Aerodynamic Turn Radius Equation

Created June 2011
Updated May 2024

This rather simple equation from Subsonic and Supersonic Anti-Ship Missiles: An Effectiveness and Utility Comparison (Jan. 1997 Naval Engineers Journal) works quite well and is accurate to within about ten feet when compared to a more complex formula/calculator (HERE).

The formula is:

R = V2 / A

Where:

R: Turn Radius (feet or meters)
V: Air Vehicle Velocity (ft/sec or m/sec)
A: Turning Acceleration Capability of Air Vehicle (ft/s2 or m/s2)

A can be calculated through the simple formula:

A = GF * G0

Where:

GF: How many G's the Air Vehicle is Pulling.
G0: Standard Acceleration of Gravity (32.17405 ft/s2 or 9.80665 m/s2)

You can also estimate the amount of time it takes to perform various turns via the following equations:



Where:

T90: Turn Time (Seconds) for 90 degree turn
T180: Turn Time (Seconds) for 180 degree turn
T360: Turn Time (Seconds) for 360 degree turn
V: Air Vehicle Velocity (ft/sec or m/sec)
A: Turning Acceleration Capability of Air Vehicle (ft/s2 or m/s2)

To make things easier, a pre-built calculator has been created for your convenience.

Pre-Built Calculator

Speed

Speed Examples:

100 MPH - WWI Biplanes
400 MPH - WWII Monoplanes
500 MPH - WWII Jets
600 MPH - F-86 / MiG-15 in Korea (Early 1950s)
900 MPH - F-100 / MiG-19 (Late 1950s)
G Loading (G's)

G-Loading Examples:

2 to 3 G - WWI German Fighter Rear Wing Spar Limit
5~ G - WWI Maximum G for British SE.5
5.5 G - WWII Unsuited Pilot
6.5 G - WWII Early G-Suited Pilot
8.5 G - 1980s F-16 Pilot with G-Suit and Reclined Seat
10 to 12 G - Structural Limit of many WWII Fighters/Dive Bombers
50 G - 1990s Air-To-Air Missiles (AIM-9X + AIM-120 AMRAAM)
100 G - 2010s Thrust Vectored AAM (A-Darter) (Drops to 50G once motor burns out)

Calculations: