Technicalities

||| |—|—| | | | Since it consists of little more than a stick at one end and a couple of ailerons at the other, I thought that hooking up the roll control system of my homebuilt would not have been much of a problem. But then you wouldn’t think anything would be much of a problem, until you try it.

The pilot’s end of the system is a sidestick that swings 30 degrees to the right and left, turning a torque tube that runs aft along the left side of the airplane to a point behind the pilot’s seat and above the rear spar. There, a crank and pushrod convert the rotary motion of the stick into a vertical, linear motion.

At this point there was, until a couple of weeks ago, a gap. Think of it as one of those blurry areas the television networks put over suspects’ faces and indecent body parts.

Jumping to the other end of the system, we find the ailerons. Their motion of about 30 degrees up or down becomes, through the intervention of a single bellcrank, an in-and-out motion of about one inch in slender pushrods that run along the rear spars and pass through small holes into the fuselage. There, until a couple of weeks ago, they ended at…the gap.

The problem was how to close this gap, which had persisted for years because, principally, of my tendency to procrastinate. You would suppose that the ends of the two aileron pushrods could simply be connected to a single bellcrank that would convert the up-and-down motion coming from the sidestick into a right-left motion of that common pushrod. And that would be that. Unfortunately, the rear spar has a couple of bends inside the fuselage, and so these pushrods have to do some acrobatics just to get near each other. And then there is an additional complication: differential.

Aileron differential is the mechanical arrangement, found in practically every airplane, that causes ailerons to deflect upward more than they do downward-twice as much, typically. Its purpose is to reduce adverse yaw-the tendency of the nose to swing out of a turn because of the excessive drag of the downgoing aileron. Adverse yaw can be controlled with rudder, but airplanes with little or no adverse yaw are more pleasant to fly than those that have a lot. We speak kindly of airplanes that stay coordinated “feet on the floor”-as if we had chronically tired feet.

To achieve aileron differential we take advantage of the geometry of circles. Think of a clock face. The tip of the minute hand moves a greater distance horizontally than vertically between the hour and five after; but it moves farther vertically than horizontally between ten and fifteen after. Using a crank that rotates the same 90 degrees, we can exploit this characteristic to produce a linear motion that is much greater in one half of the crank’s arc (aileron up) than in the other (aileron down). It should be obvious (don’t you love people who say that?) that the largest differential that can be obtained from a single bellcrank making a 90-degree arc is .7071 divided by .2929, or about 2.4:1. Since control surface deflections are usually limited to about 30 degrees, this means 30 degrees up and 12 or 13 degrees down.

The predictable behavior of circular-arc linkages breaks down when the components are close together, and, because my habitual design procedure for irksome details is to leave some empty space and worry about them later, I found, when I was forced finally to do the job, that I had very little choice about where to put the various components. I had created a situation in which various parts of the aileron linkage, a flap actuator, and a cable trolley intended to keep the right and left flaps in step with each other all had to be stuffed into a small, inaccessible corner of the fuselage behind the pilot’s seat. Thus, what looked on paper like a simple exercise in bellcrank geometry turned out to be a struggle with complication, contortion and perspiration instead.

In the end I got it done, but I had to ask myself whether it wouldn’t have been wiser just to forget about the differential and let the ailerons use their full travel. After all, reducing the down aileron deflection reduces the roll rate. Was it worth it, just to keep my feet on the floor? To answer that question, I went to the computer to compare roll rates for ailerons with and without differential.

Pilots like to talk about roll rates in terms of degrees per second, but engineers often use, instead, a figure called pb/2V, or the “helix angle.” The symbol p stands for the roll rate in radians per second (a radian is 57.3 degrees), b is the wingspan, and V is the true airspeed in the same units as were used to measure the span. Thus, an airplane with a 30-foot wingspan traveling at 300 feet per second and rolling at 114.6 degrees-or two radians-per second would have a helix angle of 2 times 30 divided by 2 times 300, or 0.10.

The idea of helix angle is similar to that of the pitch of a screw, the screw thread being represented by the spiraling path of the wingtip of the rolling airplane. If you watched the rolling airplane from the side, the helix angle would be the angle of the path of the wingtip as it passed through the horizontal. It doesn’t surpass a certain maximum value because at that helix angle the resistance to rolling produced by the wings and tail surfaces-called “roll damping”-is equal to the “rolling moment” force produced by the deflected ailerons. One advantage of thinking in terms of helix angle is that it is constant over the speed range, whereas roll rate varies in proportion to speed.

I ran a series of computer simulations of the complete airplane, assuming one aileron deflected 28 degrees upward and the other deflected downward 12, 16 and 28 degrees. As you would expect, the helix angle increases along with the down aileron’s deflection, and, incidentally, it does so in a pretty linear way. It’s .089 with 12 degrees, .098 with 16 and .126 with 28. So the roll rate is almost 30 percent worse with the maximum differential tested than it would be with ailerons that moved equal amounts upward and downward.

