How fast could rocket technology have been developed

Solid rockets you have since 13 century
Liquid fuel rocket need, in theory they had build them in 19 century

but this After 1900 Discussion
1903 Konstantin Tsiolkovsky publish his book "The Exploration of Cosmic Space by Means of Reaction Devices"
widely ignore worldwide for decades
already in 1916 Hermann Oberth proposed big solid rockets for war use
unfortunately he proposed that to Austria generals who laught at him...
1910 Robert Goddard start on Rocket research, but he get tuberculosis until recovery in 1914
1915 He start his first test of Rocket engine.
1919 Goddard write "A Method of Reaching Extreme Altitudes"
1922 Oberth's proposed doctoral dissertation on rocket science was rejected as "nonsense",
1923 Oberth publish his doctoral dissertation as book "Die Rakete zu den Planetenräumen"
1924 a writer for the Russian newspaper Izvestiia reported on "A Method of Reaching Extreme Altitudes"
USSR noticed Konstantin Tsiolkovsky oblivion work. Sergey Korolyov start private R&D on space travel
1926 Robert Goddard test at first a liquid rocket engine
1929 Oberth conducted a static firing of his first liquid-fueled rocket motor
the U.S. stock market crash makes impossble to get funding for private R&D
wat delay rocket technology for almost a decade.

so WI Goddard gets not tuberculosis ?
he conducted a static firing of his first liquid rocket engine in 1919
then is Oberth's proposed doctoral dissertation consider as "interesting" in 1922
USSR noticed Konstantin Tsiolkovsky oblivion work and Sergey Korolyov get officially order to build liquid rocket engine
so Goddard, Oberth and Korolyov got fist sounding rockets bevor U.S. stock market crash in 1929.
so we got rocket technology ten years earlier.
 
I don't mind explorering before 1900 to try and speed things up, just I consider most aviation achievements in the 1900's. Was there a diplomat or someone that could have come to power that really could have made a big impact etc...
 
Didn't Goddard try to get military funding? Maybe result in early RPGs?

yes and the guys laught at him just like at Herman Oberth
that was same generals who thought, sinking ship with Aircraft is nonsense and a attack on pearl Habor never gona happen
only after the japanese sink U.S. Battelships in Pearl Habor with Aircraft, the U.S. military gave Goddard funding and Order
give us Rocket-Assisted Take Off Gear for Aircraft ! :(

In Germany they discover fast the use of rocket for military
after the WWII the Allied were perplex on how fare the germans were
SRBM with "V-2", SAM with "Rheinbote", rocket artillery "Rheintochter", rocketlauncher "Nebelwerfer"
even first "air interception rocket" for fighter interceptor the "R4/M Orkan"
lucky for us, to late for the Nazi to use in greath scale during the war :p
 
So we'll want to get the USAAF/USN rocketplanes...

The best way I can see is to get the US into a war in the 1920s, in which the enemy sinks several battleships using aircraft. Their aircraft are better than American ones, so, as a quick patch for the problem, the USN and USAAF start attaching booster rockets to their planes to accelerate them and launch them to higher altitudes.

Would this work? And if so, who can they get into a fight with?

Alternatively, what if the Germans were to fund rocketcraft? If they could test unmanned rockets (V-2 a decade early), then we'll get somewhere. Did Versailles have any restrictions on that?
 
So we'll want to get the USAAF/USN rocketplanes...

The best way I can see is to get the US into a war in the 1920s, in which the enemy sinks several battleships using aircraft. Their aircraft are better than American ones, so, as a quick patch for the problem, the USN and USAAF start attaching booster rockets to their planes to accelerate them and launch them to higher altitudes.

Would this work? And if so, who can they get into a fight with?

Alternatively, what if the Germans were to fund rocketcraft? If they could test unmanned rockets (V-2 a decade early), then we'll get somewhere. Did Versailles have any restrictions on that?

No, Versailles did not have any restrictions on Rockets per se, but rather on conventional artillery...
As a result of this "Loophole" in the treaty, the German Army started delevoping the concept of rocket artillery, as they were not banned from doing so...
 
The big advance wasn't rockets, but guidance packages. After all, fireworks had been one of the early uses of gunpowder, more than half a millenium earlier. Without guidance packages, you have only the tiniest control where it'll go. A big rocket without guidance is just a random threat to civilians, not a help to anybody.

Guidance packages aren't the least bit easy. They still take alot of effort, even with today's computers, and Hamas' infamous rockets are unguided and rarely actually hit anybody or anything signicant. Google for Circular Error Probable, I think, will help you understand as well.

Guidance packages were just barely feasible in WW2 tech, notice, also the first generation that could just barely make computers. And, they could barely make guidance systems, either - Apparently, all the V1s and V2s were aimed at London Bridge, and not only did it stay standing, but they mostly managed to miss London. So, I'm dubious we'd see faster development. Now, you COULD have Goddard - maybe with some other, more politically oriented ally -get military funding and have and American military rocket program fun. It would, of course, tend to have similar limits to the V2.

Also, the first one of two of ANTHING new tends to be problematic.

There's another thread on a related topic, titled something like How I Came To Stop Worrying and Love the ICBM.'
 
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