In part 4 of this series, diagrams were prepared on which to base a design code.
Download code (29 KB BAS file)
The equations used in this design code were taken from Larrabee's report to the NFFS in 1979, entitled 'Propeller Design and Analysis for Modelers'. The particular section of this report entitled 'Arbitrary propeller performance' was used in novel ways.
Firstly, the definition of the blade angle BETA was changed . Rather than measure the blade angle to the chord-line, BETA was changed to the angle at the zero-lift line. This eliminated the tiresome repetition of the zero-lift angle in the maths. I also found it less confusing. The zero-lift angle only appears in the final calculation of the geometric pitch.
Secondly, a fixed value of the angle-of-attack was chosen, which hopefully corresponds to a good L/D. The variable name chosen for angle-of-attack is AOA. The choice of AOA can be guided by Rothwell's Law. In the case of a fairly flat-bottomed section, the flat should lie close to the line of advance. This empirical result is well worth a try. Note that AOA is measured to the zero-lift line, not the chordline.
Thirdly, an arbitrary radial chord distribution was chosen for a first trial value in a process of iteration. A parallel chord blade is a sgood a starting place as any. The iteration first sets out to find the downwash angle, then adjust the chord to provide the power absorption required and to make the slip constant. The chord variable name is ch(J). The blade taper is the result of forcing the slip to be constant.
The process does not compute the optimum components of efficiency, viz profile and induced, but must come close to it. The blade is numerically divided tangentially into 25 equal length elements, which are considered to act independently of each other. The power absorbed by each element is considered to be proportional to the chord of that element: the power of the proportionality is not relevant. The slip, likewise is adjusted using the chord. The slip at 3/4 radius is taken as the point for normalising the slip of the other blade elements. The power absorption and slip are adjusted simultaneously, at which time the solidity for new blade radial chord distribution is also determined.
The vector diagrams for each element are displayed as the iteration proceeds. This slows the calculation, so a subroutine 'delay:' is provided to adjust the display time. The variable 'timex' (seconds) may be varied by editing the code to suit. Like wise, the user may edit the code to adjust all the other inputs, but it is suggested that the user keep an unmodified copy in case of finger problems. The iteration converges rapidly, 6 run thru's is enough.
The code is written in Quick Basic, an easy to read and edit high-level language. The coding is heavily commented, so further description is not required here. The program is stand alone, and should run with no problems. The user may want to edit the input values to suit his own needs. The language Quick Basic is only supported on machines the can run DOS. If someone could convert the code to Visual Basic, then the code could be run on the later Windows operating systems.
No claim is made to absolute accuracy, but the results look about right. No corrections are made for Reynolds number, compressibilty or shock-wave problems. The tip speed should not exceed 300 MPH for these restrictions to be valid.
Compressibility is considered in Part 6 of this series. The correction process is a little complicated, which justifies the simple code presented here in Part 5.
Have fun! |
