How long did it take for a diplomat to travel between Berlin and Vienna in the 1770's?

Tassis operated by using a courier on horseback, riding with its maximal speed. The courier made stops every few kilometres just to change his tired horse to a fresh one, that was already awaiting for him. It could also be that there were two or more couriers along the distance travelling only some part of the way each (so they did not have to eat or sleep).

Top speed of a horse is ca. 88 km/h; I think half of it would be adequate, because of roads and that this is a top speed, and if he travelled by night, it should also be reduced. Having this in mind a way 1000 km long could be travelled in ca. 24 hours.

The message itself could be then delivered relatively fast, if it was urgent, and there was no risk of stealing the message by enemy.

Of course diplomats wouldn't spend this time on a horseback. They required more comfort and some protection, as roads were not safe enough. They need to stop for dinner or sleep. I think that time needed would be (if they were in hurry) at least ca. 3-5 days.

Let's consider a well documented journey by Napoleon in 1809, a mere 40 years later. The basic technologies are all the same, though the network of metalled roads has been steadily expanding through that time. Napoleon was in a hurry, had the resources of an Empire at his command, and travelled similarly to how a diplomat might have travelled in the preceding hundred years (in a carriage) because he had a campaign to plan and luggage to carry. Update: (And, as far as Strasbourg, Josephine to love and cherish.)

Napoleon left Paris in the wee hours of April 13, 1809, in the Imperial coach, and arrived in Donauworth in the early afternoon on the 17th. [Update #2: Dawn on the 17th, not early afternoon, so about 8 hours less travel time.] He stopped only to rest and feed the horses and to eat, choosing to sleep in the carriage while travelling. This makes a total travel time of about 108 hours.

Update #2 - This paragraph copied from comments below:
The Imperial Guard was en route from Spain and arrived some weeks later; it did not accompany Napoleon. According to Thunder on the Danube (page 159): Napoleon travelled only with his personal guard; the Imperial carriage; and Josephine as far as Strasbourg. He stopped a handful of times to reassure allies (Kings of Wurttemberg and Bavaria) and meet with his niece, the Oudinot family and a couple of others. In the absence of his own guard the Wurttemberg Guard escorted him through that territory.

The road distance today is listed as 762 km, so let's take a figure of 850 km for two hundred years ago. This direction of travel was along major trade routes from France into Central Europe, as well as along the major invasion route into (or out of) France from Central Europe. There is no reason to believe that the route was substantially less direct then than now.

This clearly shows that a determined individual, with the financial resources to acquire new horses as needed, travelling on major roads of the time in a coach, could achieve a speed about 8 km per hour. Clearly this was an in extremis situation, as is evident to anyone familiar with the Eckmuhl phase of Napoleon's 1809 campaign. It is doubtful that anyone could have achieved better in the years from between 400 CE and the onset of the railway in the 1830's. A more normal pace for a diplomat might be 1/2 or 1/3 that set by Napoleon, entailing a travel time of 8 to 13 days respectively for a distance of 850 km over a well travelled road in Central or Western Europe..

Note that a horse's working gait is typically a trot, is about 13 kph (breeds and individuals vary), and can be maintained by a well treated horse for several hours at a time over suitable terrain. The use of multiple ranks of horses to pull a carriage allows the team to pull the carriage at a trot for longer by reducing the load on the individual horses. The rule of thumb is that each pair behind the first only contributes half as much as the pair in front; however I believe the alpha horses must be put in front for the team to be well behaved (just like a dog sled).

As an aside, the network of metalled roads (pikes) was expanding across Europe through this period. The Turnpike Act in the UK (allowing the establishment of private metalled toll roads) was already 100 years old by 1770. One might reasonably expect that similar arrangements existed in the larger nations of 18th century Europe: France, Prussia, Austria-Hungary, Bavaria, though I cannot track down explicit sources for this. (Eastern Europe was a different story, which might explain why travel from Berlin to Vienna went via Leipzig.) Certainly by 1809 Bavaria was criss-crossed by a network of Pikes that both Napoleon and Charles endeavoured to make use of.

John H. Gill's 1809 Thunder on the Danube Vol. I describes Napoleon's journey in the first several paragraphs of Chapter 5.

