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Copyright 1996-2001 jsd

1   Energy Awareness and Energy Management

Note: You can buy a used airplane for about the same price as a new sports car.

Riddle: What's the main difference between the sports car and the airplane?

Answer: If you accelerate the sports car to about 75 miles per hour and pull back on the steering wheel, nothing very interesting happens.

When piloting an airplane, two of your most fundamental duties are (1) controlling the airplane's speed and (2) controlling its altitude.

Performing these duties would be easy if the airplane were equipped with ideal controls, so that you could (1) move a lever that would immediately change the airspeed by a few knots, with no change in altitude, or (2) move another lever that would immediately change the altitude by a few dozen feet, with no change in airspeed.

Alas, it is physically impossible to build an airplane with such ideal controls. One purpose of this chapter is to explain how real controls affect the airspeed and altitude of a real airplane.

For example, consider the seemingly simple maneuver of changing speed while maintaining a constant altitude. We will see that this requires a complex sequence of adjustments of several controls. There are two ways to deal with this maneuver. One way would be to discover (by trial and error) the required sequence of adjustments, and perform that sequence by rote forever after. A far easier and better way is to understand the fundamental relationships, so that the proper sequence seems logical and obvious.

Understanding how the airplane really responds to the controls makes your flying not only easier, but safer as well.

Generally, a pilot who tries to control airspeed and altitude separately winds up controlling one or the other rather poorly. Usually it is the airspeed that suffers. All too often, the airspeed gets too low, whereupon the wing stalls and the pilot rather abruptly loses control. This is the classic stall/spin accident. It is usually fatal. The good news is that if you understand what the controls really do, you can stay out of this sort of trouble.

The key to understanding the relationship between airspeed and altitude — and several other things — is the concept of energy.

Energy is not a new or complicated concept. Most pilots understand that being ``high and fast'' is very, very different from being ``low and slow''; the concept of energy just makes this notion a little more precise and gives it an official name.

Good pilots think about energy all the time. The more critical the situation, the more carefully they evaluate the energy before reaching for the controls.

Once you grasp the basic concept of energy, you will be able to apply it in many ways, to many different situations. This is a big improvement over trying to figure out all possible situations one by one. Energy gives you the ``big picture''.

1.1   Total Energy Cannot Change

As illustrated in figure 1.1, there are four types of energy that are crucially important for airplanes, namely: There are of course other types of energy, but the four forms listed above are the ones pilots use all the time, so let's concentrate on them for now.1

Figure 1.1: Total Energy Cannot Change

Energy has the remarkable property that it cannot be created or destroyed — it can only be converted from one form to another. This rule (which physicists call the law of conservation of energy) is not one of Newton's laws; it was not even known in Newton's day.

Consider the analogy with water: it can be converted to ice and back again, yet the amount of water doesn't change in the process. Even if the water leaks away and we lose track of where it is, the number of water molecules in the world hasn't changed.

The same notion applies to energy, as illustrated in figure 1.1. Fuel energy can be converted to altitude; altitude can be exchanged for airspeed; altitude can be cashed in to pay for drag; et cetera. The amount of energy in the world doesn't change.

Some of these energy conversions are irreversible. Fuel burn, for example, is a one-way street; we cannot (alas) operate the engine backwards and replenish the fuel supply. Similarly, when energy is dissipated by drag, that energy can never be recaptured in a useful form.

The airspeed and altitude together are called the mechanical energy. Engine power increases the mechanical energy, while dissipation decreases the mechanical energy.

