Pilot Training - Theory of Flightt: Dynamic Loads

45. Loads and load factors.-a. The basic load is the load on a structural member or part in any condition of static equilibrium of an airplane. It is the load due to the weight of the airplane in unaccelerated flight.

b. In accelerated flight, for each type of airplane, experience has indicated that the structure will be subjected to a load not in excess of a maximum probable load, also called maximum applied load. The limitations of the maximum applied load may be due to inherent flight characteristics of the airplane or may be due to prohibition of certain maneuvers in flight with the specific object of holding the maximum applied load to low limits. This ratio of the maximum applied load to the basic load is the applied load factor.

c. The necessity of keeping structural weight to a minimum requires the very close design of airplane parts and the elimination of all unnecessary material. To keep structural weight to a minimum, the parts are therefore designed to fail at an ultimate load which is customarily fixed at approximately 1.5 times the maximum applied load. The ratio of the ultimate load to the maximum applied load (usually about 1.5) is the factor of safety. This term as applied to airplane structures is not used in the same sense as used by the civil engineer in the design of bridges and similar structures, and its use in aeronautics results in much confusion and ambiguity.

d. The ratio of the ultimate load to the basic load is the design load factor. Since structural failure of aircraft is extremely hazardous to personnel and materiel, the design load factor must be large enough to eliminate structural failure if the airplane is flown within the limitations as to maneuvering placed on it by the regulations. Every case of structural failure is investigated, and where

repeated failure occurs during normal flying operations a revision in design load factors for subsequent types is in order.

146. Dynamic loads.-a. In flight, the dynamic loads which the wings carry depend upon accelerations which throw the airplane from its normal flight path. These accelerations may be due to sudden changes in air currents or to manipulation of the controls of

the aircraft. Since acceleration is rate of change of velocity with time, very rapid changes result in large accelerations and large dynamic loads. Thus if a pilot pulls back on the control stick suddenly, the dynamic load imposed on the airplane will be greater than if he pulls back slowly. The pilot who performs maneuvers smoothly will stress the airplane structure less than the pilot who is addicted to rough erratic maneuvers. Similarly large aircraft which maneuver slowly and for which loops, spins, rolls, and vertical dives are prohibited are subjected to lower dynamic loads than are small highly maneuverable aircraft designed for combat operations.

b. An accelerometer is an instrument which may be installed in an airplane for the purpose of recording the accelerations and hence the dynamic loads which occur in flight. The instrument is calibrated to read dynamic load factors, the dynamic load factor being unity in steady level flight. A form of accelerometer called the V-G recorder has been developed for the purpose of recording the maximum dynamic loads occurring on an airplane during the period of installation of the instrument. From this data a knowledge of proper load factors for future design may be obtained. The instrument also betrays the pilot who is inclined to perform prohibited maneuvers when unobserved.

147. Curvilinear flight;-In curvilinear motion the centrifugal force in pounds is

where   

W= the, weight of the airplane in pounds

g = the acceleration of gravity

V=velocity of the airplane in ft./sec.

r= radius of curvature of the flight path in feet.

The centrifugal force is usually expressed as so many times the weight of the airplane. The greater the speed and the shorter the radius r the greater the centrifugal force.

In a perfectly executed turn, the angle of bank must be such that the vertical component of lift will equal the weight, and the horizontal component of lift will equal the centrifugal force. The sharper the turn the steeper the bank and the greater the dynamic load supported by the wings. The conditions for equilibrium are:

148. Accelerations due to sudden change in angle of attack.-When an airplane encounters a gust, the vertical component of the gust produces a sudden change in angle of attack. Should the change occur so that the angle of attack of maximum lift is suddenly reached, the forces acting on the wings will be

where V is the original speed of flight.

When in steady flight at maximum C_L

Dividing equation 93 by equation 94

The ratio F/V is the dynamic load factor in terms of g, and it will be observed the higher the velocity of flight V the greater are the possible dynamic loads due to gusts.

Rapid changes in angle of attack may be also secured by sudden movement of the elevator control. The dynamic loads produced are of the same nature as those resulting from the action of gusts in changing angle of attack. The maximum accelerations are the result of a sudden pull up from a steep dive. Theoretically, the maximum possible dynamic load factor is the ratio , where V_T is terminal velocity in a dive and V_min the speed of flight at C_Lmax (landing speed).

Actually, the theoretical maximum dynamic loads are never attained. Gusts do not develop instantaneously and the pull up from a dive occurs over an interval of time such that the velocity of flight has dropped before the angle of attack of C_Lmax can be reached.

