Power vs Drag

For a particular plane in a particular configuration (flaps, landing gear), there's a particular airspeed at which you can cruise with the lowest drag. For a trainer flying with no flaps, this is usually around 75kts. Fly faster than this, and drag goes up as speed goes up, as parasitic drag gets higher. Go slower than this and drag goes up as speed goes down, as induced drag gets higher. It actually requires more power to maintain straight and level, constant-airspeed, flight at higher airspeeds, and also at lower airspeeds, so speeding up or slowing down increases the power required to continue level flight. This is a bit peculiar, because if we want to reduce our drag, if we're going fast we need to slow down, but if we're going slow, we need to speed up.

We're used to the idea of "drag goes up as speed goes up", because that's what we'd see in a car or on a bicycle, flying a kite, or when we do our wind tunnel experiments by making wings with our hands out the car window. The idea that drag can go up by going slower is specific to airplanes, though, and not intuitive, so it helps to see a demonstration of this for ourselves.

The typical best "demonstration" is to practice slow flight, which is flying the plane at a very slow airspeed, nearly as slowly as possible, so slow that the wings must be raised to a very high angle of attack in order to generate enough lift to support the plane's weight, just below the critical angle of attack at which the wing stalls.

When in slow flight, the plane requires a great deal of power just to fly along straight and level. When we raise the nose by applying back pressure to the elevator, the plane doesn't climb like it does when we do this at cruise, instead it slows down and starts to "wallow", may start to descend, the stall warning horn complains, and if we keep up this nonsense, we may find ourselves in a power-on stall (or, at least, in a sinking "mush").

So at cruise speed, raising the nose slows the plane and makes it go up. In slow flight, raising the nose slows the plane and makes it go down. This is a bit of a problem for us, because we need to be sure that we don't have a "stick back makes us go up" idea stuck in our head, as that can have disastrous results when we're flying very slow, such as when coming in to land. So why does "stick back" make us climb when we're fast, but descend when we're slow?

Types of energy

I think the easiest way to understand this is to think of it in terms of power and energy. You can think of "energy" as the ability to produce some change, and "power" is how fast energy is being produced or spent. A plane can have a few different types of energy:
  • kinetic energy: this is "1/2 * mass * velocity^2". So this is energy the plane has as a result of its motion. It's pretty intuitive to us to understand that an object in motion has some energy stored in it; for instance if we coast down a big hill on our bicycle, the speed we have at the bottom of the hill can propel us up the next hill without needing to pedal. It's a similar notion to momentum, which also depends on mass and velocity, but not exactly the same.
  • potential energy: potential energy is energy that is "stored" in some fashion. A plane has a couple types of potential energy:
    • Gravitational potential energy: this comes from the plane having mass and being some distance away from the center of the earth. If you pick up an object and raise it, you need to spend some energy in order to lift it. That energy doesn't disappear, it's now "potential energy". If you pick something up off the floor, and put it on a table, it now has some stored potential energy. If you nudge it off the table, and it falls, that potential energy transfers into kinetic energy as it speeds towards the floor.
    • Chemical potential energy: The fuel in the tanks has potential energy that can be released by igniting it. When fuel is mixed with air and ignited, the chemical potential energy is converted into heat, yet another type of energy.
So when we're sitting on the ramp, engine not yet started, our tanks are full of chemical potential energy, and we've got some gravitational potential energy (depending on our elevation). As we fly, we gradually convert that chemical potential energy into gravitational potential energy (as we climb), kinetic energy (as we get moving), and we release some of it as heat (via our engine exhaust), but we impart the bulk of that energy to the air around us as we push and shove it around as we fly. This pushing around of the air is what the plane feels as drag. If there was no drag, then we would only need a little bit of energy to gain some altitude (gravitational potential energy), a little bit more to give us some airspeed (kinetic energy), and then we could coast around all day long with the engine turned off. In movies, spaceships on long flights are always gunning their engines, but real-world spacecraft just need thrust to escape the planet's gravitational pull and to generate some velocity, and then they coast after that. In our real airplanes, in a long cruise at a steady altitude and airspeed, we're burning our 10GPH (or whatever) purely to feed out energy to overcome drag.

