Technical Issues Relative to High-μ Rotor Flight (μ>0.6)
Nine key technical issues had to be understood before a SR/C™ aircraft could fly at high-μ ratios. A blade element spreadsheet program developed by Carter and Carter's X-Plane based flight simulator were the two primary analytical tools used to understand these issues well enough for the CarterCopter to exceed the μ-1 ratio on 17 June 2005. The research into these and other SR/C™ technologies has resulted in 21 patents. These nine issues are as follows.
1. Flapping/excessive coning due to low centrifugal force and lift on the advancing blade
at high forward speeds (μ >0.6 to~5):
The worst case predicts a ½ rev flapping/coning when the blade is at 1:30 o'clock (45º). The max possible forward speed before this flapping divergence can occur is a function of density altitude, tip weight, blade area, forward speed, and rotor RPM. There are at least three ways to control this divergence. 1) Extra mass in the blade tips to maintain adequate centrifugal force. 2) A high degree of pitch cone coupling such that as the blade cones up say 2º, the blade pitch is reduced by 2º-4º. 3) With a stiff blade and a flapping lock-out mechanism.
Carter SR/C™ aircraft use a combination of the first two. In the 1950s, the McDonnell XV-1 was able to achieve μ-0.95 by using a combination of the last two. However, the increased structure needed to stiffen the XV-1 blades is generally much heavier than the Carter approach of adding weight to the tip. Pitch cone coupling is used to reduce vertical gusts loads in the same way it is used on helicopters, by reducing the blade pitch when there is a positive "G" load and increasing blade pitch when there is a negative "G" load. On SR/C™ aircraft, it also reduces the flapping at μ values greater than 0.8 because as the advancing blade flaps up due to increased lift, the blade coning will also increase, which pitches the leading edge of the blades down. This decreases the lift on the advancing blade, but increases the lift on the retreating blade because the airflow is now flowing from the trailing edge to the leading edge and has in effect increased the pitch of the retreating blade - thus reducing flapping.
2. Flapping due to unbalance in lift between the advancing and retreating blade
at high-μ (>0.6 to ~ 5):
Flapping automatically balances the lift between the advancing and retreating blades whether the air flows from the leading edge to trailing edge or the trailing edge to leading edge. The worst condition for flapping, called critical-μ, occurs ~ μ-0.75 when the retreating blade has the lowest average airflow velocity and therefore the least ability to produce lift. As μ increases above ~ 0.75, flapping for a given rotor lift will decrease. Flapping can be controlled with the use of rotor collective. Increasing collective will increase flapping while decreasing collective will reduce flapping. The procedure can be automated. Carter's analysis program predicts that at 400 mph and μ-4, a SR/C™ aircraft could encounter a vertical gust of 50 ft/sec without the flapping becoming excessive. If the flapping should go too high or increase too rapidly due to a gust or a high rotor loading, the rotor would automatically go to negative pitch, thus rapidly decreasing lift and flapping.
3. Blade flutter/divergence on retreating blade:
Instability on the retreating rotor blade can be caused by reverse airflow shifting the blade's aerodynamic center from the ¼ chord line to the ¾ chord line. The blades on a Carter rotor are tied together by a carbon spar. Up to a certain μ-ratio the advancing blade is more stable than the retreating blade is unstable. The stability sum of both blades can be inherently stable through μ ~ 1.4 given a certain blade planform and weight distribution, such as that shown in figure 1 above. Blade instability is manifested by the rotor going out-of-track, with the divergence increasing or decreasing with an increase or decrease in airspeed. It is not a sudden divergence, but increases rapidly in a linear fashion, thus providing the pilot sufficient time to take corrective action. This blade instability can be controlled by a control system that is very stiff, or by over mass balancing the blades, or even by a combination of both to provide the best combination of load and weight reduction. At some μ greater than 1.4, the reverse airflow velocity over the retreating blade causes the stability sum of both blades to go negative and unstable, making it necessary to have a stiff boosted cyclic and collective control. An automatic, mechanical collective pitch control (no pilot input) varies the blade pitch from jump takeoff (max pitch), through high-μ flight (min. pitch) and back to the pitch required for a near vertical zero roll landing. The pitch controller also removes any linkage deadband when the rotor is at high-μ and a stiff connection between the advancing and retreating blade is required.
Note1 Most helicopter rotors go unstable at a very low μ-ratio and as a result, boosted controls are required on even small helicopters. Carter's stable rotor system does not require boosted controls on SR/C™ aircraft less than 4,000 lbs gross weight until some value above μ - 1 is reached (μ ~ 1.4 based on Carter's calculations).
