Airplanes and Airships Evolutionary Cousins

Transcription

1 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 09-1 January 01, Nashville, Tennessee AIAA Airplanes and Airships Evolutionary Cousins Leland M. Nicolai 1 and Grant E. Carichner Lockheed Martin Aeronautics Co., Palmdale, CA This paper will discuss the relationship between aircraft and airships. For this discussion the airships will be either single-lobe bodies of revolution or multi-lobe hybrid configurations. The aircraft will be low aspect ratio (AR<4) lifting bodies and fighter type configurations. Most people will argue that the only connection between aircraft and airships is that they fly through the air. Everything else seems to be apples and oranges. The most noticeable difference is that the airship becomes airborne using buoyant lift and the aircraft using wing generated aerodynamic lift. However, all airships can generate some aerodynamic lift (it is called dynamic lift) by angle-of-attack but the lift is small compared to the buoyant lift. However, the main problem with buoyant lift is that it is constant for airships with ballonets and cannot be modulated like aerodynamic lift. This poses a problem for the airship during landing and ground operations because it needs to remain heavy as the crew and payload are removed or exchanged. Another issue has to do with the weight changes due to burning fuel. Airship lift needs to be reduced as fuel is burned off. This problem is solved by designing the airship to have the capability to have some heaviness = weight buoyant lift of about 10 to 0 percent. When properly designed this change in heaviness is offset by aerodynamic lift. So, is there a connection? This paper will show that there is a connection based on the aerodynamic forces generated by both vehicles. The specific connections are lift-to-drag ratio (L/D), lift curve slope (C L α ), and the drag-due-to-lift factor in the drag expression C D = C D0 + KC L. There is also continuous variation of L/D from the extremely low aspect ratio airships to the higher aspect ratio winged aircraft. Nomenclature AR = aspect ratio, (span) /planform area (AR = 4/π FR for bodies of revolution) BoR = body of revolution BR = buoyancy ratio, buoyant lift/weight C D = drag coefficient, drag/q (reference area) C D = zero lift drag coefficient o C L = lift coefficient, lift/q (reference area) C L = lift curve slope (per degree) α FR = fineness ratio, length/equivalent diameter K = drag-due-to-lift factor, C D / C L L/D = lift to drag ratio S Plan = planform area (ft ) q = dynamic pressure, ½ρ (velocity) Vol ⅔ = reference area for airships α = angle of attack β = (1- M) ½ = leading edge sweep angle (degrees) σ = density ratio, ρ/ρ SL 1 Technical Fellow, Advanced Development Programs, AIAA Fellow Project Engineer Senior, Advanced Development Programs, AIAA Associate Fellow 1 Leland M. Nicolai and Grant E. Carichner, 01 Copyright 01 by Leland M. Nicolai and Grant E. Carichner. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

