Guys! Don't mix apples and oranges, the ratios discussed whether 4.5:1 or 7.5: 1 are all speed to speed relationships. RPM to RPM.
Now if you want to calculate how many horsepower is required to run this generator we need to know the KILOWATT rating. Then it is a simple calculation to find required HP, using a standard rule of thumb factor.
All calculations assume that the generator is operating at FULL electric load.
For direct drive; engine to generator requires at least 1.7hp : Kilowatt (1000 watts) (this includes a power transmission loss factor).
ie; 5.5KW x1.7 = 9.35 or 5500watt needs a 10hp engine.
ie; 20KW x 1.7 = 34 or 20,000watts needs a 34hp engine.
Now if using PTO and gear box or jackshafts we need to add in an additional power loss factor of 10 to 20% for transmission losses, so to make it simple lets use 2.0 as our multiplier.
ie; 5.5KW x 2.0 = 11hp at the PTO
ie; 20KW x 2.0 = 40hp at the PTO
ok ,get r done and send pics.