5

Aircraft Load

5.1 Overview
Aircraft structures must withstand the imposed load during operations; the extent depends on what is expected from the intended mission role. The bulkiness of the aircraft depends on its structural integrity to withstand the design load level. The heavier the load, the heavier is the structure; hence, the MTOW affecting aircraft performance. Aircraft designers must comply with mandatory certification regulations to meet the minimum safety standards. This book does not address load estimation in detail but rather continues with design information on load experienced by aircraft. Although the information provided herein is not directly used in configuring aircraft, the knowledge and data are essential for understanding design considerations that affect aircraft mass (i.e., weight). Only the loads and associated V-n diagram in symmetrical flight are discussed herein. It is assumed that designers are supplied with aircraft V-n diagrams by the aerodynamics and structures groups. Estimation of load is a specialized subject covered in focused courses and textbooks. However, this chapter does outline the key elements of aircraft loads. Aircraft shaping dictates the pattern of pressure distribution over the wetted surface that directly affects load distribution. Therefore, aircraft loads must be known early enough to make a design “right the first time.”

5.1.1 What Is to Be Learned? This chapter covers the following topics: Section 5.2: Introduction to aircraft load, buffet, and flutter Section 5.3: Flight maneuvers Section 5.4: Aircraft load Section 5.5: Theory and definitions (limit and ultimate load) Section 5.6: Limits (load limit and speed limit) Section 5.7: V-n diagram (the safe flight envelope) Section 5.8: Gust envelope

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5.2 Introduction

139

5.1.2 Coursework Content This chapter provides the basic information required to generate conceptual aircraft configurations. To continue, it is recommended that readers peruse this chapter even though there is no coursework involved yet. The chapter can be skipped if the subject has been learned in other coursework. However, readers should be able to draw schematically a representative V-n diagram of their aircraft (explained in Section 5.8).

5.2 Introduction
Loads are the external forces applied to an aircraft – whether static or dynamic, in flight or on the ground. In-flight loads are due to symmetrical flight, unsymmetrical flight, or atmospheric gusts from any direction; on-ground loads result from ground handling and field performance (e.g., takeoff and landing). Aircraft designers must be aware of aircraft loads given that configurations must be capable of withstanding them. During the design study phase, aerodynamicists compute in-flight aerodynamic loads and relate the information to stress engineers, who ensure structural integrity. Computation of aerodynamic load is involved, currently undertaken using computers. The subject matter concerns interaction between aerodynamics and structural dynamics (i.e., deformation occurring under load), a subject that is classified as aeroelasticity. Even the simplified assumption of an aircraft as an elastic body requires study beyond the scope of this book. Generally, conceptual design addresses rigid aircraft. User specifications define the maneuver types and speeds that influence aircraft weight (i.e., MTOM), which then dictates aircraft-lifting and control surface design. In addition, enough margin must be allocated to cover inadvertent excessive load encountered through pilot induced maneuvers (i.e., inadvertent internal input in excess of the specifications), or sudden severe atmospheric disturbances (i.e., external input), or a combination of the two scenarios. The limits of these inadvertent situations are derived from historical statistical data and pilots must avoid exceeding the margins. To ensure safety, governmental regulatory agencies have intervened with mandatory requirements for structural integrity. Load factor (not to be confused with the passenger load factor, as described in Section 4.4.1) is a term that expresses structural-strength requirements. The structural regulatory requirements are associated with V-n diagrams, which are explained in Section 5.7. Limits of the margins are set by the regulatory agencies. In fact, they not only stipulate the load limits, they also require mandatory strength tests to determine ultimate loads. The ultimate load tests must be completed before the first flight, with the exceptions of homebuilt and experimental categories of aircraft. Civil aircraft designs have conservative limits; there are special considerations for the aerobatic category aircraft. Military aircraft have higher limits for hard maneuvers, and there is no guarantee that under threat, a pilot would be able to adhere to the regulations. Survivability requires widening the design limits and strict maintenance routines to ensure structural integrity. Typical human limits are currently taken at 9 g in sustained maneuvers and can reach 12 g for instantaneous loading. Continuous monitoring of the statistical database retrieved from

