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function calculateSRT() {
// Get input values
var tas = parseFloat(document.getElementById("tasInput").value);
var rot = parseFloat(document.getElementById("turnRateInput").value);
// Validation
if (isNaN(tas) || tas <= 0) {
alert("Please enter a valid True Airspeed greater than 0.");
return;
}
if (isNaN(rot) || rot <= 0) {
alert("Please enter a valid Rate of Turn greater than 0.");
return;
}
// Constants
var gravity = 11.26; // Constant derived for knots and feet
// 1. Calculate Bank Angle
// Formula: tan(bank) = (V * ROT) / 1091 (approx) or derived from centripetal force
// Exact relationship: Rate of Turn (deg/sec) = (1091 * tan(bank)) / TAS
// Therefore: tan(bank) = (ROT * TAS) / 1091
var tanBank = (rot * tas) / 1091;
var bankAngleRad = Math.atan(tanBank);
var bankAngleDeg = bankAngleRad * (180 / Math.PI);
// 2. Rule of Thumb Calculation
// Standard Aviation Rule: (TAS / 10) + 5
var thumbRule = (tas / 10) + 5; // Standard rule
// Alternative rule (15%): var thumbRule2 = tas * 0.15;
// 3. Calculate Radius
// Formula: Radius (feet) = V^2 / (11.26 * tan(bank))
var radiusFeet = (tas * tas) / (gravity * tanBank);
var radiusNm = radiusFeet / 6076.12; // Convert feet to Nautical Miles
// 4. Calculate Diameter
var diameterNm = radiusNm * 2;
// 5. Time for 360
// Formula: 360 / Rate of Turn
var seconds360 = 360 / rot;
var minutes = Math.floor(seconds360 / 60);
var remainingSeconds = Math.round(seconds360 % 60);
var timeString = minutes + " min " + remainingSeconds + " sec";
// 6. Load Factor
// Formula: 1 / cos(bank angle)
var loadFactor = 1 / Math.cos(bankAngleRad);
// Update DOM
document.getElementById("resultsDisplay").style.display = "block";
document.getElementById("preciseBank").innerHTML = bankAngleDeg.toFixed(1) + "°";
document.getElementById("ruleOfThumbBank").innerHTML = thumbRule.toFixed(1) + "°";
// Format Radius logic
if (radiusNm < 1) {
document.getElementById("turnRadius").innerHTML = Math.round(radiusFeet) + " ft";
} else {
document.getElementById("turnRadius").innerHTML = radiusNm.toFixed(2) + " NM";
}
document.getElementById("turnDiameter").innerHTML = diameterNm.toFixed(2) + " NM";
document.getElementById("time360").innerHTML = timeString;
document.getElementById("loadFactor").innerHTML = loadFactor.toFixed(2) + " G";
}
How to Calculate Standard Rate Turn
In aviation, specifically during Instrument Flight Rules (IFR) operations, maintaining a predictable path over the ground is critical for safety and traffic separation. A Standard Rate Turn (SRT) is defined as a turn rate of 3 degrees per second.
At this rate, an aircraft completes a full 360-degree circle in exactly 2 minutes (120 seconds). This standardization allows pilots and air traffic controllers to anticipate aircraft position and timing accurately.
The Physics of the Turn
The bank angle required to maintain a standard rate turn increases as the aircraft's speed increases. This is why faster aircraft require steeper bank angles to turn at the same rate (degrees per second) as slower aircraft.
The core formula relating Bank Angle ($\theta$), True Airspeed ($V$ in knots), and Rate of Turn ($ROT$ in deg/sec) is:
$$ \tan(\theta) = \frac{ROT \times V}{1091} $$
Rules of Thumb for Pilots
While the calculator above uses precise physics equations, pilots in the cockpit rarely calculate tangents mentally. Instead, they use proven rules of thumb to estimate the required bank angle for a standard rate turn:
- The (TAS / 10) + 5 Rule: Take your True Airspeed, divide by 10, and add 5. For example, at 120 knots: (120/10) + 5 = 17 degrees of bank.
- The 15% Rule: Calculate 15% of your True Airspeed. For 120 knots: 120 * 0.15 = 18 degrees of bank.
Radius and Diameter of Turn
Understanding the radius of your turn is vital for holding patterns and procedure turns. As speed increases, the radius of the turn increases exponentially if the rate of turn remains constant.
The radius in feet is calculated as:
$$ Radius (ft) = \frac{V^2}{11.26 \times \tan(\theta)} $$
For a standard rate turn (3°/sec), a simple approximation for the diameter in Nautical Miles is 1% of the TAS. For example, at 140 knots, the turn diameter is roughly 1.4 NM.
Why is Standard Rate Important?
- Timed Turns: If the heading indicator fails, a pilot can turn to a specific compass heading by timing the turn (e.g., turn 90 degrees by holding a standard rate turn for 30 seconds).
- ATC Expectations: Controllers base separation on the assumption that aircraft are turning at a standard rate.
- Structural Limits: At very high speeds, the bank angle required for a standard rate turn might exceed safe limits (usually capped at 25 or 30 degrees for IFR operations). In these cases, pilots default to the maximum bank angle (usually 25°) rather than the standard rate.
Using the Turn Coordinator
Most aircraft are equipped with a Turn Coordinator or Turn and Slip Indicator. The "doghouse" or aircraft symbol aligns with a specific index mark when the aircraft is turning at a standard rate. This instrument is calibrated based on the rate of yaw and roll, independent of airspeed, making it the primary reference for establishing a standard rate turn.