Sum-of Moments diagrams?
Sum-of Moments diagrams?
Raghu and all,
I still think we need to see all this on sum-of-moment diagrams – for gyros – such as Udi’s FW drawings. Gyros, are considerably more complex, and there are numbers of additional freedom’s of motion that need to moment arm change). Another issue is the offset gimbal that causes the rotor AOA to correct for change in G-Load – BUT, only if the cyclic stick is allowed to float! Another may be the differential in lift slopes between rotors and airfoils.
I still propose that we start a new thread, specifically for the “heavyweights” on gyro aerodynamics (I include myself maybe only because I am physically a heavyweight), to step-by-step walk through the pitch reactions and steady state conditions to changes in the variables. I propose that Udi’s drawing for FW be a good starting place. Start with a tailless pure CLT gyro. Do the sum-of-moments analysis for step changes in airspeed, in thrust. Look at the initial moments (just after “flapping” responds to the step change). Then do the final steady state result sum-of-moments after the transitional loads steady out.
Then do the actual sum-of-moments for progressively more complex gyros – first for tailless gyros with HTL and LTL. Then add a HS and do for all combinations of CLT, HTL, LTL with neutral, up-angled and down-angled HSs.
(Looking at a step INCREASE in airspeed – before airframe AOA or airspeed has a chance to steady out to steady state):
The “flapping” action moves the RTV forward - the RTV moment - in the nose-up airspeed restoring direction. In the FW version this does not happen. At the same time, the “flapping” action, it seems to me, also increases the actual rotor disk AOA and overall rotor thrust – at the instance of step increase in airspeed. The overall pitching moment effect of this depends on whether the RTV is forward or aft of the CG at that time – just after “flapping” changes the disk AOA. If the RTV is aft of the CG at this point, the resultant increased RTV pitching moment is nose-down – the airspeed (and G-Load) DIVERGENT direction. If the RTV is forward of the CG at this point, the resultant increased RTV moment is nose-up – the airspeed restorative direction!
Do these two effects offset each other in one case or the other? - Exactly? How and in what situation is the overall pitching moment be AOA (and airspeed) restorative upon a step change in airspeed? Would rotor design, reflex, etc. affect this? Could this be divergent? – A straight rotor is said to be airspeed unstable – thus the addition of the offset gimbal!?
That was rotor only – not considering offset gimbal or any HS. If we add a HS to this gyro, would the FW AOA stability mechanism apply? I’m thinking that it would as long as the overall rotor nose-drop pitch moment was less than the “balancing” HS moment in the opposite direction when the aircraft started to rise because of the increased rotor lift.
Again as with the FW AOA analogy question, when is an equivalent HS up-AOA equal to the resultant “equivalent” rotor AOA adequate to restore AOA and/or airspeed eventually to the initial steady state? This means, just how much HS AOI will still provide overall gyro AOA stability? And, with the variables of changes in RTV moment during all this, and possibly even a reversal in RTV moment direction, can we show that the overall AOA restorative pitch is even in the right direction for all cases? Remember, this is still pure CLT!
I’m swimming in risky muddy waters here – but just trying to think through all that myself. That’s why I suggest some Udi-like sum-of-moments analysis for successively more complex gyro configurations.
Considering all this and the posts above and on other threads concerning LTL, I’m still not able to see how any of this affects the POWER and G-Load stability issues – the change in CG/RTV moment and AOA and airspeed upon changes in propeller thrust with LTL. I certainly agree that somehow positioning the RTV aft of the CG in flight is THE thing to do – for the critical issue of G-Load stability. And holding the nose up and CG forward with a LTL will do this when there is propeller thrust! But, I fail to see, with or without a HS (of any AOI), how the CG is continued to be held in that forward position if LTL thrust is reduced.
Considering there may be (there are!) airframe aerodynamic moments that would force the nose low and CG even aft of the RTV without this LTL thrust, how are we going to hold the CG forward of the RTV if the HS is not down-lifting? It seems to me, that even a HS mounted level to the keel will be up-lifting when LTL prop thrust is holding the nose/keel attitude up. Upon reduction of the LTL nose-up moment, that up-lifting HS, as well as the other nose-down aerodynamic moments, will certainly cause the nose to drop or fly lower – there is nothing else to hold the nose up and the CG forward! And, if the HS is mounted level on the airframe – or worse angled UP – it will not even start to hold the nose level until the pitch attitude is nose-down enough to start a down-lift on the HS – the CG at this point will be AFT of the RTV! The “Holy Grail” of avoiding buntovers is keeping the CG forward of the RTV!
The only way I can see that the CG is held reasonably at the G-Load stable forward position under all conditions of power and airspeed is if the HS is at least creating a down-load in all conditions of propeller thrust. The down-lifting HS can provide a down-load component proportional to propeller propwash (thrust), while at the same time providing a proportional down-load free airstream component to “balance” out the aerodynamic nose-down moments. (And yes, Raghu, the HS moment does “balance”, or attempt to balance, the other aerodynamic moments the same at all airspeeds – both moments increase proportionately to each other!)
Now I may be all wet with this. And maybe we might prove that Airspeed (AOA) stability can be achieved with some degree of up-loaded HS. But, I would like to see someone show me on “sum-of-moments” diagrams just how an up-lifting HS can do both jobs of “balancing” a nose up LTL moment and a nose-down aerodynamic moment at the same time – under all conditions of power – without affecting airspeed (AOA) or CG/RTV moment (G-Load stability margin or sign)!
Raghu, please consider starting another thread, lay out the objective(s) of that thread, and start with some simple gyro sum-of-moments diagrams? Then, add thrustline offsets, then add HSs, then add power changes. Then, for good measure add the other aerodynamic airframe pitch moments. Look at it for step change variables (airspeed and Power and G-Load), then for the steady state balance point under these changes. I may be persuaded otherwise to my convictions on LTL. But, the arguments defending LTL (or “balanced” HTL) may not be real world either when all things are considered!
In the end, just perform the static flight tests - POWER, AIRSPEED and G-LOAD! It is my experience doing these tests, and some reported experiences of others, that convinces me to not too easily bow out of this discussion, and of my convitions, about what really happens in the "real world"!
- Thanks, Greg
If you start a new dedicated thread, please be sure to notify the individuals you want to be sure to participate – we need them all if we are ever going to show enough consensus to convince the confused! Or, let me know if you want me to do this. But, I think you and other “heavyweights” on this thread probably have the aerodynamics and physics credentials to do this. I think it is important that we stop debating and confusing people on these issues – even if I turn out to be dead wrong – we may still affect awareness enough to prevent someone from just being “dead”!
