Airplane Design 101: Part 3 - Size

Good handling qualities throughout the whole flight regime. ... As you do this, the airplane will start slowing down and climbing. In a stable airplane, when you release the ... stick-free static margin. The major ..... To download Cirrus DUATS from the World Wide Web, visit us at ... five-place homebuilt to carry his wife and three ...
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Suggested Lower Limit Suggested Upper Limit

Balancing Act NEAL WILLFORD, EAA 169108

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n the previous two articles in this series we've looked at estimating performance, estimating weights, and locating the center of gravity (CG) for a new airplane design. In this final article we'll size the horizontal tail to meet the desired CG range. We'll also size the vertical tail and ailerons and estimate the required dihedral.

much research has been done that makes this job a lot easier. The latest version of the spreadsheet (available by clicking the EAA Sport Aviation cover on the EAA website at www.eaa.org) will handle the math and make the process pretty painless. An airplane is considered stable in pitch when it tries to return to the trimmed airspeed. Say you're flying at some trimmed airspeed and then slowly pull back on the stick. As you Have you ever thought about some of the do this, the airplane will start slowing down most important factors in an airplane design? and climbing. In a stable airplane, when you Some that come to mind for me are: release the stick the nose will drop and then • Structural integrity. bobble up and down as it accelerates back to • Well-designed systems with an attention the trim airspeed. Likewise, if you push the to safety. stick forward and then release it, the nose will • Good handling qualities throughout the pitch up and again bob up and down as it setwhole flight regime. tles back on the trim airspeed. The first two items are usually transparent to It would take more force to either pull or pilots. We expect the airplanes we fly to be push the stick if the airplane's CG was at its forstrong enough to handle the loads they were ward position. If you kept moving the CG aft designed to take. We also expect airplane sysand tried the push/pull experiment, you would tems to work well and not cause a major hazeventually reach a CG position where the airard if they fail. plane would not attempt to return to its trim The third item, however, is obvious to pilots. airspeed when you let go of the stick. Instead it Whatever the flap setting, we expect the air- would want to stay at whatever the airspeed planes we fly to have enough elevator control was when you let go of the stick. In this case power to hold the nose up during landing at a the CG is at the airplane's neutral point for the forward CG position. We also expect our airgiven flight conditions. planes to have adequate stability at aft CG posiThis neutral point is not a CG location at tions and at various speeds and power settings. which most pilots will want to fly. When the When working on a new design, the airCG is ahead of this point, the airplane has a plane designer needs to consider these things positive static margin, which is presented in when sizing the horizontal tail. Fortunately, terms of the mean aerodynamic chord (MAC). Sport Aviation

57

For example, if an airplane has a MAC of 50 inches and a static margin of 5 percent MAC, this means that the CG is .05 times 50 inches, or 2.5 inches ahead of the neutral point. Actually, we'll discuss two types of static margin: stick fixed and stick free. Stick-fixed static margin is the measure of stability when flying with the control stick held firmly in place. Stick free represents the stability when flying an airplane trimmed to fly handsoff. The amount of force and the proper direction of that force (push to speed up, pull to slow down) required to move the airplane off trim speed are an indication of an airplane's stick-free static margin. The major players that determine an airplane's static margin are the wing, fuselage, power, and tail. Each has a positive or negative contribution to the static margin, and their sum tells us whether an airplane has a positive static margin. Wing Contribution

The wing's contribution to the airplane's static margin depends on the locations along the MAC of the aerodynamic center of the airfoil and the horizontal and vertical locations of the CG. The airfoil's aerodynamic center is the point on the airfoil where the pitching moment is essentially constant as the angle of attack changes. Wind tunnel data many times has this location identified for a given airfoil, and it's usually between 24 percent and 26 percent MAC.

The horizontal CG location has the biggest effect on the static margin and will increase it when the CG is ahead of the aerodynamic center of the air58

APRIL 2002

foil. As the horizontal CG location moves aft of the airfoil aerodynamic center, the static margin is reduced. The CG's vertical location with respect to the MAC has a lesser, but still important, effect. References 1 and 2 discuss this in more detail, and from Reference 2 you can approximate this effect with Formula 1. When the CG is below the MAC (as in a high-wing airplane), the distance is negative, and this will help increase the static margin. Conversely, the vertical distance is positive in a low-wing airplane, and that reduces the static margin. If you're designing a b i p l a n e , Reference 3 shows how to calculate the MAC'S location, and the vertical CG and the MAC may be fairly close to each other. The vertical CG contribution also depends on the airplane's lift coefficient (CL). The lift coefficient at sea level can be determined using Formula 2. Looking at this equation you can see that CL depends on the wing loading and the square of the airspeed. At higher airspeeds CL will be

