stabilizer volume by rotor diameter

[Vance]

Hello all, As I was following the thread that went from polishing the rotor blade to calculating rotor blade length, I became confused by Doug's spread sheet that included stablizer volume. I wondered why the rotor disk size and blade chord would affect the volume of the stabilizer, if the stabilizer is to stabilize the body and not the rotor?

I was also wondering if disk size and chord would also affect the rudder volume? How do you calculate the rudder volume?

I found the concept of blade loading interesting as somehow I have gotten stuck on disk solidity and disk area.

I would be grateful for any help in becoming less confused!
Thank You, Vance.

[Douglas Riley]

Vance, the discussions on this topic over on Norm's forum in the last couple years, combined with the discussions connected with the new Light Sport Gyro certification standard, have tended to move away from strict reliance on the "Cierva formula." That's the formula that relates rotor volume to tail volume.

You're right -- there too many other variables to allow tail sizing to be based only on rotor volume. Of course, Cierva's machines were tractor gyros with conventional airplane-style tail assemblies. As such, they all had centerline thrust (which Cierva himself patented!) and similar moments of inertia. The formula worked for that configuration and probably works well for today's tractor gyros.

It's a good starting place today for centerline thrust machines as well, but cross-checks of the results should be done using other methods at the design stage. Flight tests are the final determinant of the adequacy of a tail design on a particular gyro.

[Vance]

Thank You Douglas, I love it when I'm right to be confused. I realy like the spread sheet. When you show the rotor horsepower does that show how much horsepower it takes to fly those speeds plus the form drag times the prop eficency? This becomes very confusing when I use Mr Tervamaki's spread sheet or one of the helicopter power required spread sheets and try to combine it with a fixed wing spread sheet. Things seem to be done at 60 mph and this has not been born out by personal observation. I find tractors vs pushers dificult to quantify also. I would be grateful for any guidence in this area. Thank you again for your help, Vance

[Doug Riley]

Spreadsheet? I couldn't construct one if my life depended on it. Whatever you're looking at, Vance, someone else must have written it, not me!

[Udi]

Vance is referring to Chuck Beaty's spreadsheet HP3.

Udi-

[Vance]

Mr Beaty, Mr Riley, My apoligies, I get lost in the numbers, questions and answers and forget who I am talking to. Udi, thank you again and I'm sorry for the confusion. Mr Beaty I would be gratefull for any help with the questions. Thank You, Vance

[jucie]

Udi:"Vance is referring to Chuck Beaty's spreadsheet HP3."

Could someone post this spreadsheet to the group, please? Thanks.

[Udi]

Jucie,

I have the spreadsheet, but I cannot post it on a public forum without Chuck's permission. I will send it to you via email, if you enable your email addy in your profile, or send it to me.

Udi-

[jucie]

I already sent to you my e-mail address, Udi. Thank you.

[LGoodhind]

Kicking an old thread because I found myself asking the same question Vance asked earlier. If this was already covered earlier (I didn't find it) a link would be great.

The Cierva "rule of thumb" for horizontal stabilizer volume is based on rotor diameter.

The point has been clearly made in the past that the universal joint between the rotor and airframe effectivly isolate each from the other- control system forces are little forces and the pilot isn't wrenching the airframe around with the inputs used to control the rotor in flight.

The CG does want to lie on the rotor thrust vector which does move (a conic with the point at the center of rotation) as you stir the stick. Forward/aft placement of the rotor head puts the controls into the right place for this when the machine is in its flight attitude but this wouldn't be influenced by the size of the rotor; an effective rotor of any diameter would be generating the same thrust vector in level flight.

What bearing if any does the size of the rotor have on the calculation of the volume of an effective horizontal (and vertical) stabilizer?

I'm wondering if the rule of thumb has more to do with generating an estimate based on assumptions about the airframe based on the rotor diameter than it does with any direct link between the two.

[skier]

At least for fixed wing aircraft, this has a lot to do with the way the moment balances and force balances are done for static stability. I assume that the sizing is done similarly for rotorcraft for the same reason, though I could be wrong here.

That being said, I don't know the Cierva "rule of thumb" and am not an expert on rotorcraft by any means.

