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SamL
03-17-2006, 03:34 AM
There are many SH flying and lots of people who swear by them.
Its great to see a machine thats set up to be easy to fly and very stable.
My machine is an open frame machine and is very similar to the SH and has its CofG about 1-2 inches below the thrust line like SH.
I would like to ask a few question about the Sparrow Hawk, and airspeed stability.

If the machine is set up to fly hands off straight and level, it is then considerd to be flying in trim at its ideal cruise speed.

*****Below is a test Greg Gremminger suggest shows a machines*****

"Sum of static pitch movements"

1) Note its trim speed
2) Slowly reduce engine power to idle. Allow the nose to drop to establish a descent.
3) With stick force if necessary, adjust the gyro's airspeed to the same as was noted in level flight above. Ideally, no additional stick force, fore or aft, should be required to maintain airspeed within 10mph of the origional "trimmed" cruise airspeed.
4) If stick force is required to maintain the origional "trimmed" cruise airspeed within 10mph, the "balance" of the HS with the prop thrustline & other aerodynamic static movements is less than ideal and suggests possible stability/ safety issues.

I have trided this on mine and found the machine continued to lower its nose well past its trim speed.
I then added about an extra degree or so of neg pitch to my stab, and found its trim speed (straight and level) decreased, but the nose still dropped and accellerated past its cruise speed.
My Questions are

1) Does the Sparrow Hawk also drop its nose and speed up past its trim speed?
2) Should I add more load to the HS and lower the trim spring pressure, and try acheive the correct power off descent speed?
3) Should I set the HS so it gives me the correct power off descent speed descent speed as level trim, then move my head rewards to lower the nose?
4) Should I JUST LEAVE IT ALONE !!! as it flys like a dream and am waisting my time?


Regards Sam

Brent_Brown
03-17-2006, 03:39 AM
4.........

Doug Riley
03-17-2006, 06:11 AM
Sam, Dominators tend to do the same thing. Greg reports that his experience with a couple of different low thrustline gyros clued him in to this issue.

If you really want it perfect, you'll have to keep adding more down-load to the HS. HS's in the center of the prop slipstream and close to the prop have a couple of significant advantages. They do, however, tend to lose a lot of their power when the throttle is shut.

The problem is partly the loss of the energizing airflow from the prop, and partly the blockage of free-air flow to the HS. The blockage results from the bulk of the engine and YOU, both located upstream.

A HS with more span (to get parts of it out into cleaner air) might help. So would a longer tail boom -- but that has its own challenges.

C. Beaty
03-17-2006, 07:25 AM
This test may be a little confusing, Sam. It is or should be a fixed stick speed stability test.

With the gyro trimmed up for level flight at, say, 50 mph and with the stick locked in that position; adding or decreasing power should not affect airspeed.

Power added, the machine should nose up and climb at 50 mph.

Power reduced, the machine should nose down and descend at 50 mph.

A small variation in airspeed is not a big thing.

This test is an exercise in futility if you have a gyro that requires constant stick motion just to keep the thing right side up.

Aussie_Paul
03-17-2006, 03:17 PM
[QUOTE=C. Beaty]This test may be a little confusing, Sam. It is or should be a fixed stick speed stability test.
QUOTE]

....Chuck, that was my forte a couple of years ago when I conducted all that stick free and stick fixed stability testing with Hybrid.

I could take off and place the bar that locked the stick in position for 60 mph cruise. I could climb to altitude level off continue around the pattern, reduce power to idle and only use the stick to flare. Now the speed stayed within 5% to 8% of 60 mph for the complete flight of climb out, cruise and power off descent.

The approx 1" to 2" high thrust line with a down force loaded h/stab seems to be the most perfect.

I was very happy when I had the opportunity to instruct in a Magni for a week, and found that the Magni stability was no better than Hybrid at 60 mph. The Magni was better the faster we flew, as the Raf cab begins to have a lot of down force as you go faster. That gave me the confidence to continue the path I was on.


I flew a single seat Dominator in NZ a few weeks ago and it behaved terribly during the above test. Cruise at 50 mph; add full power and the airspeed would keep reducing until it was zero. Reduce power to idle and the speed would build up to where I was not comfortable and had to unlock the stick. Now this is no real problem at all when just flying around, BUT does not meet the tests. It could be solved by lowering the seat approx 8" for the perfect gyroplane that would be easier to mount. I enjoyed the Dom but would prefer a correctly designed nose wheel steering. The rudder authority engine idling is poor compared to a fin and rudder set as far back as practical.

