Re-engine of N19WT replaces a 60 hp VW, 3,200 rpm, with a 60 hp, Hirth 3502, geared to 2,400 rpm. I've found a flight controllable IVOprop whose moment of inertia fits within the Hirth 3502 specs. But I wondered, 'What about prop diameter?'
My first though was to keep the same pressure differential through the prop disk. The slower turning prop needs a larger diameter to move the same mass at the same pressure differential. It turns out this is the square-root of the ratio of the two rpm and moves the propeller diameter from 52" to 60". The landing gear would have to be 8"/2 or 4" taller. But is that enough?
So I looked at propeller efficiency and this led to "advance ratio." There are multiple Google references but it all comes down to a non-dimensional formula:
J = V / (n*d)
J - advance ratio
V - velocity feet/sec
n - revs/sec
d - propeller diameter in feet
So I put together a quick spreadsheet and calculated propeller efficiency at three speeds and three diameters:
- 60 mph - minimum flight speed
- 80 mph - maximum rate of climb
- 140 mph - maximum level speed
- 48" - smallest diameter available
- 52" - current prop diameter
- 60" - calculated, constant pressure differential
I also calculated the prop tip speeds to avoid high mach numbers.
The prop efficiency surprised me at 60, 80, 140 mph:
- Original 52" prop @3200 rpm, efficiency range: 27%, 38%, 68%
- Alt 48" prop @2400 rpm, efficiency range: 46%, 55%, 79%
- Alt 52" prop @2400 rpm, efficiency range: 38%, 55%, 79%
- Alt 60" prop @2400 rpm, efficiency range: 38%, 46%, 72%
I had expected the slower turning, 52" prop to be less efficient because of the higher pressure differential. Instead, it turned out to be more efficient across all speed ranges compared to the original 52" prop turning much faster. But even more surprising, the longer 60" prop was less efficient than the 52" and 48" props.
The original, fixed pitch, wooden prop would limit the VW power at low speeds and let it generate more power at higher speeds. Due to the characteristics of the Hirth 3502, the replacement prop has to be flight adjustable to stay within a narrow rpm range. But finding that the prop efficiency decreased with larger diameter has me scratching my head. I would have thought that increasing the pressure differential across the smaller propeller disk would have reduced efficiency.
The only thing that might make sense is the increased tip speed of the larger diameter prop may have a greater impact on efficiency than I originally thought:
- 48" @2400: 504, 506, 512 ft/s tip speeds at 60, 80, 140 mph
- 52" @2400: 546, 547, 553
- 60" @2400: 630, 631, 636
But these tip velocities are relatively narrow and I don't see enough, even raised to a power, to explain the lost efficiency of the larger diameter prop.
Have I missed something?