The probable loads due to gusts and the gust load factors for design purposes are based on the assumption of a, sharp-edged gust with an intensity of 30 feet per second acting in either direction normal to the flight path and at all velocities up to the maximum permissible diving speed. The structural failures that have resulted during flight in the turbulent air conditions of violent thunderstorms indicate that the gusts encountered in such meteorological conditions may impose greater loads on the aircraft structure than can be accounted for by the assumed 30 feet per second gust.

The ratio of the maximum speed in horizontal flight to the miniIlium speed (landing speed) is defined as the speed range. The square of the speed range is the theoretical maximum dynamic load at the maximum speed of flight. Airplanes with high parasite resistance and low speed range therefore are subjected to lower dynamic load factors than airplanes of clean design with low parasite resistance and high speed range.

The load factors imposed during maneuvers (maneuver load factors) are proportional to the square of the speed at the start of the maneuver (equation 95) where the angle of attack of maximum lift is reached instantaneously. Only in small highly maneuverable airplanes of the pursuit type is it possible to impose approximately the theoretical maximum load in a maneuver. Figure 115 shows the loads resulting from the rapid pull up from a dive of a pursuit airplane at various airspeeds.

In all airplanes other than the pursuit type, the magnitude of the control forces required and the slower maneuverability characteristics combine to increase the spread between the actual maneuver load factors and those theoretically possible.

149. Aerodynamic loads.-a. Generally speaking, there are two ways in which a pilot may increase the applied aerodynamic loads on an airplane in flight:

(1) By increasing angle of attack without change in airspeed. In this maneuver, the most significant change of applied load is an increase in the component of total wing force acting normal to the axis of the airplane, and the effect of this increase in normal force is to produce an acceleration of the airplane in the normal direction. This normal acceleration is usually expressed as a ratio to the acceleration of gravity.

(2) By increasing airspeed.-The second determinant of applied load, airspeed, produces simultaneous change in both the lift and the drag forces. If, as is the usual case, an airplane is maneuvered so as to experience the change in airspeed with negligible change in applied normal force, the applied drag load still is subject to variation as the airspeed is altered. But there are other consequences of airspeed change which are of even greater importance than drag forces, and these less obvious effects are caused not so much by change in the magnitude of the applied loads as by shift in their distribution over the airplane. Thus, although a steady high speed glide or dive is characterized by a small resultant applied normal force, the wing torsion, the tail load, and the resultant bending moment and shear carried by the fuselage reach exceedingly large values in this maneuver. Normal acceleration and indicated airspeed are the two fundamental criteria which determine the external loads applied to the primary structure of any given airplane in flight. The limitation of normal acceleration (load factor) and airspeed which the airplane should be capable of withstanding without permanent deformation of any structural member are prescribed as a preliminary to the design of every new airplane.

b. Obviously, the selection of load factors as well as maximum permissible diving speed depend upon the type of service for which the airplane is intended. The positive and negative applied load factors and the maximum diving speeds of the various types of Air Corps airplanes are designed so that no structural part is stressed beyond the point where permanent deformation will occur. The design load factors are 50 percent greater than the maneuver load factors and represent the point at which total failure of the structure may be expected to occur.

150. V-G diagram.-a. The limiting load factors and diving speeds are very conveniently shown on the graphical chart known a, a V-G (velocity-acceleration) diagram, a typical one of which is presented in figure 116. Taking the type BT "basic training" airplane as the example, the positive and negative maneuver load factors of plus 5.67 and minus 2.33 are represented by the lines AB and DC. These maneuver load factor lines are drawn horizontally because it is an Air Corps requirement that all airplanes be able to sustain the same given maximum value of applied load factor throughout the permissible range of airspeed. The high speed of the BT in level flight is 174 miles per hour and is identified on this diagram by the dashed line, HH. The maximum permissible diving speed for this airplane is 130 percent of 174, or 226 miles per hour, and is represented by the line BC in figure 116. The curved lines OA and OD are based upon aerodynamic rather than structural considerations, and they define the maximum positive and negative accelerations which it is possible to attain at various speeds with the fully loaded BT operating at its maximum positive and negative lift coefficients, respectively. Thus point A occurs at the lowest value of indicated airspeed at which it is theoretically possible to reach the maximum allowable positive load factor of 5.67; and, similarly, point D marks the airspeed below which the maximum negative load factor of minus 2.33 cannot be reached.

b. The closed boundary OABCDO has been drawn in such a manner as to include the full range of airspeed and applied load factor which the Air Corps requires that this airplane be capable of withstanding with complete safety. But, before these limiting flight conditions can be approved as a basis for structural design, it is necessary to determine whether or not the airplane would be in danger of experiencing an excessive acceleration if flown at high speed in a region of gusty or "bumpy" air.

c. Assuming that the maximum gust velocities encountered in flight are 30 feet per second, it may be shown that for horizontal flight

and for the vertical dive

Where n =normal acceleration in g units (load factor) m=slope of the airplane normal force coefficient vs.. angle of attack curve in absolute units per degree. V =calibrated airspeed in miles per hour. W= airplane gross weight in pounds. S= wing area in square feet.

