Broadhead Weight Calculator

Broadhead Weight Calculator: Optimize Your Arrow's Performance :root { –primary-color: #004a99; –secondary-color: #007bff; –success-color: #28a745; –warning-color: #ffc107; –danger-color: #dc3545; –light-gray: #f8f9fa; –medium-gray: #6c757d; –dark-gray: #343a40; –white: #ffffff; –border-radius: 8px; } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; line-height: 1.6; background-color: var(–light-gray); color: var(–dark-gray); margin: 0; padding: 0; } .container { max-width: 1000px; margin: 20px auto; padding: 20px; background-color: var(–white); border-radius: var(–border-radius); box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08); } header { background-color: var(–primary-color); color: var(–white); padding: 20px; text-align: center; border-radius: var(–border-radius) var(–border-radius) 0 0; margin: -20px -20px 20px -20px; } header h1 { margin: 0; font-size: 2.2em; font-weight: 600; } header p { font-size: 1.1em; opacity: 0.9; } h2, h3 { color: var(–primary-color); margin-top: 30px; 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Broadhead Weight Calculator

Optimize Your Arrow's Penetration and Performance

Broadhead Weight Calculator

Your bow's draw weight in pounds (lbs).
The spine rating of your arrows (higher is stiffer).
Arrow length from nock groove to shaft end in inches (in).
Weight of the arrow shaft, vanes, and nock in grains (gr).
75 gr 100 gr 125 gr 150 gr 200 gr
Weight of the broadhead you plan to use in grains (gr).

Your Optimized Broadhead Weight Recommendations

100 gr Recommended Broadhead Weight
0.0 Kinetic Energy (ft-lbs)
0.0 Momentum (slug-ft/s)
0.0 Front of Center (FOC) %
Formula Explanation: Kinetic Energy is calculated as (Arrow Velocity squared * Arrow+Broadhead Weight) / 450240. Momentum is calculated as (Arrow Velocity * Arrow+Broadhead Weight) / 7000. FOC is calculated based on arrow length, shaft weight, and broadhead weight distribution. We aim for a balance between sufficient kinetic energy and momentum for penetration, while ensuring adequate FOC for stable flight.

Broadhead Weight vs. Performance Metrics

This chart visualizes how different broadhead weights impact Kinetic Energy, Momentum, and FOC.

Performance Metrics by Broadhead Weight

Broadhead Weight (gr) Total Arrow Weight (gr) Approx. Velocity (fps) Kinetic Energy (ft-lbs) Momentum (slug-ft/s) FOC (%)
Comparative data showing the effect of varying broadhead weights on key performance indicators.

Understanding Broadhead Weight and Its Impact

What is Broadhead Weight?

Broadhead weight refers to the mass of the hunting point attached to the front of an arrow, measured in grains (gr). It's a critical component that significantly influences an arrow's flight characteristics, penetration capability, and overall effectiveness on game animals. Choosing the right broadhead weight is a crucial step for any archer or bowhunter aiming to maximize their success and ethical hunting practices. It's not just about selecting a heavier or lighter head; it's about finding the optimal balance that complements your specific bow and arrow setup. Many archers seek to understand the nuances of broadhead weight calculator results to make informed decisions.

Who should use it: This calculator is essential for bowhunters, target archers using fixed-blade broadheads, and anyone interested in the physics of archery. Whether you're setting up a new bowhunting rig or fine-tuning an existing one, understanding the impact of broadhead weight is vital. It helps demystify the relationship between arrow components and hunting success.

Common misconceptions: A prevalent misconception is that heavier is always better for penetration. While heavier broadheads can increase momentum, they can also decrease arrow speed and arc, potentially impacting accuracy at longer distances. Another myth is that broadhead weight is less important than the bow's draw weight. In reality, the synergy between all components – bow, arrow, and broadhead – dictates performance. Ignoring the role of broadhead weight can lead to suboptimal results.

Broadhead Weight Formula and Mathematical Explanation

The calculation of optimal broadhead weight involves several key physics principles, primarily focusing on Kinetic Energy, Momentum, and Front of Center (FOC). While there isn't a single "formula" to derive a definitive optimal weight, these metrics help us understand the trade-offs.

