Assignment 18

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SAE COMPETITION MICRO DESIGN OF AIRCRAFTs

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LITERATURE REVIEW

Aircraft design expressed the need of using empirical values for statistical analysis for various design parameters to better account for the aerodynamic parameters such as taper and wing-aspect ratios (Kawai and Rinoie, 2003). It specifically emphasized on the boundary element techniques for estimating the aerodynamic characteristics estimates for better efficiency but the greatest takeaway is the expression of aerodynamic parameters in this design process. In a separate study which sought to better express the aerodynamic stability in flight testing it concluded with a investigation on the dynamic and static longitudinal states using the maneuver point and neutral point. The takeaway from this stability assessment was that aerodynamic parameter play a vital role not in the flight testing but the initial design procedures. Among these design metrics include the aerodynamic force that affects the energy conservation especially in relation with aerodynamic breakup. The fact this parameter contains a non-linear oscillatory movement creates a technical challenge in design analysis that makes it a vital parameter.

Wing sections is another metric that affects the notional airfoil in aircrafts making a design parameter. It requires various corrections as the cambered shape, maximum chord thickness using the Reynolds Number, altitude, flight speed to appropriately develop wings with good chord specifications. In some design programs int includes developing a optimization algorithm with conjugate gradients for aerodynamic performance e.g., modifying the inboard upper surface or reducing the shock drags with respect to volume(Hicks and Henne, 1978). Also, another design criterion includes increasing the lift-drag proportion using the lifting coefficient and wing volume to achieve a better stall progression (Hicks and Henne, 1978). Despite such techniques proposing the use of numerical methods for the boundary conditions to determining the optimal design for practical wings there is a concern with the speeds among other possible design improvements (Hicks and Henne, 1978).

In blended wing-body (B.W.B) aircrafts currently operational they include the assessment of the aerodynamic behavior for optimal efficiency (Qui, et al., 2004). But most don’t include the surface optimization especially with the used aero foil, an inherent factor to the spanwise distribution for both discrete and continuous approaches. Its inclusion in the BWB sections allows the optimal improvement of the viscous flow, baseline configurations and ultimately the efficiency (Qui, et al., 2004). Other parameters closely linked the wing section include aspect ratio, pitching moment, maximum link, drag, span-load distribution, velocity factor, section lift-curve slope, wing lift-curve slop, wing span, wing area among other airfoil aspects (Abbott and Von, 2012.

BENCHMARK

This section includes the relevant technical specifications, standards/safety practices within the scope of Micro Aircrafts. Additionally, it includes the Computer-Aided Design practices with models related to the general design. Finally, it includes the virtual inspection aspects with respect to Aero Design.

Aircraft requirements commence from the 2-Dimensional drawings related to general design. It conformance in real-life using the carpenter squares and tape measures plus other tools with the parameters e.g, aircraft’s height, overall length and wingspan for this particular Micro-class of aircrafts. It also includes positive mechanical steering from the ground using the landing gear specifications and attached linkages. The aircraft specifications using the rule requirements and installed safety nuts in this particular micro aircraft. S.A.E also gives another specification for the removable and discrete red-alarming plug that should get installed externally for the aircraft’s top surface where it must be either in front or behind the propeller’s rotational plane. SAE Aero Design also specifies it should be either more than exposed male connection leads based on the aircraft’s overall length. Battery in this aero craft should fight against flight loads in the bay or battery compartment that should be free from damage using mechanical hardware especially in the event of a crash. Additionally, S.A.E also continues to specify that the battery compartment forward wall should be visible from a considerable distance. Control linkages and servos should either properly installed and secure using a mechanical keeper and a secured mounted receiver, all clearly labelled. Aircraft includes a design requirement and marking e.g., fuselages. It includes the ensuring that the location with relation to wing trailing or leading edges with the aircraft horizontally suspended or freely tilted up or down.

1. Micro class inspection items include the wingspan, battery, cargo bay and Micro Class Power Limiter specifications. First, the dimensions for this Micro class Aircraft should be less or equal to 47”. Next, the battery should be from Lithium Polymer pack with a maximum of 4 cells with clear markings based on their size and capacity. Cargo bag should contain a mechanical enclosure with payload plates. Finally, the inspection includes the mandatory specification that S.A.E Power Limiter (Limiter, Arming plug, E.S.C, Battery and RX) all should be visible, mounted securely and properly installed in the aircraft.

