I suggest you used this
calculator to estimate the potential of your engine (read the
theory to understand how it works).
The restrictor will impose a limit on the airflow rate based on
this equation:
Divide by
ρ0 to get the volumetric flow rate. Assuming a
discharge coefficient Cd of 1, SAE J1349 air conditions (99 kPa & 25°C), the maximum flow rate is 226.5 m³/h for a 20 mm restrictor.
If you play around with the calculator, assuming a
BMEPd of 12 bar, you'll notice that you cannot get more than 100 hp out of your engine, no matter how you modify your engine.
You have a 1-cyl engine, hence you're doing your intake process during ¼ of your cycle (With a 4-cyl or more, the engine is doing it throughout the cycle, as every cylinder are not doing the process simultaneously). So, in theory, your engine pulls its air during only ½ revolution instead of 2 revolutions, which means the flow rate could be 4 times as high as the one from a 4-cyl+ of the same displacement and rpm. Your limit would be 56.6 m³/h instead of 226.5 m³/h (In fact, it will be a little higher as the vacuum created inside the manifold will still pulls some air even after the intake valve is closed). That means that your 100 hp limit just dropped to 25 hp! (I told you a little more and you got 30-33 hp). That is, if you pull the air with the piston itself.
What you can do, is put a box at the inlet of the intake manifold and feed that box with an air pump. That box will act as a sub-atmosphere to feed the engine and the air pump will fill the box continuously instead of just during ½ revolution. This way, you can reach again your 226.5 m³/h limit imposed by the restrictor.
Although you can now feed 226.5 m³/h, your engine has a speed limit and the inlet pressure (boost pressure) might be a limiting factor too. So if the engine is too small, it might be impossible to accept that much air. If you play around with the calculator, you'll find out that this is your case. With extreme modifications (I mean extreme), one might bring your engine to 65-70 hp.
Turbocharged or supercharged?
Personally, I think I would prefer a supercharger to a turbocharger for the air pump. A
positive displacement compressor rather than a
dynamic compressor.
The supercharger is a relatively easy install compared to a turbocharger. The supercharger will not affect the air & exhaust flow of the engine. So you can tune the engine manifolds independently from the air pump. With a turbocharger, the flow affects the turbocharger and the turbocharger affect the flow. If you mismatch the parts, you can end up with something worse than what you started with. Since you have no reference for your engine turbocharged (especially with a restrictor), a lot of costly (time & money) testing will probably be involved. Worst, if you never done it before. With a supercharger, it is merely a question of selecting the right pulley ratio and it can be easily estimated with calculations.
In any case, an intercooler will be helpful.
A turbocharger is a dynamic compressor (DC) and, as I already mentioned, a positive displacement compressor (PDC) might be better. The PDC will raise your power curve through the whole rpm range, which I think you will need for your competition. With a DC - even as a supercharger - it will perform best at a certain rpm only. This bring us again to costly testing.
I assumed you had
this engine. By reverse engineering, I found out it had
BMEPd of 12 bar and a volumetric efficiency of 92%. By putting a supercharger, you can keep the 92%
VEun-boost, drop the
BMEPd to 9.6 bar (for power consumption, maybe better) and raise the pressure ratio to 1.8: You get 50 hp with 138 m³/h of air flow. Look at that, the http://www.oguraclutch.co.jp/e/product/supercharger/type.html (they have a
US office as well, so a possible sponsor) can produce 130 m³/h at a pressure ratio of 1.8!
For a turbocharged version, your
VEun-boost will probably drop to 80% (due to the un-tuned exhaust length), the
BMEPd to 10.5 bar (maybe better) and, with a pressure ratio of 2, you will get the same power output as the supercharger. Though, you might be able to reach a 2.8 pressure ratio for an extreme case, giving you 60 hp. But remember, that is peak power. Your average power within your rpm range might not be as good as with the supercharger. Sorry - unlike a supercharger - I can't easily give you an available compressor/turbine combination that would fit those scenarios. You would need to match
compressor &
turbine maps with the engine estimated airflow and pressure (told you it was complicated).
On the plus side for the turbocharger, note that its higher
BMEPd means that it will have a better fuel economy compared to the supercharger.