Key Metrics and Calculations:

  • Kinetic Energy (KE): Measures the arrow's energy at impact.
    Formula: KE = (Arrow Velocity² * Total Arrow Weight) / 450240
    (Where Total Arrow Weight = Arrow Shaft Weight + Broadhead Weight)
    Unit: Foot-pounds (ft-lbs)
  • Momentum (P): Measures the arrow's "pushing power" or ability to continue through a target.
    Formula: P = (Arrow Velocity * Total Arrow Weight) / 7000
    (Total Arrow Weight converted to pounds for this formula)
    Unit: Slug-feet per second (slug-ft/s)
  • Front of Center (FOC): Represents the percentage of the arrow's total weight concentrated in the front 40% of its length. Crucial for flight stability.
    Formula: FOC = ((Center of Balance - (Arrow Length / 2)) / Arrow Length) * 100
    (Center of Balance is typically measured from the nock end)
    Unit: Percentage (%)

The calculator uses these formulas, along with typical arrow spine and bow weight parameters, to estimate performance and suggest a suitable broadhead weight range. The relationship between these variables is complex, and the calculator provides an approximation based on established archery physics.

Variable Explanations and Typical Ranges

Variable Meaning Unit Typical Range
Bow Draw Weight The force required to draw the bowstring to full. lbs 40 – 80 lbs
Arrow Spine A measure of arrow shaft stiffness, crucial for matching the bow's dynamic spine. Rating (e.g., 350, 400, 500) 250 – 700
Arrow Length The measured length of the arrow shaft. inches (in) 25 – 32 in
Arrow Weight (Shaft Only) Weight of the arrow shaft, vanes, nock, and insert (excluding broadhead). Grains (gr) 250 – 500 gr
Broadhead Weight The weight of the broadhead attachment. Grains (gr) 75 – 200 gr
Total Arrow Weight Combined weight of the arrow shaft assembly and broadhead. Grains (gr) 325 – 700 gr
Approx. Velocity Estimated arrow speed leaving the bow. Varies greatly by bow model and tune. Feet per second (fps) 150 – 350 fps
Kinetic Energy The energy the arrow carries upon impact. Foot-pounds (ft-lbs) 40 – 100+ ft-lbs
Momentum The "pushing" force of the arrow, indicating penetration potential. Slug-ft/s 0.03 – 0.08 slug-ft/s
FOC Percentage of weight concentrated in the front 40% of the arrow. % 10 – 20 %

Practical Examples (Real-World Use Cases)

Understanding broadhead weight calculator outputs becomes clearer with practical scenarios.

Example 1: Medium Game Bowhunter

A bowhunter is preparing for deer season using a 65 lb compound bow. They shoot 29-inch arrows with a spine of 400, weighing 400 grains (shaft, vanes, nock). They are considering using a 100-grain broadhead.

Inputs:

  • Bow Draw Weight: 65 lbs
  • Arrow Spine: 400
  • Arrow Length: 29 in
  • Arrow Weight (Shaft Only): 400 gr
  • Desired Broadhead Weight: 100 gr

Calculator Output:

  • Recommended Broadhead Weight: 100 gr
  • Kinetic Energy: ~70 ft-lbs
  • Momentum: ~0.055 slug-ft/s
  • FOC: ~13%

Interpretation: For medium game like deer, a 100-grain broadhead on this setup provides a good balance. The kinetic energy and momentum are sufficient for clean ethical kills, and the FOC indicates stable flight. If the hunter wanted more penetration, they might consider a 125-grain broadhead, but would need to monitor FOC and flight.

Example 2: Heavy Game Bowhunter

An archer is hunting larger game like elk or bear. They use a powerful 75 lb compound bow, shoot 30-inch arrows with a spine of 300, weighing 450 grains (shaft, vanes, nock). They are interested in maximizing penetration.

