Rate of Climb (Excess Power)

This formula comes from an energy balance: the engine supplies power to the aircraft, and the portion left over after overcoming drag and other resistive effects is the power that can be converted into gain in altitude. Because climbing at a vertical speed ROC requires increasing gravitational potential energy at a rate of W × ROC, the excess power equals W × ROC, so ROC is the excess power divided by weight. A larger excess power gives a steeper climb, while a heavier aircraft climbs more slowly for the same excess power.

Use this in performance calculations for aircraft climb capability, especially when comparing climb rates at different speeds, weights, altitudes, or engine settings. It is also useful in determining how changes in available or required power affect climb performance during takeoff or en route climb.

• Using horsepower and pounds force without converting to consistent SI units
• Substituting thrust instead of power in the formula
• Forgetting that only the excess power contributes to climb, so P_a must be larger than P_r