La Paz Take-off Lab

0.0 s

Verdict (1.15 × s_LO ≤ runway)

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Density ratio σ

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Density altitude

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Avg. roll thrust

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V_stall (TAS)

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V_LO (TAS)

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V_LO (EAS ≈ IAS)

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Net force at 0.7 V_LO

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s_LO lecture formula

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1.44 W²/(g ρ_∞ S c_l,max [T − (D + μ_r(W − L))]_avg)

s_LO integrated (check)

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Runway left at lift-off

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Max mass by rule (lecture formula)

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Field and day

Field elevation (m)

Temperature offset ISA ± (°C)

Runway length (m)

LPB is about 4,000 m (approximate).

Aircraft (737-800-class)

Take-off mass (kg)

MTOW about 79,000 kg (approximate).

c_l,max (take-off flaps)

Representative: 2.0.

Static thrust per engine, sea level (kN)

Two CFM56-7B-class engines, about 117 kN each.

Wing area S	124.6 m²
Avg. roll thrust / static	0.85
Thrust lapse	T ∝ σ^0.75
c_d,0 / e / c_l in roll	0.05 / 0.8 / 0.8
Ground effect φ (h 2.5 m, b 35.8 m)	0.555
Rolling friction μ_r	0.02

Values marked representative are reasonable textbook numbers, not manufacturer data.

What to notice

The dashed EAS curve ends at the same lift-off speed everywhere (85.49 m/s at 79 t): the pilot sees the same indicated speed. The true speed, and so the ground speed, is higher by 1/√σ.
Density enters twice: the wing (s ∝ 1/ρ_∞) and the engines (T ∝ σ^0.75). At 0.7 V_LO the dynamic pressure is the same at every field, so D, L and μ_r(W − L) do not change with altitude: the net force falls faster than the thrust.
The lecture formula (forces at 0.7 V_LO) and the integrated roll agree within about 1 %: the 0.7 V_LO average is a very good one.
On a warm La Paz afternoon the main lever is weight: every +1 °C costs about 229 kg. A headwind or an early-morning (cooler) departure also helps.

Model: ISA troposphere, temperature Θ (K; T means thrust), off-standard day ρ = ρ_ISA·Θ_ISA/(Θ_ISA+ΔΘ) (same pressure). V_LO = 1.2 V_stall. Lecture formula (primary): s_LO = 1.44 W²/(g ρ_∞ S c_l,max [T − (D + μ_r(W − L))]_avg) with L = q S c_l, D = q S [c_d,0 + φ c_l²/(π e AR)], φ = (16h/b)²/(1+(16h/b)²), AR = b²/S, forces at 0.7 V_LO, c_l = 0.8 in the roll; thrust constant, T = 0.85 · T_SL · σ^0.75. Check: m dV/dt = T − D − μ_r(W − L) integrated with RK4, Δt = 0.01 s (the V(s) curves). Classroom field-length rule (lecture formula): 1.15 × s_LO must fit on the runway (a stand-in for certified take-off distance with engine-out cases). Maximum masses are rounded down to 10 kg (conservative); the "weight-limited" preset loads that mass. Aircraft data are 737-800-class and representative. Companion to the AESP 420 (Fall 2026) take-off and landing lecture, 9/29.