Figure 1.2: Energy Conversion -- Glide
Altitude is being cashed in to pay for drag. The airspeed is not changing, and no energy is being taken from the fuel tank.
Figure 1.3: Energy Conversion -- Climb
Fuel is being consumed to pay for drag and purchase altitude.
Figure 1.4: Energy Conversion – Cruise
Fuel is being consumed to pay for drag. Altitude and airspeed are not changing much.
Figure 1.5: Energy Conversion – Zoom
If you pull back on the yoke, the airplane will slow down and ascend. If you do it quickly enough, drag will not have time to consume very much energy, nor will the engine have time to convert very much fuel.
Figure 1.6: Energy Conversion – Pushover
Conversely, if you push forward on the yoke, the airplane will speed up and descend. Once again, if you do it quickly enough, drag and engine power will not affect the energy budget very much.
Figure 1.7: Energy Conversion – Initial Roll
During the early part of the takeoff roll, drag is negligible. There is no change in altitude, so virtually all engine power goes toward building up airspeed.
Figure 1.8: Energy Conversion – Flare
An important conversion is the flare maneuver, which occurs at the end of every flight. It is possible to maintain altitude without using the engine, by gradually cashing in airspeed to pay for drag.

1.2   Energy Conversion

Figure 1.2 through figure 1.8 show several examples of how one form of energy can be converted to another. We now investigate energy-conversion processes in a little more detail.

1.2.1   Converting Speed to Altitude and Back

An airplane (like any other object) has potential energy proportional to its altitude. Every increment of altitude represents an increment of energy. Similarly, any moving object has kinetic energy proportional to the square of its speed. We can easily convert back and forth between these two forms of energy. A roller-coaster is a well-known2 example of this, as illustrated in figure 1.9.

Figure 1.9: The Law of the Roller Coaster

At the left of the figure, we have a roller-coaster at a low altitude, moving quickly. In the middle of the figure, the roller-coaster has a higher altitude, but much less speed. At the right of the figure, the roller-coaster has returned to the lower altitude and regained its speed.

Since the roller-coaster carries no fuel and has very little friction, potential energy (altitude) and kinetic energy (speed) are the only forms of energy we need to take into account.

Here is the law of the roller-coaster:

Conversion factor = 9 feet per knot, per hundred knots

This law applies to airplanes, roller-coasters, or anything else that converts potential energy to or from kinetic energy. The altitude gain is proportional to (a) the amount of airspeed loss times (b) the average airspeed during3 the maneuver. Let's apply this to a couple of examples: if you are cruising straight and level at 201 knots, and you pull back on the yoke, when you reach 200 knots you will have zoomed up 18 feet. If you started at 101 knots and pulled back to 100 knots (once again a loss of one knot) you would only gain 9 feet.

This rule applies to aircraft, roller coasters, and indeed all objects in the world — in situations where friction can be neglected. The conversion factor, 9 feet per knot per hundred knots, is just the reciprocal of the acceleration of gravity4 expressed in aviation units.

The two forms of energy — altitude and airspeed squared — are deeply related, even though they are measured in different units. We need a conversion factor (9 feet per knot per hundred knots) so we can convert from one set of units to the other.

1.2.2   Energy Per Unit Mass

Since we are about to start comparing these mechanical forms of energy with other forms, we must start paying attention to an additional detail: an object's potential energy depends not only on its altitude but also on its mass. A 300-ton Boeing at any given altitude has 300 times more potential energy than a 1-ton Piper at the same altitude.

Similarly, an object's kinetic energy is also proportional to its mass. A 300-ton object at any given airspeed has 300 times more energy than a 1-ton object at the same airspeed.

Since the mass of an airplane does not usually change much during the course of a maneuver, we can often simplify the discussion by ignoring the distinction between ``energy per unit mass'' and genuine ``energy''. In cases where the distinction matters, I will remind you of it.

1.2.3   Converting Fuel to Altitude

Having understood the conversion between altitude and speed, let's bring fuel into the picture. Each pound of fuel contains a certain amount of chemical energy. The engine allows us to convert this chemical energy to mechanical energy. Assuming typical engine efficiency, the fuel-to-altitude conversion factor is:

Typical conversion factor = 6300 foot-tons per gallon

That is, climbing 6300 feet takes 1 gallon more fuel than level cruising for the same amount of time, in a typical one-ton airplane. A heavier plane would require proportionately more fuel for the same climb.

