# Polar Curve Points

> Key performance speeds derived from the Drag Polar.

- **Subject:** 081 — Principles of Flight
- **Section:** 081-08 — Flight Mechanics
- **Topic code:** 081-08-03
- **Last reviewed:** 2026-04-01
- **Author:** Pablo Asensio Martínez
- **HTML version:** https://pilotsyllabus.com/en/principles-of-flight/flight-mechanics/significant-points-on-a-polar-curve/

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## Drag Polar
A graph of Lift Coefficient ($C_L$) vs Drag Coefficient ($C_D$).
*   **Tangent from Origin**: The point of maximum **Lift-to-Drag Ratio** ($L/D_{max}$).
*   **Top of the Curve**: $C_{Lmax}$ (Stall speed).

## Significant Speeds (Thrust Required Curve)
Plotting Drag (Thrust Required) vs Speed ($V$).

1.  **Vmd (Minimum Drag Speed)**: The bottom of the U-shaped curve.
    *   Occurs where Parasite Drag = Induced Drag.
    *   Speed for **Max Range** (Jet) and **Max Endurance** (Prop - approximately).
    *   Speed for **Best Glide Angle** (Max Distance).

2.  **Vmp (Minimum Power Speed)**:
    *   Occurs at approximately $0.76 \times V_{MD}$.
    *   The point where the product of Drag $\times$ Velocity is minimum.
    *   Speed for **Max Endurance** (Jet) because fuel flow is proportional to thrust $\times$ speed (power).
    *   Speed for **Minimum Sink Rate** in a glide.

3.  **Vx (Best Angle of Climb)**: Speed where **Excess Thrust** is maximum. Close to $V_{MD}$.
4.  **Vy (Best Rate of Climb)**: Speed where **Excess Power** is maximum. Higher than $V_x$.

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