Using ORBIS which reconstructs travel through the Roman Empire circa 200CE as a basis, a fast carriage across ~700kms (I chose Naples to Verona) would have taken about 10 days. A horse relay team between the same cities only took 3.6 days to cover 763 kms. One could use these numbers as a rule of thumb for all pre-industrial travel on decent roads.

That said, I dare say that travelling down the Danube would have been preferable to the road. Again, as per ORBIS, river transport would shorten the journey between Regensburg (Castra Regina) to Vienna (Vindobona), a distance of ~440 km, from between 4 (military) to 7 days in 200CE.

Depending on whether it was a courier delivering a message to a diplomat travelling himself, it might be reasonable to estimate that the journey between Berlin and Vienna might have taken anywhere between 3 and 10 days.

(Although ORBIS does take a lot of factors into account, this answer does not account for either political and geographical roadblocks or technological improvements in 1770s Europe. It's simply an educated guesstimate.)

Straight-line distance from Berlin to Vienna is 523 kilometers or 325 miles according to Wolfram Alpha. In a car traveling at a constant speed of 55 miles per hour (ca. 88 km/h), total travel time would be 5 hours and 55 minutes. However, roads are not perfectly straight. According to Google Maps the shortest route is 678 km long and you would need at least six hours and 43 minutes by car.

Various sources state that the condition of roads in the late 18th century permitted experienced horseback riders to travel distances up to 100 kilometers per day. But you would need to change horses along the route several times. So the theoretical shortest time, assuming that the road then was as long as it is today, would be seven days.

Reproduction of German lithography (c. 1820) found on http://www.zeitspurensuche.de/04/post2.htm#Unfall

However, that is unrealistic. Roads were in varying condition then, there was no unified network. The total road distance surely was closer to 1000 km than to 678 km. All sorts of mishaps could occur along the way. To get from Berlin to Vienna you had to traverse a patchwork of principalities and fiefdoms, some of which stopped you to demand that you pay a customs fee.

You are probably right that a diplomat would have preferred to travel by carriage than on horseback. That would have limited them to a daily maximum of 80 kilometers, likely much less. So in my opinion, two weeks is probably a realistic estimate of the travel time for diplomats between Berlin and Vienna in the late 18th century.

For comparison: In the New World, going along the nearly straight Jersey Turnpike from New York City to Philadelphia entails driving about 100 miles (~170 kilometers), an hour and 43 minutes by car. In the late 18th century this trip required three days by (fast) stage coach according to Stage Coach and Tavern Days (1900). However, this was a well-established, competitive run and one should expect long hauls between less frequently paired destinations to last disproportionately longer.

Roman road column, Aoste region, present-day Italy.

_{By Lysippos (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons}

Keep in mind that the most important variable limiting travel speed was not the quality of horses (more or less constant through the ages) or carriage technology (improvements made largely affected comfort, not speed) but the condition of the roads. No major road building had been done in Europe since the Roman era. What remained of Roman paved roads was in disrepair, and the deeply rutted dirt roads were much worse.

Postal distance column in Saxon town of Annaberg, 1727. Note the distance to various destinations being given in "hours". In fact, a postal "hour" was a fixed length of 4.531 kilometers, often called a half mile (yes, the Saxon "mile" then was 9.062 kilometers long!)

_{By Oxensepp (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons}

A comparison table lists the speeds achievable for horse-drawn carriages:

(ca. 1700) approx. 2 km/h 20- 30 km per day
(ca. 1800) approx. 3 km/h 30- 40 km per day
(ca. 1815) approx. 4 km/h 40- 50 km per day
(ca. 1830) approx. 6 km/h 60- 75 km per day
(ca. 1850) approx. 10 km/h 100-120 km per day

The fivefold increase in coach travel speed from 1700 to 1850 was almost entirely due to the improvements made in the quality of overland roads. Keep in mind that a human walks at a typical speed of four to five kilometers per hour. In the Hollywood movies, when you see horse-drawn carriages they usually move at a brisk pace... but that is not what it was like for most travelers then.

(I'm actually a bit skeptical of that table, the figures for the early years are probably too low. My estimate is that a diplomat in the service of the Holy Roman Emperor could cover up to 60 kilometers of ground in a day of travel by horse-drawn carriage.)