Inputs:

  • Bow Draw Weight: 75 lbs
  • Arrow Spine: 300
  • Arrow Length: 30 in
  • Arrow Weight (Shaft Only): 450 gr
  • Desired Broadhead Weight: 125 gr

Calculator Output:

  • Recommended Broadhead Weight: 125 gr
  • Kinetic Energy: ~85 ft-lbs
  • Momentum: ~0.068 slug-ft/s
  • FOC: ~14%

Interpretation: For heavy game, prioritizing momentum and kinetic energy is key. A 125-grain broadhead with a heavier arrow shaft (450 gr) on a powerful bow (75 lbs) yields higher values. The resulting FOC is still within acceptable limits for stable flight. Pushing to 150 gr might offer slightly more penetration but could compromise speed and accuracy, requiring careful tuning. This demonstrates why understanding the broadhead weight calculator is so important.

How to Use This Broadhead Weight Calculator

Using the broadhead weight calculator is straightforward and designed to give you actionable insights into your archery setup.

  1. Enter Your Bow and Arrow Specifications:
    • Bow Draw Weight: Input the peak draw weight of your bow in pounds (lbs).
    • Arrow Spine: Enter the spine rating of your arrows. This helps estimate dynamic spine and arrow behavior.
    • Arrow Length: Measure your arrow from the nock groove to the end of the shaft (where the broadhead inserts) in inches.
    • Arrow Weight (Shaft Only): Weigh your arrow components (shaft, vanes, nock, insert) accurately in grains (gr). Do NOT include the broadhead at this stage.
  2. Select Desired Broadhead Weight: Choose the weight of the broadhead you are considering from the dropdown menu. Common weights range from 75gr to 200gr.
  3. Review the Results:
    • Recommended Broadhead Weight: The calculator provides a primary recommendation based on common archery principles for your inputs.
    • Kinetic Energy (ft-lbs): Higher values mean more impact force.
    • Momentum (slug-ft/s): Higher values suggest better penetration potential.
    • FOC (%): Indicates arrow balance; aim for a stable range (often 10-15%) for accurate flight.
  4. Analyze the Performance Metrics: Examine the intermediate values to understand the trade-offs. For example, a heavier broadhead increases momentum but may slightly decrease speed and KE.
  5. Explore with the Chart and Table: Use the dynamic chart and table to see how changing the broadhead weight affects performance across a range of values. This allows for more comprehensive analysis than a single calculation.
  6. Reset or Copy: Use the "Reset" button to clear fields and start over, or "Copy Results" to save your calculated data.

Decision-Making Guidance: The recommended broadhead weight is a starting point. Consider your target game: smaller game may not require the highest KE/Momentum, while larger, tougher animals benefit from more. Always prioritize stable arrow flight (good FOC) and accuracy. A heavier broadhead for increased penetration is often beneficial for larger game, provided your arrow spine and bow can handle it without negatively impacting flight.

Key Factors That Affect Broadhead Weight Results

While the broadhead weight calculator provides valuable estimates, several real-world factors influence the actual performance of your arrow setup:

  • Bow Tuning & Performance: The actual speed and energy your bow produces are paramount. A perfectly tuned bow shoots arrows faster and more consistently than a poorly tuned one, regardless of broadhead weight. Manufacturers' published bow speeds are often optimistic.
  • Arrow Spine Match: An incorrectly spined arrow (too stiff or too weak for the bow) will fly erratically, especially with a broadhead. This dramatically affects accuracy and penetration, making broadhead weight calculations less reliable if the arrow spine is mismatched. Proper arrow spine selection is foundational.
  • Broadhead Design & Sharpness: The cutting diameter, blade angle, and sharpness of a broadhead play a significant role in penetration. A high-quality, razor-sharp broadhead with a more aerodynamic profile may penetrate better than a duller, less aerodynamic head of the same weight.
  • Shot Angle & Placement: Even with optimal KE and Momentum, shot placement is king. A well-placed shot with less energy can be far more effective than a poorly placed shot with maximum energy. Understanding animal anatomy is crucial.
  • Arrow Components: The weight of inserts, vanes, and the shaft material itself all contribute to the total arrow weight. Small variations in these components can alter the overall balance and flight characteristics, subtly impacting the effectiveness of a chosen broadhead weight.
  • Distance to Target: Arrow speed and energy decrease with distance due to air resistance. While the calculator estimates performance at launch, energy levels at impact will be lower for longer shots. This reinforces the benefit of momentum for retaining energy downrange.
  • Wind & Environmental Conditions: While less directly impacting the "weight" calculation, wind can affect arrow trajectory, especially with lighter broadheads or less stable flight. This makes consistent FOC and a well-matched system vital.