Compromises everywhere BUT this is experimental, and we are so lucky to have the ability within the rules to play around like this. Don't you agree?


Aussie Paul.:)

C. Beaty
03-17-2006, 04:17 PM
Yes, I agree.

The Dominator would be better with the seats lowered and a fin-rudder is more powerful than an all-flying tail but I don’t agree about the nosewheel steering.

With good, progressive brakes, mainwheel steering is fine. The self acting, external band brakes used by Dominator are anything but progressive.

SamL
03-18-2006, 02:33 AM
Chuck and Paul
Yes I did try and lock the stick by hand, and it still very slowly accellerated in descent.
I didnt try the climb, but will next time I get a chance.
Doug, thanks for your feedback and I agree with with you statements.
Overall, I'm still not sure if I should continue to persue this or not.

Regards Sam.

Doug Riley
03-18-2006, 06:27 AM
Paul, I haven't found that Dominators go completely off the deep end with throttle changes as you describe. They do experience significant trim changes with throttle changes, which will indeed result in unwanted airspeed changes if the stick is not tended. With flight-adjustable trim, I apply full aft trim when powering down to idle, and full forward trim on takeoff.

Perfect static airspeed stability with respect to power setting would require than no trim adjustment be needed in order to maintain airspeed, whatever the throttle adjustment.

Udi
03-18-2006, 12:19 PM
...I have trided this on mine and found the machine continued to lower its nose well past its trim speed.
I then added about an extra degree or so of neg pitch to my stab, and found its trim speed (straight and level) decreased, but the nose still dropped and accellerated past its cruise speed...
You should have added positive pitch, Sam, not negative! Your stab is immersed inside the prop wash and adding negative pitch makes it react even more to power changes, without much effect on airspeed stability. Go the other way with your stab.

Udi

SamL
03-19-2006, 03:04 AM
Udi
At this momment my machine has the inverted aerofoil HS set to zero degrees pitch.
This is confirmed as the machines keel flys level in flight.
The machines trim is set at 50 knots and flys hands off. The last flight I made I confirmed this, then landed and added about 1-2 degrees to the trailing edge of the HS.
I then test flew it and found it would now fly hands off at 45 knotts.
I know and understand what you mean, but beleive it didnt apply to my machine as its CofG is very close to its thrustline.

Regards Sam.

StanFoster
03-19-2006, 05:27 AM
I did an airspeed stability check on my Sparrowhawk yesterday. I trimmed it out to 50 mph .....nice and steady at 4400 rpm. I slowly decreased power to 3500 rpm.....my nose went down....and the airspeed ended up at 56.

I then reset to 4400 at 50 mph....got it steady...and then slowly increased the power to 4800 rpm. My nose went up....the airspeed settled in at 48.


Not perfect....but this was hands off as well. Something I couldnt have done before for this long of experiment.

Stan

scandtours
03-19-2006, 07:28 AM
Dr Bensen in his (Bensen flying News) magazine (JUST HOW TRIM ARE YOU?) gives the answers. I really recommend everybody to find it and read it or I can scan it and post it.
He ends up like this .... your gyro should take-off, clib, level out and maintain 45 mph WITHOUT ANY STICK FORCE INPUT. ...... reduce throttle, but DONT touch the stick and your gyro should set up a glide path for you at 45 mph, and all because of proper trim the gyro will level out and fly by itself.
Giorgos

C. Beaty
03-19-2006, 08:21 AM
Unfortunately, stick free testing is a fools paradise. It is a test of the gimbal rotorhead and not much more.

A riding lawnmower fitted with a Bensen rotorhead would give similar results.

Harry_S.
03-19-2006, 08:46 AM
Is that lawnmower with or without rotor blades?!:p


Cheers :)

scandtours
03-19-2006, 09:23 AM
Unfortunately, stick free testing is a fools paradise. It is a test of the gimbal rotorhead and not much more.

A riding lawnmower fitted with a Bensen rotorhead would give similar results.
Is it a fools paradise or clevers hell to find the machine continued to lower its nose well past its trim speeds as Sam mentions above

Udi
03-19-2006, 10:43 AM
It is true that the offset gimbal head has a part in the total airspeed/G-load stability equation. But Sam's question re- airspeed stability indicates something other than the rotor head is affecting this gyro's airspeed.