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Aircraft Load

aircraft-mounted “black boxes” provides feedback to the next generation of aircraft design or at midlife modifications. A g-meter in the flight deck records the g-force and a second needle remains at the maximum g reached in the sortie. If the prescribed limit is exceeded, then the aircraft must be grounded for a major inspection and repaired, if required. An important aspect of design is to know what could happen at the extreme points of the flight envelope (i.e., the V-n diagram). In the following sections, buffet and flutter are introduced. 5.2.1 Buffet At the initial development phase of stall (or during extreme maneuvers), airflow over the wing becomes unsteady; the separation line over the wing (or over any other lifting surface) keeps fluctuating. This causes the aircraft to shudder and is a warning to the pilot. The aircraft structure is not affected and is not necessarily at its maximum loading. 5.2.2 Flutter This is the vibration of the structure – primarily the wing but also any other component depending on its stiffness. At transonic speed, the load on the aircraft is high while the shock–boundary layer interaction could result in an unsteady flow causing vibration over the wing, for example. The interaction between aerodynamic forces and structural stiffness is the source of flutter. A weak structure enters into flutter; in fact, if it is too weak, flutter could happen at any speed because the deformation would initate the unsteady flow. If it is in resonance, then it could be catastrophic – such failures have occurred. Flutter is an aeroelastic phenomenon.

5.3 Flight Maneuvers
Although throttle-dependent linear acceleration would generate flight load in the direction of the flight path, pilot-induced control maneuvers could generate the extreme flight loads that may be aggravated by inadvertent atmospheric conditions. Aircraft weight is primarily determined by the air load generated by maneuvers in the pitch plane. Therefore, the associated V-n diagram described in Section 5.7 is useful information for proposing candidate aircraft configurations. Section 3.6 describes the six deg of freedom for aircraft motions – three linear and three angular. Given herein are the three Cartesian coordinate planes of interest. 5.3.1 Pitch Plane (X-Z) Maneuver (Elevator/Canard-Induced) The pitch plane is the symmetrical vertical plane (i.e., X-Z plane) in which the elevator/canard-induced motion occurs with angular velocity, q, about the Y-axis, in addition to linear velocities in the X-Z plane. Changes in the pitch angle due to angular velocity q results in changes in CL . The most severe aerodynamic loading occurs in this plane.

5.5 Theory and Definitions

141

5.3.2 Roll Plane (Y-Z) Maneuver (Aileron-Induced) The aileron-induced motion generates the roll maneuver with angular velocity, p, about the X-axis, in addition to velocities in the Y-Z plane. Aircraft structures designed to the pitch-plane loading are the most critical; therefore, roll-plane loading is not discussed herein. 5.3.3 Yaw Plane (Z-X) Maneuver (Rudder-Induced) The rudder-induced motion generates the yaw (coupled with the roll) maneuver with angular velocity, r, about the Z-axis, in addition to linear velocities in the Z-X plane. Aerodynamic loading of an aircraft due to yaw is also necessary for structural design.

5.4 Aircraft Loads
An aircraft is subject to load at any time. The simplest case is an aircraft stationary on the ground experiencing its own weight. Under heavy landing, an aircraft can experience severe loading, and there have been cases of structural collapse. Most of these accidents showed failure of the undercarriage, but breaking of the fuselage also has occurred. In flight, aircraft loading varies with maneuvers and/or when gusts are encountered. Early designs resulted in many structural failures in flight. 5.4.1 On the Ground Loads on the ground are taken up by the undercarriage and then transmitted to the aircraft main structure. Landing-gear loads depend on the specification of Vstall , the maximum allowable sink speed rate at landing, and the MTOM. This is addressed in greater detail in Chapter 7, which discusses undercarriage layout for conceptual study. 5.4.2 In Flight In-flight loading in the pitch plane is the main issue considered in this chapter. The aircraft structure must be strong enough at every point to withstand the pressure field around the aircraft, along with the inertial loads generated by flight maneuvers. The V-n diagram is the standard way to represent the most severe flight loads that occur in the pitch plane (i.e., X-Z plane), which is explained in detail in Section 5.7. The load in other planes is not discussed herein.