A younger author trying to pick the right tail for his airplane.

lot will feel this with either increasing or decreasing stick

forces, respectively. Fuselage Contribution

When you look at the planview (top down) of a conventional airplane, notice that a certain amount of the fuselage sticks out ahead of the wing. Formula 1

Vertical CG Contribution =

lower and, consequently, will have a smaller effect on the vertical CG's contribution to the static margin. At higher lift coefficients (like in climb or in a gliding descent) it will become more of a factor. This means that compared to the static margin at top speed or cruise, a highwing airplane's static margin will improve as it slows down, whereas a low-wing's static margin will decrease. The pi-

-0.3 x CL x Vertical distance to CG

The length and width of this in relation to the rest of the fuselage will determine how much the fuselage will affect the airplane's static margin. A wider fuselage w i l l be more destabilizing than a narrow one for a given length of fuselage ahead of the wing. Reference 4 provides a good curve to estimate the fuselage effects for "regular" looking fuselages, and that's what I put in the latest version of the

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far generally reduce the airplane's static margin. The horizontal tail needs to be big enough to overcome all the negative effects on stability caused by these items and provide enough additional stability to achieve the desired positive static m a r g i n . For a conventional layout (the tail behind the wing), the amount of stability that the tail adds to - Horizontal Tail the airplane depends on these -Wing factors: • Lift slope of the wing and tail 3 4 5 6 7 8 10 • Tail volume coefficient Aspect Ratio • Rate of change of the downwash at the tail • Dynamic pressure at the Rgure 1. Comparison of lift slopes for wing and horizontal tail tail spreadsheet. gle to the thrust line. It's called • Size of the elevator The lift slope of a wing or the "propeller normal force," Power Effects and it acts like a little tail sur- tail is the change in lift coeffiThe propeller's effect on the face. When the propeller is cient it will experience for a 1static margin depends on the ahead of the wing, it acts like a degree change in angle of atvertical location of the thrust canard, which is destabilizing. tack. It's mostly a function of line with respect to the CG poOn the other hand, when the surface's aspect ratio, and sition and whether the pro- an airplane has a pusher pro- Figure 1 shows how the lift peller is located ahead of the peller it acts like an additional slope varies (based on inforCG. During powered flight the horizontal tail and increases mation in References 2 and 5). propeller can improve the stability. This effect is there As far as stability is concerned, static margin if the thrust line even at idle power with a it's the ratio of the wing and passes above the CG location. windmilling propeller. That is tail lift slopes that matter. The wing's aspect ratio deFormula 2 pends on the wing area and span chosen to meet the deWeight x 295 sired performance conditions, Wing area x (airspeed in knots)2 as discussed in Part 1. The horizontal tail aspect ratio is usuThis is true of most low-wing why it is important to check ally between 3.5 and 6 and airplanes. On high-wing air- the static margin when the should be at least 50 percent planes the CG location is prop is windmilling during a of the wing's aspect ratio, or higher because of the wing lo- glide (like on approach). This higher if possible. cation, and as a result, some will probably be the critical For a given tail area, a high-wingers have their thrust stability case for a low-wing higher aspect ratio will not line angled down to get it to airplane with the propeller up only provide a higher static pass above the CG or at least front. margin, but also allow the CG closer to it. limit to be further forward. The propeller also generates Tail Contribution However, a higher aspect ratio a force that acts at a right an- The items we have covered so tail will tend to be heavier and not as torsionally stiff. This is Formula 3 a concern if you plan on using a fabric-covered tail. This type Tail arm length x horizontal tail area of tail should have an aspect MAC x wing area ratio closer to the bottom of Sport Aviation

59

No matter what process you use to design an airplane, a competent pilot, not the first customers,

should explore its stability characteristics at the forward and aft CG limits. the range with external bracing at the leading edge and the main spar to provide enough rigidity. Formula 3 defines the horizontal tail volume coefficient. The tail arm length is the horizontal distance between the CG and the horizontal tail MAC 1/4-chord position, and t h i s arm will be its shortest when the CG is at the aft limit. A larger tail volume means more static stability, and for a given volume coefficient, you can have a large tail-arm-toMAC ratio and small tail-areato-wing-area ratio or vice versa. As mentioned in Part 2, for most airplanes the t a i l arm-to-MAC ratio is between 2.5 and 3.5. A wing generates lift by taking air and deflecting it down toward the ground at some angle. This is the downwash angle, and it's mostly a function of the lift coefficient and wing aspect ratio. The harder the wing is working, the greater the downwash angle. This downwash angle causes the horizontal tail to fly at a lower angle of attack than the airplane. The rate of change of downwash at the tail is a measure of how much the downwash angle changes for a 1-degree change in angle of attack. The larger this rate is, the worse it affects the airplane's static margin. It is largely dependent on the wing lift slope and aspect ratio, and a higher aspect ratio wing will 60

