Rules of thumb

fateric

Member
Joined
Oct 2, 2006
Messages
55
Location
UK
I have found a few rules of thumb relating to stability, but would appreciate any additonal comments. Please keep it simple, I am learning to crawl before I meet Euler and fluid dynamics :)

Please note some of these 'rules' may need to be in relevant context and may have been edited from other threads.

1 Size of Horizontal Tail.

Rotor 'volume' = Total blade area x Rotor Diameter
Tail 'Volume' = Horizontal stabiliser area x L (where L=moment arm length measured from the centre of the rotor to 1/4 chord of the tail)

Tail area should be about 12-15% of rotor volume (Cierva)

2 Thrust should be in line with the VCom and centre of drag
3 Centre of pressure should be behind the centre of mass (5-6 inches is excellent)


The rotor spin axis (spindle bolt) is usually placed behind the rotorhead pitch pivot. This allows for some feel in the stick and creates stick-free stability in the sense that an increase in rotor thrust from a gust will tend to pivot the rotor nose down , which reduces the thrust. This offset is used in conjunction with trim springs in the pitch axis.

The blades are usually balanced about the 1/4 chord point for stability and may have a reflexed trailing edge to avoid pitching moment problems if they are asymmetrical. Bensen used wooden blades that were torsionally flexible and tended to pitch nose down at advancing speed; another way to control rotor pitch stability, but most blades are metal or composite these days.

Other ways to influence rotor stability include the use of a delta-3 angle in the hub. This mechanically reduces flapping excursions and has other effects related to forward flight. Not many small gyros incorporate delta-3, but it is often used on Helos.

The COM of the coned rotor should lie at the height of the teeter bolt, which is controlled by the undersling of the rotor. This doesn't affect stability per se, but does affect 2 per rev shake.

A full span, or "tall tail" that spans the length of the prop will act as flow straightener and tend to cancel prop torque effects.

A stab that is placed in the propwash will be more effective than one that is placed out of the propwash and its lift will vary with power changes, aiding in offsetting the nose down pitching in a HTL(high thrust line) design.
Power off control will suffer, so there are different schools of thought on the best placement of the h-stab.

Negative incidence on a h-stab is often used to compensate for a HTL.

A rudder that is full flying, like on a Dominator, may need to have a so called servo-tab added for self centering and for feel in the pedals.

Twin vertical stabs can be dangerous in that one stab can fall in the shadow of the other and reduce control under certain conditions.

Other ways to control torque that have been used: differential incidence on horizontal stab surfaces and rotor offset.

Turbulators may be needed on a cabin to reduce yaw instability resulting from the effects that a sharply cut off body has on airflow.

Blade loading vs rotor diameter: Manufacturers have tables showing preferred rotor diameter for a given all up weight.
Al Hammer - 12 above


My empirical experience has been that a round mast performs better with respect to rotor shake than a square one.
C. Beaty

(1)Rotor tip speed varies as the square root of blade loading.

(2)Power consumed by rotor profile drag varies as the product of tip speed cubed and blade chord.

All things otherwise being equal.
C. Beaty


Circular section is actually stronger for weight than box section for a given bending load. Box section will buckle at the compression corners while circular section spreads the compression out over the whole "side". Best if radius is Side_Length*4 / 2*PI for same weight as box.
For same diam as box side second moment of area, hence stiffness, is lower for circular section (solid section bd^3 / 12 vs PI*D^4 / 64). Again if radius chosen as above for same weight, circular section works out roughly 55% stiffer.
Graviman


Rotor tip speed - for untwisted untapered blades set at a reasonably efficient pitch for the blade section.
RTS =~ 66 x SqRoot(Blade loading)
Blade loading is: (Gyro weight in Lbs)/(Blade area in Lbs per Sq Foot)
Answer is in Ft/Sec

Opinions vary as to the exact number, "it all depends on...." but trying to exceed a Mu of around 0.4 is either brave or foolhardy depending on your skill set.

Mu is the ratio of forward speed to tip speed, so with around 400 ft/sec of tip speed (a not unusual value) - Mu = 0.4 (max) says we should never exceed 0.4 x 400 = 160 ft/sec for fear of the retreating blade falling out of bed.

