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From Travian v2 Wiki (S2-S6), the encyclopedia anybody can edit

The Great barrack allows you to build more units in the same time but they cost thrice the original amount. While it does not actually produce more units, it provides one a second way to produce units in parallel, albeit at markedly higher costs. Upgrades to the Great barrack speeds up the rate at which new troops are made. Each successive level cumulatively reduces the training time of units by 10%.

Costs and time to build level 1:

 630 |  420 |  780 |  360 |  4 |   ?

Requirements:
Barracks Level 20 and Main Building Level 20

Level							Culture Points	Training Length
1	630	420	780	360	?	4	1	100%
2	805	540	1000	460	?	2	1	90%
3	1030	690	1280	590	?	2	2	81%
4	1320	880	1635	755	?	2	2	73%
5	1690	1125	2095	965	?	2	2	66%
6	2165	1445	2680	1235	?	3	3	59%
7	2770	1845	3430	1585	?	3	4	53%
8	3545	2365	4390	2025	?	3	4	48%
9	4540	3025	5620	2595	?	3	5	43%
10	5810	3875	7195	3320	?	3	6	39%
11	?	?	?	?	?	?	7	35%
12	9520	6345	11785	5440	?	3	9	32%
13	?	?	?	?	?	?	11	28%
14	?	?	?	?	?	?	13	25%
15	19965	13310	24270	11410	4:01:30	3	15	23%
16					?		18	21%
17					?		22	19%
18