Proceedings of PACAM XII
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
WING DESIGN WITH A TWIST: OPTIMISED GEOMETRIC TWIST
OF THE GRAND TOURING SPORTS CAR WING
Pascual Marqués-Bruna, marquesp@edgehill.ac.uk
Faculty of Arts & Sciences, Edge Hill University, St. Helen’s Road, Ormskirk, Lancashire, UK
Abstract. Wing twist gives the Grand Touring (GT) sports car an eye-catching ‘aerodynamic shape’, improves
downforce and can enhance aerodynamic efficiency if the twist is optimised. This study aimed to explore the influence
of optimum total twist and optimum twist distribution upon wing aerodynamics, using numerical analysis. Straight
baseline inverted wings with constituent NACA 651-412 and NASA LS(1)-0413 airfoils and linear taper were designed.
Complete wings consisted of the baseline wings fitted with a Gurney flap and end plates. Optimum geometric twist was
subsequently determined and applied. Aerodynamic parameters including downforce, induced drag and profile drag
were computed using a modified version of the classical Prandtl’s Lifting-line Theory. Drag polars were constructed.
The numerical analysis suggests that the twist-optimised wing duplicates the ideal aerodynamic performance of a wing
of elliptic planform and yields high downforce and minimum possible induced drag. The findings support the
implementation of the classical analytical lifting-line model and optimum wing twist at the conceptual stages of GT
sports car design.
Keywords: geometric twist, GT sports car, lifting-line theory, optimisation, wing design
1. INTRODUCTION
Modern aeroplane wings are constructed with geometric twist in a washout configuration characterized by a
progressive reduction in the angle of incidence β from wing root to wing tip (Anderson, 2007). Washout helps control
wing stall, retain aileron function and reduce induced drag (Bertin, 2002). The wing lift coefficient −𝐶𝐿 (downforce in
an inverted wing) and induced drag coefficient 𝐶D𝑖 distributions vary along the span 𝑏. Similarly, the wing of the GT
sports car requires optimised aerodynamics to attain high downforce, aerodynamic efficiency and improved safety while
conforming to the Federation Internationale de l’Automobile’s (FIA) technical regulations for car design (FIA, 2010).
However, there is a scarcity of research on the influence of optimised twist upon sports car wing aerodynamics.
Straight wings of elliptic planform attain minimum 𝐶D𝑖 and profile drag coefficient 𝐶D (Milne-Thomson, 1973), but
are more expensive to manufacture than rectangular wings. The tapered wing is typically used as a compromise
between the elliptic and the rectangular planform. However, Phillips et al. (2006) has explained that the tapered wing
requires an optimum total wing twist Ω𝑜𝑝𝑡 and optimum spanwise twist distribution 𝜔(𝜃)𝑜𝑝𝑡 to generate an elliptical
−𝐶𝐿 distribution, minimum 𝐶D𝑖 and replicate the high aerodynamic performance characteristic of a straight wing of
elliptic planform (Phillips, 2004). Recent developments of Prandtl’s Lifting-line Theory (Phillips, 2004; Phillips et al.,
2006; Phillips and Alley, 2007) allow computing Ω𝑜𝑝𝑡 & 𝜔(𝜃)𝑜𝑝𝑡 for the design of a high performance wing. This
study aimed to explore the influence of geometric Ω𝑜𝑝𝑡 & 𝜔(𝜃)𝑜𝑝𝑡 upon −𝐶𝐿 , 𝐶D𝑖 and 𝐶D in wings with linear taper. It
was hypothesised that: H1 - application of Ω𝑜𝑝𝑡 & 𝜔(𝜃)𝑜𝑝𝑡 yields a near-elliptical −𝐶𝐿 distribution that gives high
downforce and minimum 𝐶D𝑖 . The findings may be used for the implementation of optimised geometric twist at the
conceptual stages of GT sports car wing design.
2. METHOD
2.1. Airfoil and wing geometry
Wing prototypes for the GT sports car were designed using National Advisory Committee for Aeronautics (NACA)
651-412 and National Aeronautics and Space Administration (NASA) LS(1)-0413 extensive laminar flow airfoils
(Abbott and von Doenhoff, 1959). The design lift coefficient 𝑐𝑙0 is 0.4 for both airfoils and the zero-lift angle of attack
𝛼𝐿0 is -3° and -4° for the 651-412 and LS(1)-0413 airfoils, respectively (Abbott and von Doenhoff, 1959; Bertin, 2002).
