Definition
The specific excess power equation. PS is specific excess power, T is thrust, D is drag, V is true airspeed, and W is weight. The equation expresses how much power, per unit of weight, is available to either climb, accelerate, or both. When thrust equals drag, PS is zero and the airplane can only maintain its current speed and altitude. When thrust exceeds drag, PS is positive and energy can be added (climb, accelerate, or both). When drag exceeds thrust, PS is negative and energy must be lost (descend, decelerate, or both).
Plain English
This formula tells you how much spare power the airplane has at any moment. If thrust is bigger than drag, you have extra power to climb or speed up. If drag is bigger than thrust, you're running an energy deficit and must give up altitude or speed.
Context Anchor
Seen in energy management and performance discussions, especially when comparing power, drag, speed, weight, climb, and acceleration.
Derivation
PS stands for 'specific power' — 'specific' in engineering means 'per unit of weight,' which is why the formula divides by W. Dividing by weight lets you compare aircraft of different sizes fairly: a heavier aircraft needs more raw power to achieve the same climb or acceleration capability.
Why Pilots Care
Pilots use Ps values to judge whether an airplane has enough surplus energy to climb, turn, or accelerate without losing altitude or airspeed.
Grounding Statement
Excess thrust over drag, scaled by speed and weight, is what the airplane has left over to climb or accelerate.
Intuition Check
Do not read PS as total engine power. It means extra usable power after drag is accounted for, adjusted for the airplane’s weight.
Example Sentence 1
At high density altitude with a full load, PS shrinks toward zero in the climb, which is why the airplane struggles to gain altitude even at full power.
Example Sentence 2
At maximum takeoff weight the calculated PS dropped sharply, showing reduced ability to accelerate or climb until fuel burn lowered the aircraft weight.