Aviation Calcs

Thrust / power required

Thrust and Power Required Calculator

Enter weight, wing area, true airspeed, and a quadratic drag polar (CD0 and either e and aspect ratio or a direct k) to get the thrust and power required in level, unaccelerated flight. Density is taken from the U.S. Standard Atmosphere 1976 at the density altitude you enter. Optional propeller efficiency converts power required to shaft power. Speeds for (L/D)max and minimum power are shown from the same polar.

ft

Get density altitude from the density altitude calculator. Sea-level standard is 0 ft DA.

Induced-drag factor from

The polar is the same as on the drag polar page. Shaft power is Preq / η.

Thrust required

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Thrust and power in level flight

q = ½ ρ V²
CL = W / (q S)
CD = CD0 + k CL²
Trequired = D = q S CD
Prequired = Trequired × V

If you enter a propeller efficiency η, shaft power is Prequired / η. Density ρ comes from the standard atmosphere at the density altitude you type (geopotential altitude in the 1976 U.S. Standard Atmosphere).

Speeds from the polar

Minimum thrust required is at (L/D)max, where CL* = √(CD0/k). Minimum power required is at CL = √(3 CD0/k), a slower speed — the same points identified on the drag polar calculator. Feed L/D and speed into the Breguet page for a range or endurance estimate.

Sources

Anderson, Aircraft Performance and Design and Introduction to Flight; FAA PHAK (thrust and power required, L/D); U.S. Standard Atmosphere 1976; the induced-drag factor k = 1/(π e AR) as used on this site’s drag-polar page.

Frequently asked questions

Is thrust required just weight divided by L/D?

Yes, in level unaccelerated flight: T = W / (L/D) = D. This page computes L/D from the polar at your speed and density, then T and P from that drag.

Why is the minimum-power speed slower than the (L/D)max speed?

Power is drag times speed. The speed that minimizes T (and maximizes L/D) is not the speed that minimizes T×V. For a quadratic polar, minimum power is at a higher CL, so a lower TAS — the propeller-endurance condition on the drag-polar page.

Should I enter indicated or true airspeed?

True airspeed. Dynamic pressure is ½ρV² with V the true speed through the air. If you only have IAS, convert it with the true-airspeed calculator first.