2 I. Introduction An airplane is sleek and fast. An airship is bulbous and slow. Coming from opposite ends of the aerodynamic spectrum could they have similar DNA that is only revealed by careful comparison? This paper will investigate the relationship between aircraft and airships and identify a unifying concept that shows how similar yet different they really are. For this discussion airships will be comprised of single-lobed bodies of revolution and multi-lobed hybrid configurations. Representative aircraft will include low aspect ratio (AR<4) lifting bodies and fighter type designs. Obviously, airships and airplanes are drastically different and it would be foolish to suggest otherwise. Generally, airships derive nearly all of their vertical force from an enclosed lifting gas and airplanes derive their vertical force (lift) from wings (disregarding vectored thrust) flying at an angle of attack. The origin of these forces couldn t be more different as an airship s buoyant lift is simply generated by an enclosed gas volume and an airplane s wings are carefully optimized to maximize circulation while producing as little drag as possible. Buoyant lift was first postulated by Archimedes about 000 years ago while an airplane s lift obeys Bernoulli s fluid pressure laws formulated 1800 years later. If these air vehicles are related then there must be a missing link between them. What might this link be? If there is a link it will be in spite of the fact that the square-cube law is reversed between airships and airplanes as stated below. Simply stated the square-cube law for- Aircraft is: the weight increases as the cube of the scale factor and the lift (wing area) increases by the square. Airships is: the lift (volume) increases as the cube of the scale factor and the weight (surface area of envelope) by the square. Most people will argue that the only connection between aircraft and airships is that they both fly through the air. The most noticeable difference is that the airship becomes airborne using its buoyant lift and the airplane by using its aerodynamic lift. Could the missing link be an airship with wings or an airplane with a large helium filled body? For numerous reasons, which are outside the scope of this paper, neither of these configurations results in a useable air vehicle. Another approach is needed where the design has buoyant features that are packaged in an aerodynamically efficient shape. This air vehicle does exist and is commonly referred to as a hybrid airship. Hybrids attempt to capture the benefits of large volumes of lifting gas and are shaped to be more aerodynamically efficient. All airships create buoyant lift that is very cost effective (the lifting gas is purchased once) but it comes with a significant design liability. That liability is the fact that the buoyant lift cannot be turned off or modulated. For an airship with a ballonet the buoyant lift force is constant up to the maximum operational altitude. Furthermore, this means that during unloading operations airships could become too light (buoyant force is greater than weight) if too much weight is removed or new weight does not replace some of the unloaded weight. This situation presents a challenge to the airship designer to be able to accommodate changing lift demands throughout the mission. Instead of changing the buoyant lifting force it is easier to change the aerodynamic lift of an airship. But, is the airship capable of generating sufficient lift to offset the fuel burn and/or payload offloads? In the last 10 years hybrid airships have been designed and proposed for various missions. Is it because the hybrid is more efficient than an airship? No. Is it because the hybrid is less expensive than an airship? No. It is because a hybrid offers unique operational capabilities not available to standard airship designs. A hybrid s ability to modulate the amount of aerodynamic lift during cruise and its inherent compatibility with integrating air cushion landing pads is an unbeatable combination. Simply put, hybrid designs offer operational flexibility unattainable by standard airships. So where is the connection? This paper will show that the connection is the result of incorporating varying amounts of aerodynamic forces for both vehicles. The fundamental parameters lift-to-drag ratio (L/D), lift curve slope (CLα ), and the drag-due-to-lift factor K in the drag expression C D = C D0 + KC L are used to make this undeniable connection. II. Reference Area The aerodynamic forces and moments need to be non-dimensionalized into lift, drag, and moment coefficients. The lift and drag forces are made non-dimensional by dividing them by the free stream dynamic pressure (q) and a Leland M. Nicolai and Grant E. Carichner, 01

3 reference area. The moments are likewise referenced by q, reference area, and a characteristic dimension (wing span, mean aerodynamic chord, or airship length). The reference area for aircraft is by international convention taken to be the planform area, S Plan, of the main lift generating component the wing. The reference area for the airship was in debate for the first half of the 0th Century and finally established by international convention to be Vol ⅔ where Vol is the volume of the airship envelope holding the lifting gas. This convention is not completely self evident because the envelope surface area would be more logical because the airship drag is primarily due to skin friction. However, determining the airship surface area requires considerable information about the airship configuration whereas the volume is easily determined by the equation- Volume = weight/ σ where is the lifting capability for pure helium gas and σ is the ratio of the densities between sea level and the airship s maximum operational altitude for standard day conditions. So Vol ⅔ is a convenient parameter except when you want to compare the aerodynamic forces and moments of airships and aircraft. For many airship configurations the planform area of the envelope is difficult to determine but when approximated by a prolate spheroid is easily calculated. The relationship between S Plan and Vol ⅔ can be expressed as S Plan = N L Vol ⅔ (1) where N L depends upon the number of lobes in the configuration. The N L can be determined empirically from real airship/hybrid configurations as # Lobes N L Equation 1 can be used to convert airship/hybrid aero data from Vol ⅔ to S Plan for comparison with aircraft data. III. Aerodynamic Data Base Table 1 contains design and aerodynamic data on 7 body of revolution (BoR) airships, 3 multi-lobe hybrid airships, 6 lifting body research aircraft, and 7 low AR (less than 4) fighter type aircraft. Figure 1 shows a representative vehicle for each of the 4 aircraft and airship configurations in Table 1. The lifting body research configurations (Reference 5) were introduced into the data set to fill in the AR gap between airships and aircraft. The lifting bodies have shapes similar to the multi-lobe hybrids. They were designed to have blunt leading edges, providing a large bow shock to manage the high heating rate of reentry but have an L/D of 3-5 for good cross-range, down-range and low speed handling characteristics. All of the airships in Table 1 have their aerodynamic data referenced to Vol ⅔ and the lifting body and fighter type aircraft are referenced to the conventional wing planform area S Plan. This mix of reference areas is necessary in order to maintain the purity of the airship/hybrid data since the conversion S Plan = N L Vol ⅔ is approximate. 3 Leland M. Nicolai and Grant E. Carichner, 01