Other contextual inspection items from SAE Aero Design Virtual Technical and Safety Inspection;

a) No lead used in any part of the aircraft or payload.

b) No metal prop.

c) Aircraft must be structurally sound and capable of flight without payload installed.

d) If ballast used, must be securely mounted and not installed in payload bay.

a. Aircraft is powered only by the electric motor or motors installed on the aircraft, with no other forms of stored potential or kinetic energy on the aircraft.

b. The assembled aircraft has been carefully examined for warps and other misalignments in the wings and tail surfaces and that all parts are mounted securely.

c. The team has safely powered up the completed aircraft, with the prop removed, and has accomplished a complete functional check of control surface movements and motor rotation direction and confirms all systems are responding correctly.

DESIGN REQUIREMENTS

This section includes the design criteria, realistic expectations and technical challenges directly or indirectly limiting the Micro-class Aircraft especially in the efficiency. The criterion involved understanding by expressing the aerodynamics performance and analysis that includes the full-scale airplane and model difference using design parameters. These include the moments of inertia, Reynolds Number and Wing loading. The R/C model wing loading is one to two orders of magnitude less than a full-scale airplane (because of the “square-cube law” … look it up). R/C models typically have wing loadings of 1-3 lb/ft2 whereas the full-scale airplanes are greater than 10 (Cessna 172 is 12.6 lb/ft2). The impact is lower stall speeds and lower take-off and landing distances.

R/C model contains the Reynolds Numbers less than 500,000 which gives the wing a predominately laminar boundary layer. Full scale airplanes are greater than one million Reynolds Number and have turbulent boundary layer wings. The impact is that the full scale airplanes have higher maximum lift coefficients due to the turbulent boundary layer delaying flow separation over the wing better than the laminar boundary layer. The R/C models and the full scale airplanes are in a Reynolds Number region where the drag coefficients are about the same.

The R/C model will have much smaller moments of inertia than the full scale airplane. The impact is that the time-to-double-amplitude t2 from a disturbance will be much shorter for the R/C model since t2 = fn (1/(moment of inertia)½ . The R/C pilot will have his hands full with a neutral or unstable model.

COURSEWORK

This section includes the analysis and calculations with relation to Flight Dynamics based on a white-paper available from S.A.E.

CD = CDmin + K’CL2 + K’’( CL - CLmin)2 (1)

The CDmin is made up of the pressure and skin friction drag from the fuselage, wing, tails, landing gear, engine, etc. With the exception of the landing gear and engine, the CDmin contributions are primarily skin friction since we take deliberate design actions to minimize separation pressure drag (ie; fairings, tapered aft bodies, high fineness ratio bodies, etc).

The second term in the CD equation is the inviscid drag-due-to-lift (or induced drag) and K’ is the inviscid or induced factor = 1/( AR e). The e in the K’ factor can be determined using inviscid vortex lattice codes such as AVL. The e for low speed, low sweep wings is typically 0.9 – 0.95 (a function of the lift distribution).

The third term is the viscous drag-due-to-lift where K’’ is the viscous factor = fn(LE radius, t/c, camber) and CLmin is the CL for minimum wing drag. Both K” and CLmin are determined from air foil data. The K’’ term is difficult to estimate (see reference 2, page 11-11) and is often omitted. It is usually determined from 2D air foil test data and will be discussed in Section IV.

SECTION AND WING DATA

The two dimensional section data should be correct for finite wing effects. These corrections will be discussed below using the notional air foil (termed the LMN-1) shown in Figure 1. The LMN-1 air foil is a 17% thick highly cambered shape with its maximum thickness at 35% chord. This air foil is similar to the shapes used by the SAE Aero Design teams (ie; the Selig 1223, Liebeck LD-X17A, and Wortman FX-74-CL5 1223).

Figure 1: Notional LMN-1 air foil data at Re = 300,000

The first thing is to check is that the data is for the appropriate Reynolds Number. Assuming an altitude of 3000 ft, standard day conditions and a flight speed of 55 ft/sec, the = 0.002175 slugs/ ft3 , = 0.3677x10-6 slugs/ft-sec the Reynolds Number per ft is 325,000. Thus the airfoil data of Figure 1 will be good for a wing having a chord of about one foot.

From the air foil data in Figure 1 the section Clmax = 1.85 can be determined for a 2D stall = 10. Notice that the air foil has a nasty inverted stall at -2.5 (ie; the lower surface is separated). Since we do not plan on operating at negative this is OK. Notice also that the linear lift curve slope has been approximated to an OL = -8 on Figure 1.

