Unlisted Numbers

From our first day in ground school, we're told about the importance of good decision-making, the need for continually evaluating in-flight weather, the value of maintaining alternative options - you know, a Plan B - and most daunting of all, our own fallibility. Most problems are of our own making. One perennial issue is fuel management. Folks are always managing to run the tanks dry, and it's usually just a few miles short of their destination. Whether it's an unanticipated route change, calculation error, unexpected weather, or some quirk in the fuel system, it happens.

One thing often figures into the accident chain that's gotten too many pilots shackled to the post of embarrassment, or worse, eating dirt just short of a runway. That particular link - happily one of the easiest to break - is learning how to fly more efficiently.

I call these the unlisted numbers, and the directory from which they're missing is your airspeed indicator. The reason they remain unlisted is that they're often a range of weight-dependent airspeeds and not just one figure.

Moving around in three dimensions is bound to introduce more variables and unknowns than in two. So we arm ourselves with back-up systems, extra reserves, a Plan B, and any number of tricks we can use when the going gets rough: forward slips, climbing out at V_X, or slowing to maneuvering speed when it's bumpy. Some of these numbers, like V_NE or V_NO, are right there at the ends of colored arcs on the dial, but some are reclusive. Here are a few more that might prove useful someday. We'll look at three of them. They are maximum range airspeed, maximum endurance airspeed, and a third, minimum sink speed.

Maximum range airspeed: Paradoxically, airplanes go farther the slower you fly them (up to a point). If there are range profile curves in Section 5 of your airplane's manual, take a look. See how much farther you can go on 55 percent power (or 45 percent, or whatever the lowest value is). Usually that's something around 2,100 rpm (and 18 inches manifold pressure for controllable-pitch propellers). There's even a little more, beyond where the charts leave off. Generally, you'll get even more miles per gallon just a bit faster than V_Y. (Keep in mind that this is a general ballpark range.) You'll be nose high and s-l-o-w. But if you're in a miserly mood, or circumstances beyond your control have "scrooged" you, you can do it. That's a lot slower than most of us would like.

The reason that there is such a speed in the first place is simple. Think about what you learned in ground school concerning the various types of drag that an airframe experiences. As you may recall, there is one type, called parasite drag, that increases with the square of velocity. This is from the airframe itself, as well as all its appurtenances, plowing through the air. In fact if you were to dive straight down (and you didn't bust design dive speed and flutter into so much confetti trying) your aircraft would reach a "terminal velocity" because of this type of drag.

At the other end of the airspeed arc is another type of drag. Unlike parasite drag, which affects any object moving through a fluid, this other one is common only among airfoils. As we probably recall, this is the one called induced drag, as it is a byproduct of our wings generating lift. Induced drag gets worse the slower you go. (In fact, it is inversely proportional to the square of velocity.) It's at its greatest when flying slowly and at a high angle of attack.

So maximum range airspeed can be thought of as nothing more than a happy medium between the two. This is what's behind our "best glide" airspeed when the power goes away, and it's just a bit higher - a very few knots - when the propeller is working for you rather than against you. (If you like being miserly just on principle, then you might be interested in "optimum cruise" airspeed, where the fuel flow per knot is at a minimum. Generally this is about one-third again as fast as best glide.) Flying at the most efficient altitude (generally that's about two-thirds of the service ceiling) and following proper leaning procedures helps even more. (See "Controlling the Mixture," AOPA Flight Training, February 2002.) Winds don't have all that much effect on things, as a rule. Just increase it by half the headwind component and decrease it by a quarter of any tailwind component. These factors will be more than enough. Again, this is another rule of thumb.

Another economy speed is maximum endurance speed. This one is quite a ways down on the airspeed dial. This is the airspeed where you are burning the least fuel per unit of time, and you want to remain in the air for as long as possible. This could come in handy if, for example, you wanted to wait for the moon to rise on a clear but dark night, or perhaps for a ground fog to burn off a bit more if you ever find yourself in that situation.

How slow is maximum endurance speed? Believe it or not, it's usually a few knots below V_X, the best angle of climb airspeed. Engine cooling isn't really great even when you fly at V_X, so if you choose to fly this slow on a hot day, keep that in mind. This airspeed is even more nose high and slower than maximum range airspeed. And we're talking bladder-stretching durations here!

