In aerodynamics and aviation physics, calculating the correct Bank Rate (or Bank Angle) is critical for executing coordinated turns. This calculator helps pilots and aviation enthusiasts determine the necessary bank angle, turn radius, and load factor based on true airspeed and the desired rate of turn.
Aerodynamic Bank Calculator
Please enter valid positive numbers for Speed and Rate.
Required Bank Angle–
Turn Radius–
Load Factor (G-Force)–
Time for 360° Turn–
Understanding the Physics of Bank Rate
When an aircraft turns, it must bank (roll) to redirect a component of its lift horizontally. This horizontal component creates the centripetal force required to pull the aircraft through the turn. The relationship between the "Bank Rate" (angle), speed, and the rate of turn is governed by fundamental laws of physics.
The Formulas
To calculate the required bank angle ($\phi$) for a specific rate of turn ($\omega$) at a given velocity ($V$), we use the following derivation:
tan(φ) = (V × ω) / 1091
Where:
φ = Bank Angle in degrees
V = True Airspeed in Knots (KTAS)
ω = Rate of Turn in degrees per second
1091 = Constant derived from gravity and unit conversions
Standard Rate Turn
A "Standard Rate Turn" is defined as 3 degrees per second. This completes a 360-degree circle in exactly 2 minutes (120 seconds). Instrument pilots rely heavily on this standard to execute precise maneuvers without visual references.
Load Factor (G-Force)
As the bank angle increases, the total lift required to maintain altitude increases. This imposes a "load factor" on the aircraft, measured in Gs. The formula is:
Load Factor (G) = 1 / cos(φ)
For example, in a steep 60-degree bank, the load factor becomes 2.0 G, meaning the wings must support twice the weight of the aircraft.
Turn Radius
The radius of the turn is directly proportional to the square of the speed and inversely proportional to the bank angle. Faster aircraft require a much larger radius to complete a turn at the same bank angle compared to slower aircraft.
function calculateBankPhysics() {
// 1. Get DOM elements
var tasInput = document.getElementById("tasInput");
var turnRateInput = document.getElementById("turnRateInput");
var resultBox = document.getElementById("resultBox");
var errorDisplay = document.getElementById("errorDisplay");
var resBankAngle = document.getElementById("resBankAngle");
var resRadius = document.getElementById("resRadius");
var resGForce = document.getElementById("resGForce");
var resTime = document.getElementById("resTime");
// 2. Parse values
var tas = parseFloat(tasInput.value);
var turnRate = parseFloat(turnRateInput.value);
// 3. Validation
if (isNaN(tas) || isNaN(turnRate) || tas <= 0 || turnRate <= 0) {
errorDisplay.style.display = "block";
resultBox.style.display = "none";
return;
}
errorDisplay.style.display = "none";
// 4. Calculations
// Formula: tan(bank) = (V_knots * Rate_deg_sec) / 1091
// Bank Angle in Radians
var tanPhi = (tas * turnRate) / 1091;
var bankAngleRad = Math.atan(tanPhi);
var bankAngleDeg = bankAngleRad * (180 / Math.PI);
// Turn Radius in Nautical Miles
// Radius = V / (20 * PI * Rate)
var radius = tas / (20 * Math.PI * turnRate);
// Load Factor (G)
// G = 1 / cos(bankAngle)
var loadFactor = 1 / Math.cos(bankAngleRad);
// Time for 360 deg turn
var timeFor360 = 360 / turnRate; // in seconds
// 5. Display Results
resBankAngle.innerHTML = bankAngleDeg.toFixed(1) + "°";
resRadius.innerHTML = radius.toFixed(2) + " NM";
resGForce.innerHTML = loadFactor.toFixed(2) + " G";
// Format time nicely
if(timeFor360 < 60) {
resTime.innerHTML = timeFor360.toFixed(1) + " sec";
} else {
var mins = Math.floor(timeFor360 / 60);
var secs = Math.round(timeFor360 % 60);
resTime.innerHTML = mins + " min " + secs + " sec";
}
resultBox.style.display = "block";
}