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From the wiki page on ships:

[Cargo ships] improve the chances of getting certain rare resources

I know that titanium is definitely affected, but are there any other resources currently implemented in the game that are boosted by trade ships? For example, do trade ships increase the chances of getting blueprints from trading?

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No, there is no other resource you obtain by trading that is affected by the amount of Cargo ships.

The part of the code that is responsible of getting more titanium with ships is the following:

var shipVal = this.game.resPool.get("ship").value;
var shipRate = shipVal * 0.35;      //0.35% per ship to get titanium

if ( this.game.rand(100) < ( 15 + shipRate ) && race.name == "zebras" ){

    var titaniumAmt = 1.5;
    titaniumAmt += titaniumAmt * ( shipVal / 100 ) * 2; //2% more titanium per ship

    this.game.resPool.addResAmt("titanium", titaniumAmt);
    tradeRes["titanium"] = tradeRes["titanium"] ? tradeRes["titanium"] + titaniumAmt : titaniumAmt;
    //this.game.msg("You've got " + this.game.getDisplayValueExt(titaniumAmt) + " titanium!", "notice");
    }

Nowhere else something similar is found in the diplomacy source code.

spoiler about unlocking:

Of course, you'll need 100 ships to unlock the Spider clan!

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