The leading edge of the 651-412 is of small-radius, which makes this airfoil aerodynamically efficient at low incidence
(Milne-Thomson, 1973). The LS(1)-0413 is stall resistant and uses a concave pressure recovery that generates high
downforce (Bertin, 2002). Straight baseline inverted wings with linear taper were constructed with the following
geometry and aerodynamic efficiency: 𝑏 = 1900 mm, chord 𝑐 at the wing mid-span = 360 mm and at the wing tip = 324
mm, taper ratio 𝑅𝑇 = 0.90, aspect ratio 𝐴𝑅 = 5.56, planform area 𝑆 = 0.65 m2, induced drag efficiency factor 𝛿 and lift
efficiency factor 𝜏 = 0.050, and Oswald efficiency factor 𝑒 = 0.95. Straight complete wings included a Gurney flap on
the pressure side of height ℎ𝐺 = 15 mm and end plates of height ℎ𝑒𝑝 = 150 mm to comply with technical regulations
(FIA, 2010). Subsequently, the wings were twisted geometrically by applying Ω𝑜𝑝𝑡 & 𝜔(𝜃)𝑜𝑝𝑡 twist mode (Fig. 1). The
twist consisted of washout using 𝛽 at the wing tips and 𝛽 + Ωopt at the mid-span and was modelled numerically by
Proceedings of PACAM XII
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
elliptically modifying 𝛽 along 𝑏 (Anderson, 2007). Wing twist and aerodynamic computations were carried out using
spanwise 𝑛 station intervals of 0.01 m (Phillips and Alley, 2007). Thus, 8 wing prototypes were constructed: straight
baseline 651-412, straight complete 651-412, twisted baseline 651-412, twisted complete 651-412, straight baseline
LS(1)-0413, straight complete LS(1)-0413, twisted baseline LS(1)-0413 and twisted complete LS(1)-0413.
Figure 1. A complete elliptically-twisted wing fitted with a Gurney flap
and end plates installed on a GT sports car
2.2. Computation of wing aerodynamics
2.2.1. Straight baseline wings
An elliptical distribution of the circulation Γ(𝑦) was computed using a 4-stage numerical iterative method, based on
Prandtl’s Lifting-line Theory (Anderson, 2007): 1 - An elliptical Γ(𝑦) distribution designated Γ𝑜𝑙𝑑 was assumed and the
local induced angle of attack at each 𝑛 station 𝛼𝑖 (𝑦𝑛 ) was calculated; 2 - The 𝛼𝑖 (𝑦𝑛 ) was used to obtain the effective
angle of attack 𝛼eff at each 𝑛 station 𝛼eff (𝑦𝑛 ), which was subsequently used to find the lift coefficient 𝑐𝑙 of the local
airfoil 𝑐𝑙𝑛 from the airfoil lift curve using AeroFoil 2.2 software; 3 - The 𝑐𝑙𝑛 was used to calculate a new Γ(𝑦), thus
Γ𝑛𝑒𝑤 , and agreement between Γ𝑜𝑙𝑑 and Γ𝑛𝑒𝑤 was attained by further input Γ𝑖𝑛𝑝𝑢𝑡 using Eq. (1) (acceptable accuracy was
set at 0.01%); and 4 - The converged Γ(𝑦) was used to obtain −𝐶L and 𝐶D𝑖 .