Figure 1.10: Converting Fuel to Altitude

To understand where this number comes from, and what it means, consider the experiment shown in figure 1.10. First we fly straight and level for ten minutes, maintaining 90 knots; we observe the fuel flow gauge is reading 5 gallons per hour. Then we open the throttle and climb for the same amount of time at the same airspeed; we observe a vertical speed of 630 feet per minute and a fuel flow of 11 gallons per hour.

The experiment tells us that in the example airplane, climbing at 90 knots consumes 6 gallons per hour more fuel than level flight at the same speed. During 10 minutes (one sixth of an hour) the climb will eat up one extra gallon. The same 10 minutes at 630 fpm will gain us 6300 feet of altitude. The example plane weighs exactly one ton, so we get the conversion factor claimed above: 6300 foot-tons per gallon.

The exact value of the conversion factor will vary a little bit from airplane to airplane, depending on the efficiency of the engine, etc., but 6300 foot-tons per gallon is a good approximation in most cases.

To determine the fuel-to-altitude conversion factor for your airplane, you can (1) divide 6300 by the weight (in tons) of your airplane; (2) perform the experiment described above; or (3) work it out using the cruise-performance and climb-performance data in your airplane's Pilot's Operating Handbook (POH).

Here are the results for several airplanes from various manufacturers, using POH numbers:

Airplane foot-tons per gallon
Two-place, carbureted, fixed gear, fixed prop
Four-place, carbureted, fixed gear, fixed prop
Four-place, fuel injected, retractable, constant speed prop
Six-place twin, fuel injected, retractable, constant speed prop

If the airplane were 100% efficient at converting fuel to altitude, the conversion factor would be higher — but it is hard to build a really efficient engine with a reasonable size, weight, and cost.

1.2.4   Power versus Energy

Since fuel corresponds to altitude, fuel flow rate must correspond to rate of climb. Airline crews use this fact routinely: to make the transition from level flight to a 500 fpm descent at constant airspeed, they just retard the throttles until they see a certain reduction on the fuel flow gauges.

This notion of ``energy per unit time'' is officially called power. You don't want to confuse power with energy, any more than you would want to confuse a vertical speed indicator with an altimeter; the former indicates altitude per unit time, while the latter indicates altitude.

The airplane has instruments that measure most — but not all — of the relevant forms of energy and power. The energy gauges include the altimeter, airspeed indicator, and fuel gauges. These tell you how much potential energy, kinetic energy, and chemical energy there is on board.

The most common power gauges include vertical speed indicators and fuel flow gauges; these tell you at a glance how much power is flowing in and out of the potential and chemical reservoirs. Sometimes other power gauges are installed; gliders often have a ``total energy variometer'', which measures the rate of change in mechanical energy (potential plus kinetic) by measuring a combination of altitude change and airspeed change. Such a device is more useful than an ordinary vertical speed indicator for detecting updrafts, for the following reason: Inadvertently pulling back on the yoke will cause a positive indication on the vertical speed indicator (by the law of the roller-coaster) which might be confused with a real updraft; pulling on the yoke will cause no indication on the TE variometer.

Since the glider has no engine power to worry about, the TE variometer gives a reasonably complete picture of how much power is flowing in or out of the aircraft (updraft = power in; dissipation = power out). In an airplane with an engine and without a TE variometer, it is somewhat trickier to visualize what is going on.

Figure 1.11 summarizes this section by showing the various forms of energy and power, and some of the relationships between them. The ones that are circled are the ones for which aircraft gauges commonly exist.

Figure 1.11: Forms of Energy and Power

A reminder for the purists: a given quantity of gasoline contains a certain amount of chemical energy, period. In contrast, a given amount of altitude represents a certain amount of energy per unit mass of airplane. Therefore it is a slight oversimplification to suggest (as in figure 1.11) that the fuel gauge and the altimeter measure exactly the same thing, but it there is no harm in it if the mass of the airplane isn't changing. Similar remarks apply to the airspeed indicator.

