SME
Flight Mechanics, Stability & Control
Aircraft performance
Use this for “A 50,000 N airplane with S = 20 m², CD0 = 0.025 and K = 0.05 flies level at 80 m/s where ρ = 1 kg/m³. Find CL and the thrust required.”
Diagram
Level flight: L = W = 50,000 N
T
=
D
=
3,553
N,
so
L
D
=
14.1
This is an example. Type your own values to start a new problem.
W
Weight
example
ρ
Air density
example
V
Airspeed
example · m/s
S
Wing area
example · m²
q
Dynamic pressure
calculated
CL
Lift coefficient
calculated
CD0
Zero-lift drag coefficient
example
K
Induced drag factor
example
CD
Drag coefficient
calculated
D
Drag
calculated
Formulas
q
=
0.5
×
ρ
×
V
2
3,200
=
0.5
×
1
×
80
2
W
=
q
×
S
×
CL
50,000 = 3,200 × 20 × 0.7813
CD
=
CD0
+
K
×
CL
2
0.05552
=
0.025
+
0.05
×
0.7813
2
D
=
q
×
S
×
CD
3,553 = 3,200 × 20 × 0.05552
Assumptions
•
Steady, level, unaccelerated flight: lift equals weight (L = W) and thrust equals drag (T = D).
•
A parabolic drag polar: zero-lift drag CD0 plus induced drag KCL².
•
The drag D found here is the thrust required to hold this speed.
Step-by-step
WE KNOW
W = 50,000 N, ρ = 1 kg/m³, S = 20 m², V = 80 m/s, CD0 = 0.025, K = 0.05
FIND
dynamic pressure (q), lift coefficient (CL), drag coefficient (CD), drag (D)
Step 1 · Find dynamic pressure (q)
Use q = 0.5 × ρ × V²
Half the density times the airspeed squared.
q
=
0.5
×
1
×
80
2
q
=
0.5
×
6,400
q
=
3,200
Pa
Step 2 · Find lift coefficient (CL)
Use W = q × S × CL
Level
flight:
the
lift
qSCL
carries
the
weight,
so
divide
W
by
qS.
CL
=
W
q
×
S
CL
=
50,000
3,200 × 20
CL
=
50,000
64,000
CL = 0.7813
Step 3 · Find drag coefficient (CD)
Use CD = CD0 + K × CL²
Zero-lift drag plus the induced part KCL².
CD
=
0.025
+
0.05
×
0.7813
2
CD = 0.025 + 0.05 × 0.6104
CD = 0.025 + 0.03052
CD = 0.05552
Step 4 · Find drag (D)
Use D = q × S × CD
Dynamic pressure times wing area times CD; the thrust must match it.
D
=
3,200
×
20
×
0.05552
D
=
64,000
×
0.05552
D
=
3,553
N
Check
Put the numbers back in. Both sides should match.
3,200
=
0.5
×
1
×
80
2
✓
50,000 = 3,200 × 20 × 0.7813 ✓
0.05552
=
0.025
+
0.05
×
0.7813
2
✓
3,553 = 3,200 × 20 × 0.05552 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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