Γ𝑖𝑛𝑝𝑢𝑡 = Γ𝑜𝑙𝑑 + 𝐷(Γ𝑛𝑒𝑤 − Γ𝑜𝑙𝑑 )
(1)
where, the damping factor 𝐷 was 0.05. The Γ(𝑦) at each 𝑛 station was obtained from the function
2𝑦 2
Γ(𝑦) = Γ0 √1 − ( )
𝑏
(2)
where, Γ0 is the circulation at the origin (i.e., at the mid-span) obtained from Eq. (3) (adapted from Anderson, 2007)
Γ0 = 0.5 𝑐𝑙 𝑐𝑛 𝑽∞
(3)
where, the 𝑐𝑙 was obtained using AeroFoil 2.2 software based on a Reynolds number 𝑅𝑒 of 1.08 × 106 and assuming
International Standard Atmosphere (Bertin, 2002). The local wing chord 𝑐𝑛 varied linearly along 𝑏 and 𝑽∞ represents
the flow velocity vector. The 𝛼𝑖 (𝑦𝑛 ) was calculated using
𝛼𝑖 (𝑦𝑛 ) =
𝑏/2 (𝑑Γ(𝑦) ⁄
1
𝑑𝑦 )𝑑𝑦
∫
4𝜋𝑽∞ −𝑏/2
𝑦𝑛 − 𝑦
(4)
where, 𝑦 is the spanwise coordinate. Then, 𝛼eff (𝑦𝑛 ) for the iterative solution was computed from
𝛼eff (𝑦𝑛 ) = 𝛼 − 𝛼𝑖 (𝑦𝑛 )
(5)
where, α is the angle of attack. The −𝐶L and 𝐶D𝑖 were obtained by integration using Γ(𝑦), in the respective Eqs. (6)
and (7), and the 𝐶𝐷 was computed using Eq. (8).
Proceedings of PACAM XII
−𝐶𝐿 =
𝐶𝐷𝑖 =
𝑏/2
2
𝑽∞ 𝑆
2
𝑽∞ 𝑆
𝐶D = 𝑐𝑑𝑖 +
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
∫
Γ(𝑦)𝑑𝑦
(6)
−𝑏/2
𝑏/2
∫
Γ(𝑦)𝛼𝑖 (𝑦)𝑑𝑦
(7)
−𝑏/2
−𝐶L2
𝜋𝑒𝐴𝑅
(8)
where, 𝑐𝑑𝑖 is the airfoil drag coefficient 𝑐𝑑 adjusted for induced flow. The 𝑐𝑑𝑖 was obtained from graphical
experimental data (Milne-Thomson, 1973; Anderson, 2007) using the adjusted airfoil lift coefficient 𝑐𝑙𝑖 calculated from
𝑐𝑙𝑖 = 𝑎0 (𝛼eff − 𝛼L0 )
(9)
where, 𝑎0 is the airfoil lift slope in radians given by
𝑎0 ≡ d𝑐𝑙 /d𝛼
(10)
2.2.2. Twist optimisation
The normalised 𝜔(𝜃)𝑜𝑝𝑡 was given by the function
𝜔(𝜃)𝑜𝑝𝑡 = 1 −
𝑠𝑖𝑛(𝜃)
1 − (1 − 𝑅𝑇 )|𝑐𝑜𝑠𝜃|
(11)
where, 𝜃 represents the spanwise angular coordinate. The 𝜔(𝜃)𝑜𝑝𝑡 was used to elliptically vary the local 𝑐𝑙𝑛 , Γ(𝑦)
and 𝛼𝑖 (𝑦𝑛 ) consistent with the progressive non-linear twist along 𝑏 (Milne-Thomson, 1973). The planform 𝑎𝑛 and twist
𝑏𝑛 coefficients for the lifting-line solution (Phillips, 2004) were obtained from the relations
∞
2𝐴𝑅(1 + 𝑅𝑇 )
𝑛
∑ 𝑎𝑛 {
+
} sin(𝑛𝜃) = 1
𝑎[1 − (1 − 𝑅𝑇 )|cos(𝜃)|] sin(𝜃)
(12)
𝑛=1
and
𝑎0
2(1 + 𝑅𝑇 )𝐴𝑅
𝑏𝑛 = {
𝑎0
𝑎𝑛 [1 +
]
2(1 + 𝑅𝑇 )𝐴𝑅
𝑎1 − (1 − 𝑎1 )
𝑓𝑜𝑟 𝑛 = 1
(13)
𝑓𝑜𝑟 𝑛 ≠ 1
where, 𝑎 is the wing lift slope in radians computed using
𝑎=
𝑎0
𝑎0
1+(
) (1 + 𝜏)
𝜋𝐴R
(14)
The Fourier coefficients 𝐴𝑛 were calculated using
𝐴𝑛 ≡ 𝑎𝑛 (𝛼 − 𝛼𝐿0 )𝑚𝑖𝑑−𝑠𝑝𝑎𝑛 − 𝑏𝑛 Ω
(15)
where, the preset total wing twist Ω of 5° was given by
Ω = (𝛼 − 𝛼𝐿0 )𝑚𝑖𝑑−𝑠𝑝𝑎𝑛 − (𝛼 − 𝛼𝐿0 )𝑤𝑖𝑛𝑔 𝑡𝑖𝑝
(16)
The −𝐶L for the optimally-twisted wing was obtained using (Phillips, 2004)
