How was the trajectory of the V2 ballistic missile (during boost phase) calculated?

Question

I'm well aware of Helmut Hoeltzer's "Mischgerat" analog computer, and I read that it not only served as a kind of "fly by wire" computer on board of the missile, but also as a simulator on the ground that calculated V2 trajectories.

But, I didn't find any clue about how it did it - how Hoeltzer calculated optimal trajectory to hit the target (cities). I think the trajectory had to calculated accurately because only by following an accurate trajectory a ballistic missile could hit a city sized target.

Answer 1

My pardons for addressing this question six years on.

The ballistic trajectory for a particular target was calculated by hand by a computing group within the V2/A4 project. If you've seen the movie "Hidden Figures", just replace African American women with Nordic men.

Based on these calculations: 1) the heading was set by orienting the rocket with one of the fins towards the target, which properly aligned the gyroscopes; 2) the range was set by a clockwork mechanism which caused the missile to tilt a set angle at a set time during powered flight; 3) a timer to shut down the engine if needed. At that point Newton took the wheel.

The Mischgerät electronic analog guidance computer controlled pitch, roll, and yaw, reacting to inputs from the gyroscopes and optionally from a radio receiver tuned to a heading beam transmitted from the ground. When the gyroscopes' platform was tilted by the clockwork, the Mischgerät commanded the rocket exhaust deflectors and the fin trim vanes, steering the rocket so as to put the gyroscopes level again, and thus tilt the rocket towards the target.

Hoelzer developed the Mischgerät and from it his more full featured analog simulation computer. The simulation computer allowed him to validate the Mischgerat's function in two degrees of freedom prior to flight test. He built a couple of examples at Peenemüende, one of which followed him to the US.

Sources: Dornburger, Walter (1954), "V2"

Ernst, Wolfgang (2008), "Der Analogcomputer als Medium der Zeitmanipulation", Humboldt-Universität zu Berlin, Seminar für Medienwissenschaft, SoSe 2008 https://www.cdvandt.org/Busjahn_Analogcomputer.pdf

Tomayko, James E. (July 1985). "Helmut Hoelzer's Fully Electronic Analog Computer". Annals of the History of Computing. 7 (3): 227–240. doi:10.1109/mahc.1985.10025. S2CID 15986944

Ulmann, Bernd (Oct 26, 2008), "Von der Raketensteuerung zum Analogrechner Helmut Hoelzers Peenemünder Arbeiten und ihr Erbe". http://www.analogmuseum.org/library/hamburg_hoelzer.pdf

Photos: Mischgerät, opened - https://www.cdvandt.org/Mischger3-0.jpg

Hoelzer Simulation computer - https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8789827 (page 2)

Answer 2

I suspect you've seen this already, but there's a book "Analog Computing" by Bernd Ulmann which goes into some detail on the V2 guidance package. It's mostly about the hardware, not the software or governing equations, but it's an interesting read none the less.

You may also want to read through the technical publications of the time to see what the state of the art in trajectory computation was. That would at least give you some idea what trajectory models Hoelzer might have used.