[Jean Claude]

It seems to me that the tail volume is a useless concept. It is surprising that this volume is related to the dimensions of a rotor tilt. In addition, many fixed-wing aircraft have no tail volume: jets with delta wing , tailless aircraft Northrop. Others have even negative volume! (Rutan Varieze). Yet they fly!
Jean Claude

[kolibri282]

If we talk the influence of fins on the motion of the aircraft we actually talk about a moment generated by the fin eg. for damping to avoid oscillation. A moment consist of the lever arm( the distance from the center of gravity to the 1/4 chord of the fin) and the force generated by the fin. The latter depends for a given flight state upon the area of the fin (that's where volume comes into the picture) and the effective lift coefficient of the fin. This effective lift curve slope (if we take the linear part of the curve of lift versus angle of attack) depends on the lift curve slope of the airfoil used and the aspect ratio of the fin. This is fin design in a nutshell. The importance of fin volume as a variable is just one small part of the story.

Cheers,

Juergen

[LGoodhind]

My question is how does the diameter of the rotor and its solidity relate to how much damping is required by the airframe.

The Cierva “rule of thumb” for the size of a horizontal stabilizer is called out in P.B.Abbott’s “Understanding the Gyroplane” but no references to the original source are cited. Chuck Beaty is referenced in context to describe the calculation.

"If you like numbers, there's a formula for the size of horizontal tails that was worked out by the inventor of the autogiro, Juan de la Cierva, and was adopted by later designers of autogyros and helicopters. Cierva established the ratio for the size of horizontal tail, based on a measure he called "rotor volume." This is the area of the rotor blades (the blades themselves, not the full rotor disc). Cierva’s rule of thumb was that the tail area should be about 12 to 15% of the rotor volume.

[an illustration shows rotor volume = total blade area x rotor diameter and tail volume = horizontal stabilizer area x L; tail volume / rotor volume ~= .12]

If you'd like to know how to figure this out, here’s Chuck Beatty to tell you:"

"If you take the number of square feet in the tail times the moment arm length, that gives a number which is the tail volume. The moment arm length is the distance from the center of the rotor to the 1/4-chord point on the tail."

"Cierva experimented a lot before he arrived at tail volume figure of about 12 to 15%. Using these numbers you can't make a Gyro bunt over [in a power push over]. You could unload the rotor for a long period of time and the rotor would eventually stop. You’d fall out of the air but there would be no such thing as the rotor just going ‘bang!’ and going over. It's impossible to do that with that big a tail."

“area of the rotor blades [themselves, not the full rotor disk]” is Chord x RotorRadius x BladeCount … pi isn’t invited to the party. This number is multiplied by RotorDiameter (2 x RotorRadius) yielding…

RotorVolume = 3 x RotorRadius x Chord x BladeCount

…which (at my level of abstration) seems like a magical number.

The calculation of the tail volume relates to how much damping force the horizontal stabilizer can generate to rotate the aircraft around its CG in the pitch axis. The tail is assumed to be an airfoil that generates lift at the 25% chord and the rotor center is used as an approximation of the length of the moment arm as the actual CG of the aircraft in steady flight will be on the rotor thrust vector (RTV) which is typically at a 10 degree angle from a perpendicular through the rotor center; the CG for the moment arm of the tail is located several inches in front of the rotor center perpendicular.

If I understand this correctly (unlikelihood high) in the static case, with fixed incidence, the tail plane has the potential to generate a force proportional to the airspeed calculated as the sum of relative free stream and the prop thrust if incidence of the tail is anything other than zero to the relative wind. These are the “for every action there is an equivalent opposite reaction” forces from deflecting the mass of air. In the static case this sort of force would need to be overcoming a continuous force that was attempting to rotate the aircraft in the pitch axis (thrust offset, drag above/below the CG, and so on) in the opposite direction.

In the dynamic case the prop thrust vector retains the same relationship to the horizontal stabilizer throughout because both are fixed to the airframe and so only the relative portion would be expected to change. In this case the goal of the stabilizer is to provide damping inputs to counter perturbations (large or small) encountered because of changes to the RTV as the CG follows it, gusts of wind and other relative wind changes against the airframe, asymmetric changes in drag due to the shape of the aircraft and so on. To be successful the moments generated by the tail needs to be greater than the force of the perturbation combined with the inertia of the airframe.

