Greg, in response to your number :
1) The CLT configuration with RTV behind the cg and download on the stab does have a strong negative slope to the pitching moment line and therefore it is more pitch stable than a CLT with no loading.
This does not say anything about its response to having the stab in the propwash, or any other interactions.
It merely shows that you'll be AOA stable when trimmed up at a given airspeed.
2.) You said "My conculsion from this, for several reasons in this paragraph, is that the bottom two examples of HTL are not adequate design of the HS - unless it's not really HTL! "
The best pitch response of the HTL gyro comes from having a sufficiently loaded stab to force the RTV to be in front of the cg.
The other designs are less positively stable, all else being equal, although they are still stable.
3.) "In the LTL column: Again, this seems to show the less up-loaded HS provides the stronger total pitch moment. Unless I'm really missing something, this seems to support my argument that the downloaded HS is more pitch stable! Where am I going wrong? "
The 3 configs are equal in pitch stiffness: LTL with no download , HTL with large download, or CLT with download and RTV behind the cg.
Actually, the diagrams are arranged such that the top row has the best pitch stiffness.
Note that all these configs have the RTV behind the cg
The next row has medium pitch stiffness, with RTV always on the cg
and the weakest pitch response is when the gyro has RTV ahead of the cg, even if it can be made stable.
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Al, another clear (to me) conclusion that I think can be drawn from your diagrams is that the more stable pitch moment - steeper negative slope - is when the CG is forward of the RTV.
That's certainly true.
Udi,
I might be able to work up some numbers at some point, but I used good old fashioned graphical analysis. I'll, of course, be interested to see your spreadsheet figures and hope that they don't make a liar out of me.!
I know that the rotor lift slope is less than the slope of the stab(reasons given in other threads) and it will slope down or up depending on whether RTV is behind, or ahead of the cg , but I didn't try to portray an exact value, but I did try to be consistent in how I drew the lines from diagram to diagram.
The stab has a steeper slope(green line) and it always slopes down with increasing AOA.
If you add two lines, which is what we're doing graphically, the slopes will add. Two lines sloping the same direction will have a resultant line with twice the slope. If the lines are sloping in opposite directions, the slopes tends to cancel.
A line plus a horizontal line is sloping at the same angle, but shifted up or down as in thre ones where I showed prop thrust as a constant moment that doesn't change with AOA.
Using this basic reasoning it is pretty easy plot the curves. The results are only approximate, but they should give an accurate indication of the trend.
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Re; G-load stability. I always tend to think in terms of AOA stability so I don't confuse myself.
If a gust ,(or anything)increases the g-load, it must raise the AOA of the rotor. Even if the the rotor thust is on the cg and there is no moment, the stab will pitch up from the same gust and so the AOA stability (negative sope to pitch moment) provides g load stability I think.
Some other terms still confuse me. Raghu insists that the front wing be more heavily loaded than the rear lifting surface and I do not understand that rule other than to recall that it is essential in a FW design to have the front wing stall first.
Thanks again for the diagrams. Now you wouldn't want to expand your matrix of diagrams to add in the effects of airframe drag/lift moments, would you? I don't think the real story is over until ALL the moments on the aircraft are considered!
The next step would be to create a little javascript program that would run on a webpage that would generate the graphs on the fly. You'd just select the config you wanted from a pull down menu, or maybe type in some parameters and it would plot the lines and run the numbers. No big deal to do. I thought it would be better to start with static diagrams before getting too fancy with the graphics.
It would be nice to look at dynamic response by having some animation too. Chuck emphasized the fact that the spring constant of pitch stiffness helps static stability, but adds to dynamic instability becaue of overshoot.
Dynamic response could be animated but things tend to get out out of hand quickly if you try to cram too musch clever stuff into a web page script.
You guys that want to work with spreadsheets are nuts. I hate those things and am more comfortable with my other tools.