Does it matter? The ultimate answer can only be subjective, but there are published guidelines summarizing the judgments of many pilots. According to the classic elementary aerodynamics textbook known by the names of its authors, Perkins and Hage, minimum requirements for pb/2V are .07 for cargo and bombardment types and .09 for fighters. Obviously, the creator of a high-performance homebuilt is thinking fighter, not freighter.

P&H was written in 1949; a more recent publication, the 1969 bestseller Background Information and User Guide for MIL-F-8785B(ASG), “Military Specification-Flying Qualities of Piloted Airplanes,” questions the value of pb/2V as a criterion and suggests that a more useful figure is the bank angle attainable within one second. This turns out to be a pretty loose criterion, however: a hundred degrees is said to be optimum but even 50 is satisfactory for “Class IV” aircraft, meaning fighters and ground attack types. As you can see, this is getting more complicated, not less; now we have to worry not just about roll rate, but about rolling acceleration as well. Other factors affecting the “goodness” of roll performance are the presence or absence of a “dead band” in the center and the existence and amount of “breakout force” in the control system.

Confronted with a multiplicity of increasingly obscure roll criteria, I fell back on the reflection that many perfectly good airplanes were designed prior to 1949. The numbers in P&H at least suggest that my airplane will not be dangerously deficient in roll rate, the minimum pb/2V of .089 translating into roll rates of 34 degrees/sec at 70 KTAS and 98 deg/sec at 200. It’s nice to dream, but to tell the truth I don’t anticipate actually getting involved in much air-to-air combat or ground attack action anyway.

By way of comparison, P&H provide rolling performance data for several World War II fighters. The following numbers are the roll rate, in degrees per second, at 87 knots, followed by the maximum attainable roll rate with the associated true airspeed in parentheses. (Because of aileron-induced wing twist, roll rate starts to decline above a certain speed.)

Aileron deflection is of course not the only factor determining roll rate. Aileron power can be increased by increasing chord and span as well. Increasing aileron chord is comparatively ineffective, and tends to increase stick forces; for an airplane with a sidestick, ailerons of narrow chord are desirable. Increasing aileron span, on the other hand, eats into flap span, and therefore pushes you toward either a higher landing speed or, alternatively, a larger wing area with more drag and a lower cruising speed.

Early on, I did investigate the possibility of using spoilers in lieu of ailerons, or some combination of spoilers with small “feeler” ailerons. I concluded, however, that for an airplane whose wing loading would never exceed 30 lb/sq ft and would seldom exceed 22, the difficulties of such a system outweighed-both literally and figuratively-the benefits.

As far as dead bands and breakout force are concerned, they are related to the free play and friction in the system. In theory, pushrod actuation systems are superior to cables because they are more precise; but cables are used in almost all production airplanes because they are simpler to route through the structure. The problem with pushrod systems is that it’s difficult to avoid having a large number of bushings or bearings in the linkage. Each may have a small amount of play, but when you add up a dozen of them the total is fairly large.

Free play is exacerbated when, as is the case in my airplane, thin wings and cramped subfloor spaces make it necessary to use bellcranks with short lever arms; an end-play of, say, ten thousandths of an inch is more noticeable when the system pushrods move only an inch or less in all than if they moved two or three inches. On the other hand, the breakout force with pushrods is negligible, because all of the joints and bearings have low friction and the mass of the system is small.

I’ve always envied Burt Rutan’s gift for simplicity, which I don’t share. The original VariEze had the simplest imaginable roll-control system, with the canard elevators moving differentially to provide roll control. The stick and the elevons were only a few inches apart and were connected so directly that it was almost as though the pilot held the elevons in his hands. The system didn’t work worth a damn-the elevons were too small, and their span too short, to provide decent roll authority-but it sure was simple.

It did teach me an important lesson about flying qualities, however: in a little while you can get used to just about anything. When I first flew the VariEze prototype, Rutan didn’t even think to brief me on the weakness of the ailerons; I discovered it for myself while plunging groundward in the turn from base to final approach, trying to figure out, as quickly as possible, how to level the wings.

It wasn’t malice (I don’t think); he had just grown so accustomed to rolling with a combination of rudder and elevon-the VariEze’s swept wings gave it powerful yaw-roll coupling-that he was not even aware that a copious dose of rudder was sometimes indispensable to raise a wing. When I told him I thought the roll authority was unacceptable he seemed sincerely surprised; without even realizing it, he had adapted his flying technique to the airplane. There’s comfort in that as I prepare my own airplane for flight; I know that no matter how badly it handles, I’ll get used to it.