The following might help you see how the variables change during a launch:
www.braeunig.us/misc/Sputnik-1_launch.pdfThe above is the tabular summary of a computer simulated launch of Sputnik 1. I created this a few months ago to help out a friend researching the Soviet space program for a book. You can see the changing variables as each row of the table represents a time step of five seconds. Below is a description of each column:
Column 1 – Time (s) – Elapsed time from liftoff.
Column 2 – Mass, Total (kg) – Total mass including launch vehicle, propellant, and payload.
Column 3 – Mass, Fuel (kg) – Mass of propellant remaining.
Column 4 – Mass, Dry (kg) – Mass of the launch vehicle and payload, less propellant.
Column 5 – Thrust (N) – Instantaneous thrust of the operating engines.
Column 6 – Pitch (degrees) – Angle of the rocket’s longitudinal axis with zero begin parallel to the ground below.
Column 7 – Acceleration, Vertical (m/s
2) – Acceleration in the vertical direction, i.e. perpendicular to the ground.
Column 8 – Acceleration, Horizontal (m/s
2) – Acceleration in the horizontal direction, i.e. parallel to the ground.
Column 9 – Acceleration, Load (g) – The g-load on the launch vehicle.
Column 10 – Velocity, Space Fixed, Vertical (m/s) – Velocity in the vertical direction relative to space.
Column 11 – Velocity, Space Fixed, Horizontal (m/s) – Velocity in the horizontal direction relative to space. (Note that the speed of Earth’s rotation is included.)
Column 12 – Velocity, Space Fixed, Total (m/s) – Total velocity relative to space.
Column 13 – Velocity, Earth Fixed (m/s) – Velocity relative to a fixed point on Earth, e.g. the launch site.
Column 14 – Altitude (m) – Height above sea level.
Column 15 – Range (m) – Distance downrange from the launch site.
Column 16 – G (m/s
2) – The acceleration of gravity acting on the launch vehicle.
Column 17 – Atmosphere, Pressure (Pa) – Atmospheric pressure, based on model of “standard atmosphere”.
Column 18 – Atmosphere, Density (Pa) – Air density, based on model of “standard atmosphere”.
Column 19 – Drag (N) – The drag force acting on the launch vehicle.
Note the changes in mass and thrust as the rocket goes through staging, etc. Also note how the thrust increases as the air pressure drops (this is something Jay talked about in his post). The decrease in thrust between 100-105s and 285-290s is due to the engines being throttled back prior to shutdown.
In order to get the simulation to attain the desired velocity and altitude, I had the manually adjust the pitch angle via trial-and-error until I got something that worked. Everything else pretty much flows from that. For instance, if I change the pitch rate at some point in the simulation, the rocket is going to go off in some direction I don’t want and end up too high or too low or too fast or too slow, etc. Designing and controlling the rocket’s trajectory is extremely critical.
Every launch vehicle is different in regard to acceleration versus time. For instance, a rocket with a high thrust-to-weight ratio needs to fly a differently shaped trajectory than one with a low thrust-to-weight ratio. Missions also vary in regard to their orbit requirements, i.e. altitude and inclination. Figuring it all out is rather complex.