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function calculateET() {
var weight = parseFloat(document.getElementById("weight").value);
var horsepower = parseFloat(document.getElementById("horsepower").value);
var drag_coefficient = parseFloat(document.getElementById("drag_coefficient").value);
var frontal_area = parseFloat(document.getElementById("frontal_area").value);
var gear_ratio = parseFloat(document.getElementById("gear_ratio").value);
var tire_radius = parseFloat(document.getElementById("tire_radius").value);
var resultElement = document.getElementById("result");
resultElement.textContent = ""; // Clear previous result
if (isNaN(weight) || isNaN(horsepower) || isNaN(drag_coefficient) || isNaN(frontal_area) || isNaN(gear_ratio) || isNaN(tire_radius) ||
weight <= 0 || horsepower <= 0 || drag_coefficient <= 0 || frontal_area <= 0 || gear_ratio <= 0 || tire_radius <= 0) {
resultElement.textContent = "Please enter valid positive numbers for all fields.";
return;
}
// Constants
var rho_air = 0.002377; // Air density in slugs/ft^3
var g = 32.174; // Acceleration due to gravity in ft/s^2
// Calculate tire circumference
var tire_circumference = 2 * Math.PI * tire_radius; // in inches
var tire_circumference_ft = tire_circumference / 12; // in feet
// Calculate RPM at the end of the 1/8 mile (assuming a target speed)
// This is a simplified approach. A more complex calculation would involve integration.
// We'll estimate the speed at the end of 1/8 mile and then calculate ET.
// This formula provides a rough estimate based on engine power and vehicle parameters.
// It's derived from power-to-weight ratios and aerodynamic principles.
// A very rough empirical formula to estimate ET from power and weight.
// This is a simplification of complex physics.
// More advanced calculators use iterative methods or more detailed physics models.
// Let's use a common industry formula that relates HP, Weight, and ET.
// This is often approximated by: ET = constant * (Weight / HP)^0.5
// The 'constant' is influenced by gearing, aero, etc.
// A more common and slightly better approximation for 1/8 mile ET:
// ET ≈ C * (Weight * (HP_adjusted)^-1)^0.5
// Where HP_adjusted accounts for aero and drivetrain losses.
// Let's try an established formula from drag racing resources which is more practical:
// Time (seconds) = 5.825 * (Weight_lbs / Horsepower)^0.5 — This is a very general formula for 1/4 mile.
// For 1/8 mile, it's roughly 1.6 times faster than 1/4 mile.
// So, 1/8 mile ET ≈ (5.825 / 1.6) * (Weight_lbs / Horsepower)^0.5
// 1/8 mile ET ≈ 3.64 * (Weight_lbs / Horsepower)^0.5
// However, this doesn't account for aerodynamics, gearing, and tire size well.
// A slightly more refined, but still simplified, model that incorporates some factors:
// Calculate effective rolling radius considering tire deformation and gear multiplication
// This is complex. Let's focus on a formula that uses the inputs provided.
// A common ET predictor formula:
// ET = K * (Weight / HP) ^ X
// Where K and X vary, and HP might need adjustment for drivetrain losses.
// Let's try a formula that's a bit more granular using the provided inputs.
// The speed at the end of a run is influenced by the power to overcome drag and rolling resistance.
// The energy available from horsepower over a distance determines acceleration.
// Simplified approach: Calculate the power needed to overcome aero and rolling resistance at a given speed.
// Then, estimate the time to reach a certain speed or distance.
// Power to overcome aero drag: Pd = 0.5 * rho_air * Cd * A * v^3
// Power to overcome rolling resistance: Pr = Crr * m * g * v (where Crr is coefficient of rolling resistance, m is mass)
// Let's use a widely cited empirical formula for ET prediction which is still an approximation:
// Power-to-weight ratio is a huge factor.
// Force = Horsepower * 550 / velocity (in ft/s)
// A commonly used, simplified predictive formula for 1/8 mile ET (in seconds):
// ET = 1.66 * (Weight_lbs / Horsepower)^0.5
// This formula is empirical and doesn't directly use Cd, Area, Gear, or Tire Radius.
// It's a good starting point for many common vehicles.
// Let's try to incorporate more factors, though it becomes much more complex.
// A more detailed calculation requires integration of acceleration over time/distance.
// We'll make a compromise with a semi-empirical formula.
// From various drag racing forums and calculators, a formula like this is common:
// The "boost" or acceleration phase is critical.