1.2.5   Drag and the Power Curve — Introduction

The time has come to bring drag into the picture.

The power dissipation due to drag is equal to the drag force times the airspeed.5 Power is energy per unit time, which should not be confused with energy itself.

The distinction between energy and power is emphasized in the following analogy:

Altitude (energy) is like money in the bank. You pay the cost of climbing to altitude only once. If desired, you can cash in the altitude energy to do useful things.   Drag (power) is like rent; you have to pay a certain amount of energy per unit time for the privilege of flying the airplane through the air. That energy can never be recovered.

The amount of drag — the amount of rent you have to pay — depends on your airspeed6 in a complicated way. The relationship is shown in figure 1.12, and is called the power curve.

Figure 1.12: Power Curve (Engine Idle)

(You may be more familiar with this curve in an upside-down version called the ``power required'' curve. The orientation given here is preferable, for the following reason: Airplanes don't have ``power required meters'' but do have vertical speed indicators. Therefore this orientation is more meaningful in the cockpit. Also note that drag contributes a negative amount to our power budget, in contrast to the engine which contributes a positive amount.)

In the figure, airspeed is labelled in Knots of Indicated Air Speed (KIAS). A knot is a nautical mile per hour, as discussed in section 14.2.2. The meaning of indicated (versus true) airspeed is discussed in section 2.12.

This figure applies to straight-ahead gliding flight. The engine is producing zero power; for any particular airspeed, the airplane will descend at the rate specified by the power curve. Altitude — i.e. gravitational potential energy — is being cashed in to pay for the frictional losses.

The traditional units for the vertical axis in this figure would be horsepower, but I have used feet per second instead. This is intended to clarify the equivalence of all four forms of energy by measuring them in a common set of units. We have seen how to think of airspeed in terms of altitude (9 feet per knot per hundred knots) and also how to think of fuel in terms of altitude (6300 foot-tons per gallon), so it is only logical that power should be measured as vertical speed; that is, altitude-change per unit time.

The terminology and basic applications of the power curve are presented in the next couple of paragraphs; some more advanced applications will be presented in section 7.5.

Figure 1.13: Power Curve — Three Regimes

As shown in figure 1.13, the power curve is divided into three regimes. The right-hand part of the curve (from moderate airspeeds on up) is called the front side of the power curve. Normal cruising flight is conducted in this range of airspeeds.

In this regime, the faster you go, the more power is consumed by friction. This is completely unsurprising — everybody knows that moving an object through the air quickly takes more force than doing it slowly. You can see in figure 1.13 that if you glide at a very high airspeed, you will have a large rate of descent.

What is less obvious to non-pilots is that at low airspeeds there is another regime with very high drag. This is called the mushing regime, and is labelled in the figure. The logic here is that it is more efficient to visit a lot of air and yank it down gently than to visit a small amount of air and yank it down violently. In this regime the airplane must fly at a high angle of attack in order to support its weight. This creates strong wingtip vortices that in turn produce huge amounts of induced drag, as discussed in section 3.12.3. Therefore if you are in the mushing regime, flying more slowly causes more descent rate, as can be seen in figure 1.13. This is quite unlike cars — a car moving slowly incurs very little frictional loss. Of course, cars don't need to support their weight by pulling down on the air.

The dividing line between the mushing regime and the front side of the power curve is the highest point on the power curve. At this point, the airplane can fly with the minimal amount of dissipation; this is the ``low-rent district''. The airspeed where this occurs is called the best-rate-of-climb airspeed and denoted VY.7

Finally, we consider the extreme lower-left part of the power curve. This is called the stalled regime, as indicated in figure 1.13.8 Flight in this regime is very, very peculiar.

The mushing regime and the stalled regime are collectively referred to as the back side of the power curve.