When a gyro is speeding up in response to reduced power and slowing down with added power, this gyro is not power stable. This is not necessarily bad - especially in Sam's gyro where added power is obviously moving the CG fwd of the RTV. This is a better place to be than a HTL response to power where added power is moving the CG back of the RTV, moving the gyro into the region of static instability.

Nevertheless, Sam has asked the question and I assume he wants his gyro to be more balanced with regard to power vs airspeed. If added power is causing loss of airspeed and reduced power is causing a gain of airspeed, the simplest remedy is to pitch the stab one or 2 degs nose up.

Since Sam's prop-immersed stab has a negative airfoil, his (near CLT) gyro's response to power is completely logical and the best way to make it more power stable is to pitch the stab nose up, so it becomes more neutral vs. power changes.

Udi :cool:

SamL
03-19-2006, 12:56 PM
Stan, your machine sounds like mine, but next time try and drop power to idle and see if it settles to a fixed descent speed or continues past it.
Sam.

SamL
03-19-2006, 01:24 PM
Udi, by increasing the HS's leading edge angle of attack it would further add to the machine lowering its nose during power off and stick locked descent.
As far as I understand, a positively pitched HS is used for very low thrust line machines. But with my configuration this problem would be further increased.

Sam

Aussie_Paul
03-19-2006, 02:38 PM
Unfortunately, stick free testing is a fools paradise. It is a test of the gimbal rotorhead and not much more.

A riding lawnmower fitted with a Bensen rotorhead would give similar results.

Yes Chuck, as I said in another post, it is the stick fixed testing that really sorts out the last level of stability, BUT do we need it to be that good???

As a "trying to be a manufacturer", and the sort of person I am, I aim for perfection. I have the experience to not get caught with stick fixed testing, and I enjoy proving the theory in practice.

Aussie Paul.:)

Udi
03-19-2006, 03:02 PM
Sam, your stab is affecting gyro attitude in two unrelated ways. One way is the one you apparently have in mind - it reacts with the free air in a direction proportional to it's AOA vs. the free air, and airspeed.

The second way your stab affects gyro attitude is due to its reaction to the prop wash. Regardless of airspeed and gyro AOA vs free air, the stab will create a pitching moment about the CG as a function of power, unless it's AOA vs. the prop wash is neutral. It is hard to tell what this AOA would be for your upside-down airfoil, but it could be 2 or 3 degs nose up. When the stab AOA vs. the prop wash is neutral, and assuming your prop thrust line is in line with your gyro CG, changing power will not result in a pitching moment. Regardless of your thrust line vs CG, you can find a certain stab AOA that will produce a net zero moment about the CG with power changes.

The question is, with the stab mounted at a positive AOA which results in zero lift due to power change, how will it affect airspeed stability. The answer has to do with your gyro angle of dangle, which is determined by your hang test (i.e. vertical CG location). Based on your description in the first post, I believe your gyro will fly closer to its trim speed during all power settings if you pitch your stab a few degs nose up to the point where it is AOA neutral to the prop wash.

Udi
p.s. after you find a stab AOA which produces a net zero pitching moment vs. power changes, your trim speed may very well be higher than what it was before the change. Use your trim spring to get the trim speed you want.

SamL
03-21-2006, 02:39 AM
If you really want it perfect, you'll have to keep adding more down-load to the HS.

Doug, you have stated I need to keep increasing my HS's negotive AofA, I guess, until the machine adops a 50 knot power off glide slope.
This is fine, but that would mean my machines keel would now fly nose high.
I would probably also find that its hands off trim would now be reduced from 50Kt's to maybe about 30kt's.
Now I can adjust my heads trim spring, until it trims hands off 50kts again, but it wont lower my keels nose back to level.
Now I think I know what comes next, but would like it explained to me first.:confused:

If I'm right, the next bit is a lot of dicking around, and trial and error.:eek:

Regards Sam.

C. Beaty
03-21-2006, 04:21 AM
Hands off flying doesn’t prove very much, Paul, beyond the fact that an offset gimbal rotorhead works pretty well.

With the proper combination of offset and trim spring rate, almost anything that can struggle into the air will fly hands off.

Years ago, a really talented gyronut from Swainsboro Georgia, Pete Johnson, experimented extensively with various combinations of offsets and trim spring rates and concluded Bensen’s standard of 1” offset combined with softer springs was an optimum combination. I published his notes in one of the issues of the Sunstate Rotorclub’s newsletters but no longer have a copy. The 1” offset must be viewed in light of the tower height of a Bensen rotorhead.

