PHOTO ILLUSTRATION LEEANN ABRAMS
Estimating
52
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Air Loads Is your airplane strong enough for its intended use? NEAL WILLFORD, EAA 169108
L
ast summer my wife and I went to England for vacation. The long trans-Atlantic flight was a perfect opportunity to read The Spirit of St. Louis. In it, Charles Lindbergh recalled his first flight and the actions of the mechanic preparing the airplane: “Behind every movement, word, and detail, one felt the strength of life, the presence of death. There was a pride in man’s conquest of the air. There was the realization that he took life in hand to fly, that in each bolt and wire and wooden strut death lay imprisoned like the bottle genie—waiting for an angled grain or loosened nut to let it out.” Lindbergh’s observations remind me that each of us play a role in keeping that genie bottled up. Pilots need to approach each flight with seriousness and attention. Builders and mechanics must be thorough and conscientious in their work, and airplane designers must ensure that they offer pilots a design that has the proper strength for the intended aerial mission. For designers, the first step in this process is to estimate the different loads the airplane may experience and then design the structure to safely handle these loads. As with the previous articles, you can download an Excel spreadsheet download from www.eaa.org. Just click on the EAA Sport Aviation cover and scroll down to view the June links. Different Types of Loads During its flying life an airplane will likely experience a variety of loads that are in one of these categories: ■ Air loads ■ Landing or ground loads ■ Miscellaneous loads Air loads are those created by the flying surfaces during flight and will be explained more fully. Landing loads are those caused by less than perfect landings. If the landing gear attaches to the wings, the designer needs to determine if the landing loads impose greater loads than
those caused by the air loads. Miscellaneous loads include those due to the engine, loads on the control system, and those caused by an emergency landing. The last two categories of loads are discussed in detail in References 1 and 2 (see box page 59). Load Factors Centuries ago, Isaac Newton discovered that the forces acting on an object are equal to the mass of the object multiplied by the change in its velocity. This change in velocity
is acceleration, and the most common example is the acceleration due to gravity. We usually don’t notice this acceleration unless we drop something, because we’re used to living in a 1g environment. For example, you’re flying straight and level on a calm morning. In this 1g environment sitting in the pilot’s seat feels no different than your easy chair at home. But if you pull back abruptly on the control stick, the wing would assume a higher angle of attack and you would suddenly feel “heavier.” This is because the wing is creating more lift than it needs to support the airplane, and this excess force results in an added acceleration on the airplane. If this added acceleration is the same as that due to gravity, you would feel twice as heavy and the airplane would be experiencing 2g’s. Pulling the stick back farther would increase the wing’s lift, until it reached the stalling angle of attack. At a given speed, the wing can generate only so many g’s before stalling. Continuing this experiment at increasingly faster speeds would eventually cause the pilot to black out—or the wings to fail. There has to be some practical limit to the g loading an airplane is designed to take without damage. Based on years of experience, the FAA has established these limit load factors (n) for certificated airplanes. Table 1 shows these minimum Sport Aviation
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Normal
Utility
Aerobatic
Sport Pilot?
Max Positive (n1)
3.8
4.4
6.0
4.0
Max Negative (n2)
-1.9
-2.2
-3.0
-2.0
Max Positive
1.9
2.2
3.0
2.0
Max Negative
0.0
0.0
0.0
0.0
Flaps Up
Flaps Down
Table 1. Limit Load Factors load factors, and they should be considered the minimum values for a homebuilt design. The final rules for the sport pilot category have not been released as of this writing, but early indications are that the limit load factors will be the same as published in Reference 1. Positive values
represent maneuvers that try to bend the wings up (and push you into your seat), and the opposite holds for negative values. The wings will flex and the skins may “oilcan” under limit loads, but when the load is removed the structure will not have any permanent damage.