The section lift data needs to be corrected for 3D, finite wing effects. The low speed unswept finite wing lift curve slope is estimated as follows for AR > 3 (see Reference 1, page 264 or Reference 2, page 8):

dCL/d = CL = Cl AR/(2 + (4 + AR2)½) (2)

where Cl = section lift curve slope (typically 2 per radian)

and AR = wing aspect ratio = (span)2/wing area

Figure 1 shows the construction of a three-dimensional AR = 10 wing lift curve using the 2D and the section lift curve slope. The OL is an anchor point for constructing the 3D wing lift characteristics since at OL the lift is zero and there is no correction to the 3D lift curve for the trailing vortices. Estimate the 3D wing lift curve slope for the model aspect ratio using equation 2 and draw it on the Cl vs a. For large AR (ie; AR > 5) low speed, unswept wings, the wing CLmax 0.9 Clmax = 1.67 (Reference 2, page 9-15). The 3D stall is approximated using the 2D stall characteristics and is about 11.5º.

The section drag polar data is used to estimate the following wing data:

CLmin Clmin = 0.7

CDmin Cdmin = 0.0145

and the wing viscous drag-due-to-lift factor K’’ = 0.0133 as shown on Figure 2.

Figure 2 Viscous drag-due-to-lift factor for the LMN-1 airfoil

ESTIMATING MODEL DRAG

As mentioned earlier we will approximate the aircraft drag polar by the expression

CD = CDmin + K’CL2 + K’’(CL - CLmin)2 (1)

The CDmin term is primarily skin friction and the data on Figure 3 will be used in its estimation. The boundary layer can be one of three types: laminar, turbulent or separated. We eliminate the separated BL (except in the case of stall) by careful design. For Re < 105 the BL is most likely laminar. At a Re = 5x105 the BL is tending to transition to turbulent with a marked increase in skin friction. By Re = 106 the BL is usually fully turbulent. Notice that our model Re is right in the transition region shown on Figure 3.

Figure 3 Skin friction coefficient versus Reynolds Number

The methodology involves estimating the drag of a notional R/C model with the following characteristics:

Configuration: Fuselage/payload pod with a boom holding a horizontal and vertical tail.

Fuselage/boom length = 84 in,

Fuselage length = 25 in, Fuselage width = 5 in

Wing AR = 10, Wing taper = 0.5

Wing area = SRef = 1440 in2 = 10 ft2 (total planform area)

Wing span = 120 in

Landing gear: tricycle

Take-off weight w/o payload = 12 lb

Item Planform Wetted Reference

Area Area Length

(in2) (in2) (in)

Fuselage 151 605 25

Engine /mount 15 100 na

Horizontal Tail 126 252 7 (MAC)

Tail Boom 14 28 48 + fuselage

Landing gear 12 24 na

Wing (exposed) 1360 2720 12.4 (MAC)

Vert Tail 0 189 9.8 (MAC)

The drag coefficients for the model components are estimated as follows (all based on SRef = 10 ft2 ).

Fuselage

Re = 625,000, assume BL is turbulent

Fuselage CDmin = FFF Cf SWet/SRef (3)

Where FF is a form factor (Reference 1, pg 281 or Reference 2, page 11-21) representing a pressure drag contribution. Form factors are empirically based and can be replaced with CFD or wind tunnel data. SWet is the wetted area of the component (fuselage) and the Cf is the skin friction coefficient of the component (fuselage) determined from Figure 3.

FFF = 1 + 60/(FR)3 + 0.0025 FR (4)

For our model the FR = fuselage fineness ratio = fuselage length/diameter = 25/5 = 5 giving a FFF = 1.49 and a fuselage CDmin = 0.0032

Wing

Re = 310,000

Wing CDmin = FFW Cf SWet/SRef (5)

Where FFW = [1 + L(t/c) + 100(t/c)4] R (6)

and L is the airfoil thickness location parameter (L = 1.2 for the max t/c located at 0.3c and L = 2.0 for the max t/c < 0.3c)and R is the lifting surface correlation parameter. Thus L = 1.2. R is determined from Reference 1, page 281 or Reference 2, page 11-13. For a low speed, unswept wing R is approximately 1.05.

Since a wing Re = 310,000 could be either laminar or turbulent, we will calculate the minimum drag coefficient both ways and compare with the section Cdmin = 0.0145 (from Figure 1).

If the BL is laminar, the wing Cf = 0.00239 and wing CDmin = 0.0057.

If the BL is turbulent, the wing Cf = 0.0059 and wing CDmin = 0.014.

Thus the wing boundary layer must be turbulent and we will use wing CDmin = 0.0145.

Horizontal Tail

The Re = 175,000, therefore we’ll assume the BL is laminar. The tail (both horizontal and vertical) CDmin equation is the same as for the wing. For a t/c = 0.09 airfoil with L = 1.2 and R = 1.05, the horiz tail CDmin = 0.00046.