If we take-off, fly around, then land back at the same airport, from an energy perspective all we've accomplished is taken some chemical potential energy and released it into the atmosphere in the form of heat, a little of which we blew out our exhaust pipe, but most of which was the net result of all that drag. But during that flight, we climbed and descended, sped up and slowed down, so there was also a continual exchange between kinetic and gravitational potential energies as well.

Physics tells us that energy cannot be created or destroyed, it can only change forms. When flying, we're changing energy from one form to another all the time. As we're speeding along the runway to take off, we're converting chemical potential energy to kinetic energy. If, in flight, we turn off the engine, point the nose down and pick up a whole lot of speed, then we're converting potential energy (from our height) into kinetic energy. If we then pull the nose back up we'll find we're climbing, despite the engine not producing any energy, and we're now reversing that swap, trading our kinetic energy back to gravitational potential energy.

But while we can trade between gravitational and kinetic energy, we know that we can't glide forever without finding some energy source (like an updraft), because we are continually spending energy on drag. In still air, a glider can climb and descend, but it will, overall, need to allow itself to get closer and closer to the earth. While a powered plane slowly spends the chemical potential energy in its fuel tanks, a glider with no updrafts slowly spends the gravitational potential energy it got from its initial tow to altitude.

The energy both the powered and non-powered crafts spent is dissipated into the atmosphere as the result of drag. You can think of this as drag causing a transfer of energy from the plane into the atmosphere, where it takes the form of heat and kinetic energy.

A powered plane has a source of power in its engine, which serves to "spend" the chemical potential energy in the fuel, doling it out as work performed on the air by the propeller to drive the plane forward. When flying straight and level at a constant airspeed, our potential and kinetic energies are not changing, so all of the power produced by the engine is spent as drag, thus power source and power drain are necessarily exactly equal. Energy cannot be created or destroyed, so whatever we're producing we must necessarily be converting into some other energy type. In fact, you can think of the plane as settling into the exact cruise speed that generates the level of drag needed such that the power lost to drag exactly matches the power generated by the engine.

Effects of changing engine power

If we're flying along straight and level, at constant airspeed, and we open up the throttle a bit, we're now producing more power than we were before, but still expending the same amount of power to drag, so we now have an "excess" of power. This power has to "go somewhere", it must be converted into some other type of energy. As pilots, we get to decide what it gets converted into. If we maintain our altitude (typically requiring some forward pressure on the stick), then initially our excess power will be steadily converted into kinetic energy as we accelerate. But as we accelerate to an even higher cruise speed, the rate at which we lose energy to drag increases as well. At some point we'll reach an airspeed where drag has risen to match our engine power, and we'll be back in equilibrium again. The plane will stop accelerating as the power imbalance is gone. In effect, the plane has "found" a new airspeed where drag exactly matches the new power output.

Alternately, after we increase engine power, we could decide to maintain our airspeed. If we do this, then no energy goes into additional kinetic energy, and there will thus be no increase in drag to soak up that new engine power. So where does the power go? It gets converted into gravitational potential energy, as the plane settles into a climb. The greater the excess power, the greater our climb rate. Then again, potential energy is a function of both distance above the center of the earth and the mass of the object, so with a set amount of excess power, a heavy plane will climb more slowly than a light plane, as each foot of climb in the heavy plane represents a greater increase in potential energy than for the light plane.

Similarly, if we're stabilized in a straight and level, constant-airspeed cruise, and we reduce engine power, we're now (initially) generating less engine power than is being lost to drag. The energy being fed to drag must come from somewhere, though. Just as above, the pilot gets to decide where it comes from. If he maintains altitude (typically applying a little backpressure on the stick), then the plane will slow down as kinetic energy is drawn upon to feed the disparity between engine power and drag. As we slow to a slower cruise speed, though, drag diminishes, and once again the plane will "find" the airspeed where drag matches the new power output, and we'll be in equilibrium again. But during the time when there was a power disparity, some store of energy had to be tapped, and in this case it's the plane's kinetic energy.