5.5 Theory and Definitions
In steady-level flight, an aircraft is in equilibrium; that is, the lift, L, equals the aircraft weight, W, and the thrust, T, equals drag, D. During conceptual design, when generating the preliminary aircraft configuration, it is understood that the wing produces all the lift with a spanwise distribution (see Section 3.14). In equation form, for steady-level flight: L= W and T=D (5.1)

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Aircraft Load

Figure 5.1. Equilibrium flight

5.5.1 Load Factor, n Newton’s law states that change from an equilibrium state requires an additional applied force; this is associated with some form of acceleration, a. When applied in the pitch plane, the force appears as an increment in lift, L, and it would overcome the weight, W, to an increased altitude initiated by rotation of the aircraft (Figure 5.1). From Newton’s law: L = centrifugal acceleration × mass = a × W/g The resultant force equilibrium gives: L+ L = W + a × W/g = W(1 + a/g) (5.3) (5.2)

where L is the steady-state lift equaling weight, W load factor, n, is defined as: n = (1 + a/g) = L/W + L/W = 1 + L/W (5.4)

The load factor, n, indicates the increase in force contributed by the centrifugal acceleration, a. The load factor, n = 2, indicates a twofold increase in weight; that is, a 90-kg person would experience a 180-kg weight. The load factor, n, is loosely termed as the g-load; in this example, it is the 2-g-load. A high g-load damages the human body, with the human limits of the instantaneous g-load higher than for continuous g-loads. For a fighter pilot, the limit (i.e., continuous) is taken as 9 g; for the civil aerobatic category, it is 6 g. Negative g-loads are taken as half of the positive g-loads. Fighter pilots use pressure suits to control blood flow (i.e., delay blood starvation) to the brain to prevent “blackouts.” A more inclined pilot seating position reduces the height of the carotid arteries to the brain, providing an additional margin on the g-load that causes a blackout. Because they are associated with pitch-plane maneuvers, pitch changes are related to changes in the angle of attack, α, and the velocity, V. Hence, there is variation in CL , up to its limit of C Lmax , in both the positive and negative sides of the wing incidence to airflow. The relationship is represented in a V-n diagram, as shown in Figure 5.2. Atmospheric disturbances are natural causes that appear as a gust load from any direction. Aircraft must be designed to withstand this unavoidable situation up to a statistically determined point that would encompass almost all-weather flights except extremely stormy conditions. Based on the sudden excess in loading that can occur, margins are built in, as explained in the next section.

5.6 Limits – Load and Speeds

143

Figure 5.2. Typical V-n diagram showing load and speed limits

5.6 Limits – Load and Speeds
Limit load is defined as the maximum load that an aircraft can be subjected to in its life cycle. Under the limit load, any deformation recovers to its original shape and would not affect structural integrity. Structural performance is defined in terms of stiffness and strength. Stiffness is related to flexibility and deformations and has implications for aeroelasticity and flutter. Strength concerns the loads that an aircraft structure is capable of carrying and is addressed within the context of the V-n diagram. To ensure safety, a margin (factor) of 50% increase (civil aviation) is enforced through regulations as a factor of safety to extend the limit load to the ultimate load. A flight load exceeding the limit load but within the ultimate load should not cause structural failure but could affect integrity with permanent deformation. Aircraft are equipped with g-meters to monitor the load factor – the n for each sortie – and, if exceeded, the airframe must be inspected at prescribed areas and maintained by prescribed schedules that may require replacement of structural components. For example, an aerobatic aircraft with a 6-g-limit load will have an ultimate load of 9 g. If an in-flight load exceeds 6 g (but is below 9 g), the aircraft may experience permanent deformation but should not experience structural failure. Above 9 g, the aircraft would most likely experience structural failure. The factor of safety also covers inconsistencies in material properties and manufacturing deviations. However, aerodynamicists and stress engineers should calculate for load and component dimensions such that their errors do not erode the factor of safety. Geometric margins, for example, should be defined such that they add positively to the factor of safety. ultimate load = factor of safety × limit load For civil aircraft applications, the factor of safety equals 1.5 (FAR 23 and FAR 25, Vol. 3).