VERTICAL TAIL

The Re = 245,000, therefore assume the BL is laminar. For a t/c = 0.09 airfoil with L = 1.2 and R = 1.05, the vert tail CDmin = 0.00039.

Tail Boom

The reference length for the tail boom is the fuselage length plus the boom length since the BL will start on the fuselage and continue onto the boom. Thus the tail boom Re = 1.825x106 and the BL is turbulent. Thus

Tail Boom CDmin = 1.05 Cf SWet/SRef = 0.00009.

Where the factor 1.05 accounts for tail/boom interference drag.

Landing Gear

From Reference 3, page 13.14 a single strut and wheel (4 inch diameter, 0.5 inch wide) has a CDmin = 1.01 based upon frontal area. Thus the tricycle gear CDmin = (3)(1.01)(2)/1440 = 0.0042 based upon the wing reference area..

Engine

From Reference 3, page 13.4, Figure 13 the engine CDmin = 0.34 based upon frontal area. For a 6 in2 frontal area the engine CDmin = 0.002 based upon the wing reference area..

Total CDmin

The total CDmin is the sum of all the components. Thus the total model

CDmin = 0.02484 based upon a wing reference area of 10 ft2 .

Note #1: As a sanity check of our CDmin we compare it with a Cessna 172 which has a CDmin = 0.026 based upon a wing reference area of 175 ft2 .

Note #2: The wing is the largest drag item due to its large wetted area. However the second largest drag item is the landing gear which is the case for all full scale airplanes. This drag can be cut in half by putting wheel fairings over the wheels. Is it surprising that airplane designers go to the trouble of designing retractable landing gears?

Total Drag Expression

Assuming a wing efficiency e = 0.95 gives an induced drag factor

K’ = 1/( AR e) = 0.0335.

Notice that the often omitted viscous drag factor K’’ = 0.0133 is 40% of the induced drag factor. The total drag expression is

CD = 0.02484 + 0.0335CL2 + 0.0133(CL – 0.7)2

The untrimmed (neglecting the horizontal tail drag-due-to lift) model drag polar and L/D are shown on Figure 4.

Figure 4 Notional model aircraft total drag polar and L/D

VI ESTIMATING PERFORMANCE

The take-off ground roll distance SG is the distance required to accelerate from

V = 0 to a speed VTO, rotate to 0.8 CLmax and have L = W. The 0.8 CLmax is an accepted value to allow some margin for gusts, over rotation, maneuver, etc.

Assuming a W = 45 lb (12 lb model and 33 lb payload), altitude = 3000 feet (standard day) and a CLmax = 1.67 (from Figure 1) gives the following VTO

VTO = [2 W/(S 0.8 CLmax)]½ = 55.65 ft/sec = 38 mph

The takeoff acceleration will vary during the ground roll and is given by the following expression (see discussion in Reference 2, Chapter 10)

a = (g/W)[(T – D) - FC (W – L)] (7)

where g = gravitational constant = 32.2 ft/sec2 and

FC = coefficient of rolling friction = 0.03 (typical value for a Cessna 172 on an average runway).

Note: A useful ground test is to measure the coefficient of rolling friction for your airplane. The testing is fairly simple using a fish scale to measure the rolling force for different loading conditions. The value for FC can increase dramatically if the landing gear is damaged, the wheels do not track straight or the take-off is in tall grass. The landing gear needs to be sturdy with large diameter wheels.

A useful expression for the ground roll distance SG is given by the equation (from reference 2, page 10-7)

SG = VTO2/(2 amean) (8)

where amean = acceleration at 0.7 VTO

Using the notional model aircraft with the wing at 0º angle of incidence ( for minimum drag during the ground run) and data from Figures 1 and 4 gives

Ground roll CL = 0.7 (from Figure 1)

Ground roll CD = 0.0412 (from Figure 4)

CLTO = 1.34 @ = 7 (0.8 CLmax )

The static thrust available is assumed to be 20 lb. This thrust will degrade with forward speed as shown on Figure 5. The data scatter represents measurements by different SAE Aero Design teams.

Figure 5 Thrust variation with forward speed for a fixed pitch prop

A static thrust of 20 lb gives an SG = 151 feet. It is useful to examine the different pieces of this ground roll distance. The mean acceleration is

acceleration @ 0.7 VTO = (32.2/45)[ 20(0.8) – 0.68 – 1.02] = 10.25 ft/sec2

Notice that the ground roll drag (0.68 lb) and the rolling friction force (1.02 lb) are overwhelmed by the available thrust force. If the static thrust was reduced by 20% to 12 lb then SG = 210 feet. Thus the critical ingredient to lifting a certain payload is having sufficient thrust to accelerate to VTO in less than 200 feet and having a large useable CLmax so that VTO is small. Having a headwind will reduce VTO which has a significant effect on SG due to the square of the VTO in the SG equation.

