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So should I get a bigger, compounds, or twins turbos;

Compound turbos give you the best of both worlds.  The first turbo is small so it will spool fast, the number two turbo that's called the primary is big so it takes over where the small leaves off. The primary turbo feeds in to the air inlet of the small turbo the small turbo feed to the intercooler. If done right it will make a sweet setup. You can run in to problems with ETG's but it is easier to deal with. The things you need is a way to give it more fuel, fuel = boost with out fuel you can't get boost. I have seen compound gas engines if you have a block the can handle it compounds will work great.

First the big turbo; A bigger turbo works if you just want a little more horsepower. If you put a bigger turbo and a boots fooler on you can get a little more horsepower out of it. If you go with a turbo that is on the big side you can run in to problems  like high EGT's (exhaust gas temperature ) slow spool up and smoke and you need to feed it more fuel.  People run big turbos at the track with trucks in the 10 seconds range. But thay get the turbo spooled up before thay leave the line. If a turbo is to big it can be very hard to drive as a daily driver and even harder to tow with.

Twin turbos; do not work well on in line 6 or 4 cylinder. I have heard of people that took a 5.9 cummins cut the exhaust in half and tried to run twins it didn't work out. The reason 2 smaller turbos work on V6 and V8 is because the smaller the turbo the faster it spools the faster you get horsepower. The only problem is the smaller turbo gives good low RPM horsepower but dose not do as much for the top end of your RPM range.

So here the thing now you want compound turbos. So you price them out and buy the time you get the compound set up some way to add fuel and anything more you might need you are talking $6000 -$8000, OK my wife is going to kill me if I drop $8000 in my truck engine. I will explain how I did it on a budget. What I was looking for was a good tow machine and did not want to wait at on ramps. One more thing sometimes I just like to put my foot down. There are a lot of different turbo combinations the best thing is to call one of the turbo tech support and tell them what you are looking for. Be realistic with them if you tell them, I want 1200 horsepower they will sell you turbos that can make 1200 horsepower but nothing in you engine will do that so you will have a mess. I started out I bought a simple 3 position tuner ( I have a 01 Dodge cummins 6sp ) for about $300. Then I got my turbo I bought a off  brand turbo ( for sure from China ) and used my stock turbo for my first. Your exhaust wont line up ( it might not with a bigger turbo be sure to ask before you buy ) so I order new 4” exhaust and turbo ( turbo about $400 exhaust about $250 ) and built my turbo pipe not as hard as you think.

You can look at videos of how on the Dodge link I have a couple. Then I put together the turbo and ran the exhaust from there. This is all I did and drove it for about 150,000 miles on a completely stock engine with stock injectors. In between I bought a top of the line tuner. This was a mild set up but I could tell a big difference, made it fun to drive. I rebuilt the engine at 400,000 and put crank studs and head studs in with 100# injectors, 110# springs, heavy duty push rods and bigger turbo but for towing not for go fast. Now I have a lot of horsepower and I started to have problems with high ETG's. So I put a waste-gate on it and made a big difference but I still was not happy so I put water / meth and the ETG's stay where they should. I towed up a mountain with about 14,000# and held 75 my ETG's stayed around 1150 it used over a gallon of water / meth but it loves to tow now. If you don't count the engine rebuild ( that I needed to do anyway ) I have about $4000 - $5000 in upgrades counting the up grades in the engine but I did it over time so it's not so bad.

We are talking about diesel here but it is the same principal for gas.

First you have to know what you are looking for. Do you just want a little more horsepower or want to  tow better or go all out. Compound turbos get confused with twins turbos. Compound turbos have one turbo feed another and work off the same exhaust. Twin turbos are separate and work off different exhaust out lets.