It does not need to be that much bigger. Look at the air horn on the old style air cleaners. The inlet was small enough to cover with your hand but the tube that went back to the air filter box gradually increased in diameter. This allowed the air flow to slow down smoothly and fill the air cleaner can with air at a higher pressure.
If the change in size is too abrupt the air flow will tumble and separate from the walls of the ducting, greatly reducing the effective size of your duct.
You want to increase the size enough that the airflow slows down significantly, this both increases flow pressure due to recovery of kinetic energy of the moving air flow, but the slower moving air has less drag (friction) with the walls of the duct so pressure losses due to flow friction go down.
Ever notice how the blower fan on your cars heater makes almost no noise at the low speed setting but gets quite noisy at setting 3 or 4?
That is due to turbulence generated as the airflow moves faster. Same thing applies to intake ducting. You can move all the air most engines can handle with a 4 inch to a 6 inch duct.
A 6 inch duct has a cross section of 0.196 sq ft. If you are moving 1000 cfm through that duct it has to move 85 ft/second or just a tad slower than 60 mph.
As you probably know friction drag due to air flow on a car below 60 mph is so insignificant it can be largely ignored but increases rapidly as speeds go above 80-100 mph.
The same thing happens in an air duct, flow friction increases at the square of the flow velocity, so if you keep air flow velocities down around 80-90 ft per second in the duct, you will minimize friction flow (obviously a smooth duct helps too), and you get as much pressure recovery as is likely in a real world setup.
The ducting does not need to be huge, just smoothly formed and with gentle bends, that are kind to the air flow, and drops the air speed by about 1/2 of its free air velocity as it enters the intake system. That will cut flow drag by 4x, and give you 50% of the theoretical pressure recovery possible at a given speed.
Good topic Blackslax. Question for all: If the air inlet is right at the nose, doesn't that reduce drag?
internal drag is just as important as external drag. The air does not know if it is inside a tube or flowing over the outside of a body. It will still exert drag against the walls of the tube. That is one reason cars go faster if you can block off the radiator flow. By forcing the flow out over the smooth body, internal drag is reduced.
Larry