APRIL 2002

-Suggested Lower Limit - Suggested Upper Limit

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reduce the rate of change of

downwash value. The air that flows over the horizontal tail is usually moving slower than the airplane's true airspeed. The amount of lift a wing or tail generates depends on the dynamic pressure the surface experiences, and this is proportional to the airspeed squared. We only need to know the ratio of the dynamic pressure at the tail to the airplane's true airspeed dynamic pressure. Wind tunnel tests have shown this ratio to be 0.7 to 0.9, without propeller effects. Using 0.8 works well for airplanes with side-by-side seating and a reasonably streamlined fuselage. The pressure ratio at the tail will be a little higher when the

power is on. Reference 1 discusses the effects of power well, but its equation for estimating the dynamic pressure ratio at the tail with power on gives values

that appear to be too high. Reference 6 gives a more realistic equation for calculating it. The spreadsheet does not correct the dynamic pressure ratio at the tail for power-on effects, so the static margin that it calculates for the full power condition should be slightly conservative. Reference 7 recommends a m i n i m u m stick-fixed static margin of 5 percent MAC at aft CG. The elevator size does not affect the stick-fixed static margin, but it does affect the stick-free value. Because we

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must make sure we have positive

stick-free static margin at aft CG, this requires some knowledge about the elevator. When a gust hits an a i r p l a n e trimmed to fly at a given airspeed, the change in angle of attack caused by the gust causes the local angle of attack at the tail to change. This changes the air pressure distribution over the elevator and causes the elevator to try to assume a new position. This floating tendency of the elevator reduces the tail's effectiveness and results in a smaller static margin. How much the elevator hurts the static margin depends on its size in relation to the horizontal tail and whether it has any aerodynamic balance. To reduce the penalty you want the elevator to be as small as possible, but making it too small will give you fits when you try to flare the airplane during landing. Typically the ratio of elevator to horizontal tail area is 0.35 to 0.45. You can reduce the effects the elevator has on stick-free stability by placing a portion of it ahead of the hinge l i n e . Most often on lightplanes you see this as a horn balance out at the elevator's tip. It is also a handy place for the elevator balance weight. We've been talking about having a positive static margin at the aft CG, but we must also ensure that we have enough elevator power to hold the nose up while landing with flaps down at forward CG. An airplane becomes more stable as the CG moves forward. Higher stability leads to higher control forces because it takes larger control deflections to trim an airplane at a given airspeed. If the CG is too far forward, you won't have enough elevator travel to overcome the nosedown pitching moment. This only gets worse if an airplane has flaps. When deflected, flaps create a large nose-down pitching moment that the tail has to counteract. Fortunately, when they are deployed and producing a lot of lift they also

create a lot of downwash at the tail. This allows the tail to create a higher down force and prevent the airplane from pitching over. Unfortunately this downwash reduces by about 50 percent when the airplane is near the ground, so during landing you may not have enough elevator control to hold the nose up. In some cases the horizontal tail size may be determined by the forward CG with a flaps-down condition and not by the aft CG

static margin requirements. Setting the horizontal tail at a negative incidence relative to the fuselage, using a higher elevator-totail-area ratio, and choosing a large maximum elevator deflection are a few things you can do to improve an airplane's forward CG capability. For design purposes, a maximum of 25 degrees up-elevator should be considered the upper limit. As m e n t i o n e d earlier, the

amount of force and the proper di-

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Spoil Aviation

61

As pilots we learned the danger of making abrupt pitch changes when flying above the airplane's maneuvering speed (VA). rection of that force (that is, push to speed up, pull to slow down) required to move the airplane off trim speed are an indication of an airplane's stick-free static margin. It will also affect the amount of pull

force required to accelerate the airplane from Ig flight to some higher load factor. From a structural standpoint—this is important.

As pilots we learned the danger of making abrupt pitch changes when

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APRIL 2002

flying above the airplane's maneuvering speed (V^). When flying faster than this speed the airplane can reach a load factor higher than it was designed to take. In certificated airplanes, Federal Aviation Regulation 23.155 specifies the minimum control force required to go from Ig flight to the limit load factor (normal category is 3.8g, utility category is 4.4g, and aerobatic category is 6g). Even though you're designing a homebuilt, these are good minimum limits to consider. For airplanes with control wheels (yokes) the minimum force is gross weight/100 or 20 pounds,

whichever is greater. If the a i r plane has a control stick, the minimum control force is gross w e i g h t / 1 4 0 or 15 pounds, whichever is greater. Other factors that affect the stick forces are the air density, amount of elevator control travel, and whether the airplane is equipped with a down spring and/or bob weight. At higher altitudes the lower air density results in a lower stick force per g. Larger control stick or yoke throws also reduce the stick force per g. A down spring is incorporated in the control system on some airplanes to increase the stick force required to change the airspeed from the trim speed, thereby improving the apparent stability of an airplane. A bob weight is a control system addition that causes the stick to move forward. It also increases the stick force required to change the airspeed from the trim speed and increases the stick force per g. Airplanes with elevators that have no mass balance (or

