Balancing Act: Managing Aircraft Energy

The airplane is an amazing energy system—continuously transforming, transferring, distributing, storing, and exchanging various forms of energy as it moves through the air. Viewing the airplane as an energy system can enhance our understanding of the role of the flight controls for managing its energy safely and efficiently. Unfortunately, energy principles associated with motion control and performance, though well established in other disciplines, have not found their way into flight education. As a result, energy management skills, founded on those guiding principles, are not adequately taught or evaluated in primary flight training.

Here are four principles not sufficiently covered in flight training: energy coupling between altitude and speed, energy balance, energy-based integration of flight controls, and energy errors.

Energy coupling between altitude and airspeed

Altitude and airspeed, the essential elements of flight, are inescapably linked through the laws of energy conservation and motion. To understand how to control altitude and speed we must first understand their relation to the airplane’s energy. As pilots, we may think we are controlling altitude and speed but in reality we are managing energy. The airplane’s total mechanical energy is the sum of the energy in altitude (potential energy) and speed (kinetic energy). As a result, the airplane’s energy state is defined by the total mechanical energy AND its allocation over altitude and airspeed. Managing the airplane’s energy then boils down to monitoring its energy state and controlling desired changes in: 1) the amount of total mechanical energy and, 2) the distribution of total mechanical energy between altitude and speed.  For example, as the airplane gains or loses total energy through positive or negative excess thrust, the resulting change in total energy must be distributed over altitude and/or airspeed. In addition, trading altitude for speed and vice versa results in energy redistribution and thus a change in energy state even though the airplane’s total energy (at least in the short term) remains the same. Let’s examine the altitude-speed link closer by exploring the principle of energy balance.

The airplane’s energy balance

A flying airplane is an open energy system. That means energy can be added to or removed from the total mechanical energy stored in the airplane. An airplane stores mechanical energy in two forms: altitude and speed. Once airborne, the airplane gains energy from engine thrust (T) and loses energy through aerodynamic drag (D). Consequently, energy flows continuously into and out of the flying airplane. More importantly, there is a fundamental relationship between the net energy flowing through the airplane and changes in the total energy stored in the airplane. This relationship, derived from the law of energy conservation, is the airplane’s energy balance[1]:

Energy Graphic 1

The left side of the equation—a function of the difference between thrust and drag (TD)—controls the net transfer of energy into or out of the airplane; while the right side controls the distribution of the resulting change in total energy between altitude and airspeed. More importantly, any difference between energy gain and loss (on the left side) is automatically matched by an equal change in the airplane’s total energy (on the right side). Thus, even though the left and right sides may change in value, an energy balance is always maintained in steady or non-steady flight. In a perfect balancing act, as the left-hand moves energy into or out of the airplane by the action of two forces (T and D), the right-hand takes the resulting change in total energy and redistributes it over altitude and/or airspeed. For example, when TD is greater than zero, energy flows into the airplane, and that extra energy must be used to gain altitude and/or speed. Simple, right? At this point you may wonder: what controls TD on the left side of the equation, and what controls the distribution of energy between altitude and airspeed on the right side? To answer these questions, we turn to the roles of the throttle and the elevator.

Energy-based integration of the flight controls

The airplane has two primary devices to control altitude and airspeed: the throttle and the elevator. The question is: which device controls altitude and which one controls airspeed? In one of the oldest debates in aviation, some pilots believe that the throttle controls airspeed and the elevator controls altitude, while others subscribe to the opposite view. Which camp is right? As it turns out, neither is right. Because of the inherent energy coupling between altitude and airspeed, any attempt to change one variable (e.g. altitude) with a single control (e.g. elevator) always results in a change in the other variable (e.g. airspeed). Thus, neither the throttle nor elevator controls airspeed and altitude independently. The solution? To effectively change altitude and airspeed, the throttle and the elevator must be coordinated following energy management principles. Both devices are really energy controls—the throttle controlling the airplane’s total energy rate and the elevator controlling the distribution of energy rate between altitude and airspeed. In fact, this energy view of the controls is in tune with the handling techniques of experienced pilots who have learned to integrate the controls effectively to achieve any altitude and speed goals within the airplane’s performance envelope.

A reservoir analogy illustrates the integrated role of the throttle and the elevator in managing the airplane’s energy. As shown in the diagram, the airplane gains energy through thrust (T) and loses energy through drag (D). The net transfer of energy, resulting from the difference between thrust and drag, determines whether the airplane’s total energy—the sum of the energy contained in the altitude and airspeed “reservoirs”—increases, decreases, or remains constant. The throttle acts as a “valve” regulating the net flow of energy into or out of the airplane, while the elevator performs as a “valve” controlling the distribution of this energy flow between altitude and airspeed. In other words, the throttle and elevator control the airplane’s energy balance —with the throttle controlling the “energy transfer” side and the elevator controlling the “energy distribution” side of the equation.

When the throttle increases thrust above drag (TD > 0), more energy flows into the airplane raising its total energy, and when the throttle reduces thrust below drag (TD < 0), more energy flows out decreasing its total energy[2]. Energy Graphic 2This increase or decrease in total energy is distributed by the elevator into or out of the altitude and speed reservoirs. Finally, when the throttle adjusts thrust equal to drag (TD = 0), there is no net energy transfer, but the energy stored as altitude and speed can be exchanged using the elevator while total energy, in the short-term, stays constant. Now that we understand the energy role of the controls, let’s focus on how we can use them to minimize energy errors during flight.