4 Table 1 Design and aerodynamic data sheet. No. Vehicle Ref AR C L α K C D 0 Ref 1 BoR, FR=7. Vol / (3) 1 BoR, FR=6.0 Vol / (3) 1 3 BoR, FR=4.8 Vol / (3) 1 4 BoR, FR=3.6 Vol / (3) 1 5a USS Akron w/o tails, FR=5.9 Vol / (3) 5b USS Akron + tails, FR=5.9 Vol / (3) 6a ZP5K w/o tails, FR=4.4 Vol / (3) 3 6b ZP5K + tails, FR=4.4 Vol / (3) 3 7a HALE w/o tails, FR=3. Vol / (3) 4 7b HALE + tails, FR=3. Vol / (3) 4 8 P-791 Vol / HA-1 Vol / (3) 4 10 Aerocraft Vol / (3) 4 11 M-F1 S Plan M-F S Plan HL-10 S Plan X-4A S Plan X-4B S Plan Space Shuttle S Plan SR-71 S Plan F-117A S Plan F-A S Plan F-16C S Plan F-104C S Plan F-15E S Plan F-5E S Plan Notes: (1) All Re 10 7 and M < 0. () AR = 4/πFR for prolate spheroids (3) Wind tunnel C D value and models did not include features such as lines, cooling drag, and landing gear. 0 The conversion of the aero data referenced to Vol ⅔ (the primed values) to data referenced to S Plan (the unprimed values) is determined as follows using Eq. 1: [C L α ] Vol ⅔ = [C L α ] S Plan = [C L α ] N L Vol ⅔ or, [C L α ] = [C Lα ] / N L and [C D 0 ] = [C D0 ] / N L () where the value of N L depends on the number of lobes. The conversion of the drag-due-to-lift K values is discussed later. IV. Aerodynamic Lift Aerodynamic lift is generated by a fluid flowing over a carefully shaped body such that at an angle- of attack α the fluid flows faster over the top surface than the bottom surface. This aerodynamic lift (caused by circulation>0) 4 Leland M. Nicolai and Grant E. Carichner, 01

5 CA-1 Hybrid Airship BoR with tails Lifting Body Aircraft Figure 1 Representative vehicles from Table 1. relies upon a sharp trailing edge to insure that the upper and lower surface flows come together at the TE (called the Kutta condition). From Bernouilli s theorem the static pressure in the fluid decreases as the speed of the fluid increases. Thus the static pressure on the upper surface is lower than on the lower surface giving an upward force called lift. This lift is expressed as Eq. 3. Aero Lift = C L q S Ref = C L α α q S Ref (3) where C L α is the lift curve slope and α is the angle-of-attack. The C L is the non-dimensional lift coefficient referenced to S Plan or Vol ⅔. Lift generation is illustrated in Figure showing the changing flow field around a 0% thick airfoil and body of revolution. There is one flow streamline (called the dividing streamline) that smashes into the airfoil and body of revolution at the stagnation point (point A). In Figure a one streamline goes over the top of the airfoil and one goes along the lower surface and they both meet (coalesce) at point C. The flow over the upper surface initially has to speed up going around the nose (to maintain continuity with the lower surface flow) and then slow down as it approaches point C. As the flow speeds up the static pressure on the surface drops (denoted by -) and as it slows down the static pressure increases (denoted by +). The flow on the lower surface does just the opposite generating an increased pressure along the nose and a decreased pressure on the aft end as it accelerates around the aft end to meet the upper streamline at point C. The resultant summation of static pressures results in zero lift but a nose-up moment is generated. There is a drag force on the airfoil due to the skin friction. 5 Leland M. Nicolai and Grant E. Carichner, 01

6 A Lift= ~ 0 M C A: Stagnation Point B: Kutta Condition Point C: Streamlines coalesce (a) 0% thick -D airfoil at α>00 A Lift>>>0 M B (b) NACA 000 -D airfoil at α>00 α V A Lift = ~ 0 M C (c) Prolate Spheroid at FR=5 at α>00 A Lift>0 M B C Aft end modified (d) Prolate Spheroid at FR=5 at α>00 A Lift>>0 M B C (e) Prolate Spheroid of FR=5 with sharp aft end and tails, at α>00 Figure The generation of lift on airfoils and bodies of revolution. (A is stagnation point where streamlines divide and B is point of Kutta Condition) 6 Leland M. Nicolai and Grant E. Carichner, 01

