What was the first rocket with de Laval (convergent-divergent) nozzle to fly?

Question

Rocket engine Wikipedia article states that

Goddard was the first to use a De Laval nozzle on a solid-propellant (gunpowder) rocket engine, doubling the thrust and increasing the efficiency by a factor of about twenty-five. This was the birth of the modern rocket engine.

This source elaborates a bit more on this:

In 1915, as assistant professor at Clark University, Worcester, he [Robert Goddard] began experiments on the efficiency of rockets. He bought some commercial rockets and measured their thrust using a ballistic pendulum, a heavy mass suspended by ropes, to which the rocket was attached. The rocket was fired, and the height to which the pendulum rose provided a measure of the total momentum (mass times velocity) imparted to it.

Goddard experimented on his ballistic pendulum with various nozzle designs, using a small metal combustion chamber filled with a type of gunpowder, ignited by electricity. The end of the chamber was threaded, so that nozzles of various designs could be screwed onto it and tested. Using a De Laval nozzle, he obtained jet velocities between 7000 and 8000 ft/sec and efficiencies of up to 63%. Later he replaced the ballistic pendulum with a more compact device, in which the thrust of the rockets did not lift a pendulum against gravity but compressed a calibrated spring. With that device he showed that (contrary to some popular claims) rockets worked just as well in a vacuum.

De Laval's nozzle turned spaceflight from a vague dream into a real possibility. Goddard communicated his results to the Smithsonian Institution in Washington and asked for support to develop a rocket capable of probing the high atmosphere. ... In January 1917 the Smithsonian responded with a grant of $5000, and Goddard began his rocketry career.

The above describes what we would call nowadays a static fire test.

Then the storyline omits further details of the solid rocket development and continues with liquid fueled rocket:

The idea of feeding the rocket with a continuous stream of solid charges also proved unfeasible, and in 1922 Goddard went back to his alternative idea, proposed independently by Hermann Oberth in Germany and also noted by Tsiolkovsky: a liquid-fuel rocket

So, between 1915 and 1922, did Goddard build a solid fueled rocket with de Laval nozzle that actually was trialled in a real flight? If not, was it his (first ever) liquid fueled rocket "Nell", that was flight tested on March 16, 1926, to be the first flying rocket to utilise de Laval nozzle?

Sketches of the rockets from 1914 Goddard patents that show de Laval nozzles (source)

Answer 1

Based on information gathered from limited amount of sources, it looks like:

• the first solid fuel rocket with an optimized de Laval nozzle flew in summer 1916, although it is possible that some test nozzles might have flown as early as 1915;
• the earliest documented precise date of demonstration flight of bazooka prototype (equipped with de Laval nozzle) is 6th November 1918 (although the first flight tests of the bazooka prototype are very likely to have happened as early as 1917).

Below is photo of the earliest Goddard solid rocket with de Laval nozzle I could find (the bazooka prototype): Photo Credit Smithsonian National Air and Space Museum

This is a 1-inch solid fuel rocket built and tested by U.S. rocket pioneer Robert H. Goddard during 1917-1918 for the U.S. Army for potential use as a weapon during World War I. The experiments were undertaken near the Mount Wilson Observatory in Pasadena, California. Later, a trial was made before Army officers at the Aberdeen Proving Grounds, Aberdeen, Maryland, on 6 November 1918.

The trials went well and this model reached about 750 yards.

Historical timeline of related events:

• 1st October 1913 Goddard files patent application for "Rocket Apparatus", which clearly describes the use of the nozzle.

• 7th July 1914 US1102653 patent for the "Rocket Application" is granted.

• 1915 first flight tests of a solid powered rockets (although it's not conclusive what exactly those rockets were, as these flights either predated or coincided with the nozzle development work at Clark University, it might have been that some of those test nozzles flew during this time in 1915)

Source 1:

He [Goddard] began by experimenting with gunpowder, and launched his first powder rocket at Clark University in 1915, this time outside of the building. But powdered rockets were inefficient; only 2 percent of the available energy was being converted into motion.

Source 2

In 1915, Goddard initiated his first test launch of a powder rocket in the campus at the university. After many tests of optimization that took him months, Goddard managed to achieve an engine efficiency of more than 63%.

• Summer 1916. First Goddard rocket flight tests.

Source 3:

Goddard's modified black powder rockets, launched from Coes Pond, Massachusetts, reached 480 feet and demonstrated jet velocities of up to 8000 ft/sec.

These are the earliest flights that are mentioned to use rockets modified by Goddard; indicated jet velocities are inline with the optimised de Laval nozzles.

• 19 June 1917. Goddard develops bazooka

  Goddard receives $ 20,000 from US Army Signal Corps for rocket development. Together with his assistant Clarence N Hickman he develops a prototype of the World War II bazooka at the Mount Wilson Observatory in California.

• 6th November 1918. Goddard demonstrates rockets to US government.

Source 3:

After demonstrations to Army officers of work achieved at Mt Wilson, Goddard is requested to demonstrate his rockets at the Aberdeen Proving Ground in Maryland.

Source 4

Goddard, during his tenure at Clark University, and working at Mount Wilson Observatory for security reasons, designed the tube-fired rocket for military use during World War I. He and his co-worker, Dr. Clarence N. Hickman successfully demonstrated his rocket to the U.S. Army Signal Corps at Aberdeen Proving Ground, Maryland, on November 6, 1918, using two music stands for a launch platform. The Army was impressed, but the Compiègne Armistice was signed only five days later, and further development was discontinued as World War I ended.

Answer 2

Surely this manuscript on gunpowder-based fireworks rockets
by Conrad Haas (1509–1576) qualifies?

Or at the very least the followup work on multistage rockets by Johann Schmidlap who published "Künstliche und rechtschaffene Fewrwerck zum Schimpff,” firstly printed in Nuremberg in 1561?
That diagram clearly shows a divergent nozzle on a gunpowder rocket.
Obviously it was not called a "De Laval Nozzle", because that phrase was only coined by Mr. De Laval 1888