With rotorcraft, the airframe hangs from a universal joint and the horizontal CG has no direct influence on the rotor thrust line to CG relationship, whereas in a FW, the horizontal CG relative to the wing is fixed.
Here’s an article that was published in Rotorcraft several years ago:
The idea that the force to move an object should act through its center of mass is not one that suddenly arrived on the scene just a few years ago. It is a law that applies universally to all things that move, from ox carts to space ships.
Juan de la Cierva, a brilliant mathematician, engineer and the inventor of the Autogiro, first publicly addressed gyroplane propeller thrust line to CG relationship in a patent application filed in 1929 which resulted in British patent No. 330,513, issued in 1930 (Fig. 1).
The Autogiros of the 1930s generally had massive rotor systems mounted above airplane type fuselages which resulted in the machines' CGs being well above the fuselage centerline. Both tractors and pushers of that period used tilted engines to ensure passage of the propeller thrust line through the CG (Figs. 2 & 3).
Bensen and Gyrocopters
Igor Bensen, as a young engineer, worked for the General Electric Company at the Schenectady Research Center, where he learned to fly both the Kellet XR-3 Autogiro (a development of the KD-1 but with fixed rotorhead and feathering cyclic and collective pitch) and the Dobhloff tip jet compound helicopter; the object being to research the thermodynamics of tip jet propulsion.
GE provided the propulsion system of the Hughes XH-17 heavy lift helicopter; J-33 engines supplying compressed air to the blade tip burners which used J-33 burner cans. The XH-17 had a rotor diameter of 134 feet and flew at a gross weight of more than 50,000 lb. That was in 1952.
After completion of the XH-17 work, Bensen, going from one extreme to another, began playing with a British Rotachute that had been supplied to GE for an earlier study and persuaded his superiors that such a machine might be commercially viable as a vehicle for hobbyists. That was in an age before product liability lawyers became ubiquitous but even so, when word of the project reached upper management, the plug was pulled. GE's business is the manufacture and sale of everything from light bulbs to railway locomotives but not dangerous toys for hobbyists.
Bensen, after a short stint as chief engineer of Kaman Helicopters, set up shop in Raleigh, NC where he designed and perfected the Gyrocopter. Nearly all of the gyros classified as amateur built are direct descendants of a Bensen design.
The problem faced by Bensen was that small gyros with a teetering rotor system generally had the CG below the obvious location of the engine near the mast center, just the opposite of Cierva's designs. Propeller thrust above the CG is a far more serious problem than below.
Bensen was well aware of the need to have propeller thrust line pass through the CG. There is casual reference to that in Bensen literature and his designs always used McCulloch engines with the propeller end tilted upward by several degrees; not enough with steel industrial wheels and a steel fuel tank attached to the keel. Equipped with lightweight wheels and a seat tank, the propeller thrust line of a B-8 passes almost exactly through the CG.
The early imitators of Bensen's designs used inverted Rotax engines with 5 ft. diameter propellers and copied the engine tilt used by Bensen without having the foggiest notion as to why. The net result was a dangerously unstable machine that caused a rash of fatal accidents. The addition of a small horizontal stabilizer somewhat mitigated but did not solve the problem.
A common misconception is that the propeller thrust line should be applied at a point that balances rotor drag against fuselage drag, the result of an erroneous perception of rotor thrust.
An autorotating rotor is no different from a propeller, a helicopter rotor or even a windmill. It produces a line of thrust along its tip plane axis (the rotor thrust vector) that can be resolved into horizontal and vertical components if need be; lift and drag.
If, when flying a kite with a weightless string, the string exerted a pull of 10 lb. and flew at an angle of 45º, it would be possible resolve the string's pull into vertical and horizontal components and to state that the kite has a drag of 7.07 lb. and also a lift of 7.07 lb. But it is important to keep in mind that the string pulls in a single direction at any given instant.
Figure 4A illustrates this misconception. The gyro can be imagined to be a 500-lb. cannon ball attached to a stick (the mast).
An average rotor; one neither exceptionally good nor exceptionally bad, will fly at an angle of attack of about 10º at 45 mph which yields a rotor drag of 88 lb. and a rotor thrust of 508 lb. when supporting the 500 lb. cannon ball. The lift, obviously, is 500 lb. The fuselage drag of a typical open, square tube airframe with the pilot sitting bolt upright will also be of the same order.
Following this line of reasoning and assuming the cannon ball has aerodynamic drag equal to that of the rotor, 88 lb., propeller thrust should be applied midway between the cannon ball and the teeter bolt.
The necessary propeller thrust is the total of airframe drag and rotor drag; 176 lb. If the mast was 5 ft. from cannon ball to teeter bolt, propeller thrust line would have to pass 2.5 feet above the CG, producing a nose down torque about the CG of 440 ft-lb. The rotor thrust line would pass slightly more than 10 inches in front of the CG, producing a nose up torque of 440 ft-lb to achieve equilibrium.
All well and good with the mast flying vertical until a gust is encountered. If the gust should be downward, the rotor thrust would be diminished, destroying equilibrium. The machine would pitch nose down, reducing the rotor angle of attack, further diminishing rotor thrust and increasing the nose down pitching until the machine flipped inverted.
A gyro with its CG behind the rotor thrust line doesn't behave differently than a tail heavy fixed wing aircraft. It is possible for both to be flown by pilots with sufficient skill and experience but it is never safe. The tail heavy fixed wing aircraft can enter an unrecoverable spin if the pilot lets the machine get ahead of him; the tail heavy gyro performs an unrecoverable bunt if the machine gets ahead of the pilot. The final outcome is the same.
The right way
Figure 4B correctly depicts the forces acting on a gyro. If the propeller thrust line passes through the CG, then the rotor thrust line will also pass through the CG and the mast will fly leaned back at a 10º angle.
Imagine that instead of a rotor, a long rope is attached to the teeter bolt and the machine is suspended from a tall bridge with the wind blowing at 45 mph. The rope represents the rotor thrust vector. With the engine fired up and the propeller producing 176 lb. of thrust as in the previous example, the rope will be tilted 10º rearward and the machine will be in equilibrium. When the bridge bounces from heavy trucks, the gyro doesn't bobble since the projected line of the rope's pull passes through the CG.
We don't usually fly cannon balls which leaves some loose ends to be addressed.
The center of fuselage aerodynamic drag, more often than not will be somewhat below the CG from the drag of landing gear and other low placed lumps. Compensation requires the horizontal stabilizer to operate at downward lift but is complete at all airspeeds since both lift and drag are affected in the same way.
It is desirable but not essential that the CG of a gyro lead the rotor thrust vector, ensuring that the machine always heads into the relative wind. It is not essential because the lift slope of a fixed airfoil is steeper than that of a rotor. A given angle of attack change will produce a greater percentage of lift change in a horizontal stabilizer than it will in the rotor.
The angle at which a gyro hangs when suspended from a rope (the "hang test") has no primary effect on the CG to rotor thrust line relationship. There is a secondary effect inasmuch as the angle of the horizontal stabilizer is affected which can rotate the airframe in flight and swing the CG fore or aft relative to the rotor thrust vector.
The real purpose of the "hang test" is control centering.
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