For technical discussion of ALL Corvair aircraft engine conversions.

The following is from the excellent web site of John Brannen, unfortunately
the images attached would not copy so please visit the web site, there is more to see: http://www.freewebs.com/brannen/index.html

On the Corvaircraft e-mail list that I belong to there was some concern about running 72Ã¢â‚¬? props on a direct drive Corvair engine due to the asymmetric prop loads and the gyroscopic loads. I decided to perform an analysis of the loads that are experienced. The individual loads in question are the asymmetric and gyroscopic loads mentioned above and also the torsion load due to engine torque. Each load load is calculated individually and then the combined loading is calculated. The stresses due to the combined loading are then compared to the material specifications for the crank to determine the fatigue life of the crank under these loading conditions. The link below is to a Microsoft Excel Spreadsheet that I set up for this problem. The text below gives a description as to the logic behind the spreadsheet and calculations.

I spent some time looking through all of my textbooks from college, the aircraft design and engineering books that I have accumulated since college and also searching the internet for information on calculating asymmetric propeller thrust or P-factor. I found nothing. I then decided to see if I could logically derive an approximation for it. Here is my approach.

First, imagine that the prop is actually a disk that produces a certain total thrust. If the total thrust that the prop produces at a given flight condition is known, the average thrust produced by a pie shaped segment of the prop disk can be calculated. Now that we know the average thrust each segment produces, we can calculate the moment that the segment creates about the vertical and horizontal axes of the prop disk if we know where the "thrust center" of that segment is. For conservatism and a first look, I decided to assume that the thrust of the segment is centered on the wedge at the prop radius. The moment arm of each segment can be calculated easily for each segment using simple trigonometry. The figure below shows what I am talking about.

Now that I have the geometry and the thrust that each segment produces, I can calculate the moment that each segment creates on the crank and then sum these moments to get the total moment. The moment is resolved into 2 components, the moment about the vertical axis of the prop disk and second the moment about the horizontal axis of the prop disk. By inspection, the moment about the horizontal axis should be zero and was verified by calculating it in a spreadsheet. The moment about the vertical axis came out to be 5162 in-lbs.

To calculate the bending load imposed on the crank due to gyroscopic effects the following equation is used.:

GyroMoment=I*w*b

Where: I=moment of inertia of the prop, w=the rotation speed of the prop, and b=turn/pitch rate in radians/sec.

I initially used a conservative approach and calculated the moment of inertia assuming that the mass distribution from prop centerline to tip was constant. This was conservative because the actual mass distribution is biased toward the centerline. I then decided that I could do this better. I decided that the moment of inertia of the prop can be calculated relatively closely by assuming that the mass distribution is greatest at the centerline and tapers linearly to the tip. Imagine a constant width bar whose thickness tapers from some thickness at one end to a smaller thickness at the other end. This is what I used to mode the mass distribution of the prop. I used a tip thickness that is 1/10th of the thickness at the root. This is conservative since the cross sections of this bar are not shaped for the airfoil and are not tapered in plan form. I took this mass distribution and calculated the moment of inertia contribution of discretized sections and then summed them up. In other words I mathematically chopped up the bar into 20 equal length pieces, calculated the mass of each piece, and knowing what distance each piece was from center, I calculated the moment of inertia contribution of each and then added this up. I came up with a moment of inertia of one blade of 0.55. I also checked the moment of inertia calculation by saying that the thickness at the root and tip were the same, and as expected, the result matched the moment of inertia equation of a slender rod at 0.931. Using I=1.1 (remember there are 2 blades), w=314, and b=1, the bending moment from gyro loads is 362 ft-lbs, or 4350 in-lbs.

COMBINED STRESS CALCULATION

The bending moment loads were added to get a total bending moment of 4350+5162= 9512 in-lbs. The engine also introduces a torque load into the crank that must be considered. I used a torque of 170 ft-lbs = 2040 in-lbs..

To see if the crankshaft can take the loads, we should calculate the peak stresses in the crank. The stress from the bending will be highest at the outside diameter of the crank. To calculate this stress for the circular crank cross section, I used the equation sigma = M*c/I, where sigma is the tensile stress, M is the applied moment, c is the distance from the centroid of the crank, and I is the area moment of inertia of the crank. For a hollow shaft, the area moment of inertia is I=pi/4*(R1^4-R0^4) where R1=outside radius of crank and R0=inside radius of crank.

I=3.1416/4*(0.75^4-0.5^4) = 0.199 so, the maximum outer fiber tensile stress due to bending is

sigma=9512*0.75/0.199 = 35773 psi

We also want to see what that torque means to the stress, so calculate the shear stress using tau = T*r/Ip, where tau is the shear stress, T is the applied torque, r is the radius of the crank, and Ip is the polar moment of inertia of the crank. For a circular section, Ip=2I. So:

tau=(170*12)*0.75/(2*.199)=3836 psi

To calculate the combined stresses due to both of these, the combined principal stress is

Principalstress=0.5*(sigma)Ã‚Â±[(sigma/2)^2+tau^2]^0.5

Which gives 0.5*35773Ã‚Â±[(35773/2)^2+3836^2]^0.5 = 36179 and -407 psi for the principal stresses. The maximum shear stress is tau(max) = [(sigma/2)^2+tau^2]^0.5. which gives a max shear of 18293. None of these numbers even come close to the tensile ultimate, or tensile yield values for the crank material. The material properties of interest for 1045 steel are: ultimate tensile = 89900 psi, Tensile yield = 70300 psi, and fatigue limit = 45000 psi. I have been informed that the early cranks were 1045 steel where the later model cranks were 5140 steel. The material properties for 5140 are: ultimate tensile = 113000 psi, tensile yield = 66000 psi. The data I have does not list fatigue limit for 5140, but a general rule of thumb for steels is that the fatigue limit is about 50% of the ultimate tensile.

FATIGUE LIFE

The last consideration is to see what the fatigue life of the crank is. Fatigue life depends on the material, number of cycles and the cyclic stress. If we use the above maximum principal stress as the cyclic stress, and look at the S-N curve for 1045 steel, we see that the stress level is below the "knee" of the S-N curve otherwise known as the fatigue limit. This is the stress level at which the fatigue life is considered infinite. Therefore, the fatigue life of the crank for these loading conditions should be infinite.

I personally believe that the assumptions IÃ¢â‚¬â„¢ve made in these calculations are very conservative and, I would have no reservations running a lightweight 72Ã¢â‚¬? prop on a Corvair motor. Am I planning on doing it? No. Does that mean that my calculations are worthless? That is for you to decide for yourself. I also said before that each person needs to weigh each choice for their airplane themselves. If you are uncomfortable with any of these calculations, you should go with what has been tested in flight.
Go love a biplane today  Johnny luvs Biplanes
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Very nicely done.

Having owned a '66 Corvair, I know that these engines are tough, but cranks have been known to break.  Look at www.flycorvair.com and William Wynne has explained in detail his theory of a few broken cranks in airplane converted engines.

A few factors one must consider before going to a 72" prop (besides the above excellent analysis) is resonance and stress risers on the crank.  Read Mr Wynne's writeup and you'll see what I'm refering to.
crazyivan
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Yes I have followed recent postings on this closely, at the end of the day the moral is "build to WW's book"!
John
Go love a biplane today  Johnny luvs Biplanes
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