SME
Aerodynamics
Lift and drag
Use this for “A 16 m² wing flies at 60 m/s in air of 1.225 kg/m³ with CL = 0.5 and CD = 0.03. Find L, D and L/D.”
Diagram
Lift
is
⟂
the
wind,
drag
along
it:
L
D
=
16.67.
This is an example. Type your own values to start a new problem.
L (kN)
=
q (Pa)
×
S (m²)
×
CL
D (kN)
=
q (Pa)
×
S (m²)
×
CD
ρ
Air density
example
V
Speed
example
L/D
Lift-to-drag ratio
calculated
Formulas
q
=
0.5
×
ρ
×
V
2
2,205
=
0.5
×
1.225
×
60
2
L
=
q
×
S
×
CL
17,640 = 2,205 × 16 × 0.5
D
=
q
×
S
×
CD
1,058 = 2,205 × 16 × 0.03
L
D
=
CL
CD
16.67
=
0.5
0.03
Formulas are worked in N. The step-by-step shows the conversions.
Assumptions
•
The coefficients come from a wind tunnel or a polar at this Reynolds and Mach number.
•
Lift is ⟂ the oncoming flow, not ⟂ the chord; drag is along it.
Step-by-step
WE KNOW
ρ = 1.225 kg/m³, V = 60 m/s, S = 16 m², CL = 0.5, CD = 0.03
FIND
dynamic pressure (q), lift (L), drag (D), lift-to-drag ratio (L/D)
Step 1 · Find dynamic pressure (q)
Use q = 0.5 × ρ × V²
Half the density times the speed squared.
q
=
0.5
×
1.225
×
60
2
q
=
0.5
×
1.225
×
3,600
q
=
0.6125
×
3,600
q
=
2,205
Pa
Step 2 · Find lift (L)
Use L = q × S × CL
Dynamic pressure times area times CL.
L
=
2,205
×
16
×
0.5
L
=
35,280
×
0.5
L
=
17,640
N
Step 3 · Find drag (D)
Use D = q × S × CD
Dynamic pressure times area times CD.
D
=
2,205
×
16
×
0.03
D
=
35,280
×
0.03
D
=
1,058.4
N
Step 4 · Find lift-to-drag ratio (L/D)
Use L/D = CL ÷ CD
q
and
S
cancel:
L
D
is
CL
CD
.
L
D
=
0.5
0.03
L
D
=
16.67
Step 5 · Convert the answers
Change each answer back to the unit you chose.
L = 17,640 N = 17.64 kN (1 kN = 1000 N)
D = 1,058 N = 1.058 kN (1 kN = 1000 N)
Check
Put the numbers back in. Both sides should match.
2,205
=
0.5
×
1.225
×
60
2
✓
17,640 = 2,205 × 16 × 0.5 ✓
1,058 = 2,205 × 16 × 0.03 ✓
16.67
=
0.5
0.03
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Drag polar and maximum L/D
Use this for “A wing has CD0 = 0.025, AR = 8 and e = 0.8. Find CD at CL = 0.5 and the best L/D.”
Reynolds number of a wing chord
Use this for “Air at 1.225 kg/m³ with μ = 1.789 × 10⁻⁵ Pa·s flows at 60 m/s past a 1.5 m chord. Find Re.”
Skin friction, form, induced or wave drag
Use this for “Which kind of drag do a golf ball’s dimples cut, and which do long glider wings cut?”