Question about the "Disc Loading Formula"

[AirCommandPilot]

I've browsed through several threads with the "Disc Loading Formula" but have a question. Does the chord of the rotor come in play? I've got 25' Skywheels (8" chord), and an all up flying weight of 835 lbs. This is soon to change as I'm changing the engine. I should drop close 100 lbs off after the swap.
I remember doing the formula a while back and getting almost 1.9 ratio, but I want to verify my numbers.

 

[Doug Riley]

Disk loading ignores blade chord. It's simply the gyro's weight divided by the area swept by the blades. This area is a shallow cone in normal flight, but we approximate it to be a flat disk. Disk loading is one statistic to use in analyzing rotors. It's measured in pounds per square foot. For small gyros, disk loadings around 1.5 lb./sq. ft. seem about right.

It's pretty obvious that blade chord matters, though. Blades are wings, after all, and their area matters a whole bunch in fact -- just as much as chord matters for any other wing.

To capture the effect of chord, we use two other calculations.

One is "blade loading." This is figured in the same way as wing loading for an airplane -- aircraft weight divided by blade area. It tends to come out in the range of 40-50-60 lb./sq. ft. For example, a small, Bensen-style gyro with blades of 7" chord and 23 - foot diameter, grossing at 550 lb., would have a blade loading of 41 lb/sq. ft.

The other stat is "disk solidity." This is the ratio between blade area and disk area. Our little gyro with the 7" x 23 ft. rotor would have a solidity of 0.032.

To over-simplify: We juggle these stats in designing our rotors so that our blade tip speed is not so high that the compressibility of the air itself starts to eat too much power, and so that the blades operate at their most efficient angle of attack -- neither stalled nor down at 1-2 degrees.

Many of the heavier homebuilt gyros are under-rotored by any of these measures. They use brute horsepower to (inefficiently) batter their way through the air, gulping fuel, making a godawful racket and straining light frames that weren't intended for such use. E.g. the Air Command and Bensen-Brock frames were designed around 40-50-60 hp 2-strokes weighing about 75 lb.

 

[AirCommandPilot]

I had a 532 on it when I got it, but if I wasn't at full throttle, I was descending. I put more HP in it, but the weight came with it. I could fly just fine, even reduce throttle and cruise, but if I had an engine out, I sank like a rock. I didn't feel comfortable flying this tub of lard, so here I am with another engine swap.

 

[Jean Claude]

Bobby,
Why do you think another engine out will change the rate of descent?
Is the pitch setting of your rotor correct?

 

[Brian Jackson]

Disk loading ignores blade chord. It's simply the gyro's weight divided by the area swept by the blades. This area is a shallow cone in normal flight, but we approximate it to be a flat disk. Disk loading is one statistic to use in analyzing rotors. It's measured in pounds per square foot. For small gyros, disk loadings around 1.5 lb./sq. ft. seem about right.

It's pretty obvious that blade chord matters, though. Blades are wings, after all, and their area matters a whole bunch in fact -- just as much as chord matters for any other wing.

To capture the effect of chord, we use two other calculations.

One is "blade loading." This is figured in the same way as wing loading for an airplane -- aircraft weight divided by blade area. It tends to come out in the range of 40-50-60 lb./sq. ft. For example, a small, Bensen-style gyro with blades of 7" chord and 23 - foot diameter, grossing at 550 lb., would have a blade loading of 41 lb/sq. ft.

The other stat is "disk solidity." This is the ratio between blade area and disk area. Our little gyro with the 7" x 23 ft. rotor would have a solidity of 0.032.

To over-simplify: We juggle these stats in designing our rotors so that our blade tip speed is not so high that the compressibility of the air itself starts to eat too much power, and so that the blades operate at their most efficient angle of attack -- neither stalled nor down at 1-2 degrees.

Many of the heavier homebuilt gyros are under-rotored by any of these measures. They use brute horsepower to (inefficiently) batter their way through the air, gulping fuel, making a godawful racket and straining light frames that weren't intended for such use. E.g. the Air Command and Bensen-Brock frames were designed around 40-50-60 hp 2-strokes weighing about 75 lb.

You should teach classes, Doug. I would sign up for that. Always glad when your name pops up on here.

