Flight Dynamics Exam 2

Longitudinal Modes and their Details

Short Period: fast bump, mostly alpha and q
Long Period (Phugoid): long oscillations, mostly u and theta

Extracting damping ratio, natural frequency, and damped natural frequency from Eigenvalues

wn = sqrt(Re²+Im²), zeta = -Re/wn, wd = Im

CnB

Positive

ClB

Negative

Clp

Negative

Cmq

Negative

Cnr

Negative

Clr

Positive

Rudder Balance

dr = -CnB/Cndr * B

Lateral Modes and their Details

Roll Mode: mostly p, non-oscillatory, usually relatively fast
Spiral Mode: mostly phi and p, can be stable or unstable, generally a slow mode
Dutch Roll: mostly B and r, oscillatory motion, produces coupled rolling and yawing, often requires a yaw damper

Spiral Stability Condition

LB*Nr > NB*Lr

Cooper-Harper Scale

handling qualities, 1-10, 1 is good 10 is atrocious

Handling Level 1

adequate for the mission

Handling Level 2

Adequate but requires increased pilot workload

Handling Level 3

Aircraft can be controlled safely, but mission effectiveness is inadequate

Class i aircraft

small, light

Class ii aircraft

medium weight, low to medium maneuverability

Class iii aircraft

large, heavy, low to medium maneuverability

Class iv aircraft

Highly maneuverable such as fighters

Flight Phase A

Non terminal flight requiring rapid maneuvering or precise flight path control

Flight Phase B

non terminal flight involving gradual maneuvering

Flight Phase C

terminal flight such as takeoff and landings

Gliding Flight Path Angle

gamma = tan^-1(D/L)

Gliding speed

V = sqrt((2*w)/(rho*S*sqrt(CD²+CL²))

Maximize Glide Range?

Maximize L/D

Maximize Endurance?

Minimize sink rate

CL Max Endurance

CLME = sqrt(3*CDo/epsilon)

CD Max Endurance

CDME = 4*CDo

L/D ME fraction of L/D max

0.86

VME percent of V L/Dmax

0.76

Approach Speeds

Civilian: 1.3 stall

Military: 1.2 stall

Carrier based: 1.1 Stall

Empirical Landing Rule

Dlanding = 0.3*V²

Barrowman Equation

the center of pressur of the rocket is a weighted average of the individual components center of pressures

Rocket Static Margin

Xcg-Xcp/dref

Stability condition for rockets

CG must be ahead of the CP