Before using the Don Bates model to define the propeller for my "Kinda Kozy" I wanted to carry out a couple of sanity checks since I found that it was possible to arrive at a wide range of propeller designs when using his model. To this end I chose to estimate the pitch using more conventional methods thus providing a level of confidence once the model was implemented.

The first inputs result from the estimate for maximum speed in the cruise condition. This was derived from the assumption that the RG gave a speed increase of at least 14 mph. This resulted in a top cruise speed of 230 mph. This would be achieved using a Lycoming 0-360 (180 hp) engine through a fixed pitch propeller. The SVX engine in its stock form provides 230 hp and since I have no knowledge of the expected power with the small number of induction and exhaust changes, I assume that the power is unchanged.

The expected speed of an aircraft, in which the dominant drag is parasitic drag, increases with the cube root of the power so the expected speed with a 230 hp engine and RG should increase from 230 mph to 250 mph. To achieve this goal the propeller must have sufficient pitch to ensure that the blade is operating within its aerodynamic drag bucket. The drag bucket occurs when the lift to drag ratio is a maximum and typically lies in the region of AOA = 0⁰ to 2⁰.

The engine spins at 5400 rpm when operating at the maximum rated power of 230 hp. There is a reduction ratio of 1.85 : 1 in the PSRU which reduces the output (propeller) speed to 2920 rpm. For this condition and an advancement speed of 250 mph the helix cut by the propeller will have a pitch of 90.4 inches. (This is the condition for incompressible fluids or a simple screw thread.)

To achieve maximum bandwidth from the propeller the tip speed should be as high as possible with the only limitation being that the tip should not get into the region of aerodynamic compressibility. Typically a figure of Mach 0.85 is used as the magic number that should not be exceeded. (This makes some allowance for the speed increase as the air passes over the aerofoil curved surface and the increase in air velocity caused by the propeller operation.) Since the aircraft is moving forwards and some air is also being moved backwards by the propeller (A figure of 6.4 mph can be added to accommodate the induced velocity) a forward component of velocity of 256.4 mph should be considered. The tip velocity is at 90 degrees to the forward velocity and the full velocity component is calculated by Pythagoras. 

Alternatively, if the maximum tip speed is one of the design criteria then the maximum radius of the propeller may be determined:

Assuming the propeller is to be designed for an altitude of 8000 ft, Mach 1 = 1085.3 ft sec^-1

The maximum rotational tip speed may be calculated:

• Rotational Tip Speed = (0.85 Mach2 - (256.4 mph)²)^1/2

• Thus the maximum rotational tip speed is 574 mph

With the maximum engine speed of 5400 rpm spinning the propeller at 2920 rpm the maximum radius to achieve this goal may be calculated by re-arranging the relationship:

• 2 p R RPM = Rotational Tip Speed
• R = Rotational Tip Speed / (2 p RPM)
• R = 33.1 inches

Thus the propeller should be no greater than 66 inches in diameter.

The 90.4 inch helix requirement and the propeller diameter result in an angle of attack or pitch angle as a function of blade station. This relationship is indicated graphically below. Notice how steep the blade angle is, even at the tip which is why the take off performance is expected to be not too good.

Using Don Bates Model.

Application of Don Bates model with the data gathered from previous characterization and a free choice of prop diameter yield

Output data, from the program is given below. The equivalent flat plate drag has reduced from the nominal 2 ft2 to a value of 1.681 ft2. This is a substantial improvement over the stock Cozy MK IV.

My estimate of 90 inches for the Effective pitch

With a static thrust of 414 lbs the take off roll is expected to be approximately 1000ft with a 1500lb gross weight. 

Last Updated:    Thursday August 31, 2006