Until low time pilots learn to relax and float the stick, they are basically flying in fixed stick mode.

Stick fixed flight separates the wheat from the chaff.

Doug Riley
03-21-2006, 05:32 AM
Sam:

Adding negative HS incidence is one way to improve airspeed stability in power-off flight. The problem, as both you and Udi point out, is that, with your HS in the prop slipstream, this same negative incidence will jack the nose up when you add power. IOW, the HS will exaggerate the effects of your low thrust line during cruise and climb. So the LTL in a sense prevents the HS from operating normally as a contributor to static stability (it works just as well as a dynamic stabilizer, i.e a PIO preventer) .

The airframe's stance in flight feeds back into your stick pressures via the trim spring. For example, in a LTL machine, you get a nose-high stance at wide-open throttle. In this stance, the airframe hauls down hard on the spring and gives you aft stick pressure. you have to hold forward stick pressure in climb.

As Chuck suggests, a long, soft trim spring might prevent the nose movements from affecting stick pressures so much. Maybe even a long bungee cord would be the thing. Other than that, you may be stuck with a compromise between ideal HS incidence at idle (= lots of negative) and ideal incidence at high throttle (= none or even positive).

Getting the thrust line very close to CLT is the best way to reduce these problems of coupling between the throttle setting and stick force/position. There's even a school of thought that says that an inch or two of HTL, with a strong HS having negative incidence, is the most rational combination.

SamL
03-21-2006, 01:12 PM
O.k, now correct me if I'm wrong.
I keep increasing negotive pitch on HS until it glides at 50kts fixed stick.
Now machine trims out at 30 kts, and keel flys nose high.
Re-Trim machine to fly at 50kts, but keel still flys nose high.
Only way to lower nose is to move head rearward, until nose is level in flight.
Problem now is HS has not enougth load, so needs to be adjusted again.
Will probably need to adjust head and HS several times until finally machine does what I want it to do. (Like I said, lots of dicking around)
Now is this right in theory or am I just jumping the gun.
I guess I just want to get my theory and understanding right.
I will probably leave machine as is, and never touch it. To me it is probably the most stable machine (in adverse weather) I have ever flown, from GA, Trikes, and Gyros.

Regards Sam.

Doug Riley
03-21-2006, 01:38 PM
Sam, if I were trying this myself, I'd change the easy/cheap thing first and go with a long, soft trim spring. Trying to fix your glide overspeed with more negative HS incidence is just going to make everything else worse. Too much dicking around, indeed, unless you have no choice.

(If you had a low-slung, draggy cabin, you might have to use the negative HS to prevent a tendency to "drag over" in high speed glides, but that's probably not the case with an open-frame machine.)

To the extent I said something different before, I take it back with apologies. LTL machines are a different breed, and require thinking outside the usual box.

Aussie_Paul
03-21-2006, 02:19 PM
Hands off flying doesn’t prove very much, Paul, beyond the fact that an offset gimbal rotorhead works pretty well.

With the proper combination of offset and trim spring rate, almost anything that can struggle into the air will fly hands off.

Years ago, a really talented gyronut from Swainsboro Georgia, Pete Johnson, experimented extensively with various combinations of offsets and trim spring rates and concluded Bensen’s standard of 1” offset combined with softer springs was an optimum combination. I published his notes in one of the issues of the Sunstate Rotorclub’s newsletters but no longer have a copy. The 1” offset must be viewed in light of the tower height of a Bensen rotorhead.

Until low time pilots learn to relax and float the stick, they are basically flying in fixed stick mode.

Stick fixed flight separates the wheat from the chaff.

I would love to see that info Chuck. I wonder if there is any chance that someone from the Sunstate Rotorclub would have a copy that could be scanned?

Aussie Paul.:)

SamL
03-21-2006, 04:00 PM
It is amaizing just how complicated these things can get.
Most gyro pilots now understand the advantages of flying with loades HS's and lowering one's machines CofG down close to its thrustline.
But having a machine which is trully stable in speed is the next step, and big challange.
Like many of us, I used to fly Cessna's, and also trikes. Both of these machines when power is chopped will lower there nose and adoped a cruise speed glide.
But to get a gyro to do the same thing, is a real challange.
This is the reason I asked if the new Sparrow Hawk acheives this or not.
As far as I can see, it has a thrustline about 2 inches bellow its CofG, and the HS seems to be set to zero incidence. So I beleive it will most probably react similar to mine. The SH is only one of many around the world including Australia's Owen machine that would probably react in this way.
I may be mistaken, but I beleive to acheive airspeed stability, it is easier to start with a slightly high thrust line, and work from there. The use of a HS outside the propwash would also help.
I supose Magni did get it right !!!!!!!!!!

