AIRCRAFT PERFORMANCE

Drag, Thrust & Flight Envelope

One aircraft. Four forces. A changing margin.

ASTER JGeneric teaching jet · clean configuration

LIVE B / FORCE BALANCESteady-level reference · 1g

TAS

Altitude

Mass, thrust & all settings ↓

Required dragAt L = W

Selected thrustSynthetic fixed-engine model

Thrust − drag

Balance setting

Horizontal and vertical arrows use separate scales. The aircraft drawing is schematic; attitude, pitch trim and flight trajectories are not solved.

ANo reference saved

02 / WHERE THE AIRCRAFT CAN SUSTAIN LEVEL FLIGHT

The level-flight envelope

B · liveA · saved

Click or drag to choose altitude and TAS. Filled area: enough thrust at this setting or lower. Its interior usually requires reducing thrust to obtain T = D.

AT THE SELECTED ALTITUDE

Lift boundary · C_LmaxMach / dynamic-pressure limitThrust sufficient · B

1g level-flight capability
Not a manoeuvre V–n diagram

A thrust deficit can remove part or all of the speed range even when the lift limit is satisfied.

03 / ONE STATE, TWO CONNECTED VIEWS

Thrust and power

B · liveA · saved

Solid: required · dashed: available
Click either graph to change TAS.

Thrust required & available

Required thrust equals drag for steady level flight. The vertical gap shows the selected thrust surplus or deficit.

Power required & available

P_required = DV; P_available = TV. These are propulsive powers at the flight speed, not engine shaft or fuel powers.

Grey regions are outside live B’s lift or upper limits. Each case’s curves stop at its own supported boundaries. A and B share the axes.

04 / WHY THE DRAG CURVE HAS TWO SIDES

Drag at the selected speed

With weight and altitude fixed, parasite drag rises with V²; induced drag falls with 1/V² while L = W remains attainable.

05 / TWO DIFFERENT OPTIMUM SPEEDS

Minimum drag ≠ minimum power

These speeds minimise the model’s aerodynamic demand. They are not automatically attainable at the selected thrust, nor universal best-range or best-endurance speeds.

06 / HOLD ONE CASE, CHANGE THE OTHER

A / B comparison

Quantity	A · saved	B · live	B − A

Compare input settings

Input	A	B

Model, equations & interpretation

One synthetic clean aircraft

Fixed wing geometry and drag polar; straight, symmetric, 1g level-flight reference. L = W is imposed where the lift limit can be met. No pitch trim, fuel burn, wind, trajectory, stall dynamics, buffet, manoeuvre loads or transonic wave drag is solved.

Mass sets W = mg. The atmosphere is a dry two-layer approximation in geopotential metres, up to 15 km. The constant polar is an educational approximation; the chosen Mach cutoff does not establish real-aircraft accuracy.

Force and power accounting

Aerodynamic demand and excess force

q = \frac{1}{2} ρ V^{2}

C_{L} = \frac{W}{q S}

C_{D} = C_{D0} + k {C_{L}}^{2}

k = \frac{1}{π e AR}

D = q S C_{D0} + \frac{k W^{2}}{q S}

F_{x} = T - D

a_{x} = \frac{T - D}{m}

These equations impose a supported 1g level-flight reference, L = W.

Symbols & units

$L, W, T, D$: Lift, weight, thrust and drag, N. Weight W = mg.
$V, m$: True airspeed, m/s; aircraft mass, kg.
$q, ρ, S$: Dynamic pressure, Pa; air density, kg/m³; wing area, m².
$C_{L}, C_{D}, C_{D0}, k, e, AR$: Lift/drag coefficients, induced-drag factor, span efficiency and aspect ratio are dimensionless.
$a_{x}$: Along-path acceleration tendency, m/s²; no trajectory is integrated.

The acceleration readout is an instantaneous tendency with vertical balance imposed. A steady, constant-speed level state also needs T = D. The filled envelope indicates the capacity to achieve that balance by reducing the selected thrust if necessary.

A declared propulsion model

Declared synthetic thrust law

T = u 12000 σ^{0.8} (1 - 0.25 M) N

σ = \frac{ρ}{ρ_{sea level}}

0 \leq u \leq 1

Symbols & units

$u$: Dimensionless engine thrust setting; this symbol is not groundspeed on this page.
$σ, M$: Density ratio and Mach number, dimensionless.
$T$: Available thrust, N. This is a prescribed illustrative engine law, not a measured engine map.

This synthetic law makes available thrust depend on altitude, speed and setting for one fixed engine. It is not a manufacturer map, a throttle transient or the output of the separate gas-turbine design-point lab. Engine idle thrust and installation detail are omitted.

Below the lift boundary, the diagram shows a maximum-lift bound. Drag and acceleration are withheld; no post-stall model is invented.

Teaching evidence

Week 8&9 Static Aircraft Performance Analysis, Part 1 — Updated on 20 Mar 2026: drag polar, required and available thrust/power, stall and attainable speeds. All illustrations are original.

Implementation checks cover analytical landmarks, force/power identities, limiting cases, bracketed envelope roots and immutable comparisons. Experimental validation remains open.

NASA · drag coefficient · NASA · four forces