I'm sure 00Dan will be along later, after contemplating options. For now, a quick follow up regarding measurements.
Test setup; one line tapped into the aircraft static system, one line tapped into the manifold pressure instrument line (i.e. the #3 primer port), and one line connected to a static pressure tap in the side of the airbox. The tap was fabricated by drilling a small hole in the airbox wall, then gluing a barb fitting to the box exterior. See photo.
The lines required restrictors to stabilize the electronic manometer readings. A tiny notch was filed in the edge of an AN426-3 rivet head, then the rivet was pushed into the tube. See photo.
Test conditions were 2500’ PA, 67F, TAS 191 MPH (166 KTAS), at 2700 RPM.
The three pressure lines were connected to an electronic manometer in turn, with the manometer's second port open to cockpit pressure. The static port deltaP was 0.16 inH2O. The manifold pressure tap measured -21.80 inH2O. The airbox port measured 2.61 inH2O. Indicated manifold pressure was 25.6 inHg.
Given freestream 0.16 above cabin pressure and airbox at 2.61 above, the airbox rise above static is 2.61 – 0.16 = 2.594. We'll round to 2.6” H20 above static.
Pressure at the primer port was negative, so –21.8 + 0.16 = 21.64. We'll go with -21.6” H2O below static
Induction loss, airbox to primer port, is thus 21.6 + 2.6 = 24.2” H2O, or 1.78” Hg, and that value does not include the filter. No surprise. It’s a carb on an updraft sump, and both are known to be restrictive. For comparison, under similar conditions the horizontal sump on my 390 with an FM-200 had a 1.0” loss, including filter. That value should reduce even more with the manifold used on the 390-119, or possibly one of the non-Lycoming manifolds.
The above is simply pressure loss in the intake tract between the airbox and the intake valve. The original question ("Can the airbox be improved?) largely revolves around how well it converts available dynamic pressure into increased static pressure...the ram effect which allows most of us to see a rise in manifold pressure with speed rise.
The combustion air inlet is not a closed pitot, but rather, has an exit (the engine), so for a simple low Vi/Vo inlet, available dynamic pressure is based on the difference between the inlet and freestream velocities. Volumetric efficiency for a stock angle valve Lycoming is close to 0.9. Although it's surely less for the updraft parallel valve, here I'll stick with 0.9 as it won't make a large difference, and said difference would improve the ram value.
Assume the existing setup is replaced with a round, external diffusion inlet of 3” diameter feeding a large volume airbox. Given 2700 RPM and a 0.9 VE, intake volume is 6480 in^3/sec, thus inlet velocity is 45.3 knots. Aircraft velocity (the freestream) was 166 knots, so velocity for available dynamic pressure is 121 knots. So, at 2500 feet and 67F, the dynamic pressure rise should be 0.63"Hg, or 8.6" H2O, somewhat better than the 2.9"H20 measured above. Airbox total pressure for this displacement, RPM, velocity, altitude and temperature should be 27.95” Hg, so after a 1.78” intake tract loss, the indicated MP should be 26.17”Hg, or 0.57” higher than the 25.6 indicated with the Cessna airbox.
We can roughly cross check that gauge indication using the measurements. Static pressure at 2500PA and 67F should 27.315"Hg. The induction loss was 1.78, so 27.315 - 1.78 = 25.72. The slight difference between 25.72 and 25.6 indicated could reasonably be seen as the filter loss, 1.6" H2O, as the filter was not included in the measured intake tract loss. The manifold pressure gauge is probably accurate.
A 2” inlet ring is not nearly as good, with an airbox pressure rise of only 0.1768’Hg. If a 2" inlet was desired for some other design reason, it would require internal diffusion. A 4” ring would bump ram pressure to 0.85", but the additional 0.2 (0.85 - 0.63) may also net a bit more external drag, as the housing would have more wetted area. Note the pressure gain is shrinking in proportion to each additional increment in diameter. All design is the art of intelligent compromise.
Anyway, the old school GA airbox appears to be costing a potential half inch of manifold pressure. It's also leaking ram pressure into the lower cowl, deteriorating engine cooling and increasing drag. If it was my airplane, it would indeed get a flotation test in the nearest body of water. 00Dan may decide different, and that's fine too.