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are mass underbalanced) essentially have a bob weight built into the control system, and this helps increase

the stick forces. Vertical Tail Sizing

An airplane is directionally

stable when it tries to return to the sideslip angle (usually zero) at which it was flying before it was disturbed, and in large part the vertical tail determines this stability. How big it needs to be depends on the fuselage area as viewed from the side, how much fuselage is forward of the CG, the wing location and wingspan, the vertical tail arm length, airplane weight, and the vertical tail aspect ratio. Reference 8 suggests using an aspect ratio between 1.3 and 2.0. The horizontal tail acts like an endplate for the vertical tail and therefore increases its lift slope. Reference 8 also suggests that the rudder area be between 40 and 50 percent of the vertical area. If you're designing a taildragger it's a good idea to be toward the upper end of this range.

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Reference 2) gives a suggested range for aileron chord lengths aft of the hinge line as a function of total aileron span. The amount of dihedral a design requires depends largely on the wing location. Reference 8 gives some guidelines, which are shown in Figure 3. The ratio of wing location to fuselage height is measured from the bottom of the fuselage, and as a result the ratio for a low wing is zero. Using the Spreadsheet

Note: the spreadsheet can be used for conventional (tail behind the wing) configurations only! In the design example from Part 2 I pushed and shoved the different parts of the airplane around to get a CG range from 16 to 32 percent MAC. Now I

need to determine the horizontal tail size needed to cover this CG range.

More at mvw.eaa.org ) To start this process the spreadsheet estimates the required horizontal tail size based on a stick-fixed static margin of 5 percent MAC at top speed. I used this horizontal tail area and input values for the ratio of elevator-to-horizontal-tail area, tail incidence, maximum stick travel, and elevator deflection for full-up elevator. I found that the minimum estimated stick force per g falls below the recommended minimum and that the tail was too small to provide enough control power for the forward CG case. I increased the tail area and varied the other parameters just mentioned and found I needed 64

APRIL 2002

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Airplane Performance Stability and Control; Perkins, Courtland and Hage, Robert; Wiley and Sons; 1949. Engineering Aerodynamics, Revised Edition; Diehl, Walter; Ronald Press; 1936. Airplane Design Manual, 2nd Edition; Telchmann, Frederick; Pitman Publishing Company; 1942. NACA TR 711; "Analysis and Prediction of Longitudinal Stability of Airplanes;'' Gilruth and White; 1941. Aerospace Vehicle Design Volume I Aircraft Design, 3rd Edition; Wood, K.D.; Johnson Publishing Company; 1968. "The Influence of Running Propellers on Airplane Characteristics;" Journal of Aeronautical Sciences; Millikan; Clark; January 1940. Aerodynamics Aeronautics and Flight Mechanics, 2nd Edition; McCormick, Barnes; Wiley and Sons; 1995. Preliminary Design Processes; Rawdon, Hrb; Wichita State University Special Collections; 1949.

a horizontal tail area of 30 square feet. This larger tail increased the estimated gross weight to 1,170 pounds, and it caused the CG range to move aft to 18 percent to 35 percent MAC. This was not what I wanted to see, so I moved the

wing aft 1 inch. I repeated the process and this time found that I now needed a horizontal tail area of 28.5 square feet to meet the minimum stick-force-per-g and forward-CG limits. This smaller tail contributed to a lower estimated gross weight

of 1,167 pounds. The CG range also is now 16 percent to 32 percent MAC, which is

closer to the range suggested

in Part 2.

I hope that you have found these articles helpful in understanding some of what it takes to design an airplane. Remember that the results you get using these methods are only estimates and that there is no guarantee with them! No matter what process you use to design an airplane, a competent pilot, not the first customers, should explore its stability characteristics at the forward and aft CG limits. Also, any new design should be checked to ensure that it is strong enough to handle flight and ground loads it is expected to experience.

A second-generation EAAer (his dad is EAA 89), Neal Willford grew up attending EAA conSpott Aviation

65

ventions at Rockford ami Oshkosh. He learned to fly in an ultralight in 1982 and earned his private pilot certificate in 1987. He holds a mechanical engineering degree from LeTourneait College and does preliminary airplane design for a major general aviation manufacturer. In his spare time he's designing a five-place homebuilt to carry his wife and three boys.

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