go straight up into outer space; it follows a natural curve that is the result of the thrust of the engine, the speed it is moving, the cumulative effect of gravity and the changing mass of the rocket. If you look at a plot of an inverse logarithm, you will see the basic form that it follows. If you look at some of the home made rocket launches as well as some of the "anti-missile" launches, they go basically in a straight line. The reason is that the total vehicle mass (weight) is very small when compared with the thrust from the engines. These rockets achieve maximum speed just after clearing the launch gantry. Larger rockets, like the Shuttle, do not reach maximum velocity until fairly late in the power portion of their flight. So their path "bends" more because gravity has longer to work on it. When they get to max speed, the Shuttle will then travel in a straight line. That can be anywhere from 30 to 200 miles down range of the launch pad. The curve followed depends on the total mass of the vehicle (this changes as it burns fuel and drops stages), total speed (very slow at the pad, faster as it goes down range), and the angle of attack (the angle the vehicle moves through the apparent wind). Thus the curve represents a balance between thrust, speed, heading, angle of attack through the air and gravity. You can represent this mathematically in a number of ways. I worked with a NASA engineer years ago developing a Taylor Series expansion to do this. Taylor Series expansions have natural data smoothing characteristics that are very useful in finding/understanding various data anomalies recorded during flight. You have heard of the term "MAX Q"? This is a combination of the air pressure being placed on the launch vehicle and the actual speed of the vehicle through the air. Max Q is the value that everyone tries to avoid - well actually there are two values for MAX Q - the first is a design value - how much combined air pressure and speed can the vehicle stand before suffering structural damage - this is the limit that everyone wants to avoid. The second is (and the one everyone refers to during launch) is the actual value being exerted on the craft. You want the observed to be less than the theoretical - unless you like to have lots of expensive fireworks. Does this help? Derrick