Bankrate Calculator

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Banked Curve Angle Calculator

Calculate the ideal banking angle for a curved road or track based on design velocity and curve radius to minimize lateral friction requirements.

Results

Ideal Banking Angle: 0°
Transformed Velocity: 0 m/s

Understanding Road Banking Physics

In civil engineering and physics, "banking" refers to the practice of tilting a road surface toward the inside of a curve. This is done to provide a component of the normal force that assists in providing the centripetal force required for a vehicle to negotiate the curve safely without relying solely on tire friction.

The Banking Formula

The relationship between the angle of the bank (θ), the velocity of the vehicle (v), the radius of the curve (r), and gravity (g) is defined by the following equation:

tan(θ) = v² / (r * g)

Key Factors in Calculation

  • Design Velocity: The intended speed limit for the curve. Note that speeds higher or lower than this "perfect" speed will require friction to stay on track.
  • Radius of Curvature: Sharper curves (smaller radius) require steeper banking angles for the same speed.
  • Frictionless Stability: The result provided by this calculator is the angle at which no lateral friction is required to keep the car on the road.

Example Calculation

If a highway engineer is designing a curve with a 300m radius for a design speed of 120 km/h:

  1. Convert 120 km/h to m/s: 120 / 3.6 = 33.33 m/s.
  2. Square the velocity: 33.33² = 1111.11.
  3. Calculate the denominator (Radius * Gravity): 300 * 9.81 = 2943.
  4. Find the tangent: 1111.11 / 2943 = 0.377.
  5. The inverse tangent (arctan) of 0.377 is approximately 20.68°.
function calculateBankAngle() { var v_kmh = parseFloat(document.getElementById('velocityInput').value); var r = parseFloat(document.getElementById('radiusInput').value); var g = parseFloat(document.getElementById('gravityInput').value); var resultDiv = document.getElementById('resultArea'); var angleSpan = document.getElementById('angleResult'); var mpsSpan = document.getElementById('metersPerSecond'); if (isNaN(v_kmh) || isNaN(r) || isNaN(g) || r <= 0 || g <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Convert km/h to m/s var v_ms = v_kmh / 3.6; // Formula: tan(theta) = v^2 / (r * g) // theta = arctan(v^2 / (r * g)) var tanTheta = (v_ms * v_ms) / (r * g); var thetaRadians = Math.atan(tanTheta); var thetaDegrees = thetaRadians * (180 / Math.PI); mpsSpan.innerText = v_ms.toFixed(2); angleSpan.innerText = thetaDegrees.toFixed(2); resultDiv.style.display = 'block'; }

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