The equation 96, plotted for the BT, is shown by the lines KP and KQ in figure 116, and equation 97 is expressed by lines OM and ON.

d. It will be noted that the first mentioned gust lines, KP and KQ most nearly represent the conditions which prevail in steady flight

at speeds up to and including the high speed for level flight. The lines ON and ON have no real significance except at the terminal velocity which is the only steady flight condition attainable in the vertical attitude. Between level flight at high speed and the terminal velocities, it is assumed arbitrarily that the attitude of the airplane changes from horizontal to vertical in a manner such that the applied gust load factors over this range in speed can be expressed by the straight lines PH and QN. The maximum applied gust load factors through the entire speed range of the BT airplane are represented by the lines KPN for positive gusts and by the lines KQM for negative gusts.

e. Inspection of the V-G diagram shows that, within the permissible range of airspeed for this airplane, all positive and negative gust load factors are within the corresponding maximum safe limits of plus 5.67 and minus 2.33. Therefore, the gusts are not critical for this airplane and no account need be taken of them in designing the structure for the full-loaded gross weight condition. From equation 96 it is evident that the increment of load factor due to a vertical gust of given velocity is inversely proportional to the wing loading at the time of encountering the gust, and this fact indicates that an airplane lightly loaded is subjected to greater gust acceleration than when at normal gross weight. These latter comments are presented merely to show that certain structural parts of an airplane, particularly motor mounts and other members which carry loads that are independent of the airplane gross weight, may be overstressed by excessive gust accelerations due to abnormally low gross weight.

f. Evidently the limiting accelerations and airspeed represented in figure 116 by lines AB, DC, and BC are at once the minimum values for design purposes and the maximum safe limits to be attained in flight. Thus, it is the designer's responsibility to make the BT airplane capable of withstanding all applied loads represented by the V-G points included in the configuration OABCDO in figure 116, but he is under no obligation to provide greater strength than this because to do so would require an unnecessarily heavy structure.

g. The essential features of the V-G diagram are reproduced in slightly different form on the operating chart in figure 117, which is issued for the information of all personnel flying airplanes of the BT series. For simplicity of application, airspeeds specified in figure 117 are "airspeed indicator reading" and an airspeed calibration curve for the BT airplane is presented in order that indicator readings may be converted to calibrated airspeed if desired. A diagram of this kind may be prepared for each new type of airplane. It will be noted that the permissible high speed given in figure 117 is somewhat lower than the corresponding value which appears on the V-G diagram of figure 116, and this added margin of safety is provided to allow for calibration differences.

h. In certain instances it becomes necessary in view of demonstrated structural deficiencies, to issue special flight restrictions. Such action is not taken unless clearly warranted, and it is of the utmost importance that all special restrictions of this kind be carefully observed.

151. V-G Recorder.-The V-G recorder developed by the N. A. C. A. records on the smoked surface of a small glass plate variations of airspeed and of normal acceleration. The airspeed is recorded as the abscissa and the load factor as the ordinate, so that each point on the smoked glass record corresponds to a similar point on a V-G diagram such as that in figure 116. The plot of the peak readings from a large number of V-G records obtained from instruments installed in BT airplanes is shown in figure 118.

a. For several years the Air Corps, with the full cooperation of the National Advisory Committee for Aeronautics, has used the N. A. C. A. V-G recorder in a study of velocity-acceleration conditions imposed upon service airplanes of various types, and this investigation has been expanded to the extent that there now are about 80 of these instruments in use at principal Air Corps stations throughout the United States. Ordinarily, the recorders are assigned to representative airplanes of the newer types. Record glasses, changed at monthly intervals, are forwarded to the Materiel Division for evaluation and compilation of results. Altogether, more than 1,300 of these records, covering over 46,000 flight hours and representing every type of airplane, have been obtained.

b. The maximum values of speeds and the acceleration are plotted on charts similar to that in figure 118, which affords a convenient representation of the data according to airplane type. Any excess of airspeed or acceleration is readily apparent from these charts and each such case is brought to the attention of the proper authorities. Over a period of the past 2 years a study of the results obtained from the records of the V-G recorder indicate that very rarely are excessive load factors imposed, but that very frequently permissible diving speeds are exceeded. Every pilot should realize that modern aircraft of clean design attain high diving speeds very quickly and that when the diving speed exceeds the permissible safe limit, the risk of dangerous structural failure is very great.