While the controls themselves don’t provide enough leverage to wrench the airframe around they do allow you to move the RTV which accomplishes the same thing; if the diameter was directly related to either the scale or speed of changes in the RTV resulting in pitch perturbations then the relationship makes sense. The only thing I see happening as the diameter of a rotor increases is that (to maintain an optimal tip speed) it will slow down. That impacts the lag between when control inputs are made and when they are realized at the rotor but I don’t know why it would increase the size of perturbations that could be expected by an airframe hanging underneath it and if anything it would slow them down.

[Jean Claude]

A small and quick (*) increase of the free stream angle causes an increase of lift of the rotor and of the HS. So, total increase applies at a point behind the RTV (focus). More it is far behind, more the stability is great. The distance is related to the volume of the rotor because, for a same diameter, small chord blades are faster: his extra lift is less influenced by variation.
* : No change r.p.m
Jean Claude

[Doug Riley]

A point related to what Jean Claude said:

The rotor itself provides some pitch and roll stabilization -- thta is, it provides forces that create moments that tend to resist sudden rotations of the airframe. The rotor does this by not reacting instantly to cyclic pitch changes. The rotor lags cyclic inputs, and so generates a restoring moment. This effect is, by custom, called rotor damping.

The magnitude of the rotor-damping moment is a function of total rotor thrust, the slope of the rotor blades' lift curve, the mass of the rotor and the rotor's RPM.

Lift curve slopes don't vary much. Large-diameter, slow rotors lag more. Heavy rotors lag more. More lag = more damping if other things are equal. Obviously, the more total rotor thrust, the larger the moment that a given lag angle produces. The wider the blades' chord, the slower the rotor, other things equal.

What's interesting about the Cierva Formula is that some of its results seem perverse if we think of a H-stab as only a stabilizer (not a control surface). Narrow-chord blades turn faster (other things equal) and so have lower rotor volume. This dictates a small H-stab. But a low-volume rotor has less rotor damping. With less rotor damping, we might think we ought to have MORE HS-induced damping, not less.

I wonder if the formula was developed back when gyro H-stabs had elevators. That would explain why it tells us to use a smaller H-stab on a narrow-chord rotor, when arguably the opposite should be true if the rotor is controlled by direct cyclic pitch. The narrow-chord rotor does not "fight" control inputs from the elevators as much as a wide-chord one would.

In the end, Larry, I think you are right that formula mostly serves as a scaling device. It ignores such important facts as the moment of inertia of the airframe, misalignment of thrustline and CG and the non-identicality of a large H-stab on a short moment arm and a small H-stab on a long moment arm. The second arrangement provides more dynamic stability than the first, even if their volumes are equal.

[Vance]

The Predator's horizontal stabilizer volume is close to 17 percent of rotor volume and is essentially a tube and fabric flat plate.

What is the down side of two large a horizontal stabilizer?

Mariah Gale is predicated to come in at 23 percent of rotor volume and the stabilizer is an airfoil shape making it, in my opinion more effective for its size.

Thank you, Vance

[Doug Riley]

No dark path and no downside, Vance, unless you fly mustering or crop-dusting missions.

Too much airframe stability in an aircraft whose lifting surface is rigidly bolted to the frame may not be great. In such a setup (the usual FW design), you can't alter the AOA of the lifting surface without rotating the frame. If the frame resists changing its orientation in space, handling will be sluggish.

OTOH, in a craft where the AOA of the lifting surface can be changed independently of any rotation of the frame (rotorcraft with direct cyclic, trike, controlwing, etc.), there's not much to gain by having the frame swing about. All you care about is that the rotor can be made to change its orbit. Having the frame simply align itself with the direction of travel is the most convenient and natural setup. For that purpose, the more HS power, the better.

A few types of trick flying may benefit from a frame that swings about readily.

