- In the diagrams below, the flyer is hovering and thrust is sufficient to maintain altitude. Because the thrust is not vertical, the system is accelerating to the left. The CG shown is combined CG of pilot + flyer. Vector components are shown in some cases but it only necessary to look at the two "resultant" vectors to visualise the overturning couple.
So, you take “one moment in time” (one instant) for which you show the thrust force T which is offset to the overall center of gravity.
Then you replace the thrust force by an equal / parallel force passing from the overall center of gravity (the direction of this force in the FBD should be opposite, I think) and a moment (the “circular” arrow at top) equal to the thrust force T times its eccentricity from the overall center of gravity (how many forum members do really understand and can apply this “equivalency”?).
Then we should add the overall weight (a vertical – downwards looking – force from the overall center of gravity).
Then we should take the sum of all forces (which is a force acting on the overall center of gravity, is normal to the T, and is looking to the left / left-bottom) and the free moment and calculate their effect.
The result would be an acceleration of both parts (the thruster and the pilot) towards the left / left-bottom ( I called this acceleration an “oblique free fall”), and an accelerating clock-wise rotation of the assembly about its center of gravity.
Now comes the “living” pilot to control the situation:
The pilot displaces – either by his hands or by his feet (or lower legs) – the pole / stick until the thrust T to point to the right creating a reverse moment and a (more or less) “opposite” overall force (it will point to the right / right-bottom).
Now the Flyer/Pilot assembly accelerates at the ”reverse direction” (to the right / right-bottom) and turns “counter-clock-wise”.
- For those who still doubt
The angular displacement of the thruster about the pivot at the feet of the pilot causes an “opposite” displacement of the pilot.
Just think what happens during a skydive:
Can the skydiver open widely and then close completely his legs?
Can the skydiver retract his limbs / head to form a “ball” and then extent his body parts to straight his body and continue his fall like an arrow head-down?
The same happens when the pilot holds the Broom-Flyer thruster: the thruster is (becomes) a part of pilots body; the pilot can displace it at all directions, provided his legs, head and arms are displaced properly to “balance” the displacement (linear and angular) of the thruster.
If the thruster was a rocket, and the assembly was in the space (no air), the oscillation would continue.
But being in the air, the oscillation will progressively fade-out due to the aerodynamic friction of the parts with the surrounding air.
And if the pilot uses his head / limbs (being in the downstream of the propellers), he can almost instantly cancel out the above linear and angular oscillations and turn to “stable” hover (correcting continuously the instability by smooth , almost unnoticeable, movements of his body parts (which hold and displace the pole)).
You also write:
- The shoulder-mounted flyer (without handlebars) is less stable. The system is experiencing a moment which is tending to rotate the thrust further away from vertical. Also the mass of the flyer creates a moment which tends to increase the difference between the thrust axis and the pilot axis (the axis passing through the hinge and the pilot's CG). To recover from this position to a stable hover requires the pilot to reverse the angle of the hinge to move the CG to the right of the thrust axis. To operate this system without handlebars requires a rigid connection at the shoulders with zero backlash. If this action requires "arching" his back, it will be impossible to recover from extreme angles.
I can’t follow.
So, when the pole is pivotally mounted to (near) the feet of the pilot, the system can recover to hovering, but when the pivot is closer to the overall center of gravity the recovery is problematic?
The thrust of the Portable Flyer (say, the plane defined by the axes of the propellers) cannot lean this way:
What is shown at right is a thrust at an eccentricity of about 0.5m from the overall center of gravity, and a pivot at the top of pilot’s head. No matter how hard the pilot tries, it is impossible to achieve such eccentricity of the thrust.
The actual arrangement of the Portable Flyer:
keeps this eccentricity much smaller (the pivot / gimbal joint is the spinal cord of the pilot in his upper torso).
Drawing the thrust at the allowable eccentricity, the pilot in order to recover just bends a little his waist and more his legs to the right displacing the overall center of gravity to the right of the thruster axis.
This creates an opposite moment that turns the Portable Flyer clockwise. Etc, etc. . .
It is similar to the way Mayman controls his JetPack.
As for the:
- Also the mass of the flyer creates a moment which tends to increase the difference between the thrust axis and the pilot axis (the axis passing through the hinge and the pilot's CG).
If you agree with the above, please explain them to the rest forum members: you are a third party and you are English speaking.