# Relationship between CL and Speed

> Balancing lift and weight in steady level flight.

- **Subject:** 081 — Principles of Flight
- **Section:** 081-01 — Subsonic Aerodynamics
- **Topic code:** 081-01-07
- **Last reviewed:** 2026-04-01
- **Author:** Pablo Asensio Martínez
- **HTML version:** https://pilotsyllabus.com/en/principles-of-flight/subsonic-aerodynamics/the-relationship-between-lift-coefficient-and-speed-in-steady-straight-and-level-flight/

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## The Balance
In steady, straight, and level flight:
$$ Lift = Weight $$
$$ C_L \cdot \frac{1}{2} \rho V^2 \cdot S = Weight $$

## The Relationship
Since Weight ($W$) and Wing Area ($S$) are constant (mostly):
$$ C_L \cdot V^2 \approx Constant $$

*   **High Speed ($V$)**: Requires **Low $C_L$** (Small Angle of Attack).
*   **Low Speed ($V$)**: Requires **High $C_L$** (Large Angle of Attack).

## Flying Slower
To maintain level flight while decelerating:
1.  Speed ($V$) decreases -> Dynamic pressure decreases -> Lift would decrease.
2.  Pilot increases Angle of Attack -> $C_L$ increases -> Lift is restored to equal Weight.
3.  Limit: Eventually $C_{L_{max}}$ is reached (Stall Speed).

## Altitude Effect
$$ EAS \approx Constant \cdot \sqrt{Weight} $$
Typically cruise is flown at specific Mach or CAS.
*   As altitude increases ($\rho$ decreases), TAS must increase to maintain same Lift (if $C_L$ is constant).

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