160 x 60/88 = 109 mph - if you trust your ASI completely!

95 mph would feel safer, imho. Guard banding is no bad idea.
Ben Mullett

Static Thrust
The laws that govern all whirling bits is the same whether rotor or props. The static thrust of an ideal prop at SL is given by:

Static thrust (pounds) = 10.41*[Diameter(ft) * Power(HP)]^0.67

A real world fixed pitch prop (pitched for all-round performance) typically achieves 70 to 75 % of the ideal static thrust value . The results at ROC agree well with the above relationship. Significantly lower values than 70% of the ideal is often due to stalled tips. Of course in flight, as forward speed picks up, the tips will unstall and perform better.

One can achieve up to about 85% of the ideal thrust if the prop is optimally pitched. Though such a fixed pitch prop would be far from the optimum at even moderate speeds, as it would over rev and not be able to absorb the power of the engine.

Static thrust is important for brisk takeoff and acceleration in the low speed regime. In addition, in draggy open frames where the best climb is in the region of 40-50 mph, they have moderate impact on climb rate. At the top end ( over 70 mph) the difference between a 5 foot and 6 foot prop, though, is just a few percent. A good example is Wallis's record breaking gyros. They all are driven by a small prop ( 4 ft) and engine but still achieve record breaking speeds and climb rates.
Raghu

Example calc -Udi
Tim Verroi Dominator Rotax 582 2.58 Ivo 60" 342Lb

The 582 has a nominal power of 64 HP. So the formula would be:

Static thrust (pounds) = 10.41*[Diameter(ft) * Power(HP)]^0.67

Static thrust (pounds) = 10.41*[60/12 * 64]^0.67=

10.41*(320^0.67) = 10.41*47.7 = 496.5 lbs

Prop efficiency = 342/496.5 * 100 = 68.9%
Udi

Thrust (non static)
as airspeed increases ideal thrust generated will reduce so as the power of the engine is fixed. The relationship, though, is a little more involved (be warned) than the case for static thrust. If you are interested here is the relationship:

First find the prop characteristic speed, Vchar, which is given by:
Vchar(ft/sec) = 41.86*[power(hp)/Diameter(ft)^2)^.33

Next find the velocity Ratio,Vr using
Vr= V/Vchar, where V is the speed in ft/sec and is the speed for which you want to know the thrust

Then calculate the thrust ratio Tr = T(at required speed)/Static thrust which is given by:

Tr = 0.794*[ (1+(1+0.233*Vchar^3)^0.5)^0.33 - ((1+0.233*Vchar^3)^0.5 -1)^0.33 ]

Finally, T (at some forward speed) = Tr*Static thrust

As in the case of static thrust the real thrust you obtain at forward speed will be less than the ideal thrust. Typically at the design point of the prop it will be ~75% of the ideal value and at all other speeds less than that.
Raghu


Power to Weight & Weight to blade area
To have a flyable gyro, you must have:
less than 10 lb of weight by hp of power;
less than 1.8 lb of weight by foot squared of rotor area;
a solidity ratio between 0.035 and 0.040. (between 35 to 45 lb/ft2 of blade).
Quadrirotor

Thrust to Weight
The old Bensen rule for thrust-to-weight ratio was that a small pusher gyro needed 1 lb.of thrust for every 2 lb. of weight.
Disk loading
1-place gyros run around 1.3 lb./sq. ft.
Doug Riley

Blade Clearance
I think a sensible rule of thumb would be to allow enough clearance for the coning angle to reverse to -1G without the rotor's hitting anything. Bensen pointed out that he designed to that criterion. He specified six inches between the prop and the rotor, when the rotor was at its aft control and teeter stops, which, as it happened, was enough to allow -1G clearance.
Doug

Rotor tip speed sets top speed; a gyro won’t go much faster than ~ 35% of tip speed
Disc loading sets the minimum flight speed; with a disc loading of 1 lb/ft², a gyro of limited power will fly quite slowly
Centrifugal force varies as rpm² so the shorter blades will generally have the greater centrifugal force and operate at a shallower coning angle.
CF = W x R x rpm²/2900 (R being the distance from center of rotation to blade CG)
Coning angle is part of the problem with longer blades on lightweight machines. Extra tip weight is one way out.
Chuck B
 
Last edited:
My understanding of the concept of tail volume is that it was originally used in airplane design. There is no particular reasoning behind it, but rather, it is based on statistics. I certainly don't know of any good explanation of how Cierva came up with his rule of thumb.
In practice, it seems no pusher gyro obeys the rule, but I think it may be followed more in tractor designs.

