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Presentation 2011
Thrive Technology & Innovation Club
Friday 15th July
Stability & Control Characteristics
RAeS 2016 Light Aircraft Design Conference14th November 2016
Who are Swift?
Who are Swift?
The concept of the Swift is to produce a one airframe “Multi-Function Platform” that will fulfil a varietyof requirements and missions.
Who are Swift?
Who are Swift?
We have implemented a philosophy that is described below. There is a high reliance on our corespreadsheet tool.
What are S&C Characteristics?
What are S&C Characteristics?
AERODYNAMIC FORCE & MOMENT COEFFICIENTS
STABILITY & CONTROL DERIVATIVES
EQUATIONS OF MOTION
What are S&C Characteristics?
Longitudinal Coefficients
𝐶𝐿 = 𝑓1(𝑅𝑒,𝑀, 𝛼, 𝛿𝑒)
𝐶𝐷 = 𝑓2(𝑅𝑒,𝑀, 𝛼, 𝛿𝑒)
𝐶𝑚 = 𝑓3(𝑅𝑒,𝑀, 𝛼, 𝛿𝑒)
Lateral Coefficients
𝐶𝑦 = 𝑓4(𝑅𝑒,𝑀, 𝛽, 𝛿𝑎, 𝛿𝑟)
𝐶𝑛 = 𝑓5(𝑅𝑒,𝑀, 𝛽, 𝛿𝑎, 𝛿𝑟)
𝐶𝑙 = 𝑓6(𝑅𝑒,𝑀, 𝛽, 𝛿𝑎, 𝛿𝑟)
Taylor’s Series Form:
𝐶𝐿 = 𝐶𝐿0 + 𝐶𝐿𝛼𝛼 + 𝐶𝐿𝛿𝑒𝛿𝑒
AERODYNAMIC FORCE & MOMENT COEFFICIENTS
What are S&C Characteristics?
Longitudinal Derivatives
𝑑𝐶𝐿
𝑑𝛼=𝑑𝑓1𝑑𝛼
= 𝑪𝑳𝜶
𝑑𝐶𝑚
𝑑𝛼=𝑑𝑓3𝑑𝛼
= 𝑪𝐦𝜶
Lateral Derivatives
𝑑𝐶𝑦
𝑑𝛽=𝑑𝑓4𝑑𝛽
= 𝑪𝐲𝜷
𝑑𝐶𝑛
𝑑𝛽=𝑑𝑓5𝑑𝛽
= 𝑪𝐧𝜷
Control
Longitudinal Derivatives
𝑑𝐶𝐿
𝑑𝛿𝑒=
𝑑𝑓1𝑑𝛿𝑒
= 𝑪𝐋𝜹𝐞
𝑑𝐶𝑚
𝑑𝛿𝑒=
𝑑𝑓3𝑑𝛿𝑒
= 𝑪𝐦𝜹𝒆
Stability
Lateral Derivatives
𝑑𝐶𝑦
𝑑𝛿𝑟=
𝑑𝑓4𝑑𝛿𝑟
= 𝑪𝒚𝜹𝒓
𝑑𝐶𝑛
𝑑𝛿𝑟=
𝑑𝑓5𝑑𝛿𝑟
= 𝑪𝐧𝜹𝒓
STABILITY & CONTROL DERIVATIVES
Stability Control
Longitudinal: Lift 𝑑𝐶𝐿
𝑑𝛼=𝑑𝑓1𝑑𝛼
= 𝑪𝑳𝜶𝑑𝐶𝐿
𝑑𝛿𝑒=
𝑑𝑓1𝑑𝛿𝑒
= 𝑪𝐋𝜹𝐞
Longitudinal: Pitching Moment
𝑑𝐶𝑚
𝑑𝛼=𝑑𝑓3𝑑𝛼
= 𝑪𝐦𝜶
𝑑𝐶𝑚
𝑑𝛿𝑒=
𝑑𝑓3𝑑𝛿𝑒
= 𝑪𝐦𝜹𝒆
Lateral: Sideforce 𝑑𝐶𝑦
𝑑𝛽=𝑑𝑓4𝑑𝛽
= 𝑪𝐲𝜷
𝑑𝐶𝑦
𝑑𝛿𝑟=
𝑑𝑓4𝑑𝛿𝑟
= 𝑪𝒚𝜹𝒓
Lateral: Roll 𝑑𝐶𝑙
𝑑𝛽=𝑑𝑓5𝑑𝛽
= 𝑪𝐥𝜷𝑑𝐶𝑙
𝑑𝛿𝑟=
𝑑𝑓5𝑑𝛿𝑟
= 𝑪𝐥𝜹𝒓
What are S&C Characteristics?