−𝐶L = 𝐴𝑅𝜋𝐴1
(17)
Proceedings of PACAM XII
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
and Ω𝑜𝑝𝑡 was given by
Ω𝑜𝑝𝑡 =
𝑘𝐷𝐿 𝑐𝑙0 1
×
2𝑘𝐷Ω 𝑎
(18)
whereby, the lift-twist factor 𝑘𝐷𝐿 and twist factor 𝑘𝐷Ω were obtained, respectively, from
𝑘𝐷𝐿 ≡
𝜋𝑎0
𝛿
(1 + 𝑅𝑇 )𝑎
(19)
and
𝑘𝐷Ω ≡ (
2
𝜋𝑎0
) 𝛿
2(1 + 𝑅𝑇 )𝑎0
(20)
The 𝐶𝐷𝑖 for the optimally-twisted wing was calculated using Eq. (21) (Phillips, 2004)
𝐶𝐷𝑖 =
−𝐶𝐿2
𝛿
𝜋𝑎0 Ω 2
+
[−𝐶𝐿 −
]
𝜋𝐴𝑅 𝜋𝐴𝑅
2(1 + 𝑅𝑇 )
(21)
2.2.3. Complete wings
The 𝑐𝑙 and AR were adjusted to account for the increased downforce provided by the Gurney flap (Wang et al.,
2008) and the flow control and increased 𝐴𝑅 effects achieved by the end plates (Phillips, 2004), respectively, using
∆𝑐𝑙 = √
ℎ𝐺
𝑐
(22)
and
ℎ𝑒𝑝
𝐴𝑅𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 = 𝐴𝑅𝑎𝑐𝑡𝑢𝑎𝑙 [1 + 1.9 ( )]
𝑏
(23)
where, ∆𝑐𝑙 is the increment in 𝑐𝑙 caused by the Gurney flap and 𝐴𝑅𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 is the effective AR attained using the
end plates. A new −𝐶L for the complete wings was obtained by modifying wing 𝑎 to account for ∆𝑐𝑙 and 𝐴𝑅𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒
−𝐶L = 𝑎(𝛼 − 𝛼L0 )
(24)
where, wing 𝑎 was adjusted by using 𝐴𝑅𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 in Eq. (14). The 𝐶𝐷 and 𝐶𝐷𝑖 associated with the installation of the
Gurney flap and end plates were obtained using the new −𝐶L and 𝐴𝑅𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 in Eqs. (8) and (21), respectively.
2.3. Modelling of wing aerodynamics
Wing aerodynamics were simulated for -4° ≤ 𝛼 ≤ 12° at 1° intervals; based on wing-tip α in the case of twisted
wings. Drag polars were plotted for the assessment of wing downforce and aerodynamic efficiency.
3. RESULTS
3.1. Airfoil and wing aerodynamics and normalised 𝜔(𝜃)𝑜𝑝𝑡
Installation of the Gurney flap changes the 𝛼𝐿0 from -3° to -5.11° and from -4° to -5.86° in the 651-412 and LS(1)0413 airfoils, respectively, and causes a Δ𝑐𝑙 of 0.205 and an increase in wing 𝛿 and 𝜏 to a value of 0.055. Mounting the
end plates increases the effective AR from 5.56 for the baseline wing to 6.39 for the complete wing. The Ω𝑜𝑝𝑡 for the
651-412 wing is 4.6° and for the LS(1)-0413 is 4°. The normalised spanwise 𝜔(𝜃)𝑜𝑝𝑡 is near-elliptical, thus the rate of
geometric twist increases rapidly in the regions near the wingtips, which causes a near-elliptical −𝐶L distribution.
