Energy Height and Specific Excess Power (flight-mechanics/performance/energy-height)
Use when the task is the energy state analysis of an aircraft:
specific excess power, energy height, kinetic height, zoom climb,
and the speed-altitude energy trade for performance and
maneuverability assessments.
Domain quick reference
- Excess power in watts: P_xs = (T - D) * V, with thrust T, drag
D in newtons (N) and true airspeed V in m/s.
- Specific excess power (the energy rate, in m/s):
Ps = (T - D) * V / W, with weight W in newtons (N). Ps is the
rate of change of the energy height and equals the rate of
climb in steady unaccelerated flight.
- Kinetic height (the speed expressed as an equivalent altitude):
h_k = V^2 / (2 * g0), with g0 = 9.80665 m/s^2.
- Energy height (total mechanical energy per unit weight):
h_e = h + V^2 / (2 * g0), with geometric altitude h in meters
and h_e in meters.
- Zoom climb gain: the extra altitude reachable by converting all
kinetic energy to potential energy, equal to h_k = V^2 / (2 * g0).
- Speed bleed for an altitude gain (climb-cruise trade):
V2 = sqrt(V1^2 - 2 * g0 * delta_h), the airspeed left after
climbing delta_h meters from V1.
- Altitude gain from a speed bleed: delta_h = (V1^2 - V2^2) /
(2 * g0), the height recovered by slowing from V1 to V2.
- Units are SI throughout: forces in N, speeds in m/s, altitudes
and heights in m, powers in watts. Energy height analysis sits
in the FAR-25 / CS-25 transport performance context for climb
and cruise capability checks.
Workflow
- Collect thrust, drag, speed, and weight for the condition.
- Compute the excess power with excess_power and the specific
excess power with specific_excess_power.
- Express the energy state with kinetic_height and energy_height
from the altitude and the true airspeed.
- Recover the speed for a target energy height with
speed_from_energy_height when the reverse question is asked.
- Trade energy forms with zoom_climb_gain,
speed_after_climb_bleed, or altitude_from_speed_bleed for the
climb and cruise exchange.
- Check that the specific excess power is positive before
trusting a climb capability verdict.
Pitfalls
- Using weight in kg instead of newtons: W must be mass * g0, or
Ps and the energy trade results come out wrong.
- Confusing Ps with excess power: excess power is a rate of energy
in watts, Ps divides by the weight and is an energy rate in m/s.
- Treating the kinetic height as an airspeed: h_k = V^2 / (2 * g0)
is a height in meters, not a speed.
- Asking for a speed from an energy height below the geometric
altitude: the kinetic energy would be negative, so
speed_from_energy_height raises ValueError.
- Bleeding more speed than the kinetic energy holds: when
V1^2 - 2 * g0 * delta_h goes negative, the climb is impossible
and speed_after_climb_bleed raises ValueError.
- Applying the trade formulas to accelerated flight: the energy
height identity assumes no work beyond the excess power and no
energy added or removed by the throttle during the exchange.
Behavior contract (gate 3)
The excess power, specific excess power, energy height, kinetic
height, zoom climb, and speed bleed logic is exercised by the gate
3 contract test: scripts/test_energy_height.py against
scripts/energy_height_logic.py (stdlib unittest, offline). Run:
python3 scripts/test_energy_height.py
Compliance
- Standards referenced, not reproduced: FAR-25 is US government
work (public domain) and CS-25 is a free EASA download; energy
height and specific excess power are common flight-mechanics
methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.