Just my 2 cents :)

Regards Sam.

C. Beaty
03-21-2006, 06:45 PM
I would love to see that info Chuck. I wonder if there is any chance that someone from the Sunstate Rotorclub would have a copy that could be scanned?
Aussie Paul.:)
I doubt it, Paul. That was over 30 years ago.

Pete Johnson got interested in offset/spring rate after flying my gyro whenever he’d come down to SRC flyins.

I was using Hughes-269/OH-6 rotor blades at the time and found the necessary trim spring tension very annoying while on the ground so reduced the pivot bolt offset to 5/8”. This permitted the removal of the trim springs and provided hands off flight at ~50 mph.

Pete always commented that hands off stability didn’t seem to be as good as he thought it should be. My thoughts were that it didn’t matter much; hands on stability isn’t really affected and hands off flight is just a show off trick.

Pete ran a tool and die shop in Swainsboro and had access to all the tools and materials he needed, including spring winding equipment.

My recollection is that he claimed that with the standard 1” Bensen offset and softer springs, his Bensen B-8 would fly indefinitely without touching the stick. Pete would have been using needle bearings in the pitch/roll pivots so low friction probably was a contributor.

My Bensen would fly quite a while hands off even with no springs and a 5/8” offset but would eventually roll off to one side. Propeller torque, I suppose.

SamL
03-23-2006, 01:36 AM
Hi Chuck

You mensioned previously
"My Bensen would fly quite a while hands off even with no springs and a 5/8” offset but would eventually roll off to one side. Propeller torque, I suppose".
That leads me to another interesting question.

Is it torque that causes most gyro's to slowlly roll over during hands off flight?

I say this as mine does just that, but some times she will fly along for many minutes before doing it, and sometime it happend right away. Hmmmmmmmm

Wounder if anyone can shed some light on this :confused: :confused: :confused:

Regards Sam.

C. Beaty
03-23-2006, 10:46 AM
The prop torque might be the trigger, Sam, but a gimbal rotorhead is somewhat unstable laterally.

With a bit of yaw, the rotor flaps in the opposite direction, rolling the machine over into an ever tightening spiral.

This can be minimized in a couple of ways.

Use a pair of trim springs that are splayed out about the yard arm or a full span vertical stabilizer that cancels prop torque and keeps turns coordinated, preventing yaw.

SamL
03-24-2006, 01:59 AM
I found this on the web.
HHHmmmmmm
Sam.

Aussie_Paul
03-24-2006, 02:46 AM
The prop torque might be the trigger, Sam, but a gimbal rotorhead is somewhat unstable laterally.

With a bit of yaw, the rotor flaps in the opposite direction, rolling the machine over into an ever tightening spiral.

This can be minimized in a couple of ways.

Use a pair of trim springs that are splayed out about the yard arm or a full span vertical stabilizer that cancels prop torque and keeps turns coordinated, preventing yaw.

I might end up with an answer I have wondered about!!!!

I fly a stable gyro with adjustable pitch and roll trim.

By using the rudder I can stop the machine rolling. It behaves like the secondary effects of rudder in a fixed wing.

I have never really known how this worked on a gyro. I have not asked as I feel a bit "stupid":confused: and it really is not a high priority "need to know" subject.:D

I know how roll, the secondary effect of rudder works, but achieving the same response in my gyro happens and I don't know why, it just does.:o

Aussie Paul.:)

C. Beaty
03-24-2006, 04:19 AM
When you get on the rudder and yaw the nose of the machine to the left, for example, the rotor disc leans away from the yaw as the result of cyclic flapping. Because the roll pivot is several inches below the teeter bolt, the rotorhead also tilts to the left if not restrained, no different from having applied left stick.

The machine would be stable in roll if the rotorhead was locked in the roll axis.

Both of Dick DeGraw’s gyros have spring detent stick locks and can be flown indefinitely with the stick locked. Both employ a form of cyclic pitch control that does not feed a component of rotor thrust back into the control system. But a gyro must be stable in pitch to be flown with the stick locked.

Doug Riley
03-24-2006, 08:42 AM
Chuck's right. A rotor with flap hinges has a weak dihedral effect. You can actually get a shallow banked turn out of the machine with rudder only (like a 2-axis U.L. plane) if you're patient enough. I recall seeing plans for an R.C. gyro that had no rotor-roll channel, just rudder for turns.

