#### Jean Claude

##### Junior Member

- Joined
- Jan 2, 2009

- Messages
- 2,631

- Location
- Centre FRANCE

- Aircraft
- I piloted gliders C800, Bijave, C 310, airplanes Piper J3 , PA 28, Jodel D117, DR 220, Cessna 150, C

- Total Flight Time
- About 500 h (FW + ultra light)

My spreadsheet uses 15 tables of 11 columns (blade parts) and 24 lines (azimuth positions).Of course nothing wrong with your assumption of disc AOA increase due to gust, but maybe you can explain in a little more detail how you used that to arrive at instantaneous load/thrust increase. I suspect that will explain the discrepancy.

table 1: Tangential airspeeds of each blade segment for each azimuth

Table 2 Multiplier coefficient for average induced speed (non-uniform)

Table 3 Air velocity component perpendicular to section trajectory (takes into account previous tables and conicity)

Table 4 Relative air velocity (combination of tangential and "axial" velocities)

Table 5 Angles of attack according to previous tables

Table 6 Slope correction dCL/di as a function of Mach Number

Table 7 CL calculation based on tables 5 and 6, taking into account possible stall and aspect ratio

Table 8 Lift calculation based on tables 4 and 7

Table 9 Cd0 calculation based on table 5 and cd min initially entered

Table 9 bis Calculation of Cd according to tables 7 and 9 and possible stall

Table 10 Drag calculation based on tables 9 and 4

Table 11 Angle of pressure resultant relative to axis of rotation based on tables 9,7,5 and pitch setting initially entered

Table 12 Resultant thrust based on tables 10 and 8

Table 13 Torques based on tables 12 and 11

Table 14 Flapping torques as a function of tables 12 and 10

Table 15 Axial thrust components based on tables 12 and 11

(I can send you the file if you give me your e-mail address)

After a few checks, I can't find any errors in my spreadsheet, and the results that seem surprising to you seems confirmed by the simple reasoning:

My spreadsheet finds that the steady rpm is around 400 when the rotor load is 2144 N at 34.2 m/s (i.e. mu = 0.25).

This calculation is not in doubt, given the numerous comparisons with accurate in-flight measurements that have already been published in the past by Naca.

For that, the indicated angle of attack of the disk is 7° or 0.122 rad, which should give a perpendicular disk speed of 34.2 m/s * 0.122 = 4.17 m/s (only for such small angles)

The induced velocity found of 0.78 m/s is not in doubt either, in this case of high Mu ratio, where the disk behaves almost like a circulare fixed wing. This means that the flow through the disc has a perpendicular component of 4.17 - 0.78 = 3.39 m/s.

At 3/4 of R, which is assumed to represent the mean effective radius, the circumferential speed is

*100 m/s.*So, the mean aerodynamic A.o.A. of blades with pitch setting of 3.5° (0.061 rad) is therefore 0.061 + 3.4/

*100*= 0.095 rad (or 5.4 degrees) when load factor=1

A vertical gust of 2.5 m/s now occurs. It increases the angle of attack of the disc by 0.073 rad, which becomes 0.122 + 0.073 = 0.195 rad, giving a speed component perpendicular to the disc of 34.2 m/s * 0.195 = 6.7 m/s (If we still confuse the angle with its tangent).

The average A.o.A of the blades would now be 0.061 + 6.7/

*100*= 0.128 rad, giving a load factor of 0.128 / 0.95 = 1.35

Except that this overload obviously implies an induced speed correction which increases by about 0.27 m/s (*) The speed of the flow perpendicular to the disc is therefore rather 6.7 m/s - 0.27 m/s = 6.43 m/s

And the average A.o.A of the blades is therefore 0.061 + 6.43/

*100*= 0.125 rad,

**giving a load factor of 0.125 / 0.95 = 1.33**, a value close to that obtained from the spreadsheet

(*) 1.055 m/s is the induced speed with factor load 1.33