Testing Theory: Prop efficiency vs. effective pitch

[hevansrv7a]

Theory says that the RPM difference cubed should equal the Horsepower (HP or BHP) difference. Another theory says that

change in effective pitch equals change in prop efficiency. We need the first to test the second.

------------------------ testing the first theory ---------------------------------
This can be done on any certified airplane's POH with similar data, but this is from the 1979 C-152.

At 2000', using 2100 and 2400 rpm's, the ratio is 1.143 for which the cube is 1.493. The BHP ratio is 1.415.Theory produces an answer that is 5.5% high.

At 8000', using 2100 and 2400 rpm's, the ratio is, again, 1.143 for which the cube is 1.493. Now the HP difference is 1.333. Theory is 12% high.

---------------------- testing the second theory ----------------------------------------------
Still using C-152 POH:

For 2000', moving from 2100 to 2400 rpm, the effective pitch changes from 49.7 to 51.1 (2.8%).

For 8000', same rpm's, the effective pitch changes from 48.0 to 50.1 (4.375%).

In both cases, the effective pitch increased with higher RPM and speed, but the difference was greater at 8000'. This observation is not affected by engine performance.

At 2000' the BHP increased 41.5% while the effective pitch increased 2.8%. 41.5:2.8 = 14.82
At 8000' the BHP increased 33.3% while the effective pitch increased 4.375%. 33.3:4.375 = 7.61.

So there is a very weak relationship between BHP and effective pitch between altitudes. This implies that the second theory fails, but doesn't really prove it.

All the above data can be taken and calculated from the POH. If we include the drag curve for this airplane which can be obtained from the experiments with the "propless" C-152, then we can compute the thrust HP (THP) at those speeds and thus the net prop efficiency: THP/BHP x 100. Follow the last link below for a spreadsheet showing the drag curve for the C-152 which also includes a copy of the relevant POH page.

For 2000' for 2100 to 2400 rpm, the prop efficiency goes down from 65.52% to 64.85%.
That's a change of -1.0%.

For 8000' for 2100 to 2400 rpm, the prop efficiency goes up from 64.39% to 65.34%.
That's a change of +1.475%.

At 2000' the "spread" is 2.475% for prop efficiency but the values are opposite polarity.
At 8000' the "spread" is 1.575% for effective pitch and both values are positive.

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CONCLUSION
Perhaps in a wind tunnel without a fuselage behind it the effective pitch and the efficiency would move in perfect synch. But at least in the case of this real world airplane, they don't. Neither theory is supported by this real world data.