Aerodynamics
Homework Solutions
SYST 460
Instructor: Lance Sherry
Question
Build Aircraft simulation model using equations for Flightpath
Axis
– Plot:
•T on x axis, Airspeed and Ground Speed (primary y axis), FP Accel
(secondary y)
• T on x axis, Altitude (primary y axis), Vertical speed (secondary y)
• T on x axis, Airspeed and Ground Speed (primary y axis), Thrust
(secondary y)
1. Initialize to 5000 ft at 250 knots. Fly for 60 seconds then
climb at 2000 fpm, to 7000’. Increase speed to 260 knots.
(Adjust FPAng and Thrust)
2. Fly a glideslope of -3º from -6nm from 2000’ at 160 knots.
(Adjust FPAng and Thrust)
Model of Manual Flight
γ (Gamma)
Push yoke forward to pitch down/
Pull yoke back to pitch up
T (Thrust)
Push Throttles forward to increase thrust
Pull Throttles back to decrease thrust
3
YOKE
Model of Manual Flight
Gamma
Gamma (degrees)
M dV/dt = T – DWsin(gamma)
Thrust
Integ
Airspeed
(knots)
Flightpath
Accel
(ft/sec2 or
g’s)
Ground
speed
(knots)
THROTTLES
Vertical
speed
(fpm)
Integ
Integ
Distance
(nm)
Altitude
(ft)
True Airspeed (ft/sec)
Altitude Rate = Vertical Speed (ft/sec)
Flightpath Angle
Sin (Flightpath Angle) = Vertical Speed (ft/sec)
True Airspeed (ft/sec)
4
Aircraft Equations of Motion
• Newtons 3rd law
ma = ∑ Forces
• Applied to aircraft
Mass * Flight Path Acceleration = Sum of the Forces on
Flightpath Axis
mass * FPAccel = Thrust – Drag – (Weight * sin (Flightpath Angle))
• Rearranging terms:
Thrust = Drag + (Weight * sin (gamma)) + (mass * FPAccel )
Thrust = Overcome Drag + Overcome Gravity + Overcome Inertia
Procedure
1. Set Flightpath Angle to meet trajectory requirements
Note:
•
Level flight  Gamma = 0
•
Descend on 3 degree glideslope  Gamma = -3 degrees
•
Climb at 2000 fpm  sin (gamma) = Vertical Speed / True Airspeed
(make sure units are same)
2.
Compute Thrust for each trajectory maneuver
Thrust = Drag + (Weight * sin (gamma)) + (mass * FPAccel )
–
Rank Thrust from Highest to Lowest
1. Thrust to climb while accelerating (Drag + Gravity + Inertia)
2. Thrust to climb at constant speed (Drag + Gravity)
3. Thrust to maintain level while accelerating (Drag + Inertia)
4. Thrust to maintain level while at constant speed (Drag)
PROBLEM #1
Flight Path Angle
Gamma = Sin-1 (2000 fpm/250 knots)
Time (s)
0 degrees = level flight
THRUST
0 degrees = level flight
Thrust and
FPAngle to
achieve
Desired
Trajectory
T = Drag + W
Sin (Gamma)
T = Drag + (mass * FPAccel
T = Drag
T = Drag
Altitude
T = Drag
Time (s)
7000’
5000’
Time (s)
Vertical Speed
Climb 2000 fpm
Time (s)
0 fpm = level flight
Airspeed
250 knots
0 fpm = level flight
260 knots’
Time (s)
Desired
Trajectory