Planet full of factories or planet kicking out a tiny/small ship with nothing but a colony module on it.  Manufacturing bonus tiles help, but aren't strictly necessary.  Generally you'll want your first mining base to be up before you actually start -building-...that extra 4-5 industry actually helps quite a bit.

Then again, I've been taking military production bonuses as of late.  Running with a custom race gives me 10% homeworld production bonus (from the moon), in DA I pick up 30% from techs early on (25% in TA as planetary improvements isn't as easily accessible), and I've got another 50% from customization points, so I've got a total of essentially an 80 or 90% bonus to my military production output.

I'm amazed you're able to weather the storm at all playing on Maso with a 6-8 turn colony ship build.  I assume you're referencing a traditional factory, at a rush buy cost of 438BC, which is 4 industry.  Not accounting for racial bonuses, that brings your homeworld to 28 industry.  6-8 turns would be 168BC to 224BC for a colony ship at 100% funding, 100% military.  While 168 is not outlandish, 224 is.  What on earth are you putting on them?  Focusing on research at 100% military would give 21 industry, at 6-8 turns is 126BC to 168BC-far more reasonable.  Is that what you're doing?

In any case, you should be able to get enough industry to knock it down to a two turn build.  Try buying factories on the longest lease-but don't go overboard.

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My initial colony ship costs me 92BC-a basic support, a colony module, and on a small hull.  After I've gotten enough infrastructure in place on my homeworld, I typically shift that world and that world alone over to a ~165BC-175BC (178BC at most) cargo hull containing a colony module, an impulse drive and an ion drive or three ion drives, and perhaps a basic or general support.  However, this is DA-specific, and I haven't played that much TA still.  It's looking like I won't be doing cargo colony ships in TA, as I'd have to get them definitely below 150BC, and probably below 130BC, so this is an engine or two at best (ion drives), which doesn't justify the additional cost or build time.

Recruiting center.  10% economic bonus, 20% population growth bonus (planetary, obviously), and only costs 25 industry.  One per planet.  Only two races that don't get them are Thalan and Arcean.

Fertility clinic is a DA improvement that you can build as many as you'd like per planet that increases the growth on that planet by 25% per.  It costs 25 as well, but requires fertility acceleration, a 1500RP tech, whereas recruiting centers are unlocked with the tech preceding space weapons.

To sustain a colony rush you need more money.  Although it can be somewhat costly to build, a transport with two colony modules and preferably an ion engine or better, allows you to get people off your homeworld and any other colonies that have become full up, and take them to colonies which aren't yet geneerating enough income to pay for themselves.  The population of the worlds you're tranplanting from will soon recover, so the loss of tax income from having 500M citizens in transport is quickly recovered.

My concern with slow ferries is not just the lost tax income, but by the time they arrive, the receiving planet grew in population and no longer needs the help.   Notable exception is the Korath.

The base speed is still 1.  But in TA some races get inherent bonuses to speed - Terrans, for example.  They also get the Innovation Center which allows a further +1 speed to ships built on that planet.

+1 speed doesn't make a lot of difference on short runs, but on the longer hauls it definitely pays off.

Base speed in TA is 2.

The main problem I have with the colony rush is maintaining a decent economy, which is very difficult when your pumping out colonies as fast as possible. Newly founded colonies are massive cash sinks until their populations grow to a decent size. The Drath are particuarly bad at this stage of the game because of their population growth penalty.

When playing the Drath the solution I found was two-fold. Firstly don't build anything apart from a recruiting centre on new colonies until the population builds up, otherwise your economy will get knackered by the maintenance and building costs. Second you should make a beeline for the Invisible Hand and War Profiteering technologies (just after Universal Translator) as fast as you can. Once you have these make contact with as many races as you can, and get them to go to war with each other. Then cackle madly as the cash rolls in.

For sheer building speed on colony ships nothing beats using asteroid mining to boost your production. Get as many asteroid mines as you can and focus their output onto your homeworld (or wherever your building colony ships).

Er, asteroid production isn't free-you still pay for it.  There's no maintenance, sure, and there's no "build cost", but the production itself is far from free.

I typically buy the first industrial complex, but nothing past that.

Jonnan