Aero 317 Flashcards
Surge
Linear movement along the x-axis
Sway
Linear movement along the y-axis
Heave
Linear movement along the z-axis
Aileron
Controlled by rotation of the stick. Primary control for roll.
Elevator
Controlled by fore/aft stick. Primary control for pitch.
Rudder
Controlled by pedals. Primary control for yaw.
Stability
The tendency of a system to return to its initial condition when disturbed from an equilibrium/trim position.
Two types of stability
Static and dynamic
Static stability
The initial tendency of an aircraft following a disturbance.
Three possibilities of static stability
- Return towards trim position (statically stable).
- Diverge away from trim position (statically unstable).
- Neither (statically neutral).
Dynamic stability
How an aircraft behaves once it enters an oscillation.
Two dynamic stability possibilities
- Oscillation damps out (dynamically stable).
- Oscillation amplifies over time (dynamically unstable).
Centre of pressure
The point on a body where the pressure field acts, i.e. where lift and drag act from if modelled as single forces.
Aerodynamic centre
The point on a aerofoil where the moment doesn’t change with lift, i.e. dCm/dCl = 0. It’s denoted xac.
Finding the moment at the aerodynamic centre.
Cmac = Cm0
If A.C. is in front of the C.G., an increase in alpha will…
- Increase lift
- Increase nose-up moment
- Increase alpha further, hence statically unstable (dM/dL > 0).
If A.C. is behind the C.G., an increase in alpha will…
- Increase lift
- Increase nose-down moment
- Decrease alpha back towards trim, hence statically stable (dM/dL < 0).
Dimensionless form of the pitching moment equation
Cm = Cl(h-hac) + Cm0wb - CltVt
Vt (v bar, technically)
ltSt/Sc
Effective tailplane angle of attack, alphat
alpha + phit - epsilon
Epsilon
(∂epsilon/∂alpha)*alpha
Neutal point, hn
hac + Vt(a1/a)(1-(∂epsilon/∂alpha))
Static margin, Hn
hn - h, where hn is the neutral point and h is the centre of gravity location.
Controls free neutral point, hn’
hac + Vt(a1/a)(1-(∂epsilon/∂alpha))*(1-(a2b1/a1b2))
Controls free static margin, Hn’
hn’ - h
Alpha
Cl/a
Cmh
Cmh0 + (b2/a2)(1/Vt)(h-hn’)Cl
Load factor, n
L/mg
Tail lift coefficient, Clt
a1alphat + a2eta + a3*beta
Three traits of the phugoid dynamic mode
- Long period
- Large amplitude
- Low frequency, characterised by large changes in flight speed and altitude.
Determinant of a 2x2 matrix, det(A)
ad - bc
If A is a 2x2 abcd matrix, what’s the adjugate of A, adj(A)?
d -b
-c a
Open loop system
No feedback outside of the pilot applying control inputs to change the aircraft state as they want.
Closed loop system
Use feedback about aircraft states to apply control inputs to the aircraft system.
Limited authority system
The feedback control law is only allowed to make small adjustments to the pilot’s control inputs to modify the response of the aircraft.
Full authority system
Allows the control law jurisdiction over the entire range of control surface deflections.
Root locus rules 1-5
- The number of lines (loci) is equal to the greater of m or n (the orders of the numerator or denominator) and hence the number of zeros or poles.
- As K increases from zero to infinity, the roots of the characteristic equation move from the open loop poles of G(s) to the open loop zeros of G(s).
- If m=n, then roots move from poles to zeros in pairs, but if there are excess poles (n>m), then the poles migrate along asymptotes towards infinity. The number of asymptotes is equal to the number of excess poles, n-m.
- The portion of the real axis to the left of odd numbers of open loop poles are part of the loci.
- The angle that the asymptotes make is a function of the number of asymptotes, N: thetan = (180-360N)/(n-m).
Root locus rules 6-8
- The asymptotes meet at a point defined by the centroid of the real parts of the roots and zeros: sigma = (∑real parts of poles - ∑real parts of zeros)/n-m
- Lines break out, or in to, the real axis at 90˚
- The points on the locus where the poles leave the real axis are the values of s which satisfy: (d/ds)G(s) = 0.
What’s the modulus of complex number equal to?
The gain.
What’s the phase of a complex number equal to?
The argument/angle.
Nichols plot
Plots the gain and phase of a transfer function.
Nyquist plot
The frequency response in the complex plane.
Nyquist stability criterion
The Nyquist plot must not enclose the critical point if the closed loop system is to be stable.
Phase margin
The amount of phase lag a system can experience before the Nyquist locus will touch the critical point.
Gain margin
The gain multiplier required to cause a loss of stability, defined by the control gain, K, and the system gain where the phase = -180˚.