Figure 1. Flight envelope
Figure 2. Wing forces at condition A 54
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For design purposes, it is important to know that the loads in the Table 1 conditions must be multiplied by a safety factor. This safety factor allows for variations in the structural materials or assembly, for uncertainties in stress analysis, and for those pilots who sometimes fly their planes outside the recommended limits. The FAA requires a safety factor of 1.5 for certificated airplanes, but a higher value might be wise if you’re building a composite airplane. Some parts of the airplane require even higher safety factors (such as fittings and hinges), and those factors can be found in Reference 1 (see box page 59). Flight Envelope Figure 1 shows a diagram designers use to describe a new design’s critical flight conditions. Called a V-n diagram, it represents the airplane’s flight envelope. Figure 1 is for a generic fixed-wing light-sport sport aircraft, and for design purposes it’s calculated using the airplane’s maximum gross weight. (For those unfamiliar with it, Reference 3 discusses V-n from a pilot’s perspective.) Each letter shows an airspeed and load factor combination where the air loads must be estimated. Some conditions will lead to higher loads than others. Conditions A and G represent the airplane’s positive and negative maneuvering speeds. Any abrupt changes in pitch above that speed can lead to load factors higher than the limits of the airplane. Conditions C and F are at the max structural cruising speed, the top of the green arc on an airspeed indicator. It is at this speed where the maximum vertical gusts are considered, and why you are advised to fly only in smooth air above this speed. These two conditions may not be critical unless the airplane has a low wing loading and a high cruise speed. In that case, the limit load factor could be noticeably higher to account for severe gusts. Points D and E represent the maxi-
mum dive speed conditions, and if the airplane has flaps, the loads also need to be considered at the maximum speed for deploying the flaps. As a starting point, Reference 2 provides the equations to calculate the airspeed (in knots) for each of the points on the V-n diagram: VFlaps = 11 x n1 x max wing loading VA,G min = 15 x n1 x max wing loading VC,F min = 17 x n1 x max wing loading VD,E min = 24 x n1 x max wing loading
It is important for designers to realize that these equations will give design speeds for an “average” airplane. An airplane with high-lift air-
The wing pressure also varies along the airfoil chord and is usually greater at the leading edge (especially at high angles of attack). foils will have a lower design maneuvering and flaps-down speed. Similarly, the maximum structural cruising and dive speeds may be greater for an airplane with very low drag. Wing Loads We need to estimate the air loads on the wing for each condition in Figure 1. At each condition, the wing will generate a certain amount of lift, drag, and pitching moment. The direction of the lift is always perpendicular to the angle of attack, and drag is always parallel to it. But the wing doesn’t know what the angle of attack is; it just knows that
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it’s being pulled in various directions. Because most wing spars are oriented perpendicular (or normal) to the airfoil chord line, stress engineers convert the lift and drag loads into forces that are parallel and perpendicular to the airfoil chord line. It is the normal loads that largely determine how big the wing spars need to be.