LONGITUDINAL
EQUATIONS OF MOTION FOR STRAIGHT LINE FLIGHT
𝛼˚𝛿𝑒˚
=𝐶𝐿𝛼 𝐶𝐿𝛿𝑒𝐶𝑚𝛼
𝐶𝑚𝛿𝑒
𝐶𝐿1 − 𝐶𝐿0 − 𝐶𝐿𝑖ℎ𝑖ℎ
−𝐶𝑚0− 𝐶𝑚𝑖ℎ
𝑖ℎ
−1
LATERAL
𝛽˚𝛿𝑎˚𝛿𝑟˚
=
𝐶𝑦𝛽 𝐶𝑦𝛿𝑎 𝐶𝑦𝛿𝑟𝐶𝑙𝛽 𝐶𝑙𝛿𝑎 𝐶𝑙𝛿𝑟𝐶𝑛𝛽 𝐶𝑛𝛿𝑎 𝐶𝑛𝛿𝑟
(−𝑚𝑔𝑠𝑖𝑛𝜙 cos𝛶 + 𝐹𝑇1)
𝑞1𝑆
−𝐿𝑇1𝑞1𝑆𝑏
−𝑁𝑇1 − 𝛥𝑁𝐷1
𝑞1𝑆𝑏
−1
How do we calculate S&C derivatives?
How do we calculate S&C derivatives?
SEMI-EMPIRICAL
EXPERIMENTAL
COMPUTATIONAL
How do we calculate S&C derivatives?
Experimental
How do we calculate S&C derivatives?
Semi-empirical
How do we calculate S&C derivatives?
Computational
How do we use these derivatives?
How do we use these derivatives?We want to fix the roll characteristics of our aircraft. Lateral roll stability depends on the roll due to sideslip angle Cl𝛽. Cl𝛽depends heavily on the dihedral angle of the wing.
Taylor’s series form of roll coefficient: 𝐶𝑙 = 𝐶𝑙𝛽𝛽 + 𝐶𝑙𝑑𝑟𝑑𝑟 + 𝐶𝑙𝑑𝑎𝑑𝑎
Roll due to sideslip as a function of dihedral: Cl𝛽= 𝑓 𝜞 | 𝜞˚= Wing dihedral
How do we use these derivatives?
Consider CS-VLA requirement 177 (a2) for static lateral roll stability.
“Static lateral stability, as shown by the tendency to raise low wingin a slip…
…The angle of slip for these tests must be appropriate to the typeof aeroplane, but in no case may the slip angle be less than thatobtainable with 10˚ of bank.”
How do we use these derivatives?Criteria for setting dihedral angle.
Reasonable values of 𝛽, dr and da using the equations of motion for lateral straight line flight.
Negative roll due to sideslip derivative is stabalising: 𝐶𝑙𝛽 < 0
CS-VLA requirement: 𝐶𝑙𝑑𝑟𝑑𝑟 − 𝐶𝑙𝛽𝛽 ≤ 0
How do we use these derivatives?We ran simulations of different 𝜞 at [Flight case] for 𝐶𝑙𝛽
𝜞˚ 𝐶𝑙𝛽
0 0.019
2 -0.0024
4 -0.025
6 -0.046
Therefore,𝐶𝑙𝛽 = 𝑓 Γ = 0.00004𝜞2 − 0.011𝜞 − 0.0196
y = 4.4544E-05x2 - 1.1294E-02x + 1.9595E-02R² = 9.9985E-01
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0 1 2 3 4 5 6 7
𝐶𝑙_𝛽
𝜞
𝐶𝑙_𝛽(𝜞)
How do we use these derivatives?If 𝜞=4 Then for 𝜙=10˚ all three criteria are satisfied.
Satisfy Criteria 1: Equations of Motion requirement.
𝜞 = 4˚ implies
𝛽˚𝑑𝑎˚𝑑𝑟˚
=50.612
Satisfy Criteria 2: Negative 𝐶𝑙𝛽
𝜞 = 4˚ implies
𝐶𝑙𝛽 = −0.025
Satisfy Criteria 3: CS-VLA 177 (a2) requirement.
𝜞 = 4˚ implies
𝐶𝑙𝑑𝑟𝑑𝑟 − 𝐶𝑙𝛽𝛽 =
\0.6*0.002\ -\-5*0.025\=−0.1016 ≤ 0
4˚
How do we use these derivatives?
Therefore, we set
𝜞 = 4˚
* Other derivatives involed.
Aircraft Wing Dihedral, 𝜞˚
Diamond DV-20 Katana 4
Aquila A210 4.5
CAP 10B 5
Chipmunk 5
Tecnam P-2002 5
SR22 G3 5
ESDU Datcom VLA CFD
𝜞˚ 4 4 4 4
𝐶𝑙𝛽∗ -0.15 -0.06 -0.058 -0.026
|𝑑𝑟𝐶𝑙𝑑𝑟|− |𝛽𝐶𝑙𝛽|
-0.7 -0.77 -0.8 -0.11
Summarise
What are S&C Characteristics?
How can we calculate them?
How can we use them?
Q&A
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