Proceedings of PACAM XII
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
3.2. Wing 𝐶D𝑖 and drag polars
The use of the LS(1)-0413 airfoil, application of wing twist and installation of the Gurney flap and end plates are all
factors that augment 𝐶D𝑖 (Fig. 2). Complete wings and twisted wings generate greater −𝐶𝐿 than baseline wings and
straight wings, at the expense of additional 𝐶D and lower aerodynamic efficiency (Fig. 3). In Fig. 3, data at α = 5° has
been marked using arrows to help compare data for different wing prototypes. Wings built with a constituent 651-412
airfoil attain higher aerodynamic efficiency but wings constructed with an LS(1)-0413 airfoil yield greater −𝐶𝐿 in all 8
wing prototypes.
Straight baseline
0.6
0.6
Twisted baseline
Twisted complete
0.4
CDi
CDi
Straight complete
0.2
0.4
0.2
651-412
0.0
LS(1)-0413
0.0
-4
-2
0
2
4
6
8
10
12
-4
-2
0
2
α (°)
4
6
8
10
12
α (°)
Figure 2. The 𝐶D𝑖 for the prototype wings
2.5
2.5
Straight wings
2.0
2.0
α = 5°
1.5
α = 5°
1.5
Baseline 651-412
1.0
-CL
-CL
Twisted wings
Baseline 651-412
1.0
Complete 651-412
Complete 651-412
Baseline LS(1)-0413
0.5
Baseline LS(1)-0413
0.5
Complete LS(1)-0413
Complete LS(1)-0413
0.0
0.0
0.0
-0.5
0.1
0.2
CD
0.0
0.3
-0.5
0.1
0.2
0.3
CD
Figure 3. Drag polars for the straight and twisted wings (-4° ≤ 𝛼 ≤ 12°)
4. DISCUSSION
Use of the LS(1)-0413 airfoil for wing construction results in higher downforce primarily due to the larger leading
edge radius and 1% greater thickness than in the 651-412 airfoil (Abbott and von Doenhoff, 1959), however such
geometric features augment 𝐶D𝑖 and 𝐶D (Figs. 2 & 3). The twisted complete LS(1)-0413 yields the largest −𝐶𝐿 and 𝐶D𝑖
of all wings (Figs. 2 & 3) due to the large β and α in the mid-span region, the presence of the Gurney flap and the use of
the LS(1)-0413 airfoil. The larger mid-span β and α of the twisted wings causes an increase in 𝐶D𝑖 (Fig. 2). Nonetheless,
the increase in 𝐶D𝑖 can be considered small and solely attributed to mid-span β and α. This suggests that a twistoptimised wing with a linearly-tapered planform for the GT car nearly duplicates the high performance of an elliptic
wing and satisfies the requirement for minimum possible 𝐶D𝑖 , consonant with theory (Milne-Thomson, 1973; Phillips
and Alley, 2007); thus, H1 was accepted. This is because, with the exception of an elliptic planform, a straight wing is
optimised for a design lift coefficient of zero. However, Ω𝑜𝑝𝑡 & 𝜔(𝜃)𝑜𝑝𝑡 considerably reduces 𝐶D𝑖 when the wing
operates at any other −𝐶𝐿 (Phillips, 2004). The Gurney flap forces the wake downwards and is primarily responsible for
increased −𝐶𝐿 with further increments in downforce achieved by the installation of the end plates (Wang et al, 2008). In
fact, the use of end plates reduces Oswald efficiency, however the augmented effective 𝐴𝑅 associated with the end
Proceedings of PACAM XII
12th Pan-American Congress of Applied Mechanics
January 02-06, 2012, Port of Spain, Trinidad
plates curtails the additional 𝐶D𝑖 and 𝐶D caused by the Gurney flap and helps maintain efficiency (Milne-Thomson,
1973). In a high-downforce racing circuit with slow turns, the additional downforce achieved by the use of the twisted
complete LS(1)-0413 will compensate for the performance losses caused by the extra induced drag (Wang et al.,
2008)).