Not to hijack this thread, but I may be in trouble after running some numbers based on the above. Or at least conflicted. The GyroBee was originally flown by Ralph Taggart with 24' blades and was reported as satisfactory if I recall correctly. An educated guess is an AUW of 500 lbs. That puts the disc loading at 1.106, which I understand is way lower than optimal, perhaps hazardous. Mine (under construction) is intended to fit these same numbers (500 AUW, 24' GyroTech carbon blades). Now I am second-guessing things. VNE on the blades is 70 mph if that makes a difference. I was assured by the manufacturer these blades would perform well on a ship of these specs, but I'm seeing contradictory data. Since I have zero experience with this, how does one reconcile this discrepancy?

 

[AirCommandPilot]

Bobby,
Why do you think another engine out will change the rate of descent?
Is the pitch setting of your rotor correct?

My rate of descent has always been horrible with this heavy engine. It only took a few "throttle at idle" landings to make me realize I didn't like the way it was coming in. I've flown other machines and they seem to float a bit more on landing.
I believe making the machine 100 lbs ( 45kg) lighter with this other engine, will give me more rate of climb, and less rate of descent. Am I thinking this wrong?

 

[Doug Riley]

Brian: I haven't explored the low-disk-loading regime methodically. All I have is anecdotes.

My 'Bee has 24.5-foot Rotordynes and an ultra-stripped configuration. I weigh 180 or less. The result is a disk loading of about 1.0. The machine flew fine, and climbed reasonably well with its 447 and wood prop. It would do over 70 mph flat out, but was happier ghosting along at 40.

By "climbed reasonably well," I mean in comparison to my 1980's 447 Air Command, which had a rate of climb down in the 200 FPM range in the summer. I found that rather scary (the saving grace was that we don't have much summer here in VT). The Air Command was heavier than the 'Bee and used 23-foot McCutchens.

I'm not certain what people believe is the danger of moderately low disk loading in gyros. Obviously, the secret of a gyro's "stall-proofness" is the fact that the wings (blades) travel at a tip speed of 3, 4, 5 or more times the aircraft's forward speed. As you slow the rotor down with lower disk loading, this margin gets smaller... but not radically smaller. The ratio of tip speed to forward speed is still on the order of 3:1.

As this ratio (known as the mu ratio) gets smaller thanks to low disk loading, you encounter more and more stalling of the inner portion of the rotor at high cruise speeds. I SPECULATE that this does not become catastrophic, however, with disk loadings in the 1 lb./sq.ft. level. Rather, the rotor flaps back more and becomes increasingly draggy at higher forward speeds until you run out of power. Again, this is speculation based on limited experience in just two gyros with low disk loading -- my 'Bee and my tandem Dominator.

The latter gyro actually had a rotor tach. Solo, it had a disk loading of about 1.15 and flew very nicely at 100 mph, at mu= 2.9 or so. Interestingly, though, it, too, used least power cruising at about 45, solo.

NACA gathered some data on these topics and published them in their 1930's reports about autogyro rotors. IIR, they found that mu= 0.4 was the most efficient ratio.

Chuck Beaty reported experimenting with a very slow rotor (like 220 RPM) on a light Bensen-style gyro. He found that the gyro would barely move forward, though it did leave the ground. Most likely, the large stalled region of the rotor acted as a drag brake.

 

[Kevin_Richey]

You should teach classes, Doug. I would sign up for that. Always glad when your name pops up on here.

Not to hijack this thread, but I may be in trouble after running some numbers based on the above. Or at least conflicted. The GyroBee was originally flown by Ralph Taggart with 24' blades and was reported as satisfactory if I recall correctly. An educated guess is an AUW of 500 lbs. That puts the disc loading at 1.106, which I understand is way lower than optimal, perhaps hazardous. Mine (under construction) is intended to fit these same numbers (500 AUW, 24' GyroTech carbon blades). Now I am second-guessing things. VNE on the blades is 70 mph if that makes a difference. I was assured by the manufacturer these blades would perform well on a ship of these specs, but I'm seeing contradictory data. Since I have zero experience with this, how does one reconcile this discrepancy?

I seem to recall that Ralph T. & Don C. flew their GyroBee on 25' diameter rotors, not 24'.

 

[Jean Claude]

I believe making the machine 100 lbs ( 45kg) lighter with this other engine, will give me more rate of climb, and less rate of descent. Am I thinking this wrong?

Same power with 50 kg less will give a climb rate much better, but the rate of descent will barely reduced.
Remember that in the descent, it is the weight that provides the energy.