Letter to Kenneth Huff, Chief Engineer Huff Helo, Warner Robins GA, September 19, 2023

Hello Kenneth,

In our last conversation I didn’t do a very good job of explaining the machine or where I was in the project up to the point where I had the calamity.

To recapitulate, it is a bi-canopied reciprocating apparatus that exploits the phenomenon of drag for gaining altitude under human power. Along with the introduction of some new terms, the principles are as follows: A given framed parachute-like canopy of a given size will have a specific rate of descent and terminal velocity that varies according to the canopy size and shape, and it will present a different drag coefficient when driven in the opposite direction if the canopy is designed to minimize drag on the upstroke, which it is. This principle of function is easily demonstrated by an umbrella being thrust and pulled back quickly. There is a resistant asymmetry in the two strokes due to the different coefficients of drag depending on direction of motion. It is possible to exploit this asymmetry for propulsion if two such umbrellas or canopies attached to a given system were to operate in opposite directions.

Two such canopies are mounted and cable braced horizontally on two coupled and vertical mirror-symmetrical towers on a bearing/rail system that can reciprocate an amount equal to that of a stroke of a human. Attached at appropriate locations on the two towers are hand grips and peddles that are used to deliver a stroke. The stroke motion to operate the machine is identical to the motion one makes when ascending a ladder. There is a lot of biomechanical energy transfer in this particular motion, I’d surmise some substantial amount greater than that made by pedal powered drivetrains.

Pedals are strapped, so leg movements upward also deliver energy. Unlike cycle power where power phase is limited to about a half cycle, this biomechanical movement is at near maximum efficiency throughout the stroke.

In motion, one half of the machine and one canopy is in descent and the canopy is slowing the overall fall rate of the machine, and the other half of the machine is in ascent and heading for a point where its task will change to slowing descent. The net result of this oscillation of canopies will be incremental climb.

It is a certainty that a sufficiently designed reciprocating machine of the kind I imagine can gain altitude. There is nothing in laws of aerodynamics that precludes such a machine from being capable of climb. All that has to be done is to sufficiently optimize all variables.

There are five main variables of such a machine. They are weight, drag coefficient(s) ascending, drag coefficient(s) descending, length of stroke of operator, and operator power. This is a pure problem of minima and maxima.

I committed an error in my first design. I had sufficiently low drag (F-drag) on the ascent, but I grossly underestimated parasitic losses on the drag maximized portion (D-drag) with my ultra-light weight multiple folding louver design, and I was at the point where I realized a canopy redesign from the ground up was necessary. It’s a triviality that has no bearing on the machine’s eminent viability. MacCready and Co. went through about twelve iterations before getting it right. I was on number one.

I was about to start new drag canopies coming at the problem in an entirely new way. They will be two very large inverted arcs. Think Sydney Harbor Bridge covered on the top and sides by lightweight impermeable fabric.

Of necessity, the curve which the canopy frames will possess is that of a spline, since this is the easiest method of generating very large curves over very long lengths of carbon fiber tubing. One merely has to pull lengths into bows to form a solid foundation for frame and wire bracing.

There’s irony in the theoretical existence of a human powered vertical flying machine design for which the use of the simple spline and bows would be demanded since throughout early history these exact things facilitated the explorer courtesy of many a shipbuilder. Yesterday meets tomorrow.

There are strong asymmetries in the motion when viewed from the front or rear. The canopies will partially glide rather than fall straight down; they’ll lurch from side to side. Although the machine will make wild motions at the top, the net movement over time will be incremental vertical climb, that is assuming the energy committed to both left and right strokes is the same. If it's not, the machine will have an imbalance and will drift in the opposite direction of the faster stroke. By this means, the operator should be able to control side to side motion by simply imparting more energy over time in either the left or right tower. The canopies - relative to the towers - are positioned to optimize

fore/aft balance with the operator at a given position, but his body mass can move in and out from the two towers to some degree, altering the center of gravity. This ability to lean in an out of the machine along with some body English should provide some very modest forward & reverse control.

One interesting question is, just what is this machine? Or what might one most properly call it? A bi-canopied reciprocating drag machine just doesn’t seem appropriate. We might turn to common airplane terminology for some help in finding a suitable term to adopt.

The motions described by an airplane are pitch, roll, and yaw. The question is, which one of these terms furnishes the best heuristic aid in understanding the way this machine works. If we consider the canopies as an analog to wings, the motion of pitch is virtually zero unless leaning in and out of the machine and thus pitch is not under consideration. Roll is a viable analog because the motion of the wings of a plane are opposite to one another during same, and this machine makes opposite canopy motions, but if we imagine an extreme roll oscillation of an airplane, it is lacking the lateral component that will result from the strong dynamic asymmetries in flight which manifests as a decidedly nontrivial diagonal displacement of both canopies during both cycles. Yaw is also a viable analog in that the canopies make motions that are opposite to one another as on a plane, and it has the benefit of having a displacement in the horizontal component. Therefore, if the way the canopies will behave most analogously resembles yaw, then it would make some sense to call it a yawway machine.

Designing a sufficiently light and rigid framed canopy is a challenge.

An inverted and louvered rectangular parallelepiped of high aspect ratio where the sides (depth) are equal to one half diameter of the canopy width presented the largest theoretical F-drag to D-drag ratio, but the problems of using multiples of ultra-light fins or louvers are intractable, as I discovered.

The next machine will have a slightly lower F to D-drag ratio, but the canopy frames will also use less tubing and yet will be more rigid due to the new shape.

Two large arcs under bending load – like that which a taught bow presents – will form a solid foundation for bracing, much more so than any rectangular canopy frame. While I would have used the two towers for the next iteration, since they were destroyed I would re-engineer them from the ground up.

The biggest changes would be to make them taller and gently tapered.

Rectangular towers are less efficient since they raise the center of gravity when the objective is to make it as low as possible. Weight reduction is another benefit.

Two liabilities that all human powered rotorcraft possess are the inability to fly in a desired direction and a tendency to drift unpredictably. As you know, this is due in part to the lengthy time lag between detecting a drift, making corrections, and having those corrective actions manifest. In contradistinction, every stroke of a yaw-way machine has the potential to introduce a change in course because there is a much more direct correspondence of energy input to flight action than there is with human powered rotorcraft.

CFD and FE analysis were not viable for a few reasons but none greater than my desire to solve the problem the way Da Vinci or the Wright Brothers would have had to solve it. Nevertheless, it is easy to infer that the kinematics & dynamics of such a discrete impulse propulsion machine in action are inordinately complex. As such, there is an entire science to be discovered that underlies the function of the MacArthur Yaw-Way Machine.

I came up with the core idea in a flash of inspiration while imagining human powered flight one day (this was long before I ever heard of the Sikorsky Prize) but my initial conceptualization had what appeared to be an insurmountable liability for actual construction. During rumination some thirty years later in 2010 I theoretically solved this particular liability, which then set me on course to try to make an assault on the Sikorsky Prize. But I have to confess I have no desire to resume anytime soon. It is a project for some point long in the future.

My destiny seems to oscillate in a manner not dissimilar to my machine, only with an inordinately long period.

George