Our current situation
Beakers per tech: 2442. We produce 696 science/turn. To get 3 turns/tech, we need to increase beaker output to 814+/turn.
Moreover, before the game ends, we will be running 5 turns/tech, down from our current 4, unless we a) increase beaker production from key cities and/or b)supplement beaker output with regular caravan deliveries.
We can increase beaker production in 4 ways - increasing science as a percentage of wealth production from the current 50%; increasing population by growing our cities faster (to work more tiles); building science improvements; and delivering a lot more Freights.
1)Increasing science at the expense of luxuries will put several cities into unrest. While science could be increased at the expense of taxes, revenues would be at a bare minimum - and probably need to be supplemented with Freight delivery.
2)We have lots of cities that could celebrate up to size 12 quite easily and thereby work more tiles and produce more science (Seville, Cordoba, Valencia, Salamanca, WhereItsAttown, Granada, and Pamplona all have tiles improved but no population to work them). Unfortunately, without Cure for Cancer, they won't celebrate right now - even with 100% luxuries!
3) Possible science improvements - University in St Praski - 18 more beakers per turn. Avila Univerity would yield 22 additional beakers/turn. Leon University - 15 additional beakers/turn. Total: 55 beakers, or less than 1/2 of what we need to get to 3 techs/turn.
Superhighways are a good option as trade from roads is increased 50%. A city with a lot of worked roaded squares (as opposed to sea squares) will produce nearly as much more science by adding SH, as it would by adding a University. The other big SH bonus is that trade goods will be worth a LOT more, delivered to or from a Superhighwayed city.
4) Freight: St Praski and Avila could each produce a Freight in 3-4 turns which when delivered, would probably yield 4 times as many beakers as a University would per turn, so that may be a better option. Even undemanded goods could yield close to 50 beakers when delivered to a large city, along with an equivalent amount of cash.
RECOMMENDATIONS:
My suggestion - build Superhighways in Capitol, Cadiz, and Avila, for a start. Immediately afterwards start producing Freight in Cadiz as it has 3 free commodities - Silk and Spice are highly demanded!
Deliver all demanded Freight ASAP (not delivering it when science box is already full, of course). However, if a city is about to produce a Superhighway, hold off delivery until completion. Deliver undemanded Freight afterwards (in case demand opens up).
Focus more on building Freight and Science improvements than on building Offshore Platforms, and Harbours for cities that have a food surplus and aren't using it up by celebrating.
If we trade enough, and boost our base trade with SH, we can build up enough cash and science to buy the spaceship, instead of needing the shields to build it.
Tech path: Research Mass Production as it leads to desired techs (Space Flight, Plastics) - but be careful to not start Apollo until we can be sure to complete the spacecraft in a short time. Computers would help immensely as well - a Research Lab in CAPITOL would yield 54 additional beakers/turn, and even more with Superhighways. SETI, IIRC, only assists cities which have a University - so if we're going to build SETI we need to get some more Universities in place.
Poll to follow.
Beakers per tech: 2442. We produce 696 science/turn. To get 3 turns/tech, we need to increase beaker output to 814+/turn.
Moreover, before the game ends, we will be running 5 turns/tech, down from our current 4, unless we a) increase beaker production from key cities and/or b)supplement beaker output with regular caravan deliveries.
We can increase beaker production in 4 ways - increasing science as a percentage of wealth production from the current 50%; increasing population by growing our cities faster (to work more tiles); building science improvements; and delivering a lot more Freights.
1)Increasing science at the expense of luxuries will put several cities into unrest. While science could be increased at the expense of taxes, revenues would be at a bare minimum - and probably need to be supplemented with Freight delivery.
2)We have lots of cities that could celebrate up to size 12 quite easily and thereby work more tiles and produce more science (Seville, Cordoba, Valencia, Salamanca, WhereItsAttown, Granada, and Pamplona all have tiles improved but no population to work them). Unfortunately, without Cure for Cancer, they won't celebrate right now - even with 100% luxuries!

3) Possible science improvements - University in St Praski - 18 more beakers per turn. Avila Univerity would yield 22 additional beakers/turn. Leon University - 15 additional beakers/turn. Total: 55 beakers, or less than 1/2 of what we need to get to 3 techs/turn.

Superhighways are a good option as trade from roads is increased 50%. A city with a lot of worked roaded squares (as opposed to sea squares) will produce nearly as much more science by adding SH, as it would by adding a University. The other big SH bonus is that trade goods will be worth a LOT more, delivered to or from a Superhighwayed city.
4) Freight: St Praski and Avila could each produce a Freight in 3-4 turns which when delivered, would probably yield 4 times as many beakers as a University would per turn, so that may be a better option. Even undemanded goods could yield close to 50 beakers when delivered to a large city, along with an equivalent amount of cash.
RECOMMENDATIONS:
My suggestion - build Superhighways in Capitol, Cadiz, and Avila, for a start. Immediately afterwards start producing Freight in Cadiz as it has 3 free commodities - Silk and Spice are highly demanded!
Deliver all demanded Freight ASAP (not delivering it when science box is already full, of course). However, if a city is about to produce a Superhighway, hold off delivery until completion. Deliver undemanded Freight afterwards (in case demand opens up).
Focus more on building Freight and Science improvements than on building Offshore Platforms, and Harbours for cities that have a food surplus and aren't using it up by celebrating.

Tech path: Research Mass Production as it leads to desired techs (Space Flight, Plastics) - but be careful to not start Apollo until we can be sure to complete the spacecraft in a short time. Computers would help immensely as well - a Research Lab in CAPITOL would yield 54 additional beakers/turn, and even more with Superhighways. SETI, IIRC, only assists cities which have a University - so if we're going to build SETI we need to get some more Universities in place.
Poll to follow.
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