7 The airfoil in Figure b is the same as in a except that the aft end has been made sharp and approximates a NACA 000 airfoil. Physically the lower surface flow cannot negotiate the sharp trailing edge and flow forward to meet the upper surface flow. Consequently the upper and lower surface streamlines coalesce at the trailing edge (point B) resulting in the upper surface streamline having gone further and faster than the lower surface. This coalescing of the flows at the trailing edge is an important physical phenomena called the Kutta condition and results in a differential pressure between the top and bottom surface generating a lift force (and a nose up moment). A necessary condition for generating significant lift on an airfoil or body is a sharp TE to satisfy the Kutta condition. The modification of the airfoil in Figure a by adding a sharp TE results in a very efficient airfoil for generating lift. Figure c shows a prolate spheroid (body of revolution) of fineness ratio FR = 5 (0% thick) inclined at α > 0. Again, there is no lift generated (same as in Figure a) due to the lower surface streamline flowing around the body and coalescing with the upper surface flow at point C. The blunt aft end is unable to support a Kutta condition. There is a moment generated due to the up force on the forebody and the down force on the aft body and there is a drag force as well. Figure d shows the same body from Fig. c except a semi-sharp cone has been attached to the aft end. The semisharp cone on the aft end forces the upper and lower flow (single streamline) to coalesce at point C which generates a small amount of lift (due to a weak Kutta condition). Because of the higher pressure on the lower surface there is a flow around the entire body reducing the pressure differential between the upper and lower surface which reduces the lift generated. Figure e shows the same body from Fig. d except that horizontal tails have been attached to the aft end for pitch stability. The horizontal tails interrupt the flow from the lower surface to the upper surface at the aft end which reinforces the Kutta condition and increases the lift generated. The tails also generate lift adding to the overall body lift and decreased nose-up pitching moment. V. Comparison of Lift Curve Slopes A useful expression for C L for aircraft is (from reference 8) α C L α = π AR AR β (1+ tan ) β (4) where β = 1 M, is the sweep of the wing leading edge and AR = (span) / S Plan. For slow speed < 100 kt, β «1 and Eq. 4 becomes C L α = π AR AR (1+tan ) (5) and for tan «1 equation (5) becomes the familiar Helmbold equation (from Reference 7) C L α = π AR AR (6) And finally for AR < 1 which is the case for airships (AR = 4/π FR) the equation for C L becomes the slender body α expression CLα = π AR/ (7) The C vs. AR for the data set of Table 1 is shown on Fig. 3. The C L for the airships and hybrids has been α Lα referenced to S Plan using Eq. so that all coefficients are referenced to the same reference area. It is observed that the 7 Leland M. Nicolai and Grant E. Carichner, 01

8 , per degree Lift Curve Slope, CLα b 5a 1 3 Slender Body Equation C Lα = π AR 10 6b 4 6a 8 9 7b 7a SR-71 F-117A F-104C F-A F-15E C Lα = F-16C π AR AR Bodies of Revolution w/o tails BoR with tails and Hybrids Lifting Bodies Aircraft Data from Table 1 All C L α referenced to S Plan F-5E Aspect Ratio, (span) /Splan Figure 3 Lift Curve Slopes for the vehicles from Table 1. single-lobe body of revolution (BoR) without tails is a poor lifting body. This is partially due to the fact that BoR typically do not have a sharp trailing edge (TE) and the lower surface flow rolls around the aft end (from the high pressure to the low pressure regions) with the flows coalescing upstream of the TE. Adding a semi-sharp cone on the aft end gives a weak Kutta condition generating a small lift. Lift generation improves substantially when tails are added (see configurations 5a to 5b and 7a to 7b) as the tails interrupt the lower surface flow around the aft end reinforcing the Kutta condition but it is still poor. The aerodynamic lift advantage of a multi-lobe, hybrid airship configuration is evident with a lift increase of to 4 times that for a single lobe BoR configuration. This is due to the hybrid having an increased aspect ratio and a geometry conducive to a sharp trailing edge. VI. Aerodynamic Drag The drag is all aerodynamic and is expressed as Aero Drag = C D q S Ref = (C D 0 + KC L ) q S Ref (8) where C is the zero lift drag coefficient and KC D 0 L is the drag-due-to-lift coefficient. The C D is due primarily to skin 0 friction acting on the wetted area of the vehicle with some pressure drag on the aft body. The C D for the aircraft and 0 airships in the data set is shown in Table 1. Once again the reference area for the aircraft is S Plan and for airships it is Vol ⅔ such that the C value for airships/hybrids referenced to S D 0 Plan is given by Eq.. The drag-due-to-lift coefficient C D is composed of inviscid (induced) and viscous terms and is expressed as L C D L = K' C L + K" C L (9) 8 Leland M. Nicolai and Grant E. Carichner, 01