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Table 5.1. Typical permissible g-load for civil aircraft
Type FAR 25 Transport aircraft less than 50,000 lb Transport aircraft more than 50,000 lb FAR 23 Aerobatic category (FAR 23 only) Ultimate positive n

Aircraft Load

Ultimate negative n −1 to −2 −1 to −2

3.75 [2.1 + 24,000/(W + 10,000)] Should not exceed 3.8 6

−3

5.6.1 Maximum Limit of Load Factor This is the required maneuver load factor at all speeds up to VC . (The next section defines speed limits.) Maximum elevator deflection at VA and pitch rates from VA to VD also must be considered. Table 5.1 gives the g-limit of various aircraft classes. For military aircraft applications, in general, the factor of safety equals 1.5 but can be modified through negotiation (see Military Specifications MIL-A-8860, MILA-8861, and MIL-A-8870). Typical g-levels for various types of aircraft are shown in Table 5.2. These limits are based on typical human capabilities. 5.6.2 Speed Limits The V-n diagram (see Figure 5.2) described in Section 5.7 uses various speed limits, defined as follows: Stalling speed at normal level flight. Stalling speed at limit load. In a pitch maneuver, an aircraft stalls at a higher speed than the VS . In an accelerated maneuver of pitching up, the angle of attack, α, decreases and therefore stalls at higher speeds. The tighter the maneuver, the higher is the stalling speed until it reaches VA . VB : Stalling speed at maximum gust velocity. It is the design speed for maximum gust intensity VB and is higher than VA . VC : Maximum level speed. VD : Maximum permissible speed (occurs in a dive; also called the placard speed). An aircraft can fly below the stall speed if it is in a maneuver that compensates loss of lift or if the aircraft attitude is below the maximum angle of attack, αmax , for stalling.
Table 5.2. Typical g-load for classes of aircraft
Club flying +4 to −2 Sports aerobatic +6 to −3 Transport 3.8 to −2 Fighter +9 to −4.5 Bomber +3 to −1.5

VS : VA :

5.7 V-n Diagram

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5.7 V-n Diagram
To introduce the V-n diagram, the relationship between load factor, n, and lift coefficient, CL , must be understood. Pitch-plane maneuvers result in the full spectrum of angles of attack at all speeds within the prescribed boundaries of limit loads. Depending on the direction of pitch-control input, at any given aircraft speed, positive or negative angles of attack may result. The control input would reach either the CLmax or the maximum load factor n, whichever is the lower of the two. The higher the speed, the greater is the load factor, n. Compressibility has an effect on the V-n diagram. In principle, it may be necessary to construct several V-n diagrams representing different altitudes. This chapter explains only the role of the V-n diagram in aircraft design. Figure 5.2 represents a typical V-n diagram showing varying speeds within the specified structural load limits. The figure illustrates the variation in load factor with airspeed for maneuvers. Some points in a V-n diagram are of minor interest to configuration studies – for example, at the point V = 0 and n = 0 (e.g., at the top of the vertical ascent just before the tail slide can occur). The points of interest are explained in the remainder of this section. Inadvertent situations may take aircraft from within the limit-load boundaries to conditions of ultimate-load boundaries (see Figure 5.2). 5.7.1 Low-Speed Limit At low speeds, the maximum load factor is constrained by the aircraft maximum CL . The low-speed limit in a V-n diagram is established at the velocity at which the aircraft stalls in an acceleration flight load of n until it reaches the limit-load factor. At higher speeds, the maneuver-load factor may be restricted to the limitload factor, as specified by the regulatory agencies. Let VS1 be the stalling speed at 1 g. Then:
2 VS1 =