Birdy has described fast-reversal maneuvers where he needs to get the prop pushing in a new direction right NOW -- before the aircraft has itself reversed its path. In fact, engine thrust is used to augment rotor thrust to accomplish the turnaround. This might be called the "engine as retro-rocket" mode. If that's what you really need, limit your HS power -- but be extra careful to stick with CLT.

[Vance]

Thank you Doug,

That was sort of my thinking.

It seemed to me that to apply rotor input from a stable platform would increase the precision of my ability to command the rotor. I felt more precise command of the rotor would translate to more precision in controlling the aircraft.

My experience with raising the engine in the Predator that made her less low thrust line reinforced my affection for center line thrust. I changed the relationship of thrust line to CG about 1.25 inches and it made landing much more elegant.

The horizontal stabilizer on Mariah Gale is below the propeller wash as it is on the Predator.

As you predicted I do lose rudder authority in a power off vertical descent with the Predator. As little as 10kts of forward speed will return my some rudder authority and any power at all makes her responsive to rudder inputs. I have found that a power off vertical descent helps me determine which way the wind blows.

The rain has stopped and I am off to fly.

Thank you, Vance

[kolibri282]

Larry Goodhind wrote:
My question is how does the diameter of the rotor and its solidity relate to how much damping is required by the airframe.

To answer that question you want to calcualte the rotor derivatives for the pitch moment (traditionally designated M or m ) with respect to forward speed disturbance (u), pitch rate (q) and vertical velocity (w). The moment increase from your tail fin for the three disturbance cases has to be greater than that from the rotor (and opposite in sign). This condition gives you three equations for your fin area. You'll finally select the largest of the three to be on the safe side.

Forumlae 7.53 7.54 7.55 of the book below give an approximation to those derivatives which you might calculate with a slide rule (if you wanted to)
http://www.scribd.com/doc/20309082/Bramwell-s-Helicopter-Dynamics

I'm sorry Larry but as Dirty Harry would put it: "You've asked for it, chap..;-)"

Cheers,

Juergen

[Jean Claude]

What is the down side of two large a horizontal stabilizer?
I suppose that HS very large can completely prevent the change of angle of the structure relative to free flow. So, the angle of descent can never exceed 15 ° (rotor tilt max. / neutral)
Jean Claude

[Vance]

I suppose that HS very large can completely prevent the change of angle of the structure relative to free flow. So, the angle of descent can never exceed 15 ° (rotor tilt max. / neutral)
Jean Claude

I am having trouble grasping your concept of a large volume for a horizontal stabilizer limiting the angle of descent.

My gyroplane, The Predator can go straight down with the nose pointed up.

It is easy to point the nose at the ground at any speed.

It seems to me if I reduce the lift of the rotor that the nose would point further and further down. It seems to me that a gyroplane with a very large horizontal stabilizer like the Predator, 19.5 square feet, would point into the relative wind.

On the Predator the 25% chord line of the horizontal stabilizer is 66 inches behind the center of gravity with full tanks and Ed and I on board. The area of the stabilizer is 19.5 square feet giving a volume of 17% of the rotor volume. I am not able to imagine how the large horizontal stabilizer limitis the angle of descent.

Please help me understand what you are saying.

The horizontal stabilizer on Mariah Gale is almost 23 square feet and projected to be 77 inches behind the center of gravity giving a stabilizer volume of 146 square feet or 23% of the rotor volume. I do not understand how that would limit the angle of descent.

I am in early days now and it is easy to change things, if I am going down a dark path now is the time to discover it and change the design.

It would be hard to reduce the area of the horizontal stabilizer on Mariah Gale but I could reduce the moment arm by 18 inches with should bring the tail volume down to around 112 square feet or 17.6% of rotor volume. Would there be an advantage in this?

Thank you, Vance

[Jean Claude]

Vance, I just wanted to say what would happen with a very very larger HS. With only your surface , no problem: Efficiency is not sufficient to counteract the torque RTV / GC: it is reduced by
- Low speed
- Stall airfoil
http://img24.xooimage.com/files/a/a/1/sans-titre-1a82f79.jpg (http://autogire.xooit.fr/image/24/a/a/1/sans-titre-1a82f79.jpg.htm)
Jean Claude