Figure 2 shows the lift and drag forces acting on our example airplane for condition A (which is the high angle of attack case). Each of the forces acts along the aerodynamic center of the wing, which is usually close to the 25 percent chord location. Notice that the chord component is actually pointed forward, even though the drag load is pointed aft. This is because Sport Aviation
55
the lift force is tilted far to the pilot deflecting that enough forward (with aileron down. That was respect to the chord line) probably not on purpose, as to overcome the drag force. he was pulling 9g’s during For condition A, the chord that particular maneuver! load in the forward direcFortunately, researchers tion can be up to 25 perwere eventually able to esticent of the normal load. mate how the air pressure Early airplane designers did distributes itself over the not understand this (they wing. Reference 5 presents were worried more about a “cookbook” method for the drag loads), and there estimating the spanwise lift were some instances where distribution on a wing, and wings failed by folding forReference 6 presents a simward in flight! ple method for estimating Figure 2 also shows the the chordwise lift distribuFigure 3. Pressure distribution during a 9g pullout wing pitching moment. tion. Both of these methods Most wings use airfoils that are incorporated in the have a pitching moment that tries shape and the lift coefficient the air- spreadsheet available at to twist the leading edge down and foil is generating. Early researchers www.eaa.org. the trailing edge up. Lowering the did a lot of wind tunnel and flight Figure 4 shows the estimated flaps or using full aileron deflection testing to understand how the air chordwise pressure distribution for at high speeds aggravates this twist- pressures varied on the wings and our example airplane at the wing ing tendency. These pitching tail for different conditions. root. The pressures vary quite a bit, moments are reacted by the wing skins, but on fabric-covered wings this moment is ultimately reacted by the front and rear spars. This usually increases the load on the rear spar, and consequently, its critical load condition will probably be with down aileron deflection at point C or D. The forces shown on Figure 2 give the big picture of the loads acting on the wing. What it doesn’t show is how the loads are spread over the wing. For example, if your airplane has a wing loading of 10 pounds/feet2, in 1g flight the wing must generate Figure 4. Lift distribution along the wing chord an average lifting pressure of 10 pounds/feet2 to keep the airplane in the air. This pressure is not spread Figure 3 shows the results when depending on the flight condition. out evenly over the wing; it’ll be NACA researchers instrumented a Conditions A and E have the largest higher at the wing root and start military biplane to measure air pres- pressures on the leading edge, so the falling off toward the tip. How fast sures on the wing and tail and put it leading edge ribs would need to be the pressure falls off as you move through the ringer, including an strong enough to handle the loads. outboard depends on the wing abrupt pull-up at high speed The average of the chordwise planform, twist, and the particular (described in Reference 4). You can pressures can also be plotted along flight condition. see how the air pressures are pulling the wingspan. Figure 5 shows this The wing pressure also varies up on the leading edges of the wings for condition A. You can see that along the airfoil chord and is usual- and the horizontal tail. You can also like Figure 3, the pressures fall off ly greater at the leading edge (espe- see that the pressures drop off toward the wingtip. By multiplying cially at high angles of attack). How toward the tips. The second bump the pressures from Figure 5 by a litit varies depends on both the airfoil on the top wing pressure plots is due tle strip of wing area, you will get 56
JUNE 2003
the load in pounds at a particular station. If you start at the wingtip and add up the loads at each wing station as you move inboard, you will get the total amount of shear at that wing station where you stop. Designers use these shear values to size the spar webs. Similarly, if you again start at the wingtip and take the average shear between two wing stations, multiply this by the distance between those stations, and add these up as you move inboard, you will get the bending moment along the wingspan. Figure 6 shows this for condition A. You can see that the bending moment gets very large as you move inboard. This is why the inboard end of a spar for a can-
The designer’s part in keeping the genie bottled up is making sure he has designed an airplane that is structurally safe for its intended role. tilever wing looks so much beefier than the outboard end. If the wing has two spars to handle the bending loads, then the bending moment will be split between the two spars. How much each spar carries depends on the spar locations as well as the flight condition. The air loads on the wing really don’t care whether the wing’s strut is braced or not, but using a strut does significantly affect the size of the wing spar. Figure 6 shows what happens to the bending moment on a strut-braced wing. For the chosen strut location, the maximum bending moment is only 27 percent of what it would be for a cantilever
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wing (where the wing joins the fuselage), and this often leads to a strut-braced wing being lighter weight. If you move the strut location farther outboard, the maximum bending moment will continue to decrease. However, after a certain point, the outboard bending moment, compression load due to the strut, and air loads over the wing inboard of the strut can cause
the moment inboard of the strut to start increasing. Older aircraft stress analysis books show how to analyze this for this condition. Aircraft certification rules in the 1930s did not allow the wing outboard of the struts to be more than 1.75 times the wing chord unless the struts were braced internally to handle the wing torsion. A properly sized metal or plywood-covered Sport Aviation
57
Figure 5. Lift distribution along the wingspan for condition A wing can handle the torsion, and most wings of this type have a greater amount of overhang. Finally, if you are considering a biplane design, you will need to determine how the lift is shared between the two wings before you can calculate the air loads on each. The gap, stagger, angle between the two wings—as well as the wing area of each—all play a role. References 5 and 6 provide the methods for doing this. Tail Loads For each point on Figure 1, the required horizontal tail load to balance out the lift, drag, and thrust is easily calculated. Estimating the tail loads would be easy if these were the only tail loads to be considered. Unfortunately, they aren’t. The reason is that greater tail loads are usually the result of abruptly deflecting the elevator up or down or hitting a gust. This causes the fuselage to pitch up or down at some rate of angular acceleration and the higher the angular acceleration, the higher the resulting tail load when the pilot tries to stop this rotation. This angular acceleration depends on the mass of all the airplane’s different parts and where they are located. 58
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Consequently, trying to calculate all the different possible horizontal tail loads can become a big job. About 50 years ago the CAA (the forerunner to the FAA) realized this and developed a simplified, usually conservative method for estimating the maximum horizontal and vertical tail loads. This is the method presented in Reference 2 and is used in the downloadable spreadsheet. This method is only for conventional (tail behind the wing) configurations.
