If I understand them correctly you need 4 turnout switches for a crossover such as this…
correct?
What is the purpose of the different ‘angles’ of crossovers?
Also, if I simply want to be able to turn my loco in the opposite direction using a couple of turnouts and a single crossover track, placed near an end loop (loop to loop style layout}, wouldn’t that work or do I need the double style crossover to come back again in the opposite direction?
I hope this makes sense! 
Jarrell
Several manufactures make double crossover’s already. but if you want to make one yourself, it’s going to require 4 Turnouts and a lot of cutting, soldering and manufaturing of guardrails. Similar to this: http://www.walthers.com/exec/productinfo/381-20210 or http://www.walthers.com/exec/productinfo/552-54 or http://www.walthers.com/exec/productinfo/948-812
If all you want to do is turn a train by a loop at the end, a single turnout will suffice.
You can also put a pair of crossovers end to end , it is longer, but that’s how a real railroad would do it. “Scissors” crossovers are extremely rare on real railroads.
The X in the middle is called a crossing. The angle of the crossing has to match the angles of the switches (the frog angle). On a real railroad the different frog angles mean different speeds a train can go over them. Most frog angles aren’t expressed as angles , but as a ratio. A number 6 frog “or switch” has the two routes diverge 1 unit in six. So 6 feet from the point of the frog, the rails will be 1 foot apart. Real railroads use #10 frogs for yard and industry tracks (10-15 mph), #14’s for slow sidings and crossovers (30 mph) and #20’s for high speed (50-60 mph).
The only reason you need a double crossover is to allow you to go from either track to the other track in either direction. If you have double track coming into the loop and always want right hand running you don’t need any crossover at all. If you want to enter the loop from either track and have the flexibility to exit the loop onto either track then you need a two crossovers, either the scissors type you have drawn or just 4 switches in two crossovers end to end. A pair of crossovers end to end is often called a “universal” crossover on the prototype.
The cheapest way to do it is to just have two crossovers end to end. It uses just 4 regular switches.
Dave H.
If I understand that you want to turn the locomotive end for end, you either need a turntable, a wye, or a loop. The crossover will allow you to run around your train but the locomotive will be backing up when you need to get to the other end of the train.
Will