SME
Flight Mechanics, Stability & Control · Problem type
Stall speed
Use this for “A 10,000 N airplane has S = 16 m² and CLmax = 1.6. Find its stall speed at sea level, ρ = 1.225 kg/m³.”
Diagram
Level flight: L = W = 10,000 N
This is an example. Type your own values to start a new problem.
Vₛₜₐₗₗ (m/s)
=
2
×
W (N)
ρ (kg/m³)
×
S (m²)
×
Formulas
Vₛₜₐₗₗ
=
√(2
×
W
ρ
×
S
× CLmax
)
25.25
=
√(2
×
10,000
1.225 × 16 × 1.6
)
Assumptions
•
Level flight, so lift equals weight, at the largest lift coefficient CLmax the wing reaches.
•
Any slower and the wing cannot carry the weight: the airplane stalls.
•
Flaps raise CLmax and so lower the stall speed Vₛₜₐₗₗ.
Step-by-step
WE KNOW
W = 10,000 N, ρ = 1.225 kg/m³, S = 16 m², CLmax = 1.6
FIND
stall speed (Vₛₜₐₗₗ)
Step 1 · Find stall speed (Vₛₜₐₗₗ)
Use Vₛₜₐₗₗ = √(2 × W ÷ (ρ × S × CLmax))
Set
W
=
1
2
ρV²SCLmax
and
solve
for
V:
double
W
,
divide
by
ρSCLmax,
take
the
root.
Vₛₜₐₗₗ
=
√(2
×
10,000
1.225 × 16 × 1.6
)
Vₛₜₐₗₗ
=
√(2
×
10,000
19.6 × 1.6
)
Vₛₜₐₗₗ
=
√(2
×
10,000
31.36
)
Vₛₜₐₗₗ
=
√(
20,000
31.36
)
Vₛₜₐₗₗ
=
√
637.8
Vₛₜₐₗₗ = 25.25 m/s
Check
Put the numbers back in. Both sides should match.
25.25
=
√(2
×
10,000
1.225 × 16 × 1.6
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Aircraft performance
Main lesson
Jet range (Breguet)
Use this for “A jet cruises at 230 m/s with L/D = 16 and cₜ = 0.6 per hour. It starts the cruise at 600,000 N and burns 120,000 N of fuel. Find its range.”
Rate of climb from excess thrust
Use this for “A 50,000 N airplane at 80 m/s has 6000 N of thrust and 3553 N of drag. Find its rate of climb and climb angle.”
Load factor and radius of a level turn
Use this for “An airplane flies a level turn at 80 m/s, banked 60°. Find the load factor, the turn radius and the turn rate.”
Density at an altitude (standard atmosphere)
Use this for “Find the standard-atmosphere temperature, pressure and density at 3000 m.”