After the ground roll, the aircraft rotates to 0.8 CLmax = 1.34 and lifts off. Note that this rotation will take a certain distance (typical rotation time is 1/3 second) and is part of the 200 feet takeoff distance limit. After liftoff the model accelerates and climbs to a safe altitude where the is reduced to ~ 0 (CL = 0.7) and the power reduced for a steady state L = W, T = D cruise.

Bottom line for the notional model in this white paper is a max payload of about 33 lb for a no wind takeoff at 3000 feet standard day.

Maximum Level Flight Speed

The maximum level flight speed occurs when T = D at L = W as shown on Figure 6. For the notional model at L = W = 45 lb and 3,000 ft altitude the maximum speed is 144 ft/sec or 98 mph where T = D = 6.6 lb.

Figure 6 Thrust available Vs required (drag)

WORK PLAN

The following section contains the Gantt Chart for this Micro-level Aircrafts.

Figure showing Ms. Project file for the Gantt Chart related to this project.

Figure showing the Project’s Timeline.

MINUTES OF MEETINGS

TEAM SIGMA- CHAMPION FIGHTERS UNIVERSITY MINUTES
Members in Attendance	William, W.K., Sharon K.N, Keith, A.N., Caroline, M.N., McAdams, C., Shebi, N.J. and Peter, K.H
Members not in Attendance	None
Guests (Department Leaders)	Dr. Tafara, E.D., Dr. David. W.N, Dr. Welma, E.P.
Call to Order	A regular meeting discussing the Design and Implementation for the Micro-level Aircrafts for S.A.E
GENERAL OVERVIEW
	· Members developed a vision board for this Project by defining the key goals and objectives. · Members discussed the future scope of Micro-level Aircraft Design. · Dr. Tafara, the Chairman of Department noted the importance of this project and cleared the air concerning the budget allocations. · Dr. Welma, volunteered to be the Project Supervisor with the team agreeing that they would consult with her every Wednesday. · Dr. David, agreed to work with the team to include futuristic technologies e.g., Artificial Intelligence in this S.A.E Micro-level Aircrafts.

REFERENCES

Abbott, I. H., & Von Doenhoff, A. E. (2012). Theory of wing sections: including a summary of air foil data. Courier Corporation.

Hicks, R. M., & Henne, P. A. (1978). Wing design by numerical optimization. Journal of Aircraft, 15(7), 407-412.

Kawai, T., & Rinoie, K. (2003). Studies on Aircraft Conceptual Design Incorporating Boundary Element Method for University Design Education. Japan Society of Aeronautical Space Sciences, 51(594), 371-379.

Qin, N., Vavalle, A., Le Moigne, A., Laban, M., Hackett, K., & Weinerfelt, P. (2004). Aerodynamic considerations of blended wing body aircraft. Progress in Aerospace Sciences, 40(6), 321-343.

Siren, W. H. (1975). A flight test determination of the static and dynamic longitudinal stability of the Cessna 310H aircraft. NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF.

20406080100

V (mph)

Nicolai-05 06-18-09

0.5

1.0

Static

20406080100

V (mph)

Nicolai-05 06-18-09

0.5

1.0

Static

20406080100

V (mph)

Nicolai-05 06-18-09

0.5

1.0

Static

406080100

V (mph)

Nicolai-06 06-18-09

Force

(lb)

Altitude = 3,000 ft

Weight = 45 lb

Thrust

Drag

Max Speed

406080100

V (mph)

Nicolai-06 06-18-09

Force

(lb)

Altitude = 3,000 ft

Weight = 45 lb

Thrust

Drag

Max Speed

2D Lift Curve

AR = 10

Lift Curve

1.8

1.6

1.4

1.2

1.0

-8-6-4-2024681012141618

Approximation

0.9

max

LMN-1 Airfoil

= 300,000

Section Drag

min

dmin

Degrees

Nicolai-02 06-18-09

0.010.020.03

0.04

0.01

0.20.40.60.81.01.21.41.61.82.0

Nicolai-04 06-18-09

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

= 0.02484 + 0.0335 C

+ 0.0133(C

–C

Lmin

)

Ref= 10 ft

0.01

0.20.40.60.81.01.21.41.61.82.0

Nicolai-04 06-18-09

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

= 0.02484 + 0.0335 C

+ 0.0133(C

–C

Lmin

)

Ref= 10 ft