5. Aerodynamics

5.1. Objective

A good aerodynamics design is vital to the success of a supersonic aircraft, with

the two main objectives as the ability of supersonic flight and the reduction of take off

gross weigh. The design of the wing must provide sufficient lift to meet performance

requirements, while the overall aircraft design is required to minimize drag to reduce total

fuel required.

The Sentinel is designed for the highest performance with the lowest possible cost

in terms of total fly away cost or the amount of fuel burned.

5.2. Wing Design

5.2.1. Airfoil Selection

Although the geometry of a thin airfoil does not make a significant difference

during supersonic flight, it does greatly influence the subsonic performance of the

aircraft. The NACA 64-206 airfoil was chosen for the Sentinel based on the airfoil

thickness and the availability of airfoil wing tunnel data. The airfoil has a 6% chord

thickness to reduce the negative shockwaves effect for supersonic performance while the

slight camber enables the airfoil to produce lift even at zero angle of attack. The NACA

64 series was reverse designed for the minimization of drag comparing to the other

NACA airfoils. The geometry layout of the airfoil can be seen in Fig. 5.1.

-0.1

0

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 5.1. Non-dimensional geometry of NACA 64-206 airfoil.

5.2.2. Wing Geometry and Performance

The Sentinel was designed with a swept wing with an aspect ratio of 3.25, a taper

ratio of 1/3, and leading edge sweep angle of 50 degree. Fig. 5.2. illustrates the wing

geometry and Mach cone generated by supersonic flight.

-20

0

20

40

-40 -20 0 20 40

Figure 5.2. Graphic illustration of the wing geometry with a Mach cone at Mach 2.2.

The wing was strategically positioned to be completely engulfed by the Mach cone,

which results in reduced flow velocity over the wing. This setup is advantageous since a

wing in a subsonic flow produces approximately twice the lift as a wing in supersonic

flow according to the conical flow theory [1]. Spanwise dimension [ft]

Leng

thw

ise

dim

ensi

on [f

t]

Effects such as downwash, wing twist, and taper ratio all have influence on the

transformation between airfoil aerodynamic data and the aerodynamic properties of a

three dimensional finite wing. DATCOM charts provided by Raymer were used to

predict the performance of the wing under various flow conditions.[2] This data was

compiled into Fig. 5.3, providing a correlation between maximum lift coefficients at

various Mach numbers, although it should be noted that the maximum lift produced at

higher Mach numbers depend more on the structural strength of the wing.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5M

CL,

max

Figure 5.3. Maximum lift coefficient versus Mach number.

5.3. Drag Prediction

Drag prediction is essential to the success of designing a supersonic aircraft. A

reduction in drag produced by the aircraft would result in an increased access thrust, thus

greater climb rate and higher overall performance; it would also reduce the fuel

consumption and decreased the take off gross weight required for the mission.

Drag forces on an aircraft are formed by three main components: the lift induced

drag which is caused by the pressure difference between the front and back of the wing,

the parasitic drag which is mainly consist of skin friction and turbulence formed behind

the aircraft due to the shape or “form” of the components, and the wave drag which is

caused by the formation of shock wave during transonic and supersonic flight. Fig. 5.4

compares the wave drag of the Sentinel with various historical aircrafts.

00.0020.0040.0060.0080.01

0.0120.0140.0160.0180.02

0 0.5 1 1.5 2 2.5M

CD

,wav

e

B-70F-106SentinelF-4

Figure 5.4. Wave drag comparison between the Sentinel and F-106, F-4 and B-70.

A combination of parasitic drag and wave drag at various Mach number and

altitude is shown in Fig. 5.5. Calculations based on the Boeing estimation approach yield

a drag divergent Mach number of 0.894; at which point the wave drag becomes a

significant part of the overall drag produced by the aircraft.[2] Data from this plot and the

lift induced drag were combined to estimate the thrust required for steady level flight.

0.014

0.018

0.022

0.026

0.03

0.5 1 1.5 2 2.5M

CD

o

40000 20000

10000 SL

Figure 5.5. Parasitic drag and wave drag at various altitudes [ft] and Mach numbers.

Another essential parameter in determining the aircraft performance is the lift to

drag ratio, usually obtained from the drag polar plot of an aircraft. This ratio is essential

in predicting the optimal altitude, fuel consumption, best cruise velocity and bestloiter

velocity. It is also used to predict the maximum climb rate velocity. Fig. 5.6 displays the

drag polar diagram of the Sentinel.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4CD

CL

Subsonic SpeedM=1.2M=2.2

Figure 5.6. Drag polar of the Sentinel at 40,000 ft.