Alternately, if after reducing engine power the pilot decides to maintain airspeed, then there's no change in kinetic energy nor in drag, so the plane must find some other source of power to tap, and in this case it draws that power from its store of gravitational potential energy by entering a descent.

Two ways to spend the same power

So while we're maintaining a level altitude, the power generated by the engine equals the power spent by drag. At any power setting, there are two airspeeds that will yield level flight, a fast one and a slow one.

So imagine yourself at a moderate cruise speed, say 90kts. Haul back on the yoke and slow down. The plane will, of course, begin to climb, as we convert kinetic energy (as we slow) into potential. Also, as we slow, drag will initially decrease, contributing to our climb rate. As we pass through the airspeed that yields the lowest drag for the current configuration, then as we continue to slow our drag will start to rise again. At some point, we will reach a slow airspeed where drag is equal to our 90kts cruise "fast" airspeed. Without ever touching the power, we can level off at this airspeed and maintain level flight again. We will have, of course, climbed to a higher altitude through this experiment, having traded some kinetic energy for potential.

The experiment can also be performed in the opposite direction, as we nose over and accelerate back to 90kts, again without changing power. We'll descend, of course, as we trade our potential energy back to kinetic energy as we accelerate, and eventually reachieve level flight at 90 kts.

(By the way, I've never tried this experiment. Once I do, I'll describe the results here. If anybody else has tried this, please drop me a note to tell me how it worked!)

Why it matters

Well, this has been a long trip, and you're thinking that by now somebody might have mentioned why we bothered. We don't, in general, cruise at 60 kts when we could, for the same power, cruise at 120, so who cares?

Really, the importance of all this comes into play when we're intentionally flying slow, typically for approach and landing. It becomes really important when we're gliding to a particular spot (e.g. in an engine-out scenario), and we need to "modulate" our glide in order to hit a particular spot.

In a "normal" approach and landing, our final approach airspeed is on the "backside" of the power required curve, such that hauling back on the yoke will have a brief, short-term climbing effect (as we swap out some kinetic energy for potential), but by slowing and increasing our angle of attack, this action increases our drag, and thus creates a longer term tend towards increasing our descent rate. Since we probably hauled back on the yoke because we wanted to climb, presumably because we're too low (and those trees are getting bigger in the windshield), this long-term effect is likely to make things worse. If we continue to respond by hauling back on the yoke, things are not going to go very well. As we slow, we're going to find that we need to bring in more and more power to overcome drag.

For this reason, the usual recommendation is to control your glidepath on final approach with power, and modulate pitch to maintain a constant airspeed. Your constant airspeed will keep drag constant, so your rate of descent will change directly as a result of your engine power changes (ignoring changing winds for now).

What happens when we find we've misjudged our approach, and are too high? Well, once power is pulled to idle, it can't go any idler. To steepen your approach further requires increasing drag. There are two ways to do this. One is to perform a forward slip, by stepping on the rudder to yaw the plane into a high-drag "sideways" flying attitude, and modulate bank to maintain the runway centerline and prevent a yawing turn to a different heading.

Forward slips certainly work, though they have a few downsides. One of the greatest is that they can be extremely disturbing to passengers, as the plane appears to be doing something dramatic and disturbing, and the passengers can feel that the plane isn't flying in a coordinated fashion (they'll feel the bank as a tendency to slide in their seat towards the lower wing). There's also a tendency in this maneuver to drop the nose and pick up speed, partly out of fear of stalling uncoordinated, and partly because the contribution to drag of the forward slip increases with airspeed.

This often yields an "illusion" that the pilot is in a better position to land than he really is, because he can forward slip himself down into a position close to the normal glidepath, but by arriving with a great deal of excess airspeed, he then floats and floats and floats along the runway, which we then begin to hope is long enough.

The alternate approach to increasing drag is to slow down, thus flying at a higher angle of attack, and increasing induced drag. This has the advantage that it looks and feels to the passengers like normal flight. It also gives the pilot a more realistic judgement of his readiness to land, because if he reachieves a position on the normal glidepath, then he should be fine because he has no excess airspeed.

The downside to slowing down on final approach is that it reduces the margin above the stall, increasing susceptibility to wind shear.

Harry Mantakos / harry@meretrix.com