Disk Loading

[eruttan]

Some time ago I read a post by craig wall on norms forum that suggested that gyros were most limited by disk loading.

I would prefer to go back and refresh my memory, but alas...

There is a lower limit and upper limit to how you high you can load the disk, which translates to a limited range between upper and lower weight and that means limited cargo. If I remember you can only vary by about 30% gross.

Airplanes can do 100% and some way more than that.

I was wondering if I remembered this correctly and if there was any further developments or known techniques that might allow us to mitigate this. I think craig suggested carrying hub bars of different lengths so one could switch for load changes.

[C. Beaty]

Eric, the drag/power consumption of a rotor is customarily split into two parts;
(1) Power consumed in dragging the blades through the air. (profile drag)
(2) Power consumed producing a downward momentum of an air mass. (induced drag)

PROFILE POWER

Profile drag power varies as the cube of tip speed and linearly with blade area.

What that means is that if you double the tip speed, power required to drag the blades through the air is increased by a factor of 8.

It also means that if you double the blade area, profile power is doubled at the same tip speed.

But there’s a close relationship between tip speed and blade area. Just as the stall speed of a fixed wing craft is set by wing loading, tip speed of a rotorcraft is set by blade loading.

The top speed of a rotorcraft is limited by stalling of the retreating blade; typically about 35% of tip speed.

Unlike a helicopter rotor where the stall begins abruptly and often violently at the tip of the retreating blade, stall in a gyro is soft and begins at the root of the retreating blade. As forward speed increases and the stall spreads outward on the retreating blade, the stick must be gradually moved forward to maintain level flight and will reach the forward stop when forward speed reaches something in the range 35% of tip speed. After that, an increase of power will cause the machine to climb at the same airspeed.

If the desired top speed is to be 100 mph, blade area should be chosen to produce a tip speed of 100/.35 = 286 mph = 420 fps.

INDUCED POWER

The lift produced by a flying machine is of the same nature as the recoil of a shotgun. F = M* A; Force = mass * acceleration. If a 12 gauge shotgun throws twice the weight of shot as a 16 gauge at the same muzzle velocity, the recoil will be twice as great.

Flying machines work by imparting a downward acceleration to a mass of air and the recoil, acting upward, is lift.

If the rotor disc area is doubled by using a rotor diameter 1.4 times as great, the air mass is doubled and the acceleration imparted to it need be only ½ as great for the same lift. The energy imparted to the airstream varies as the square of velocity so we have a net saving by increasing disc area.

Based on momentum theory, the power consumed by a rotor in the production of lift can be expressed as follows:

Induced HP = (AUW^2)/(Radius^2 * Airspeed * 8) Airspeed = fps.

This tells us that doubling weight without changing anything else requires 4x as much power.

Doubling rotor radius reduces power to ¼ of its previous value.

Doubling the airspeed reduces induced power by ½.

Momentum theory doesn’t account for air accelerated in unproductive directions nor for nonuniformity of airflow through the rotor disc but produces useful results for airspeeds above 30 mph or so. Below 30 mph, the results become increasingly optimistic.

Some examples: 500lb. AUW, 22’ rotor, 50 mph (73.5 fps).

HPi = (500^2)/(11^2*73.5^2*8) = 3.5 HP

Same except 24’ rotor:

(500^2)/(12^2*73.5*8) = 3 HP

Going from a 22’ to a 24’ rotor hasn’t made a much better 50 mph flying machine.

The bottom line is that if you want to fly at 12 mph, all the rotor possible is needed.

At speeds of 50 mph and up, rotor diameter doesn’t make much difference and too much rotor makes things squirrelly.

In the upper speed range of a gyro, drag due to lift becomes increasingly insignificant and profile drag power dominates. One of the reasons that low drag rotors so significantly improve the performance of underpowered gyros.

[automan1223]

Mr Beaty, you are truly a gift to this group. We all appreciate your insights and excellent explainations for truly complex questions. On my best day I dont think I could grasp all that you seem to know like the back of your hand.

The only thing I can impart here is that the larger rotor will lift the weight but the delay in control and stick inputs make a smaller rotor at higher rpm more desirable to the beginner.

Jonathan

[C. Beaty]

“…..Said ***** to Owl; “You elegant Fowl, how charmingly sweet you sing.”…..”

[GeorgeHedinger]

Whoa! Now I'm starting to scare myself!
Chuck, I understood every word you wrote!
Thanks!!
(boy, have I got a lot to learn!!)

[barnstorm2]

Excellent Question and Answer.

This forum ROCKS :cool:

[StanFoster]

Chuck: You are a wealth of knowlege and when I read your intensive posts... I look like the RCA dog with my head tilted 10 degrees. :rolleyes:

..the more I reread your posts...the leveler my head becomes. :D

Thanks for your contributions.

Stan

[RHerron]

Chuck,

When comparing disc loading of a gyro to that of a helicopter with the same weight and rotor diameter, is the gyro's rotor more heavily loaded proportionally?

(ie., only the outer sections of the gyro rotor are contributing to lift while the helicopter with negatively-twisted blades has a more linear lift distribution).

Ron H

[C. Beaty]

Interesting question, Ron.

Although the angle of attack distribution along the span of a rotor blade is different and reversed between helicopter and gyro, the mean angle of attack is nearly the same for both.

Both operate at a mean angle of attack of something in the range of 5 degrees.

The helicopter, with collective set somewhere in the range +5 to +15 degrees, has blade angle of attack reduced by flow downward through the rotor disc.

The gyro, with fixed blade incidence of +2 degrees of so (above angle of zero lift), has blade angle of attack increased by upward flow through the rotor disc.

The lift distribution along the span of a rotor blade depends more on velocity than anything else. Inner sections of a rotor can’t produce much lift on helicopter or gyro because velocity is so low.

Helicopter design is driven by the military so the designers don’t view rotor efficiency by the same measure we do or even Arthur Young did.

For them, lifting efficiency is less important than speed and overall dimensions. Just hang on a bigger gas turbine.

[eruttan]

Chuck;
Thanks for the answer.
What I mean to ask is what would a gyro look like that
1) had a weight of 1000 #'s
2) could carry 0-1000#'s cargo
I understand from a blade loading point of view this would be impossible to accommodate without changing the rotor diameter.

[Spaced]

It would look like this
http://www.russian.ee/~star/vertigo/foto/fairey_rotodyne.jpg
Rotor Diameter, 27.4m, MTOW 17500kg

[eruttan]

again I apologize as I have been unclear.

What I mean to ask is what would a gyro look like that
1) had an empty weight of approximatly 1000LBS
2) could carry 0-1000LBS cargo
I understand from a blade loading point of view this would be impossible to accommodate without changing the rotor diameter as the weight changed
Is this true?