One puzzle that might occur to you about this maximum endurance speed, which is generally about halfway between V_X and a stall, is that, since induced drag is so high when we fly that slowly, how in the world can we stay in the air longer? The answer is that the engine is pulling against it at a much slower speed. Think of it this way: Which seems easier, walking up a few flights of stairs carrying your flight bag, or sprinting madly up carrying nothing?

Finally, below this, there's still one more: minimum sink speed, which is just above a stall. It's no news to sailplane pilots. This is exactly what they use when circling around inside of a thermal (which is nothing more than a rising column of air). And it could be welcome news for you if your engine quits and you already have the field made. Don't just barrel down at best glide, especially if you're stuck with a rough surface or worse. Since impact forces increase with the square of the velocity, it stands to reason that if you slow down (which you would do in a full-stall landing anyway), you will be that much better off.

Just remember two rules here: You'll reach this airspeed at just a few knots above the stall, so you don't have much wiggle room, and the main reason folks sometimes come to grief in a forced landing is that they're so busy doing fancy footwork to maneuver around some obstacle they see at the last minute that they forget rule number one. So even though there's no way to stretch a glide (which is absolutely true), there is a way to stretch a glide, at least in terms of time. Actually, at the lower minimum sink speed, a propeller might stop windmilling, which would actually give you back a little of that lost glide range (but not as much as you'd get at best glide speed, where the lift-to-drag ratio is greatest).

A further caution: Going that slow, you've got precious little protection against wind shear, and you won't get much of a flare. And if you ever need to make a course reversal with a minimum altitude loss, do what glider pilots do during simulated rope breaks: a 180 into the wind at minimum sink speed plus 20 percent. Why 20 percent? Because they're in a 45-degree bank! (Since the load factor is the reciprocal of the cosine of the bank angle, and the stall speed goes up with the square root of load factor, the stall speed increases by a little less than 20 percent.) And why are they in a 45-degree bank? For the same reason that you learned in high school physics as to why a projectile travels the farthest when fired at an angle 45 degrees above the horizon. It's just another compromise between forward velocity and gravity. (I emphasize emphatically that this is not to be used to the exclusion of all else in an engine failure scenario at low altitude. Too many pilots have found that out the hard way!) Like best glide and best range, which are a few knots apart, best endurance and minimum sink speeds are too - the power-on state being the faster, in both cases. Again, this is because the propeller is working in your favor at maximum endurance airspeed and becomes an opponent at minimum sink speed.

Maximum range airspeed, best glide, maximum endurance airspeed, and minimum sink airspeed are all related. The last two can be grouped as one of two "bottom" points on two different parabolic curves: the first of them being a plot of power versus airspeed, the latter on another similar curve of sink rate vs. airspeed (see p. 38). Here, they are represented by V_ME and V_MS on these two curves, respectively. Of the latter, sailplane pilots know that in a zero-wind situation, best glide (here shown by V_BG) is given by the point on the sink rate/airspeed curve tangent to a line drawn from the zero airspeed origin (or from farther along the airspeed axis with a headwind, or behind the origin in the "negative" X-axis range for a tailwind) and that minimum sink speed lies at this curve's minima, or bottom. And with maximum endurance airspeed, at the bottom of the power vs. airspeed curve (any slower being in that often-cited "region of reversed command") is the maximum range airspeed (V_MR), similar to that for best glide on the other curve, which lies where a line drawn from the zero-airspeed origin just touches it. For math types anyway, this is pretty cool stuff.

These numbers aren't precise. They don't have to be. Most of us consult our POH, choose a manifold pressure setting (and propeller rpm, if required) appropriate to our altitude, and monitor our fuel situation with an "ops check" every few minutes. And most of us start to get a bit nervous when the fuel needles move toward the one-quarter mark. We don't fly to dry tanks, after all, even though that's the only time when the fuel gauges are required to be accurate.

Speaking for myself, I'd be loosening my collar and starting to look like Rodney Dangerfield if I wasn't on the ground with an hour's fuel still aboard. So anything to widen that safety zone is fair game to me. Think of these performance numbers simply as more arrows in the quiver against outrageous fortune - or our own fallibility.