How do I find the average velocity of an airplane by year?

I want to compare how the top aircraft models have gotten faster year over year, or how airlines have changed their flight patterns to fly more quickly, but I can't find an average speed.

The National Transportation Safety board does annual accounts of car miles, but reports aircraft in hours flown. I want to know how many miles (rough estimate) yearly aircraft fly. My current idea is to multiply flight hours times average speed… But I can't find that anywhere!

Cruising speeds for jets haven't really changed over the past 50 years. Acceleration on takeoff and rate of climb have improved, but there's a practical limit to cruising speed. For example, a Boeing 727 cruised around Mach 0.84, which is about the same as the Boeing 777. The 787 Cruises at about Mach 0.85, but the 747 that predates it by 35 years cruises at 0.86.

In fact, it can be argued that overall, cruise speeds have decreased a little bit because the most common aircraft (Boeing 737 and Airbus 320) only cruise at Mach 0.78 which is slower than the most common planes used in the 1960's and 70's.

What has improved the theoretical "block time" is point-to-point GPS navigation, improved weather information (particularly winds aloft forecasts), decreased aircraft separation and improvements in the ATC system. However, due to increasing air traffic congestion, ATC has to limit aircraft speeds in order to meter the flow of traffic smoothly in and out of the larger airports, which negates the improvements in efficiency. And, on short flights the average speed is much slower than long flights because a greater percentage of the flight is taken up by the much slower speeds during the departure and arrival phases.

So what you're trying to do is problematic to say the least because you'd have to analyze the tens of thousands of daily flights to come up with a baseline. In the USA alone there are 87,000 airline flights daily. You'd find it easier to compare published airline flight schedules from decades ago (if you could find them) with those covering the same routes today. For non-stop flights between any two destinations, you'll find that things haven't really changed at all unless you start looking at the 1950's when most airliners were propeller-driven.

That said, when it comes to smaller cities, there are a lot more point-to-point flights now days than there used to be, thanks to smaller regional jets. So, it isn't always necessary to change planes like was more common in the past. When almost everything went through a major hub airport.

Look up DC-3 cruising speed, then on to the other DC models and Lockheed Constellation of the 1950s. After 1960's 707 and DC-8, cruising speed hit a wall (not counting the Concorde). That and what "Zaphod" tells is all that you need.

That is because, with the exception of the now gone contribution of the Concorde, the speed of the fastest airliners has NOT gone up since 1958 (the Boeing 707 cruise speed was Mach 0.88; a Boeing 787 cruises at Mach 0.85; essentially the same speed).
Now, the average speed would have to take into account the takeoff/climb and descent/landing which are not flown at cruise speed; but if a plane arrives at a busy airport and has to circle in the sky for 20 minutes while waiting for a runway, it is not really going anywhere even if it is flying at 250 knots; do you count this?
Because that would indicate a problem with the saturation of the airport infrastructure, not a drop in performance.

African or European?

If you want to find out how far planes fly now then go on something like flightaware.com and you can get the statistics for individual flights and see where planes fly. See e.g. The flight history of A7-AND an A350-1000 for Qatar Airways.

The longest flight is around 7000 miles from Doha to JFK, then 4000 miles to Singapore, then 3400 miles to London, 3100 to Frankfurt, 560 miles to Muscat and 410 miles to Kuwait as typical operations.

The recently delivered A350-900ULR with Singapore Airlines have recently started flying SIN-EWR-SIN on a round the world flight if you want the extreme.

which is around 18hrs for each segment and over 10300miles.

Because of ATC air corridors planes of similar types fly at similar speeds to maintain separation and this hasn't really changed for about 50 years, since there have been jets that can fly up to M0.85. What has changed is that the 18hr flight of today would have been flown in maybe 3x6hr segments several decades ago maybe leading to a total of nearer 22hrs with the stops and maybe a longer total distance because the stopping points wouldn't coincide with the non-stop route.

Old timetables are a guide to the past, but the main differences will be in flights that are now direct that used to have stops. A short-medium haul flight that took 3 or 4 hours in the 1960s will take 3 or 4 hours these days. A 7hr transatlantic flight was a 7hr flight in the 1960s as it is now.