Unsymmetrical Loads All the conditions we’ve considered so far are for conditions where the ailerons are not deflected. In reality, the ailerons are often deflected during maneuvers (like shown in Figure 3). When deflected, the ailerons increase the twisting moment on one wing panel and decrease it on the other. Depending on the wing configuration and airfoil used, this may be the critical torsion case. Deflecting the ailerons also causes the lift load to be different on each wing. This is due to the down aileron acting like a flap and increasing the lift on that wing panel, and the up aileron decreasing lift on its wing. This unsymmetrical load is hard on the bulkhead or location where the wings attach to the fuselage. These bulkheads experience a loading similar to taking a picture frame in your hands and pushing one side up and pulling the other side down. The horizontal tail can also experience unsymmetrical loads during a slip or spin, and the resulting loads will also try to deform the fuselage bulkheads where they attach. In conclusion, the designer’s part in keeping the genie bottled up is making sure he has designed an airplane that is structurally safe for its intended role. Estimating the air
Figure 6. Wing bending moment comparison
References 1. Design Standards for Advanced Ultra-Light Aeroplanes, DS 10141E, Light Aircraft Manufacturers Association of Canada, 2001. (Note: This is a boiled-down version of the U.S. FAR 23 certification standards and is recommended reading for those considering designing a small airplane. $30 Canadian, plus shipping and handling, from www.bushcaddy.com.) 2. Code of Federal Regulations Airworthiness Standards, Appendix A to Part 23 (Amendment 48), 1996. Website: www1.faa.gov/certification/air craft/
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3. “Maneuvering Diagram,” Kolano, Ed, EAA Sport Aviation, February 2002. 4. NACA TR 364, “The Pressure Distribution Over the Wings and Tail Surfaces of a PW-9 Pursuit Airplane in Flight,” Rhode, Richard, 1930. 5. Civil Aeronautics Manual 04, “Airplane Airworthiness,” 1944. Website: http://specialcollections.tasc.d ot.gov/scripts/ws.dll?login&site= dot_cams 6. Design of Light Aircraft, Hiscocks, Richard. Published by author, 1995. loads the airplane may experience is the first step. Once built, the airplane should be proof loaded to ensure that it will in fact be able to safely handle those loads.
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Using the Spreadsheet There are two spreadsheets on the EAA website’s EAA Sport Aviation page. One is for a stressed skin wing design (where the wing skin resists all the torsion loads). The second
More at www.eaa.org Click on the EAA Sport Aviation magazine cover for more info.
spreadsheet is for fabric-covered wings that have front and rear wing spars. The spreadsheets include graphs so that you can compare the loads for the different conditions. I can’t overemphasize the importance for those interested in designing an airplane to get copies of References 1 and 2 and become familiar with them. Sport Aviation
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