Life would be simpler if manufacturers would explicitly show the power curve somewhere in the POH, but they don't. You have to figure it out for yourself. Fortunately, the general shape of the power curve is more-or-less9 the same for all airplanes, so the concepts discussed here are very widely applicable.

1.2.6   Rates of Energy Conversion

An airplane can very rapidly and efficiently convert airspeed to altitude, and vice versa. Because of this, these two forms of energy are often considered together, and are collectively referred to as the mechanical energy.

In contrast, it is difficult to convert fuel to mechanical energy quickly, and it is difficult to dissipate large amounts of mechanical energy via drag quickly (especially while maintaining a safe airspeed).

A rapid conversion of airspeed to altitude is called a zoom — a fairly common maneuver.10 You should always be careful when performing a zoom, because if the airspeed gets too low there could suddenly be very unpleasant consequences.

The airplane's ability to convert airspeed to altitude and back again is the key to many aerobatic maneuvers. There is no way you could perform a loop using engine power alone; you have to zoom. Bob Hoover's airshow routine typically closes with a spectacular energy management demonstration. After shutting down the engine, he performs a series of complex aerobatic maneuvers, including an eight-point roll and a hammerhead.11 He then returns for landing and coasts to the reviewing stand, all without restarting the engine. It is quite a fascinating lesson in pilot technique.

1.3   Effect of Controls on Energy

The previous section introduced the main forms of energy that affect flight. The next step is to discuss how the pilot can control the energy in various ways. This section doesn't introduce very many additional concepts; it mainly just combines and applies the concepts introduced previously.

We continue to use the analogy between energy and money. Therefore, deciding how much power should flow from one reservoir to another is called the power budget.

1.3.1   Power Budget — Using the Engine

Figure 1.14 shows how engine power affects the power budget.12 The bottom curve applies when the engine is operating at 1700 RPM, the middle curve applies at 2000 RPM, and the top curve applies at 2300 RPM.

Figure 1.14: Power Curve (Various Engine Power Settings)

Point A indicates a 500 fpm descent at 80 knots. Point B indicates level flight at the same airspeed, and point C indicates a 500 fpm climb still at the same airspeed. The rule is simple: if the engine produces more power, the airplane will descend at a lesser rate or even ascend.

Point D corresponds to level flight at 110 knots. The power setting is the same as at point C — but the energy that was being used to purchase altitude (point C) is now being used to pay for the higher drag at the new airspeed (point D). If engine power exactly equals frictional losses, the airplane will stay level — fuel energy is being used to pay for the friction.

The numbers in this example are consistent with a rule of thumb that applies to a wide range of light aircraft: starting from level flight, to set up a 500 fpm descent, This rule works surprisingly well over quite a range of different makes and models. Make a point of learning whatever version of this rule applies to your airplane. It is a big improvement over blindly guessing at throttle settings.

1.3.2   The Effects of the Throttle

I make sure all my students really understand the effects of a power change. In the first or second lesson, we get the airplane trimmed for straight and level flight (using a moderate power setting). We then push the throttle a little more open. The student may be expecting that the airplane will respond by accelerating, just like a car. But airplanes are not the same as cars! In most airplanes (including all the common trainers) the airplane will actually slow down slightly.13 This experiment — observing how power changes affect the trim speed of the airplane — is one of the first things I do not just for students but also for myself when I am learning to fly a new make & model of airplane. (It is also important to learn how flap extension affects the trim speed, and how the flaps and power interact.)

The throttle14 controls power. What could be simpler? The throttle controls power. (Remember, power is energy per unit time.)

There are three things this power could be used for:
  1. Power is needed to overcome drag. Flight at speeds above or below VY requires more power than flight at VY.
  2. Climbing requires more power than level flight, other things being equal.
  3. Acceleration requires more power than unaccelerated flight along the same path.
It may seem obvious that engine thrust ``should'' cause the airplane to accelerate, but usually that's not what happens. Although the airplane is being pulled forward, the trim mechanism notices what is going on and immediately converts the new energy to altitude. Therefore the throttle can be reliably used to control up/down motion. As discussed in chapter 6, this is the normal, natural aerodynamic behavior.