9 where K' and K" are the inviscid and viscous drag-due-to-lift factors respectively and are usually combined into the drag-due-to-lift factor K = K' + K". The inviscid K' C L term is due to the flow rolling around the wing tip or body edge from the high pressure to the low pressure region on the wing or body. The flow creates a vortex which trails behind the vehicle and is referred to as a trailing vortex or wing vortex (the source of the destructive wake turbulence behind an aircraft which can cause a small aircraft trailing a large aircraft to be flipped upside down). This trailing vortex induces a downwash at the aerodynamic center of lift which results in an induced drag. This drag coefficient is expressed theoretically as K' C L = C L /π AR e (10) where e is the wing efficiency factor. For airships the e «1 and resulting in a large induced drag for airships. The e for aircraft is typically 0.5 to 1.0. The viscous drag-due-to-lift coefficient K" C L is due to the pressure drag on the hull of the airship or wing of the aircraft as lift is generated for α > 0. The combined drag-due-to-lift factor K = C D / C L for the data set of aircraft and airships is determined from wind tunnel or flight test data and presented in Table 1. The K values for the airships and hybrids of Table 1 are multiplied by 4/ N L and plotted vs. AR on Fig. 4. Since K is dependent upon C L the K for the body of revolution airships is α extremely large, whereas the K for the multi-lobe hybrid airships is in line with that of the lifting bodies and low AR fighter type aircraft. K = CD/C L b 6b 5a 6a 3 7b 4 7a Bodies of Revolution (BoR) Hybrid Airships Body of Revolution, w/o tails Body of Revolution & Hybrids, with tails Lifting Bodies Aircraft 1 All K s Referenced to S Plan Data from Table Aspect Ratio, (span) /S plan Figure 4 Drag-due-to-lift factor, K, for vehicles in Table 1. 9 Leland M. Nicolai and Grant E. Carichner, 01

10 VII. Conclusion Aircraft and airship designs matured at roughly the same time in history as both were attempting to meet man s dream of flying with the birds. In a short period of time this dream became a fundamental need to stay aloft for long periods and move cargo from one point to another. Optimizing airship and aircraft designs were very different pursuits yet their aerodynamic characteristics are shown to be on the same continuous line when hybrid airships and lifting bodies are included. So, aircraft and airships are related by their common dependence on aerodynamic forces regardless of the size of the buoyancy term. At one end of the spectrum the neutrally buoyant airship needs no added aerodynamic lift whereas the airplane depends solely on aerodynamic lift to stay aloft. In between, lifting body and hybrid airship data bridge the gap showing the relationships for lift and drag-due-to-lift to be a continuous relationship. The data for lifting bodies are readily available from standard NASA sources but data for hybrid airships is harder to find. Although a few hybrid designs have emerged in recent years it is difficult to get much pertinent information on them. However, looking at the data in Figures 3 and 4 leaves no doubt that buoyant vehicles are directly related to aircraft. They are distinctly different but definitely related. The range/endurance and takeoff/landing performance analysis for airships and aircraft is exactly the same due to their aerodynamic connection. However, the strategies for using their performance is different for these cousins. References 1 Abbott, I.H., Airship Model Tests in the Variable Density wind Tunnel, NACA TR-394, 1931 Freeman, H.B., Force Measurements on a 1/40 Scale Model of the US Airship Akron, NACA TR Ross, S.A. and Liebert, H.R., LTA Aerodynamics Handbook, Goodyear Aircraft Corp., Akron, OH Carichner, G.E. and Nicolai, L.M., Fundamentals of Aircraft and Airship Design, Volume II Airship Design, AIAA, 1801 Alexander Bell Dr., Reston, VA , 01 5 Saltzman, E.J., Wang, C.K. and Iliff, K.W., Flight-Determined Subsonic Lift and Drag Characteristics of Seven Lifting-Body and Wing-Body Re-entry Vehicle Configurations With Truncated Bases, AIAA Paper 0383, 37th AIAA Aerospace Sciences Meeting, Reno NV, Jan Nicolai, L.M. and Carichner, G.E., Fundamentals of Aircraft and Airship Design, Volume I Aircraft Design, AIAA, 1801 Alexander Bell Dr., Reston, VA , Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Addison-Wesley, Reading MA Lowry, J.G. and Polhamus, E., A Method for Predicting the Subsonic Lift Curve Slope for Straight Taper Wings, NACA TR 3911, Leland M. Nicolai and Grant E. Carichner, 01

11 11 Leland M. Nicolai and Grant E. Carichner, 01