1 0.5ρCLmax

W S

or

2 L = W = (0.5ρ Vs1 S)CLmax

Let VSn be the stalling speed at ng, where n is a number. Then:
2 nW = 0.5ρ Vsn S CLmax

Using Equations 5.1 and 5.2,
2 2 n × 0.5ρ Vs1 S CLmax = 0.5ρ Vsn S CLmax

or
2 2 n = VSn /VS1 = 2 (0.5ρ CLmax )Vsn until n reaches the limit-load factor (W/S)

(5.5)

VA is the speed at which the positive-stall and maximum-load factor limits are simul√ taneously satisfied (i.e., VA = VS1 nlimit ). The negative side of the boundary can be estimated similarly.

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Aircraft Load

Figure 5.3. Aircraft angles of attack in pitch-plane maneuvers

5.7.2 High-Speed Limit VD is equal to the maximum design speed. It is limited by the maximum dynamic pressure that an airframe can withstand. At high altitude, VD may be limited by the onset of high-speed flutter. 5.7.3 Extreme Points of a V-n Diagram The corner points of the flight envelope (see Figure 5.2) is of interest for stress engineers. Enhancing structures would establish aircraft weight that must be predicted at the conceptual design phase. Figure 5.3 shows various attitudes in pitch-plane maneuvers associated with the V-n diagram, each of which is explained herein. The maneuver is a transient situation, and the various positions shown in Figure 5.3 can occur under more than one scenario. Only the attitudes associated with the predominant cases in pitch-plane maneuvers are addressed below. Negative g is when the maneuver force is directed in the opposite direction toward the pilot’s head, irrespective of his or her orientation relative to the Earth.
Positive Loads This is when an aircraft (and its occupants) experiences a force more than its normal weight. An aircraft stalls at a maneuver reaching αmax ; following are the various scenarios. In level flight at 1 g, the aircraft angle of attack, α, increases with slowing down of speed and reaches its maximum value, αmax , at which the aircraft would stall at a speed VS .

1. Positive High Angle of Attack (+PHA). This occurs during a pull-up maneuver that raises the aircraft nose in a high pulling g-force, reaching the limit. The aircraft could stall if it is pulled harder. At the limit load of n, the aircraft reaches +PHA at aircraft speeds of VA . 2. Positive Intermediate Angle of Attack (+PIA). This occurs at a high-speed level flight when control is actuated to set the wing incidence at an angle of attack. The aircraft has a maximum operating speed limit of VC when +PIA reaches the maximum limit load of n, in maneuver; it is now in transition. 3. Positive Low Angle of Attack (+PLA). This occurs when an aircraft gains the maximum allowable speed, sometimes in a shallow dive (dive speed, VD ). Then, at a very small elevator pull (i.e., low angle of attack), the aircraft would hit the maximum limit load of n. Some high-powered military aircraft can reach VD during level flight. The higher the speed, the lower is the angle of attack, α, to reach the limit load – at the highest speed, it would be +PLA.
Negative Loads This is when an aircraft (and its occupants) experiences a force less than its weight. In an extreme maneuver in “bunt” (i.e., developing – negative g in a nose-down

5.8 Gust Envelope

147

(a) Gust boundary crossing limit-load

(b) Finished V-n diagram

Figure 5.4. Example of a V-n diagram with a gust envelope (FAR/JAR 25)

curved trajectory), the centrifugal force pointing away from the center of the Earth can cancel the weight when the pilot feels weightless during the maneuver. The corner points follow the same logic of the positive load description except that the limit load of n is on the negative side, which is lower because it is not in the normal flight regime. It can occur in an aerobatic flight, in combat, or in an inadvertent situation caused by atmospheric gusts. 1. Negative High Angle of Attack (–NHA). This is the inverted scenario of +PHA explained previously. With –g, the aircraft must be in a maneuver. 2. Negative Intermediate Angle of Attack (–NIA). In +PLA, the possibility of – ve α was mentioned when the elevator is pushed down, called the “bunting” maneuver. Negative α classically occurs at inverted flight at the highest design speed, VC (coinciding with the PIA). When it reaches the maximum negative limit load of n, the aircraft takes the NIA. 3. Negative Low Angle of Attack (–NLA). At VD , an aircraft should not exceed zero g.

