/* Calculator Widget Styles */
.turn-rate-calculator-container {
max-width: 600px;
margin: 20px auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
border: 1px solid #e2e8f0;
border-radius: 8px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
background: #fff;
padding: 25px;
}
.trc-header {
text-align: center;
margin-bottom: 25px;
border-bottom: 2px solid #3b82f6;
padding-bottom: 10px;
}
.trc-header h2 {
margin: 0;
color: #1e293b;
font-size: 24px;
}
.trc-input-group {
margin-bottom: 20px;
}
.trc-input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #475569;
}
.trc-input-group input {
width: 100%;
padding: 12px;
border: 1px solid #cbd5e1;
border-radius: 6px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.2s;
}
.trc-input-group input:focus {
border-color: #3b82f6;
outline: none;
}
.trc-button {
width: 100%;
padding: 14px;
background-color: #3b82f6;
color: white;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
}
.trc-button:hover {
background-color: #2563eb;
}
.trc-results {
margin-top: 25px;
padding: 20px;
background-color: #f8fafc;
border-radius: 6px;
display: none;
border: 1px solid #e2e8f0;
}
.trc-result-item {
display: flex;
justify-content: space-between;
margin-bottom: 12px;
padding-bottom: 12px;
border-bottom: 1px dashed #cbd5e1;
}
.trc-result-item:last-child {
border-bottom: none;
margin-bottom: 0;
padding-bottom: 0;
}
.trc-result-label {
color: #64748b;
font-weight: 500;
}
.trc-result-value {
font-weight: 700;
color: #1e293b;
}
.trc-highlight {
color: #3b82f6;
}
.trc-error {
color: #ef4444;
text-align: center;
margin-top: 10px;
display: none;
}
/* Article Styles */
.turn-rate-article {
max-width: 800px;
margin: 40px auto;
font-family: Georgia, serif;
line-height: 1.6;
color: #333;
}
.turn-rate-article h2 {
font-family: -apple-system, sans-serif;
color: #1e293b;
margin-top: 30px;
}
.turn-rate-article p {
margin-bottom: 20px;
}
.turn-rate-article ul {
margin-bottom: 20px;
padding-left: 20px;
}
.turn-rate-article li {
margin-bottom: 10px;
}
.trc-info-box {
background: #eff6ff;
border-left: 4px solid #3b82f6;
padding: 15px;
margin: 20px 0;
font-family: sans-serif;
}
function calculateTurnMetrics() {
// 1. Get input values using var
var tasInput = document.getElementById("tasInput").value;
var bankInput = document.getElementById("bankAngleInput").value;
var resultBox = document.getElementById("resultBox");
var errorMsg = document.getElementById("errorMsg");
// 2. Parse values
var tas = parseFloat(tasInput);
var bankDeg = parseFloat(bankInput);
// 3. Validation
if (isNaN(tas) || isNaN(bankDeg) || tas <= 0 || bankDeg = 90) {
errorMsg.style.display = "block";
resultBox.style.display = "none";
return;
}
errorMsg.style.display = "none";
// 4. Constants and Conversions
// Convert Knots to Feet per Second (1 Knot = 1.68781 ft/s)
var velocityFps = tas * 1.68781;
// Gravity (ft/s^2)
var g = 32.174;
// Convert Degrees to Radians for Math functions
var bankRad = bankDeg * (Math.PI / 180);
// 5. Calculation Logic
// Rate of Turn (Degrees per Second)
// Formula: ROT = (1091 * tan(bank)) / TAS (Approximation used in aviation)
// Physics Formula: omega = (g * tan(theta)) / V
// Using physics formula for precision:
var rotRadPerSec = (g * Math.tan(bankRad)) / velocityFps;
var rotDegPerSec = rotRadPerSec * (180 / Math.PI);
// Turn Radius (Feet)
// Formula: r = V^2 / (g * tan(theta))
var radiusFeet = (velocityFps * velocityFps) / (g * Math.tan(bankRad));
var radiusNM = radiusFeet / 6076.12; // Convert feet to Nautical Miles
// Diameter (Nautical Miles)
var diameterNM = radiusNM * 2;
// Load Factor (G)
// Formula: G = 1 / cos(theta)
var loadFactor = 1 / Math.cos(bankRad);
// Time for 360 degree turn (Seconds)
// Formula: T = 2 * pi * r / v
// Or simply 360 / degrees per second
var timeSeconds = 360 / rotDegPerSec;
var timeMinutes = Math.floor(timeSeconds / 60);
var timeRemSeconds = Math.round(timeSeconds % 60);
// 6. Formatting and Display
document.getElementById("resRate").innerHTML = rotDegPerSec.toFixed(2) + " °/sec";
document.getElementById("resRadius").innerHTML = radiusNM.toFixed(2) + " NM (" + Math.round(radiusFeet).toLocaleString() + " ft)";
document.getElementById("resDiameter").innerHTML = diameterNM.toFixed(2) + " NM";
document.getElementById("resLoad").innerHTML = loadFactor.toFixed(2) + " G";
// Format time string
var timeString = timeMinutes + " min " + (timeRemSeconds < 10 ? "0" : "") + timeRemSeconds + " sec";
document.getElementById("resTime").innerHTML = timeString;
// Show results
resultBox.style.display = "block";
}
Understanding Aircraft Turn Rate Physics
The calculation of turn rate, radius, and bank angle is a fundamental concept in flight dynamics and aerodynamics. Whether you are a student pilot, a flight simmer, or an aviation enthusiast, understanding the relationship between speed (True Airspeed) and bank angle is critical for safe maneuvering and standard instrument procedures.
Standard Rate Turn: In instrument flying, a "Standard Rate Turn" is defined as a turn rate of 3 degrees per second. This completes a full 360° circle in exactly 2 minutes.
How the Calculator Works
This calculator uses standard physics formulas derived from circular motion dynamics. Unlike a car on a road, an aircraft must bank to turn. The horizontal component of lift creates the centripetal force required to change the aircraft's heading. The physics involves three main variables:
- True Airspeed (TAS): The speed of the aircraft relative to the air mass, entered in Knots (KTAS).
- Bank Angle: The angle at which the wings are tilted relative to the horizon, entered in degrees.
- Gravity (g): The constant acceleration due to gravity (approx 32.17 ft/s²).
Key Formulas
The logic behind our calculator uses the following aerodynamic equations:
1. Rate of Turn (ROT):
The rate at which the aircraft changes heading, measured in degrees per second. As speed increases, the rate of turn decreases for a fixed bank angle.
Formula: ROT = (1,091 × tan(Bank Angle)) / TAS
2. Radius of Turn:
The horizontal distance from the center of the turn to the aircraft. Higher speeds result in a much wider turn radius.
Formula: Radius = V² / (11.26 × tan(Bank Angle))
3. Load Factor (G-Force):
The apparent weight felt by the pilot and airframe during the turn. This increases exponentially as the bank angle approaches 90°.
Formula: Load Factor = 1 / cos(Bank Angle)
Practical Application
Pilots use these calculations to ensure they stay within protected airspace during holding patterns or instrument approaches. For example, if you double your airspeed, your turn radius quadruples, which could push the aircraft outside of safe boundaries if the bank angle is not increased. Conversely, a steeper bank angle tightens the turn but significantly increases the G-load on the airframe.