--by Juan Merkt, FAA Safety Briefing Guest Writer
“Without concepts there can be no thought, and without analogies there can be no concepts.”
— Douglas Hofstadter and Emmanuel Sander
Whether you realized it or not, the first time you increased back pressure on the elevator as you rotated the nose of your airplane for liftoff and left the ground without assistance from your instructor, you became an energy manager. Managing energy in the form of altitude and airspeed is a required skill for anyone who flies an airplane. Without it, you are more prone to bending one accidentally and even killing yourself in the process.
Learning to manage an airplane’s energy is critical for all new pilots. The Airman Certification Standards, or ACS, requires private pilot-airplane candidates to demonstrate understanding of energy management concepts. To help new pilots understand these concepts and put them into practice, I use an analogy everyone can relate to: money. This analogy is an excellent way to develop the correct mental model of the airplane as an energy system. This mental model will be the foundation to help you master managing your airplane’s energy safely and efficiently.
Manage Your Airplane’s Energy Wisely to Avoid Going Bankrupt
Like money, energy can be earned, spent, saved, withdrawn, and even transferred from one “account” to another. Think of the airplane as the energy bank and the pilot as the owner of the bank accounts. The pilot/owner’s job is to manage energy transactions competently and to avoid becoming energy bankrupt. While running out of money is a bad thing, hitting the ground if you run out of altitude and airspeed energy could easily kill you.
Viewing the Airplane as an Energy System
Pilots control the airplane’s altitude and airspeed by managing its energy state. A flying airplane is an “open” energy system, which means that the airplane can gain energy from some source (e.g., the fuel tanks) and lose energy to the environment (e.g., the surrounding air). It also means that energy can be added to or removed from the airplane’s total mechanical energy — the total amount of energy stored as altitude (potential energy) and airspeed (kinetic energy).
Let’s expand the money analogy to help us understand the airplane as an energy system. An airplane has two savings accounts for storing mechanical energy. One account stores energy as altitude and the other one as airspeed (Figure 1). Once airborne, the airplane earns energy from engine thrust (T), or income. It spends energy on aerodynamic drag (D), which is an expense (Figure 1). The difference between energy earned and spent (T – D) is the net income, which determines whether total mechanical energy — the savings — increases, decreases, or remains the same. At any given time, the energy state of the airplane is determined by the total amount and distribution of energy saved as altitude and airspeed.
When energy income exceeds the amount needed to pay for drag (T – D > 0), the pilot can deposit the surplus energy and save it as increased altitude or airspeed. For example, if the pilot decides to put all the surplus energy into the altitude account, the airplane can climb at a constant airspeed (Figure 2A). But if the pilot opts to place all the surplus energy into the airspeed account, the airplane can accelerate while maintaining altitude (Figure 2B).
When the airplane does not have enough energy income to pay for drag (T – D < 0), then the pilot must dip into the savings accounts. For example, the pilot may choose to let the airplane descend at a constant airspeed (Figure 2C) or slow down while maintaining altitude (Figure 2D) as energy is withdrawn out of one of the savings accounts to help pay for drag. When energy gained equals that spent (T – D = 0), all thrust is spent on drag. Nothing is added or removed from the savings accounts. In this case, the total amount of mechanical energy and its distribution over altitude and airspeed does not change. Both remain constant as the airplane maintains a constant altitude and airspeed (Figure 2E).
Also like money, energy can be transferred from one savings account to the other by exchanging the energy between altitude and airspeed. For example, when you trade airspeed for altitude, you will notice that as altitude increases, airspeed decreases. In other words, when energy is exchanged, altitude and airspeed always change in opposite directions (absent any other energy or control inputs). As one goes up, the other one must come down. Also note that even though the distribution of energy over altitude and airspeed may change dramatically during energy exchange, the total amount of mechanical energy remains the same in the short term (Figure 2F). In the long term, thrust would need to be adjusted to match drag as the latter varies with changes in airspeed.
Like Managing Money, Managing Energy is a Balancing Act
Since the airplane gains energy from engine thrust (T) and loses energy through aerodynamic drag (D), energy flows continuously into and out of the airplane while in flight. Usually measured as specific excess power (Ps), or energy rate of change, the energy flow is a direct function of the difference between thrust and drag (T – D). More importantly, there is a fundamental relationship between changes in the airplane’s total energy resulting from this energy flow on one hand, and changes in the energy stored as altitude and airspeed on the other. This fundamental relationship can be summarized through the airplane’s energy balance equation (Figure 3).
If energy were money, the left side of the energy balance equation would represent the airplane’s “net income,” while the right side would reflect matching changes to the airplane’s “savings accounts” (Figure 3). Thus, the left side controls changes to the airplane’s total energy, while the right side regulates the distribution of the resulting change in energy over altitude and airspeed.
Because energy cannot be created or destroyed, a change in total energy resulting from the difference between thrust and drag (left side) always matches the change in total energy redistributed over altitude and airspeed (right side). Although the energy rate of change varies during flight — becoming positive, negative, or zero — both sides of the equation are inexorably balanced regardless of whether the airplane is accelerating, decelerating, climbing, descending, or maintaining constant altitude and airspeed. (Note: This simplified balance equation does not account for long-term changes in total mechanical energy caused by the reduction in aircraft weight as fuel is gradually burned in flight. Although the effect of weight loss on total energy becomes critical when solving long-term aircraft performance problems of range and endurance, it is negligible when considering short-term flight control problems.)
Of course, the pilot controls the change in total energy on the left side of the equation, as well as the distribution of any changes in energy over altitude and airspeed on the right side. How the pilot coordinates the throttle and elevator to achieve and maintain desired altitude and airspeed targets, as well as avoid energy “crises” and “bankruptcies,” is at the core of energy management and would be a topic for another time.
A FRAME OF REFERENCE FOR MANAGING ENERGY STATE
To manage the airplane’s energy state, we need a frame of reference for tracking altitude and speed that is independent of varying terrain elevation and wind conditions. Luckily, we already have such a reference system. The indicated altitude displayed in the altimeter and its associated potential energy are based on the height of the airplane above a fixed reference point (mean sea level or MSL), not on the height above ground level (AGL), which changes with variations in terrain elevation. Likewise, the indicated airspeed displayed in the airspeed indicator and its associated kinetic energy are based on the speed of the airplane relative to the air, not on the speed relative to the ground below which varies with changes in wind speed and direction. This terrain/wind-independent frame of reference is essential for managing energy state, whether the airplane is maintaining a constant indicated altitude and airspeed, or whether it is climbing, descending, accelerating, or decelerating. Note that changes in indicated altitude and airspeed are attained through forces resulting from the pilot’s direct manipulation of the controls. These “internal” factors determine the airplane’s ability to climb/descend or accelerate/decelerate. In contrast, AGL-altitude and groundspeed are dependent on “external” factors, terrain elevation and wind condition, that change independent of pilot input. Of course, the pilot can manipulate the airplane’s energy in such a way as to minimize any risks associated with terrain or wind. Using the money analogy, you can think of a tailwind as a “dividend” and a headwind as a “tax” on groundspeed. Likewise, you can view descending terrain as a “dividend” and rising terrain as a “tax” on AGL-altitude. For example, the pilot may seek to manipulate energy state so as to maximize the airplane’s energy gains and minimize energy loses when faced, for example, with increasing terrain taxes.
Juan Merkt (merktj@erau.edu) is chair of the department of Aeronautical Science at Embry-Riddle Aeronautical University in Prescott, Ariz., and he is a flight instructor. He developed and teaches a course on “Safety Principles of Aircraft Energy Management” at Embry-Riddle.