1---2name: energy-height3description: Use when you must compute the energy state of an aircraft for performance and maneuverability analysis: derive the specific excess power Ps from thrust, drag, speed, and weight, express the total energy as the energy height combining the geometric altitude with the kinetic height from the airspeed, convert between kinetic and potential energy in climb and cruise trades with the zoom climb gain and the speed bleed for an altitude gain, and recover the speed from a target energy height. Produces the excess power in watts, the specific excess power in m/s, the energy height in meters, the zoom climb gain, and the speed after the energy trade that gate the energy maneuverability assessment. Trigger: energy height, specific excess power, zoom climb, energy maneuverability, kinetic energy.4license: Apache-2.05---67# Energy Height and Specific Excess Power (flight-mechanics/performance/energy-height)89Use when the task is the energy state analysis of an aircraft:10specific excess power, energy height, kinetic height, zoom climb,11and the speed-altitude energy trade for performance and12maneuverability assessments.1314## Domain quick reference1516- Excess power in watts: P_xs = (T - D) * V, with thrust T, drag17 D in newtons (N) and true airspeed V in m/s.18- Specific excess power (the energy rate, in m/s):19 Ps = (T - D) * V / W, with weight W in newtons (N). Ps is the20 rate of change of the energy height and equals the rate of21 climb in steady unaccelerated flight.22- Kinetic height (the speed expressed as an equivalent altitude):23 h_k = V^2 / (2 * g0), with g0 = 9.80665 m/s^2.24- Energy height (total mechanical energy per unit weight):25 h_e = h + V^2 / (2 * g0), with geometric altitude h in meters26 and h_e in meters.27- Zoom climb gain: the extra altitude reachable by converting all28 kinetic energy to potential energy, equal to h_k = V^2 / (2 * g0).29- Speed bleed for an altitude gain (climb-cruise trade):30 V2 = sqrt(V1^2 - 2 * g0 * delta_h), the airspeed left after31 climbing delta_h meters from V1.32- Altitude gain from a speed bleed: delta_h = (V1^2 - V2^2) /33 (2 * g0), the height recovered by slowing from V1 to V2.34- Units are SI throughout: forces in N, speeds in m/s, altitudes35 and heights in m, powers in watts. Energy height analysis sits36 in the FAR-25 / CS-25 transport performance context for climb37 and cruise capability checks.3839## Workflow40411. Collect thrust, drag, speed, and weight for the condition.422. Compute the excess power with excess_power and the specific43 excess power with specific_excess_power.443. Express the energy state with kinetic_height and energy_height45 from the altitude and the true airspeed.464. Recover the speed for a target energy height with47 speed_from_energy_height when the reverse question is asked.485. Trade energy forms with zoom_climb_gain,49 speed_after_climb_bleed, or altitude_from_speed_bleed for the50 climb and cruise exchange.516. Check that the specific excess power is positive before52 trusting a climb capability verdict.5354## Pitfalls5556- Using weight in kg instead of newtons: W must be mass * g0, or57 Ps and the energy trade results come out wrong.58- Confusing Ps with excess power: excess power is a rate of energy59 in watts, Ps divides by the weight and is an energy rate in m/s.60- Treating the kinetic height as an airspeed: h_k = V^2 / (2 * g0)61 is a height in meters, not a speed.62- Asking for a speed from an energy height below the geometric63 altitude: the kinetic energy would be negative, so64 speed_from_energy_height raises ValueError.65- Bleeding more speed than the kinetic energy holds: when66 V1^2 - 2 * g0 * delta_h goes negative, the climb is impossible67 and speed_after_climb_bleed raises ValueError.68- Applying the trade formulas to accelerated flight: the energy69 height identity assumes no work beyond the excess power and no70 energy added or removed by the throttle during the exchange.7172## Behavior contract (gate 3)7374The excess power, specific excess power, energy height, kinetic75height, zoom climb, and speed bleed logic is exercised by the gate763 contract test: scripts/test_energy_height.py against77scripts/energy_height_logic.py (stdlib unittest, offline). Run:78python3 scripts/test_energy_height.py7980## Compliance8182- Standards referenced, not reproduced: FAR-25 is US government83 work (public domain) and CS-25 is a free EASA download; energy84 height and specific excess power are common flight-mechanics85 methodology, summary-only per standards-map.yaml.86- compliance: STANDARDS-REF, gated: false.
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