Of course, if you defeat the trim mechanism, all bets are off. For instance: I reiterate that in flight, if you (and the autopilot) leave the yoke and trim alone, opening the throttle just makes the airplane climb. If you want to accelerate or decelerate without an altitude excursion, you will need to adjust the throttle and the yoke, as discussed in section 7.2.

A car, of course, will speed up when you open the throttle. But this has got nothing to do with the behavior of an airplane in flight.

An airplane is not the same as a car. Cars don't have trim. Cars aren't free to move in the third dimension.

Now that we understand the effects of opening the throttle, the effects of closing the throttle should be no surprise. The airplane will maintain its trim speed (or possibly speed up very slightly) and descend. This is easy to understand in terms of energy; compare points B and A in figure 1.14. If engine power is reduced, the only way to pay the rent is to cash in altitude energy at a steady rate.

1.3.3   The Effects of the Yoke

Now let's do a slightly different experiment: pulling on the yoke. As before, start with the airplane nicely trimmed in straight and level flight. Then pull the yoke back a little ways and hold it there. What happens next? Several things will happen, on various time-scales: Let's clarify the long-term behavior by considering two versions of this experiment. In the first version, as illustrated in figure 1.15, the airplane is initially on the front side of the power curve — cruising at 105 knots, which is definitely on the front side of the power curve. Pull back on the yoke a little, and hold it.

Figure 1.15: Pulling on the Yoke — From Cruise

What happens to the airspeed and altitude?17 The first thing that happens is that the airplane slows down from 105 knots to 100 knots. You should think of this as the primary effect of moving the yoke. This is a short-term and long-term effect.

As a consequence of this speed change, the airplane will zoom up about 45 feet, according to the law of the roller coaster: 9 feet per knot, per hundred knots. This is a short-term, one-time effect.

Also, we can see from the power curve that 100 knots is a more-efficient airspeed. Less power will be consumed by drag, so the airplane will ascend. (Remember we've kept the engine power unchanged.) The airplane will continue to climb at a steady rate for a long time.

The short-term altitude change is governed by the law of the roller-coaster, while the long-term altitude change is governed by the power curve.

So far this all seems pretty normal — but the second version of the experiment is much more interesting, as shown in figure 1.16. Let's reconfigure the airplane for flight on the back side of the power curve — say 58 knots. Trim the plane for straight-and-level flight, then pull back on the yoke a little and hold it there.

Figure 1.16: Pulling on the Yoke — From Slow Flight

The first part of the story is the same: you will slow down. Let's say the new speed is 53 knots. As always, you should think of this as the primary effect: if you pull back on the yoke you will slow down.

The second part of the story is also the same: there will be a one-time increase in altitude. This time it will be about 25 feet. The zoom is less than in the previous case, because the initial airspeed was less.

The final part of the story contains the surprise: because the new airspeed represents a higher-drag (less-efficient) point on the power curve, the airplane will enter a steady descent. At the new airspeed, it will descend and descend and descend.

As always, the short-term altitude change is governed by the law of the roller-coaster, while the long-term altitude change is governed by the power curve.

. This scenario (a short-term ascent followed by a long-term descent) is called a zoom.18 It is the bane of student pilots when they start learning to perform landings. Starting from a low airspeed a few feet above the runway, they pull back on the yoke The airplane obediently zooms upward, then (alas) descends at a tremendous rate and makes an airplane-shaped hole in the runway.

Students who have not been taught the distinction between the short-term and long-term effects have a hard time figuring out this situation.

Note: this treacherous behavior (short term ascent followed by long-term descent) does not imply that the airplane is stalled or about to stall. As mentioned in section 1.2.5, the mushing regime is not the same as the stalled regime. In the mushing regime, induced drag is the culprit; stalling is a completely different issue, which is discussed in chapter 5.