5.8 Gust Envelope
Encountering unpredictable atmospheric disturbance is unavoidable. Weather warnings are helpful but full avoidance is not possible. A gust can hit an aircraft from any angle and the gust envelope is shown in a separate set of diagrams. The most serious type is a vertical gust (see Figure 5.1), which affects load factor n. The vertical gust increases the angle of attack, α, developing L. Regulatory agencies have specified vertical gust rates that must be superimposed on the V-n diagrams to describe the operation limits. It is common practice to combine the maneuver and gust envelope in one diagram, as shown in Figure 5.4. The FAR provides a detailed description of required gust loads. To stay within the ultimate load, the limits of vertical gust speeds are reduced with increases in aircraft speed. Pilots should fly at a lower speed if high turbulence is encountered. The gust envelope crosses the limit load and its boundary varies with increases in speed. Equation 5.5 shows that

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Table 5.3. FAR-specified gust velocity
Altitudes 20,000 ft and below VB (rough air gust) VC (gust at max design speed) VD (gust at max dive speed) 66 ft/s 50 ft/s 25 ft/s

Aircraft Load

Altitudes 50,000 ft and above 38 ft/s 25 ft/s 12.5 ft/s

aircraft with low wing-loading (W/SW ) and flying at high speed are affected more by gust load. VB is the design speed for maximum gust intensity. This definition assumes that the aircraft is in steady-level flight at speed VB when it enters an idealized upward gust of air, which instantaneously increases the aircraft angle of attack and, hence, the load factor. The increase in the angle of attack must not stall the aircraft – that is, take it beyond the positive or negative stall boundaries. From statistical observations, the regulatory agencies have established the maximum gust load at 66 ft/s. Except for extreme weather conditions, this gust limit is essentially all-weather flying. In a gust, the aircraft load may cross the limit load but it must not exceed the ultimate load, as shown in Figure 5.4. If an aircraft crossed the limit load, then an appropriate action through inspection is taken. Table 5.3 outlines the construction of a V-n diagram superimposed with a gust load. Flight speed, VB , is determined by the gust loads and can be summarized as shown in the table. Linear interpolation is used to obtain appropriate velocities between 20,000 and 50,000 ft. The construction of V-n diagrams is relatively easy using aircraft specifications, in which the corner points of V-n diagrams are specified. Computations to superimpose gust lines are more complex, for which FAR has provided the semiempirical relations. Vertical-gust velocity, Ug , on forward velocity, V, would result in an increase of the angle of attack, α = Ug /V, that would generate an increase in load factor n = (CLα Ug /V)/(W/S). Airspeed V is varied to obtain n versus speed. DATCOM and ESDU provide the expressions needed to obtain CLα . A typical V-n diagram with gust speeds intersecting the lines is illustrated in Figures 5.2 and 5.4. VC is the design cruise speed. For transport aircraft, the VC must not be less than VB + 43 knots. The JARs contain more precise definitions as well as definitions for several other speeds. In civil aviation, the maximum maneuver load factor is typically + 2.5 for aircraft weighing less than 50,000 lbs. The appropriate expression to calculate the load factor is as follows: n = 2.1 + 24,000/(W + 10,000) up to a maximum of 3.8 (5.6)

This is the required maneuver-load factor at all speeds up to VC , unless the maximum achievable load factor is limited by a stall. Within the limit load, the negative value of n is –1.0 at speeds up to VC , decreasing linearly to 0 at VD . The maximum elevator deflection at VA and pitch rates from VA to VD also must be considered.