Managing energy errors

When managing the airplane’s energy we are mainly concerned with changes to vertical flight path and airspeed. The need to change flight path and/or speed arises in two situations: when initiating a new maneuver (e.g. entering a climb from straight-and-level) or when correcting deviations from the desired path/speed profile. Here I focus on the latter since most in-flight energy crises start as undetected or ignored deviations from the target flight path or airspeed. For example, being below the glide slope at a slower speed than desired on final is an unsafe deviation requiring prompt flight path and speed correction. Thus, an important aspect of learning to manage the airplane’s energy safely and efficiently is to develop mitigation skills to recognize, correct and prevent energy errors.

Since the airplane’s total energy is distributed over altitude and airspeed, one can distinguish two types of energy state deviations: 1) total-energy errors and 2) energy-distribution errors. In total-energy errors, the airplane has too much or too little total energy. In this type of error, altitude and speed usually deviate in the same direction (e.g., low-and-slow or high-and-fast). In energy-distribution errors, the aircraft may have the proper amount of total energy but its distribution over altitude and speed is incorrect. In this type of error, altitude and speed typically deviate in opposite directions (e.g., high-and-slow or low-and-fast). Just remember, here we are interested in relative deviations—not absolute altitude and speed. According to energy management principles then, total energy errors should be corrected by increasing or decreasing energy using the throttle, while energy distribution errors should be corrected by exchanging energy between altitude and speed using the elevator. For example, when flying an ILS approach, being low and slow is fundamentally different than being high and slow. The airplane is slower than desired in both cases, but the former deviation calls for adding thrust with the throttle to increase total energy (and slight elevator control to ensure the added energy is distributed correctly) while the latter one calls for down elevator to null the energy distribution error. In cases where both total energy and its distribution have deviated, the throttle and elevator must be coordinated to bring the airplane back into its proper energy state. In addition, once energy deviations are corrected, the airplane will need to be trimmed to maintain the desired vertical flight path and airspeed.

To Sum Up…

At its core, managing the airplane’s energy is a “balancing act”; best embodied by the energy balance equation—a fundamental, yet little-known concept. On the surface, the balance equation is a simple equality that applies to any phase of flight—where a change in the amount of energy flowing through the airplane is matched by an identical change in the total energy stored in the airplane. But as we dig deeper into the equation, we discover other “balancing acts.”

On the left side of the equation, a “tug-of-war” between two opposing forces—thrust and drag—determines whether the airplane’s total energy will increase, decrease, or remain constant. On the right side, any resulting change in the airplane’s total energy is reallocated over altitude and/or speed. If energy were cash, the left side would account for changes in the airplane’s “cash flow,” while the right side would reflect matching changes to the balance in the airplane’s altitude and speed  “saving accounts.”

The master performers in the airplane’s energy “balancing act” are, of course, the throttle and the elevator. Desired changes in energy on both sides of the balance equation (e.g. to initiate a new maneuver, or to correct trajectory/speed deviations) require the balanced coordination of the throttle acting on the left side and the elevator acting on the right side. By regulating engine thrust, the throttle controls the net transfer of energy and thus the rate of change of the airplane’s total energy, albeit imperfectly since the throttle cannot regulate aerodynamic drag. The elevator, which per se does not contribute to energy gain or loss, is simply an energy distribution device whose primary role is to correctly allocate changes in total energy between altitude and speed.

The concepts that I describe in this article are the result of the work by many people. Here I would like to acknowledge four of them: Matthijs Amelink, Tony Lambregts, Colin Pennycuick, and Edward Rutowski. Full references to their work and that of others are found in the link below.

Juan Merkt, member of SAFE, is chair of the Aeronautical Science Department at Embry-Riddle Aeronautical University in Prescott, AZ. He has been involved in programs that educate and train professional pilots for 20 years and has served on the board of trustees of the Aviation Accreditation Board International (AABI) since 2001. For more information on energy management, see Merkt’s study “Flight Energy Management Training: Promoting Safety and Efficiency”, published in the Journal of Aviation Technology and Engineering (JATE). The paper can be viewed at http://docs.lib.purdue.edu/jate/vol3/iss1/6. Merkt welcomes comments and feedback at merktj@erau.edu.



[1] The airplane’s energy balance is usually expressed as a rate equation in units of energy/time (power). Note that in the simplified equation depicted here we are not accounting for the change in total mechanical energy caused by the change in aircraft weight as fuel is gradually burned in flight. Although the effect of weight change is negligible when applying the energy approach to solve short-term control problems (as we are doing here), it becomes critical when solving long-term performance problems such as those involving range calculations.

[2] Even though a change in the airplane’s total mechanical energy is a function of both thrust (energy gain) and drag (energy loss), the amount of drag mainly varies due to long-term changes in airspeed or limited deployment of high lift/drag devices that can only increase drag. Therefore, most changes in total energy—demanded by new or corrective maneuvers—are initiated by changing thrust, not drag.

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