The effect really is wimpy, though, and would never satisfy a crank-and-bank guy like Ron Awad.

Aussie_Paul
03-24-2006, 11:33 AM
Chuck's right. A rotor with flap hinges has a weak dihedral effect. You can actually get a shallow banked turn out of the machine with rudder only (like a 2-axis U.L. plane) if you're patient enough. I recall seeing plans for an R.C. gyro that had no rotor-roll channel, just rudder for turns.

The effect really is wimpy, though, and would never satisfy a crank-and-bank guy like Ron Awad.

No it certainly wouldn't, but it is intersting when I am so keen on stability, to see what a correctly set up gyo can actually do without using the stick. Just interests my curiosity. I know, I know, it killed the cat!!:eek:

What is the prognisis of Sams sketch he found on the net??

Aussie Paul.:)

C. Beaty
03-24-2006, 11:58 AM
What is the prognisis of Sams sketch he found on the net?? Aussie Paul.:)
That sketch illustrates offset flap hinges, a feature incorporated on most helicopters having 3 or more blades. It increases control power so that control doesn’t depend upon rotor thrust vectoring alone.

Doesn’t work for two blades unless you enjoy riding jackhammers.

Steve McGowan
04-16-2006, 06:40 PM
WoW..

You guy's are so far over my head it hurts.. Chuck,, me and you gotta go party for a while and talk about this..

Steve

C. Beaty
04-16-2006, 07:02 PM
When the Demon Rum is present, Steve, I can’t even pronounce some of the words.

But I’m not much into Cool-Aid parties.

BigBen
05-09-2006, 08:15 PM
Chuck:
Can you explain further the effect off-set flapping hinges have on a two bladed rotor (i.e., why the "jackhammer effect)?

Al_Hammer
05-09-2006, 10:38 PM
Ben, if you go back in this thread and look at the sketch of the offset flapping hinges, it shows that they produce a torque on the mast when the blades flap up or down on the hinge, unlike a teetering rotor which can't produce torque.

What you need to try to visualize, is that the blades are continually changing their flap angles during each revolution and the sketch only captures the instant when the blades are flapped at their maximum point. At the 3-9 o'clock position the 2 blades are midway between the extremes of their flapping travel, and both blades are now AT THE SAME ANGLE with respect to the flap hinges. At this point there is no moment being produced. Thus, the moment imparted to the mast varies at a 2 per rev rate between maximum effect and no effect. A teetering rotor would act the same way if it had a hub spring.

With 3 blades, if you break the rotor disc into 2 arbitrary halves, say a front and rear half, an equal number of blades are entering or leaving that half at any one time and the torque of each is such that there is a steady torque imparted to the mast rather than one that varies at 2 per rev. It reminds me of a 3 phase motor which runs smoothly for the same sort of reasons- the phases are 120 degrees apart just like the blades on a 3 bladed rotor.

BigBen
05-10-2006, 09:11 AM
Thanks AL:
I understand the situation you are describing for a fixed shaft hub such as used on a helo or a swashplate controlled gyro, however I thought that on a gyro with a direct control hub (where the hub is pivoted into the desired rotor plane) the blades would align themselves very quickly with the new hub plane (the non-flapping axis).

Al_Hammer
05-10-2006, 10:14 AM
Ben, the rotor does quickly align with the hub plane, but whenever you have forward speed the rotor will have a flap angle.

It's usually just a couple of degrees, but this means that the spin axis of the rotor hub is not exactly aligned with the rotor plane axis. The teeter joint, acting as a hookes joint accomodates the non aligned planes at the expense of a cyclic variation in speed and a varying angle between blades and hub.

If you introduce offset hinges, then the previously described 2-per rev moment will be a problem on a gyro as it will on a swashplate controlled helicopter. Essentially a swashplate and tilt head gyro hub do the same thing in terms of cyclic control.
A tilt of the hub causes one blade to increase pitch at one instant while the opposing blade decreases pitch.
A swashplate, when used for cyclic input will do the same thing; it rotates the blades in such a way that they could just as well be joined as a unit as they are on a gyro. The only time they rotate differentially is during collective input. Otherwise, the blades, as a unit, basically tilt or rotate about the feathering axis and this causes the disc to realign until the tilt goes away. Flapping introduces a cyclic variation that can't be taken out with stick input.