Partial wing stall is an important parameter in wing design that may contribute to safety in motor racing by
preventing a sudden loss of downforce when the car decelerates upon entering a slow curve (Bertin, 2002). Geometric
twist may be effective in achieving a partial stall of the wing since the mid-span region, which is set at a higher 𝛼, will
stall first (Anderson, 2007). Greater safety, as well as higher downforce, can be attained by using the LS(1)-0413 airfoil,
which is stall resistant (Bertin, 2002). Also, the small 𝑅𝑇 helps preserve 𝑐 length and prevent a low Re and the stall in
the wing tip region (Abbott and von Doenhoff, 1959). Thus, the use of a LS(1)-0413 airfoil, geometric twist and a small
𝑅𝑇 help control, and perhaps prevent, wing stall.
The data in Fig. 3 help prioritise either downforce or aerodynamic efficiency in wing design to adjust the GT car to
the characteristics of the racing circuit (Wang et al., 2008). Greater downforce is attained using the twisted complete
LS(1)-0413 wing but higher efficiency is achieved using the straight complete 65 1-412 wing. The higher aerodynamic
efficiency attained when using the 651-412 airfoil over the full range of 𝛼 (Fig. 3) is due to the small-radius leading
edge and 1% thinner profile of the constituent airfoil (Abbott and von Doenhoff, 1959). Phillips et al. (2006)
demonstrated the validity of the modified lifting–line numerical solution for the prediction of the 𝐶D𝑖 associated with
optimised wing twist. The computational fluid dynamics validation performed by Phillips et al. (2006) suggests that the
lifting-line method slightly underestimates the decrease in 𝐶D𝑖 caused by optimum twist. The complexity of flow over
complete optimally-twisted wings may be examined in a wind tunnel to further validate the numerical methods.
5. CONCLUSIONS
An optimally-twisted wing is complex to fabricate, as the twist varies elliptically along 𝑏. However, the findings
suggest that a twist-optimised wing with a linearly-tapered planform for the GT car replicates the high performance of
an elliptic wing and fulfils the requirements for high downforce and minimum possible 𝐶D𝑖 . A twisted complete
LS(1)-0413 wing yields high −𝐶𝐿 , at the expense of greater 𝐶D𝑖 and 𝐶D , and is suitable for a high-downforce racing
circuit. The geometric twist and small 𝑅𝑇 help achieve a partial wing stall that contributes to safety in motor racing. The
complete straight 651-412 wing achieves superior aerodynamic efficiency and may be used in fast circuits.
6. ACKNOWLEDGEMENTS
The author acknowledges the financial support provided by Marques Aviation Ltd for this project.
7. REFERENCES
Abbott, I.H. and von Doenhoff, A.E., 1959. “Theory of Wing Sections”, Dover Publications, New York.
Anderson, J.D., 2007. “Fundamentals of Aerodynamics”, McGraw-Hill, London.
Bertin, J.J., 2002. “Aerodynamics for Engineers”, Prentice Hall, New Jersey.
FIA, 2010. Technical Regulations for Grand Touring Cars (Group GT1 and GT2), Annexe J, Appendix J, Article 257,
Paris, pp. 1–15.
Milne-Thomson, L.M., 1973. “Theoretical Aerodynamics”, Dover Publications, New York.
Phillips, W.F., 2004. “Lifting-Line Analysis for Twisted Wings and Washout-optimized Wings”, J. Aircr., Vol. 41, No.
1, pp. 128-136.
Phillips, W.F. and Alley, N.R., 2007. “Predicting Maximum Lift Coefficient for Twisted Wings Using Lifting-Line
Theory”, J. Aircr., Vol. 44, No. 3, pp. 898-910.
Phillips, W.F., Fugal, S.R. and Spall, R.E., 2006. “Minimizing Induced Drag with Wing Twist, Computational-fluiddynamics Validation”, J. Aircr., Vol. 43, No. 2, pp. 437-444.
Wang, J.J., Li, Y.C. and Choi, K.S., 2008. “Gurney Flap: Lift Enhancement, Mechanisms and Applications”, Prog.
Aerospace Sci., Vol. 44, No. 1, pp. 22-47.