Here are a few more rules of thumb off the top of my head:

The rotor spin axis (spindle bolt) is usually placed behind the rotorhead pitch pivot. This allows for some feel in the stick and creates stick-free stability in the sense that an increase in rotor thrust from a gust will tend to pivot the rotor nose down , which reduces the thrust. This offset is used in conjunction with trim springs in the pitch axis.

The blades are usually balanced about the 1/4 chord point for stability and may have a reflexed trailing edge to avoid pitching moment problems if they are asymmetrical. Bensen used wooden blades that were torsionally flexible and tended to pitch nose down at advancing speed; another way to control rotor pitch stability, but most blades are metal or composite these days.

Other ways to influence rotor stability include the use of a delta-3 angle in the hub. This mechanically reduces flapping excursions and has other effects related to forward flight. Not many small gyros incorporate delta-3, but it is often used on Helos.

The COM of the coned rotor should lie at the height of the teeter bolt, which is controlled by the undersling of the rotor. This doesn't affect stability per se, but does affect 2 per rev shake.

A full span, or "tall tail" that spans the length of the prop will act as flow straightener and tend to cancel prop torque effects.

A stab that is placed in the propwash will be more effective than one that is placed out of the propwash and its lift will vary with power changes, aiding in offsetting the nose down pitching in a HTL(high thrust line) design.
Power off control will suffer, so there are different schools of thought on the best placement of the h-stab.

Negative incidence on a h-stab is often used to compensate for a HTL.

A rudder that is full flying, like on a Dominator, may need to have a so called servo-tab added for self centering and for feel in the pedals.

Twin vertical stabs can be dangerous in that one stab can fall in the shadow of the other and reduce control under certain conditions.

Other ways to control torque that have been used: differential incidence on horizontal stab surfaces and rotor offset.

Turbulators may be needed on a cabin to reduce yaw instability resulting from the effects that a sharply cut off body has on airflow.

Blade loading vs rotor diameter: Manufacturers have tables showing preferred rotor diameter for a given all up weight.

I've got a bunch more formulas and mathematical rules of thumb in my notes, but will have to look them up. Meanwhile, I'm sure others will come up with a few.
 
I've got a bunch more formulas and mathematical rules of thumb in my notes, but will have to look them up. Meanwhile, I'm sure others will come up with a few.

Thats a brilliant list Al and greatly apprectiated. I will make up a complete list at the end - or perhaps a running list that people can add to. Look forward to your formulas and mathematical rules. :) It will help me get a better understanding of what makes the gyro tick - create loads more questions (sorry) and hopefully make a better pilot of me.
 
Thank You Al

Very nice list and informative.

We all look forward to your formulas and math rules.

Fateric. Thank you for bringing it up.

Regards.
Rehan
 
Rule of Thumb

Rule of Thumb

Rotor tip speed - for untwisted untapered blades set at a reasonably efficient pitch for the blade section.

RTS =~ 66 x SqRoot(Blade loading)

Blade loading is: (Gyro weight in Lbs)/(Blade area in Lbs per Sq Foot)
Answer is in Ft/Sec

Surprising how accurate this can be!

Somewhere else Chuck posted a brief guide to blade loading vs max speed choice, will pop a link to it here if I find it again.

Opinions vary as to the exact number, "it all depends on...." but trying to exceed a Mu of around 0.4 is either brave or foolhardy depending on your skill set.

Mu is the ratio of forward speed to tip speed, so with around 400 ft/sec of tip speed (a not unusual value) - Mu = 0.4 (max) says we should never exceed 0.4 x 400 = 160 ft/sec for fear of the retreating blade falling out of bed.

160 x 60/88 = 109 mph - if you trust your ASI completely!

95 mph would feel safer, imho. Guard banding is no bad idea.

All the best, Ben
 
Top