Hi again,

After I started looking at RPMs from our planes, I wanted to see if we were using their propellers efficiently.

Now, the most efficient range for any given propeller is when the TIP of the propeller turns below 82% sound barrier - but the closer the better.

Between 88% to 92% time the sound barrier speed being the redline and over being noisy and inefficient.

Since I don't intend on reinventing the wheel (prop), I went on the Internet (where else) and dug out the formula

to calculate Prop Tip Speed. The calculation came from the Ponk Propeller website thru the WarpDrive website

( http://www.pponk.com/HTML%20PAGES/propellers.html ) and reads like this :

To determine propeller tip speed:

Prop Diameter X Pi / 12 X RPM X 60 / 5280 = Tip Speed in MPH

Example: 86" prop turning at 2800 RPM
86 X 3.1416 / 12 X 2800 X 60 / 5280 = 716.4 MPH

To determine the speed of sound:

Square Root (absolute temp + ambient temp) X 33.4 = Speed of Sound

Example: 59 degree F. day
Square root (460+59) X 33.4 = 760.9 MPH (speed of sound)

To determine propeller tip mach speed:

Tip Speed / Speed of Sound = Tip Mach Speed
716.4 / 760.9 = .942 MACH (too fast)

For the sake of discussion, we'll be using real data collected from 3 different airplanes running WarpDrive props at

FULL THROTTLE during takeoff where all power available is used to get us out fast and safe.

Data collected :

Owner/pilot             Takeoff RPM                                       Cruise RPM            Aircraft 

Bob M.              : 2385 RPM   (72 inch - 3blades)    2140 RPM   (5200 RPM)     CH750

Bob S.              : 2085 RPM   (72 inch - 3blades)    N/A   1775 RPM    (85%)     CH701

Normand L.       : 2430 RPM   (70 inch - 3blades)    2175 RPM   (5000 RPM)      CH701

For argument sake, I decided to use 70F as outside temperature for our calculations.

So, for the TIP speed calculation in MPH, we have Prop Diameter X Pi / 12 X RPM X 60 / 5280 = Tip Speed in MPH :

Bob M.       : 72inch X  3.1415926 / 12 X 2385rpm X 60 min / 5280 ft = 18,84 X 2385rpm X 60 /5280 = 510,86 MPH

Bob S.       : 72inch X  3.1415926 / 12 X 2085rpm X 60 min / 5280 ft = 18,84 X 2085rpm X 60 /5280 = 446,37 MPH

Normand L.: 70inch X  3.1415926 / 12 X 2430rpm X 60 min / 5280 ft = 18,33 X 2430rpm X 60 /5280 = 506,15 MPH

For speed of sound at 70F, we have the basic calculation :

Square Root (absolute temp + ambient temp) X 33.4 = Speed of Sound 

It becomes SQRT(460 +70F) X 33.4 = 23.0217289 X 33.4 = 768,86 MPH

So, what are our TIP speeds (pct sound barrier) ?

Bob M.        : 510.86 / 768.86 = 66%

Bob S.        : 446,37 / 768.86 = 58%

Normand L. : 506.15 / 768.86 = 65%

We all are FAR from exceeding the 88% to 92% range. We should strive to get closer to 88%. Not bad ! 

Now, WarpDrive states : 

If you want the quietest and most efficient propeller propulsion system,

select a prop configuration (and reduction drive ratio) that will keep the tip

speed for your cruise RPM at or below 700 feet per second or 475 mph. 

Above this speed "compressibility" of the air in front of the prop leading

edge begins to occur which begins to degrade the performance of your

propeller and make more prop noise.

With this knowledge, we have our CRUISE data:

Bob M.       : 72inch X  3.1415926 / 12 X 2140rpm X 60 min / 5280 ft = 18,84 X 2140rpm X 60 /5280 = 458,15 MPH

Bob S.       : 72inch X  3.1415926 / 12 X 1775rpm X 60 min / 5280 ft = 18,84 X 1775rpm X 60 /5280 = 380,01 MPH

Normand L : 70inch X  3.1415926 / 12 X 2175rpm X 60 min / 5280 ft = 18,33 X 2175rpm X 60 /5280 = 453,04 MPH

As can be seen, we don't have any problems keeping close/below and near 475 mph.

The closer to 475mph, the better efficiency we get. 

Hope this helps.

Regards.

Normand