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    Re: Cel nav in space
    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
    
    
    

       
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