Note2 The Delta-tip design shown in figure 1 (above) allows the weight/dynamic center of gravity (DCG) to be placed as far forward in front of the blade aerodynamic center (AC) as possible while the trailing edge extension also increases this distance by moving the AC aft. The further the DCG is in front of the AC, the greater the blade stability. Weight placed at the tip increases its stored energy efficiency. The 45º slope on the delta tip significantly reduces the rotor drag at high tip-speeds and/or aircraft forward speeds.
4. Rotor diving force sensitivity at high speeds where the rotor is mostly unloaded - the rotor plane of rotation less than 5º off air-stream:
Following a zero-roll takeoff, an infinitely variable rotor RPM is achieved by tilting the rotor aft as the aircraft speed increases until the rotor is driven via autorotation, wherein the rotor RPM and lift is controlled by the amount of air flowing through the rotor disk. Once the rotor is in autorotation and the aircraft speeds up and the wings provide more of the lift, the rotor lift and RPM are reduced by tilting the rotor forward. This reduces the angle "alpha" between the rotor plane of rotation and the air stream, and reduces the flow of air through the rotor and its driving force with a resulting reduction in rotor RPM and lift. As the rotor RPM slows and the forward airspeed increases (increased μ-ratio), alpha becomes small, so that a slight change in alpha results in a large percent change in air flow (driving force) and rotor RPM. A spindle trim tilts the rotor spindle/rotor plane of rotation relative to the control stick and horizontal stabilizer position, allowing the rotor angle to be trimmed/adjusted to maintain the desired RPM. The high rotor inertia helps stabilize the RPM and makes the rotor easier to control.
5. Control response at slowed rotor RPM:
As the rotor RPM is reduced, the rotor control response and the aircraft maneuverability are reduced. When fast control responses are critical, the RPM controller will be directed to hold a higher RPM with a corresponding reduction in aircraft efficiency. Normally the lowest rotor RPM is used during high speed, high altitude, long range cruise when efficiency is most important and fast control response is not required or desirable, due to the near max lift condition required for best wing efficiency and the wing's potential to stall with a fast control response.
6. Tilting the mast to control rotorcraft pitch and rotor RPM:
A long tilting mast as shown in Figure 2 can move the rotor center of lift fore and aft relative to the aircraft CG, which causes the aircraft to pitch up or down. As long as the rotor is providing a significant part of the aircraft's lift, a rearward movement of the mast will lower the aircraft's nose while a forward movement will raise the nose. During this period of significant rotor lift, the tilting mast can hold aircraft pitch as needed to keep the wings at their most efficient L/D, greatly improving the aircraft's efficiency and performance. Once the wings are providing most of the lift and control, the tilting mast controls the rotor RPM by tilting the rotor plane of rotation relative to the airstream. Tilting the rotor aft increases airflow through the rotor and the RPM increases. Tilting the rotor forward decreases the airflow and RPM.
7. Rotor operation over a wide RPM range:
Unlike helicopters, which operate over a small RPM range, rotors for SR/C™ aircraft must operate over a large RPM range; from high RPM during takeoffs and hover to very low RPM during cruise flight. The Carter rotor design enables its first in-plane natural frequency to be higher than the highest RPM the rotor will ever see. This is achieved with an I-beam shaped spar with the spar caps positioned far enough apart to provide a sufficiently high edgewise stiffness to produce the desired edgewise natural frequency. Because of the high centrifugal force generated by the mass at the tip, any flat-wise natural frequencies encountered are heavily damped such that even if a flat-wise natural frequency is encountered, there is no build-up in stresses. This feature greatly simplifies the rotor design by being able to basically ignore any build-up in stresses when operating the rotor at some flat-wise natural frequency.
8. High hub drag normally associated with rotorcraft:
Historically, about 1/4 to 1/3 of the total rotorcraft aerodynamic drag can be attributed to the rotor hub. The Carter design reduces this drag over conventional helicopters by a very large factor. It is accomplished by using a twistable spar for collective, a tilting hub for cyclic, and a single pass-through 2-bladed I-beam spar which is very stiff in the edgewise direction and soft in the flat-wise direction, which further eliminates a blade coning hinge and the need for the associated lead-lag mechanisms, permitting the use of a very small, integrated, root fairing that remains nearly aligned with the air-stream during cruise flight.
9. Simplified, intuitive control between rotor and aircraft modes:
The pilot is able to control the aircraft in essentially the same manner whether he is flying in hover or slow speed mode where the rotor is providing most of the lift and control, mid-speed where the rotor and wings are each providing a significant part of the lift and the aileron and horizontal stabilizer are providing some control input, or high-speed where the rotor is unloaded and providing only 5-20% of lift and control.