Rate of Turn Calculation

Calculate aviation and nautical turn dynamics based on velocity and bank angle.

Rate of Turn

0.00

Degrees per Second

Turn Radius

0.00

Nautical Miles (NM)

function calculateROT() { var tas = parseFloat(document.getElementById('tas_input').value); var bank = parseFloat(document.getElementById('bank_input').value); if (isNaN(tas) || isNaN(bank) || tas <= 0 || bank = 90) { alert("Please enter valid speed and a bank angle between 1 and 89 degrees."); return; } var bankRad = bank * (Math.PI / 180); // Formula for ROT (deg/sec) = (1091 * tan(bank)) / TAS var rot = (1091 * Math.tan(bankRad)) / tas; // Formula for Radius (NM) = TAS^2 / (11.26 * tan(bank) * 6076.1) // Or simpler using ROT: Radius (ft) = V^2 / (11.26 * tan(bank)) var radiusFt = Math.pow(tas, 2) / (11.26 * Math.tan(bankRad)); var radiusNM = radiusFt / 6076.115; document.getElementById('rot_output').innerText = rot.toFixed(2); document.getElementById('radius_output').innerText = radiusNM.toFixed(2); var turnTypeLabel = ""; if (rot >= 2.8 && rot 3.2) { turnTypeLabel = "Above Standard Rate Turn"; } else { turnTypeLabel = "Below Standard Rate Turn"; } document.getElementById('turn_type').innerText = turnTypeLabel; document.getElementById('rot_results').style.display = 'block'; }

Understanding the Rate of Turn (ROT)

In aviation and marine navigation, the Rate of Turn (ROT) is the number of degrees per second or minute that a vehicle changes its heading. Understanding ROT is critical for maintaining safe separation between aircraft and ensuring precise navigation during approach and holding patterns.

The Standard Rate Turn

A "Standard Rate Turn" (also known as a Rate One turn) is defined as a turn of 3 degrees per second. This results in a full 360-degree circle in exactly 2 minutes. Pilots use this standard to predict exactly where they will be after a specific duration of turning, regardless of their airspeed.

The Mathematics of the Turn

The calculation for Rate of Turn is derived from the balance of aerodynamic forces (lift) and centrifugal force. The two primary factors affecting your turn are:

• Airspeed (TAS): As your speed increases, your turn radius increases and your rate of turn decreases for a constant bank angle.
• Bank Angle: Increasing your bank angle increases the horizontal component of lift, resulting in a higher rate of turn and a smaller radius.

Key Formulas Used:

ROT (deg/sec) = (1,091 × tan(Bank Angle)) / TAS

Radius (NM) = TAS² / (11.26 × tan(Bank Angle) × 6,076)

Practical Example

Imagine an aircraft flying at a True Airspeed of 150 knots with a bank angle of 20 degrees:

1. Calculate Tan(20°): Approximately 0.364.
2. Apply ROT Formula: (1091 × 0.364) / 150 = 2.65° per second.
3. Calculate Radius: 150² / (11.26 × 0.364 × 6076) = 0.90 Nautical Miles.

In this scenario, the pilot is turning slightly slower than a standard rate turn. To achieve a standard 3°/sec rate at 150 knots, the pilot would need to increase the bank angle to approximately 22-23 degrees.

Why Rate of Turn Matters

Precise turn calculations are essential for several reasons:

Application	Benefit
Holding Patterns	Ensures the aircraft stays within the protected airspace.
Instrument Approaches	Allows for accurate course interception.
Air Traffic Control	Predictability helps controllers maintain separation.

Note: These calculations are based on standard aerodynamic formulas for coordinated level turns and do not account for wind drift or density altitude variations.