Kinematics with respect to the HIR Airframe and CG "Flex"(My Theory)

KINESTHETIC MECHANICS
 PHYSICS & GEOMETRY MATHEMATICS
AFFECTING GIMBALED AIRFRAMES
Kinesthetic Mechanics: The interaction of the human body with any mechanical device that may be controlled by the movement of the extremities and/or body weight in order to attain a desired result or change in the device attitude or configuration. Such results may be any range of motion, mechanical frame attitude control or the movement of a prescribed load or cargo from one point to another. An exoskeleton mechanical device may be rigid or move with the body, combining kinesthetics in an exoskeleton mechanical frame to control it’s attitude, function or range of motion. Control may be facilitated by computer aided sensory devices, hydraulics or pneumatics. How can it be applied in the aerospace industry? Where does practical application end & “novelty” begin?
Can we question if there is a correlation between the mathematics of geometry & all of the forces of physics which have an affect on any airframe? Does the end result of a man made mathematical change, cause an equal change in any part of physics? Perhaps one can consider this to be true when thinking “for every action there is an equal and opposite reaction. Can all of these effects of physics interacting with the mathematics of geometry be controlled at equal moments to attain a positive result in transitional flight?
Picture your childhood see-saw. It is nothing more than a lever centered on a fulcrum. The center of gravity of the two loads is balanced & in line or just below the board or for the sake of Geometry, we’ll call it the “horizontal lever reference line“. It can be affected by the shifting of weight and/or applied force to the balanced load. Force is applied at one end resulting in the far end moving in the opposite direction at equal distance because the applied force is redirected through the centered fulcrum to the opposite end of the lever. Now apply this mental picture to the airframe of a helicopter. Move the fulcrum higher above the “horizontal lever reference line” giving it a much lower center of gravity with regard to weight distribution at both ends of our “airframe lever”. This gives us more stability. In our case it is the upper airframe w/ the pilot at one end and the power plant, electronics, etc.  at the other. During fabrication, portions of the helicopter may be moved around before being permanently fastened together to insure balance. This is why we do mockups. Fuel cells may be placed under the CG like that of the “saddle” fuel cells on a Bell 47G which solves the positioning of fuel on the airframe with regard to the CG. Fuel is burned off and the airframe becomes lighter. The fulcrum is the lower airframe with a gimbal joint or spherical bearing. The upper airframe “lever” is attached at more than one point to the lower airframe “fulcrum” to facilitate rigid control of the upper airframe “lever“. Now add an additional longitudinal lever near the center of gravity. Applied force (pilot input) will manipulate our horizontal airframe “lever“ from the center of the balanced load via the longitudinal lever. Now set the entire assembly within an imaginary cone or pyramid. The point of the cone/pyramid will be the location of the gimbal fulcrum and the longitudinal lever will extend down through the center. The area within the cone will be the only area in which the CG can be manipulated.

Now let’s talk about traditional weight shifting & CG manipulation concepts in helicopters. Traditional CG/weight shifting manipulates the CG within a static airframe or tilting the mast from a point on a static airframe. All of the forces act accordingly, some being negative. The CG is shifted to another portion of the airframe, even in small amounts, outside the “perfect balance of all forces” acting on that aircrafts’ CG/balance. Lift, thrust and all of these forces act on any airframe…….gyroscopic precession whatever, all must be taken into account. Vibrations can result…..the usual “for every action there is an equal & opposite reaction”. So, how do we work with these forces so that the end-state of lift & transitional flight are efficient? Lets go back to the basics of Geometry again. I hope we all can agree that the mathematics of geometry are in perfect harmony with all of the forces of physics. Look at anything in nature. The forming of a crystal for example…..perfect geometry. Why should physics be different than anything else in nature? If both are equal then all is well and in balance. We can change it, but we must deal with the “opposite reaction”. If we change it equally, in theory, the opposite reaction should be positive provided that the applied force is calculated & flight control inputs are made & limited accordingly. Precise inputs are determined through testing. One must be careful never to add too much “applied force” which can result in over correction. The applied force being greater than the positive & equal balance of forces affecting the center of gravity/weight configuration of the aircraft can cause negative “opposite reactions”. Unwanted or even violent vibrations at minimum can occur and perhaps cause a moment during which other negative forces may surface affecting your airframe adversely such as fastener or material degradation. Back to the see saw, balance of two loads w/ force applied, but with a twist. Instead of shifting the weight or CG to attain the desired affect, let us use the “for every action there is an equal & opposite reaction”  to our advantage. Of course this methodology is theoretical because we understand that there are some things in physics we cannot control. The affects of some forces are just too great. Let us not shift the CG in mast orientation form alone or simply move any given load or a portion of that load in linear fashion to affect the CG. Applied force can be introduced to  tilt or “flex” the CG within a given area (imaginary cone/pyramid) and the necessary levers & fulcrums to support movement within this area. Further, the airframe will also change equally every time the CG changes. Both move together as a result of equal moments of applied force. The CG is manipulated at the lower end of the longitudinal lever which hangs down through our imaginary pyramid or cone.  The rotor disc at the higher end of the longitudinal lever moves in calculated shorter spans of movement as opposed to the lower end of the longitudinal lever where applied force (pilot input) is introduced. Utilizing two airframes, leaving the rotor system completely within one of the frames gimbaled to the other, results in the applied force  tilting of the rotor disc/mast as well as the center of gravity in equal amounts. More stability in the dimension of “UP” is always a benefit the higher we maneuver the aircraft in altitude. The longitudinal lever receives applied force which is transmitted through the fulcrum and results in force or movement in the opposite direction than where the applied force was introduced. This force “result” tilts the upper airframe & rotor disc yet with a smaller span of motion at the upper end of the longitudinal lever near the fulcrum to vector the thrust. This also prevents over correcting. The lower end of the longitudinal lever is where the weight and center of gravity are most stable. It is also the area in which the lever has the most area to move, flexing the CG within the largest area of our imaginary cone. For example, applied force (pilot input) tilts or flexes the CG -2 degrees aft causing the horizontal upper airframe to tilt forward and the rotor disc also moves in like manner +2 degrees forward. This morphing affect also places the airframe into the most optimal configuration to hold the balance of forces in physics within the area of the imaginary cone. Changes are made in equal increments in the airframe, center of gravity & rotor disc attitude. Of course this is just a theory of mine. We’ll see if it works.

D. Hickman