5.4. Comparison with Delta Wing

Delta wing configurations are common among modern supersonic aircrafts such

as the Eurofighter, Dassault Rafael, and Saab Gripen. The delta wing is known to have

good transonic and supersonic performance due to the highly swept leading edge, which

also contributes to the formation of leading edge vortex (LEX). The resulting LEX

effectively provides additional lift production at higher angles of attack. In order to

justify the decision to employ a swept back wing instead of delta wing, drag analysis and

CL,max data from DATCOM[2] for both wing types were compiled and compared in Fig. 5.7

a) and b).

a)

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.5 1 1.5 2 2.5Mach Number

CD

Swept Wing 35000ftDelta Wing 35000ft

b)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5M

CL,

max

Swept WingDelta Wing

Figure 5.7. The comparison between swept wing of Sentinel and a delta wing of the same wing area for a) drag forces at various Mach number and b) Maximum lift coefficient at various Mach number using DATCOM data

. As illustrated in the above plots, the delta wing produced slightly less drag at

transonic and supersonic regime comparing to the swept back wing. However, the

maximum lift coefficient of the delta wing is significantly lower than that of a swept back

wing. A swept back wing was chosen based on the above statement in addition to the

known property of having a higher aspect ratio at a given wing loading value, thus

producing less induced drag.

5.5. Lift Distribution

In order to study the effect of downwash, as well as to decide on the setup of

structural components to withstand the lift generated by the wing, an approximation of

lift distribution along the wing is required. There are various methods that can be used to

solve for the lift distribution of a tapered swept wing, with the most influential one as the

modified lifting line theory proposed by Weissinger [3]. However, due to numerical

difficulty, it was decided to use a simpler approximation suggested by Schrenk [4] which

uses equation 5.1.

( 5.1),

where c(y) is the variation of chord length with respect to spanwise location. The

resulting half span lift distribution of the wing is shown in Fig. 5.8.

0

0.001

0.002

0.003

0.004

0.005

0.006

0 0.2 0.4 0.6 0.8 1Normalized y location

CL /

y

Figure 5.8. The spanwise lift distribution of the wing at zero degree angle of attack.

5.6. High Lift Devices

Extra lift is needed during take off and landing as the aircraft is traveling at a

slower velocity, which would require a larger CL value to stay aloft. High lift devices

were introduced in order to generate adequate lift for take off, landing, and high g turns.

The Sentinel employed 70% span leading edge slats and Fowler type flaps that cover the

inner 30% of the exposed wing area, similar to the setup illustrated in Fig. 5.9. A Fowler

type flap was chosen since it generates the highest lift among the flap types and can be

reasonably equipped on an airfoil of 6% chord thickness. The increase in lift from the

usage of high lift devices under various conditions is demonstrated in Table 5.1.

Figure 5.9. F-18 with full span leading edge slat.[5]

Table 5.1. Contribution of high lift devices for various maneuvers.Altitude SL 35000 35000Mach # 0.2 0.7 1.2Maneuver Landing Turn1 Turn2c'/c flap 1.1 1.001 1.025c'/c slat 1.025 1.00025 1.0125ΔCDo 0.0523 0.0476 0.0487ΔCDi 0.0163 0.0142 0.0147ΔCL,max,total 0.5522 0.5157 0.5258

5.7. Interdisciplinary Trade Study

The instantaneous turn rate is one of the most demanding requirements set by the

RFP. The aircraft stall limit and 7 g structural limit was plotted to obtain the corner speed

at which the maximum instantaneous turn rate occurs. A trade study of various flap

configurations was done to optimize the flap setting as discussed in section 3.2.

5.8. Conclusion

A good aerodynamics design is essential for a successful supersonic aircraft. The

analysis presented above has illustrated that the Sentinel is optimized for supersonic

operation as well as subsonic maneuvers. Various obstacles were encountered and

overcame during the design process, demonstrating the TSN design team motto “Think,

Create, Integrate.”

Reference:

[1] Bertin, J. “Aerodynamic for Engineeers”, 4th edition, Princeton Hall Publication, 2001.

[2] Raymer, D. “Aircraft Design: A Conceptual Approach”. 3rd edition, AIAA, 1999.[3] Weissinger “Lift Distribution of Swept-Back Wing” NACA TM 1120, 1947.[4] Schrenk “A Simple Approximation Method for Obtaining the Spanwise Lift

Distribution” NACA TM 948, 1940.[5] Yves Fauconnier “J-5005 about to land after a nice in flight display at Nancy air

show. June 2002.” [http://perso.wanadoo.fr/aeromil-yf/F18l%205005%20landing.jpg.  Accessed 4/12/06.]