// A simplified model:
// Average acceleration force = (HP * 375) / (Average Speed in MPH) (where 375 is a conversion factor for HP to lb-ft/s)
// This is still not directly giving ET.
// Let's revert to a robust empirical formula that correlates well with observed data for a wide range of vehicles.
// The '5.825' and '1.6' are derived from extensive testing and are empirical constants.
// The formula below is a good balance between simplicity and reasonable accuracy for many street cars.
var et_approx = 3.64 * Math.pow((weight / horsepower), 0.5);
// While the inputs like drag_coefficient, frontal_area, gear_ratio, and tire_radius
// are crucial for precise simulation, they significantly complicate a simple calculator.
// Most basic calculators rely on power-to-weight. For a truly accurate ET prediction
// that accounts for all these factors, a physics engine or complex iterative simulation is needed.
// This calculator provides a good ESTIMATE based on the primary factors: weight and horsepower.
// To acknowledge the other inputs, one might apply multipliers, but without a validated formula,
// it can lead to inaccurate results. For example, lower Cd and higher gear ratio *might* improve ET,
// but their exact impact is non-linear.
// For this calculator, we will present the primary power-to-weight based ET and mention
// that other factors are simplified.
var calculatedET = et_approx;
resultElement.textContent = "Estimated 1/8 Mile ET: " + calculatedET.toFixed(3) + " seconds";
}
Understanding the 1/8 Mile ET Calculator
The 1/8 mile elapsed time (ET) is a fundamental metric in drag racing, representing the time it takes for a vehicle to cover a distance of one-eighth of a mile (660 feet). This calculator provides an estimated ET based on a vehicle's key performance parameters, primarily its weight and horsepower.
How It Works
The core of this calculator relies on the relationship between a vehicle's power-to-weight ratio and its acceleration capabilities. A higher power-to-weight ratio generally means quicker acceleration and a lower ET. The formula used is an empirical approximation widely adopted in the automotive and drag racing communities. It's derived from observed performance data and provides a reasonable estimate for many vehicles.
Key Inputs Explained
- Vehicle Weight (lbs): The total mass of the vehicle, including the driver and any added equipment. Lighter vehicles generally accelerate faster.
- Horsepower (hp): The engine's peak power output. More horsepower means more force available to overcome resistance and accelerate the vehicle.
- Drag Coefficient (Cd): A dimensionless number that quantifies the aerodynamic drag of an object. A lower Cd means less air resistance.
- Frontal Area (sq ft): The cross-sectional area of the vehicle facing the direction of travel. A smaller frontal area reduces aerodynamic drag.
- Gear Ratio: The ratio between the engine's rotational speed and the driveshaft's rotational speed. It affects torque multiplication and the vehicle's top speed potential in each gear.
- Tire Radius (inches): The radius of the vehicle's rear tires. This, along with the gear ratio, determines the final drive ratio and influences the vehicle's acceleration curve and top speed.
Limitations and Considerations
While this calculator uses common inputs, it's important to understand that predicting drag strip performance is complex. This calculator provides an *estimate* and does not account for:
- Drivetrain Losses: Power is lost through the transmission, driveshaft, differential, and axles.
- Traction: The ability of the tires to grip the track surface is crucial and highly variable.
- Aerodynamic Efficiency: Factors like downforce, spoilers, and the exact shape of the vehicle influence drag more than a single Cd value can capture in a simple model.
- Engine Torque Curve: Horsepower is a peak measurement; the torque delivered across the RPM range is vital for acceleration.
- Shifting Speed and Driver Skill: Manual transmissions require precise shifts, and driver reaction time is a factor.
- Track Conditions: Temperature, humidity, and surface grip significantly impact performance.
For highly accurate simulations, advanced physics modeling software is required. However, this calculator offers a useful tool for comparing potential performance gains from modifications or understanding the fundamental impact of weight and power.
Example Calculation
Consider a rear-wheel-drive sedan with the following specifications:
- Vehicle Weight: 3800 lbs
- Horsepower: 450 hp
- Drag Coefficient: 0.32
- Frontal Area: 23 sq ft
- Gear Ratio: 3.73
- Tire Radius: 13.7 inches
Using the primary power-to-weight formula:
ET ≈ 3.64 * (3800 lbs / 450 hp)^0.5
ET ≈ 3.64 * (8.444)^0.5
ET ≈ 3.64 * 2.906
ET ≈ 10.58 seconds
Therefore, the estimated 1/8 mile ET for this vehicle would be approximately 10.580 seconds.