Calculate Rate of Turn, Radius, and Load Factor based on Airspeed and Bank Angle.
Rate of Turn:– deg/sec
Turn Radius:– NM
Load Factor (G-Force):– G
Time for 360° Turn:– sec
function calculateBankRate() {
// Get input values using var
var tas = parseFloat(document.getElementById("tasInput").value);
var bankAngle = parseFloat(document.getElementById("bankAngleInput").value);
var resultDisplay = document.getElementById("resultDisplay");
var errorDisplay = document.getElementById("errorDisplay");
// Reset display
resultDisplay.style.display = "none";
errorDisplay.style.display = "none";
errorDisplay.innerHTML = "";
// Validation
if (isNaN(tas) || tas <= 0) {
errorDisplay.innerHTML = "Please enter a valid True Airspeed greater than 0.";
errorDisplay.style.display = "block";
return;
}
if (isNaN(bankAngle) || bankAngle = 90) {
errorDisplay.innerHTML = "Please enter a valid Bank Angle (0-89 degrees).";
errorDisplay.style.display = "block";
return;
}
// Logic Implementation
// Convert degrees to radians for JS Math functions
var bankRadians = bankAngle * (Math.PI / 180);
var gConstant = 11.26; // Constant derived from gravity and nautical mile conversion
// 1. Calculate Rate of Turn (ROT) in degrees per second
// Formula: ROT = (1091 * tan(bankAngle)) / TAS
var rot = (1091 * Math.tan(bankRadians)) / tas;
// 2. Calculate Turn Radius in Nautical Miles (NM)
// Formula: r = TAS^2 / (11.26 * tan(bankAngle))
var radius = (tas * tas) / (gConstant * Math.tan(bankRadians));
// 3. Calculate Load Factor (G)
// Formula: n = 1 / cos(bankAngle)
var loadFactor = 1 / Math.cos(bankRadians);
// 4. Time for standard 360 degree turn (2 minutes for standard rate)
// Formula: Time = 360 / ROT
var timeForTurn = 360 / rot;
// Display Results
document.getElementById("rotResult").innerHTML = rot.toFixed(2) + " deg/sec";
document.getElementById("radiusResult").innerHTML = radius.toFixed(2) + " NM";
document.getElementById("loadFactorResult").innerHTML = loadFactor.toFixed(2) + " G";
// Format time (min:sec or just sec)
if (timeForTurn > 60) {
var mins = Math.floor(timeForTurn / 60);
var secs = Math.round(timeForTurn % 60);
document.getElementById("timeResult").innerHTML = mins + " min " + secs + " sec";
} else {
document.getElementById("timeResult").innerHTML = timeForTurn.toFixed(1) + " sec";
}
resultDisplay.style.display = "block";
}
Understanding Aircraft Bank Rate & Turn Dynamics
In aerodynamics and aviation physics, the "Bank Rate" or "Rate of Turn" is a critical flight parameter determined by the aircraft's True Airspeed (TAS) and the angle at which the wings are banked relative to the horizon. Unlike financial calculators, a physics-based bank rate calculator focuses on the forces of flight: lift, gravity, and centrifugal force.
The Physics of the Turn
When an aircraft banks to initiate a turn, the lift vector is tilted. The vertical component of lift continues to oppose gravity, while the horizontal component acts as the centripetal force that pulls the aircraft around the turn. The steeper the bank angle, the greater the rate of turn, provided airspeed remains constant.
Key Parameters Calculated
This tool helps pilots and aviation students compute four essential metrics:
Rate of Turn (ROT): The number of degrees of heading change per second. A "Standard Rate Turn" is defined as 3 degrees per second, completing a 360° circle in 2 minutes.
Turn Radius: The physical distance (radius) of the circle flown. As speed increases, the radius of the turn increases significantly for the same bank angle.
Load Factor (G-Force): In a level turn, the aircraft structure must support more than the aircraft's weight. At a 60° bank angle, the load factor is exactly 2.0 Gs, meaning the wings are supporting twice the weight of the aircraft.
Formulas Used
For those interested in the underlying math, the approximations used in standard aerodynamics are:
Rate of Turn (deg/sec) = (1,091 × tan(Bank Angle)) / TAS
Radius (NM) = TAS² / (11.26 × tan(Bank Angle))
Load Factor (G) = 1 / cos(Bank Angle)
Practical Application
Understanding these relationships is vital for Instrument Flight Rules (IFR) operations. For example, to maintain a Standard Rate Turn (3 deg/sec) at higher speeds, a pilot must increase their bank angle. However, banking too steeply increases the stall speed due to the increased load factor (G-force), creating a limit on safe maneuvering speeds.