Sometimes the mushing regime is called the ``regime of reversed control'', but this is not a very good term. The following table summarizes the actual effects of pulling back on the yoke:

Front-side effect
Mushing effect
Airspeed decrease decrease no
Short-term altitude increase increase no19
Long-term altitude increase decrease yes

By two votes out of three, we conclude that the term ``regime of reversed control'' is not a good description of the mushing regime.20

1.3.4   Sizes of Energy Reservoirs

The following observation may help put into perspective the sizes of the various energy reservoirs. First, consider normal cruising flight: the energy in the fuel tank is enough to ``pay the rent'' (overcome drag) for several hours. Second, consider a power-off glide: starting from a reasonable cruising altitude, altitude energy can be cashed in to pay the rent for several minutes. Finally, consider the flare maneuver: it is possible to arrest a power-off descent and maintain level flight by cashing in airspeed for a few seconds. To summarize:

You can pay for drag by cashing in fuel ... for a few hours.
You can pay for drag by cashing in altitude ... for a few minutes
You can pay for drag by cashing in airspeed ... for a few seconds.

So, we see that the available energy reservoirs have very different sizes.

This difference in sizes has many consequences, but the most important one is this: you cannot make large altitude corrections (only small ones) by borrowing from the airspeed reservoir.

That is, suppose you are a few feet below your desired altitude. The quickest way to get back up is to pull back on the yoke. You thereby cash in some airspeed energy to buy altitude, according to the law of the roller-coaster. On the other hand, if you try to go up some more by pulling back some more, you will very soon run out of airspeed.

The bottom line is: you should feel guilty about borrowing energy from the airspeed reservoir. There just isn't very much energy there to begin with, and letting the airspeed get too low can have serious consequences.

The pros and cons of controlling altitude by borrowing airspeed are discussed in more detail in chapter 7.

1.4   Energy Management Strategy

The next step is to combine what we know about energy and develop general rules for energy management. Let's consider the four situations depicted in figure 1.17.

Figure 1.17: Energy Management — Four Situations

In the figure, as we go from left to right the kinetic energy increases; similarly as we go from bottom to top the potential energy of the situation increases.

Let's start by considering the situation in the upper-left corner: the altitude is a bit high and the airspeed is a bit low. If we're lucky, the total energy might be about right. Therefore, the obvious thing to do is to push on the yoke. That will get rid of some altitude by converting it to airspeed, which is basically what we want.

In the lower-right corner we have the complementary scenario: the altitude is a bit low and the airspeed is a bit high. Once again, if we are lucky the total energy might be about right. Therefore, the obvious thing to do is to pull on the yoke (in moderation). That will convert some of the excess airspeed into altitude, which is basically what we want.

The situation in the upper-right corner is more challenging: both the airspeed and the altitude are too high. Unlike in the previous two scenarios, we clearly have an energy problem: the total energy is too high. There is nothing you can do with the yoke that will make the altitude better without making the airspeed worse,21 and vice versa, so we have to find something else to do. The first step is to retard the throttle, the sooner the better; every bit of power that the engine produces only adds to the energy problem. The other way to get rid of energy is to increase drag. This can be done by extending the landing gear, extending the flaps, slipping, et cetera. Over time, the increased drag will take energy out of the system, which is what you want. If drag is not taking energy out of the system fast enough, you may have to perform a 360 degree turn or something in order to buy some more time.

Finally, let's consider the lower-left corner of figure 1.17. In this case, both the airspeed and the altitude are too low. This is the proverbial coffin corner. You have an energy problem, and having too little energy is even worse than having too much energy. You should open the throttle immediately; this will (over time) convert some fuel energy into new airspeed and/or altitude.

If no power is available, do not try to ``stretch the glide''. There is nothing you can do with the yoke that will add new energy to the system; all you can do is minimize the loss by maintaining the canonical best-glide airspeed. Since you are too slow, push on the yoke to re-establish that airspeed. Since you are too low, choose a closer place to land.

This discussion of how the yoke and the throttle are used together for energy management is continued in chapter 7.

1.5   Summary: Energy Management

Question: What makes the airplane gain altitude? Answer: four things: The most common way of reducing drag is by selecting an airspeed closer to VY. (Of course it also pays to get rid of any extraneous drag, perhaps by retracting the flaps, retracting the landing gear, and/or reducing the amount of slip.)

Suppose you are on final approach for landing. You notice that you are below the glideslope. What should you do? Add power?? Pull back on the yoke?? — This is asking the wrong question. The glideslope indication alone doesn't give you enough information to decide what to do.

You need to perceive the airspeed as well as the height. Think about your energy: potential energy plus kinetic energy. Being low and slow is very different from being low and fast.

Instructors: on final, ask your students ``Are we high or low, fast or slow?'' Make sure they evaluate the energy situation continually and correctly.

Altitude and airspeed tell you your total mechanical energy. In the short run there is nothing that will change the total mechanical energy; all you can do is use the yoke to trade energy back and forth between altitude and airspeed. The conversion factor is nine feet per knot, per hundred knots.

In the long run, the throttle (engine power) and the power curve (drag power) control the rate at which energy is entering and leaving the ``airspeed plus altitude'' system. To establish a long-term climb, add power and/or trim for a speed closer to VY. To overcome drag (in unaccelerated level flight) requires power. To climb (while maintaining constant airspeed) requires added power. To accelerate (while maintaining constant vertical speed) requires added power.

The amount of energy in the airspeed reservoir is very small compared to the energy in the altitude reservoir, which is in turn very small compared to the energy in the fuel reservoir.

If you value your life, look at the airspeed indicator before pulling on the yoke. Looking at just one indicator (altitude or airspeed) for making a decision about just one control (yoke or throttle) is poor pilot technique and could well lead to a stall/spin accident. You must look at both indicators, size up the energy situation, and then decide what to do with both controls.

For instance, solar energy can produce updrafts and windshears. Sometimes the airplane's ability to extract energy from these is important, as discussed in section 7.5.6 and section 16.14.2.
Langewiesche (reference 1) devotes an entire chapter to ``The Law of the Roller Coaster''.
To be exact: Take the initial airspeed and final airspeed and average them.
... that is, g = 9.807 meters per second per second; 1/g = 8.8537 feet per knot, per hundred knots.
The relationship between force and power is discussed in more detail in section 4.4.
As we shall see, it would be more precise to say that the drag depends on angle of attack — but airspeed is often a convenient stand-in for angle of attack, as discussed in section 2.12.
a more precise definition of VY will be given in section 7.5.
Section 5.3 gives a precise definition of stall, and section 5.3.2 explains why the power curve hooks back to the right in the stalled regime.
Section 7.6 explains the slight variations from plane to plane, and how to sketch the power curve for your particular airplane.
The reverse conversion, altitude to airspeed, is equally common but does not have a correspondingly colorful name.
A hammerhead involves flying vertically upward until the airspeed is practically zero, turning 180 degrees around the now-horizontal yaw axis, and then retracing your steps vertically downward.
This is slightly idealized. See section 7.5 for more details.
The rare exceptions are discussed in section 6.1.4.
... in conjunction with the RPM control if you have a propeller governor.
Having a particular pitch attitude is rarely an end in itself. Instead, you should use it as a good means of controlling other things, such as angle of attack; see section 2.6 and section 2.10. Also note that abrupt movement of the yoke will provoke phugoid oscillations, as discussed in section 6.1.12.
The aerodynamics of how the yoke and trim govern airspeed is discussed in chapter 6.
Again, note that discussion of pitch changes is being postponed until section 2.6.
Some older books call it ``ballooning''.
... unless you pull back very, very slowly, in which case the short-term ascent might be masked by the long-term descent.
Similarly, in the mushing regime, other controls (such as the ailerons) become less effective, but they do not reverse.
... in the short run, at least — but see section 7.7.1.

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