seen a few posts saying reactors and relays are worthless and not worth researching or putting on ship. this post is to explain them in depth and put all the arguements to rest. Note my math will not be exact, just rounding things off through the equations. But you will get the point. One thing about this game is at first something may seem small, but as you learn better versions their worth will shine.

Ok first some assumptions for the following equations
1)assume you don't sleep and never take the relays out (in the first few types the energy bar will still fill up before 8 hours)
2)assume you only build the mark 4 versions of reactors. This is my personal strategy. I learn all 4 versions of a reactor type then build 3 of the mark 4 version. then i build the relay I can learn right after it.
3)you always build 3 reactors and 4 relays (max per ship). and you should be doing this!!
4)assume you have the Omicron Injector in (one of the first tier rewards that give you a +10 seconds to energy recharge rate)
5)skip the +1 Relays


Reactors and Relay Tree in order:
-Power Conduit -- +1 sec recharge (+4 total) and -5 max energy (-20 total)
-Fusion Reactor mark 4 -- +19 energy (+57 for 3)
-High Energy Relay -- +3 sec recharge (+12 total) and -10 max energy (-40 total)
-Graviton Core Mark 4 -- +35 energy (+105 total)
-Plasma Relay -- +6 sec recharge (+24 total) and -20 max energy (-80 total)
-Quantum Capacitator Mark 4 -- +55 energy (+165 total)
-Wave Conduit -- +9 sec recharge (+36 total) and - 30 max enegy (-120 total)
-Antimatter Reactor Mark 4 -- +83 energy (+249 total)
-Positron Relay -- +12 sec recharge (+48 total) and -40 max energy (-160 total)
-Singularity Core Mark 4 -- +123 energy (+369 total)
-X conduit -- +15 sec recharge (+60 total) and -50 max energy (-200 total)
-Zero-Point Reactor Mark 4 -- +175 energy (+525 total)
-Transconduit -- +18 sec recharge (+72 total) and -60 max enegy (-240 total)

Now for the math:

combo 1) no reactors or relays -
max energy = 80
recharge rate = 170 seconds (2min 50 sec)
21 energy/hour - 508 energy/day

combo 2) 3x Fusion Reactor mark 4 and 4x High Energy Relay
max energy = 97
recharge rate = 158 seconds (2min 38 sec)
22 energy/hour - 546 energy/day

combo 3) 3x Graviton Core Mark 4 and 4x Plasma Relay
max energy = 105
recharge rate = 146 seconds (2 min 26 sec)
24 energy/hour - 591 energy/day

combo 4) 3x Quantum Capacitator mark 4 and 4x Wave Conduit
max energy = 125
recharge rate = 134 seconds (2 min 14 sec)
26 energy/hour - 644 energy/day

combo 5) 3x Antimatter Reactor Mark 4 and 4x Positron Relay
max energy = 169
recharge rate = 122 seconds (2 min 2 sec)
29 energy/hour - 708 energy/day

combo 6) 3x Singularity Core Mark 4 and 4x X conduit
max energy = 249
recharge rate = 110 seconds (1 min 50 sec)
32 energy/hour - 785 energy/day

combo 7) 3x Zero-Point Reactor Mark 4 and 4x Transconduit
max energy = 365
recharge rate = 98 seconds (1 min 38 sec)
36 energy/hour - 881 energy/day

combo 8) haven't learned these yet but the improvements of the modules are constant therefore you can assume
max energy = 517
recharge rate = 86 seconds (1 min 26 sec)
41 energy/hour - 1004 energy/day

By the end you have doubled your efficency and believe me you will need it with the amount of xp needed to level. Also if you remember to unequip your relays when you level you will get alot more energy recharged to use as a great boost in xp on your next level. This is where the greatest value is.

here is your energy without relays on each combo.
combo 1) 80
combo 2) 137 (1.7x energy on lvl compared to no reactors)
combo 3) 185 (2.3x energy on lvl)
combo 4) 245 (3.0x energy on lvl)
combo 5) 329 (4.1x energy on lvl)
combo 6) 449 (5.6x energy on lvl)
combo 7) 605 (7.5x energy on lvl)
combo 8) 797 (9.9x energy on lvl)

THANK YOU!!!!!!!
This helps allot.