Determining Best Climb Speeds (Vx & Vy): A Brief for Students

Concept: Best Rate vs. Best Angle of Climb

When climbing, pilots often target specific airspeeds for optimal performance. Two key speeds are:

1. Best Rate of Climb Speed (Vy): The airspeed at which the aircraft gains altitude the fastest (maximum vertical speed or Rate of Climb, RoC). This is used to reach a desired altitude in the minimum amount of time. Vy occurs where there is the maximum excess power (Power Available - Power Required).

2. Best Angle of Climb Speed (Vx): The airspeed at which the aircraft gains the most altitude over a given horizontal distance. This is used for clearing obstacles shortly after takeoff. Vx occurs where there is the maximum excess thrust (Thrust Available - Thrust Required).

Typically, Vx is slower than Vy. This flight test focuses primarily on finding Vy, as it's often determined by plotting climb performance, but the data collected can also hint at Vx.

Physical Origin: Power Available vs. Power Required

• Power Available (Pa): The power generated by the engine/propeller combination. It's calculated as Thrust * True Airspeed (TAS). Thrust typically decreases slightly with airspeed for propeller aircraft and can vary significantly for jets.

• Power Required (Pr): The power needed to overcome the aircraft's total drag at a given airspeed in level flight. It's calculated as Drag * TAS. Since Drag varies significantly with speed (high at low speeds due to induced drag, high at high speeds due to parasitic drag), the Power Required curve has a characteristic "U" shape when plotted against TAS.

• Excess Power (Pe): The difference between Power Available and Power Required (Pe = Pa - Pr). This excess power is what allows the aircraft to climb. The Rate of Climb (RoC) is directly proportional to excess power: RoC = Excess Power / Weight.

• Finding Vy: The Best Rate of Climb (Vy) occurs at the airspeed where the difference between the Power Available curve and the Power Required curve is greatest (maximum Excess Power).

(Note: For Best Angle of Climb (Vx), we look for the maximum difference between the Thrust Available and Thrust Required (Drag) curves, which generally occurs at a lower speed than maximum excess power).

Flight Test Proposal using OpenFlight Simulator

This test involves performing steady climbs at various airspeeds to find the speed that yields the highest rate of climb.

1. Setup:

   • Select an aircraft model.

   • Configure mission for a safe starting altitude (e.g., 500m - low enough to allow a significant climb segment but clear of initial ground effects).

   • Set a long data recording window (e.g., 0-300 seconds or more) to capture multiple climb segments.

   • Set maximum continuous thrust (usually key '9', check controls) for the climb.

2. Procedure (Series of Steady Climbs):

   • Initial State: Start at the initial altitude at a speed slightly above the expected climb speed range. Apply maximum continuous thrust.

   • Target Speed 1: Using pitch control ('A'/'Q' keys), establish a steady climb at a specific target Equivalent Airspeed (EAS) or Indicated Airspeed (IAS) if EAS isn't directly available (EAS is preferred as it relates more directly to aerodynamic performance). Choose a speed within the expected climb range.

   • Stabilize & Record: Maintain this constant EAS climb (allow altitude to increase) for a sufficient period (e.g., climb through 300-500m or for 30-60 seconds) to ensure the rate of climb stabilizes. Record the data.

   • Target Speed 2: Smoothly adjust pitch to stabilize the climb at a different constant EAS (e.g., 5 knots faster).

   • Stabilize & Record: Maintain this new constant EAS climb and record data.

   • Repeat: Continue this process, establishing steady climbs at various constant EAS values, covering a range from slightly above stall speed up to a typical cruise climb speed. Aim for 5-10 different speed points.

3. Recording: Ensure data is recorded throughout all steady climb segments.

Data Analysis

1. Load Data: Use the Flight Data Visualization tool or other analysis software.

2. Identify Steady Climb Segments: For each target EAS climb, identify the time interval where the EAS (or TAS if using that) was constant and the rate of climb (VSI_ms) was also relatively constant and positive.

3. Extract Average Values: For each steady climb segment:

   • Calculate the average Rate of Climb (VSI_ms).

   • Note the corresponding average EAS (or TAS) for that segment.

4. Plot RoC vs. Speed: Create a plot of the average Rate of Climb (VSI_ms on the Y-axis) against the average EAS (or TAS on the X-axis).

5. Identify Best Rate of Climb Speed (Vy):

   • Find the peak (maximum value) on the RoC vs. Speed plot. The airspeed (EAS or TAS) at this peak is the Best Rate of Climb Speed (Vy) for the tested conditions (altitude, weight, configuration).

(Note: Finding Vx precisely often requires plotting Thrust Available and Drag vs. Speed, which might need data not directly available in the standard telemetry, like instantaneous thrust. However, Vx generally occurs at a lower speed than Vy, often near the speed for minimum drag or maximum L/D).

Additional References

• Aircraft performance sections in standard aerodynamics and flight dynamics textbooks.

• Anderson, J. D. (2016). Fundamentals of Aerodynamics. McGraw-Hill Education. (Covers power required/available curves).

• Dole, C. E., et al. (2017). Flight Theory and Aerodynamics: A Practical Guide for Operational Safety. Wiley.

• Pilot's Operating Handbook (POH) for real aircraft list Vy and often Vx speeds for various conditions.

This test provides a practical way to determine the speed for the most efficient climb in terms of time to altitude using the simulator.