Auto Gravity-Turn Launcher 1.11

A rather boring rocket that delivers a 1t mass to low Droo orbit. But it does so with a script that can take almost any (orbit capable) rocket into the lowest safe orbit that can be efficienctly reached with unparalleled accuracy and as little dV as possible.

I've used this on everything from tiny rockets to behemoths, from ones that use 3 stages to those that do it in a single one. The results have been close to ideal every time. The script includes some parameters (top left, with explanatory comments) that can allow fine tuning of performance, but playing with them is not necessary for it to work with any sensible craft.

The script does multiple things during launch:
• Automatically stages as fuel runs out.
• Maintains heading to have lowest inclination possible for the launch site.
• Goes straight up until the craft is out of the thickest part of the atmosphere, then turns down range to initiate the ideal gravity turn estimated for its TWR (tuneable).
• Continues this gravity turn by keeping to prograde, smoothly switching from tracking surface to orbital prograde.
• Adjusts the throttle to prevent excessive loss to atmospheric drag (tuneable).
• Continues doing this until the apoapsis is above the minimum safe altitude (tuneable).
• Calculates live how long the circularization burn will take, and by how much time the apoapsis will be pushed back while this burn is happening.
• Uses this prediction to start the circularization burn as late as safely possible to have the lowest, most accurate, and most efficient insertion.
• Controls the throttle to "surf" the apoapsis and complete the circularization burn smoothly just as it is reached, taking into account engine spooling time (tuneable).
• Reports what is happening at every point through the flight log so you can sit back and enjoy the automated show.

For the rocket uploaded, the screenshots show the different stages of going from the desert launch pad to orbit. The results shown are typical: it takes under 4.8 km/s of dV to end up with an apoapsis and periapsis within 1km of each other around 85km ASL.

UPDATE 1.11: Improved presentation of code to make it easier to integrate your own customization to the launch (ie, retracting landing legs, ejecting side tanks) as launch thresholds are reached, and removed empty input fields in vizzy (thanks to @Ambarveis). Actual performance unchanged.