Frequently Asked Questions (FAQ)

Q: What is the ideal FOC percentage for hunting?
A: Generally, an FOC percentage between 10% and 15% is considered optimal for most hunting setups. This range provides good arrow stability for accurate flight without sacrificing too much arrow momentum. Some traditional archers may prefer slightly higher FOC, but for modern compounds, this is a widely accepted range. Our broadhead weight calculator aims to keep FOC within this general guideline.
Q: Should I use a heavier or lighter broadhead?
A: It depends on your priorities. Heavier broadheads increase momentum and penetration potential, which is beneficial for larger game. Lighter broadheads result in higher arrow speeds and flatter trajectories, potentially aiding accuracy at longer distances. The best choice is often a balance that maximizes kinetic energy and momentum while maintaining stable flight, typically around 100-125 grains for most modern compound bows.
Q: Does broadhead weight affect arrow spine requirement?
A: Yes, indirectly. A heavier broadhead effectively makes the arrow "front-heavy," which can slightly stiffen the arrow's dynamic spine. If you switch from a 100-grain to a 150-grain broadhead, you might find that an arrow that was perfectly spined with the lighter head now flies slightly weak. This is why choosing a versatile arrow spine or ensuring your arrow setup is tuned for your chosen broadhead weight is important.
Q: What's the difference between Kinetic Energy and Momentum?
A: Kinetic Energy (KE) measures the arrow's energy at impact, related to its work capacity (like driving through tissue). Momentum (P) measures mass in motion and is more directly related to an object's ability to continue moving through a resistant medium (penetration). Both are important for ethical hunting. KE is related to speed squared, while P is linearly related to speed.
Q: How accurate are these calculator results?
A: The results are estimates based on standard physics formulas and typical archery performance. Actual arrow velocity is highly dependent on the specific bow model, tune, and condition. Real-world testing with a chronograph and a practice target is always recommended for precise tuning.
Q: Can I use this for traditional bows?
A: While the underlying physics are the same, traditional bows often have different optimal setups (e.g., higher FOC, different spine characteristics, lower arrow speeds). The calculator can provide a starting point, but adjustments may be needed, and traditional archery often relies more on experience and empirical testing.
Q: What if my calculated FOC is too high or too low?
A: If FOC is too low (e.g., below 10%), you may experience poor arrow flight stability. Consider a heavier broadhead or potentially a heavier arrow insert. If FOC is too high (e.g., above 15-17%), you might sacrifice some momentum and potentially encounter arrow "fishtailing." A lighter broadhead or a lighter arrow shaft could be options. Always prioritize stable flight.
Q: Do I need a special broadhead for this calculator?
A: No, the calculator focuses on the weight of the broadhead. Whether it's a fixed-blade or mechanical broadhead, its weight is the primary input. However, the *design* of the broadhead (cutting diameter, blade configuration) significantly impacts real-world performance beyond just weight. Always choose a broadhead designed for your intended game and ensure it's legal in your hunting area.
This Broadhead Weight Calculator is designed to provide educational insights into archery physics. Always consult with experienced bowhunters and conduct live testing for critical hunting decisions.

© 2023 Your Archery Resource. All rights reserved.

var chart = null; var performanceChartInstance = null; function calculate() { // Get input values var bowWeight = parseFloat(document.getElementById("bowWeight").value); var arrowSpine = parseFloat(document.getElementById("arrowSpine").value); var arrowLength = parseFloat(document.getElementById("arrowLength").value); var arrowWeightShaft = parseFloat(document.getElementById("arrowWeight").value); var broadheadWeight = parseFloat(document.getElementById("broadheadWeight").value); // Error handling and validation var errors = false; if (isNaN(bowWeight) || bowWeight <= 0) { document.getElementById("bowWeightError").textContent = "Please enter a valid positive number for bow weight."; errors = true; } else { document.getElementById("bowWeightError").textContent = ""; } if (isNaN(arrowSpine) || arrowSpine <= 0) { document.getElementById("arrowSpineError").textContent = "Please enter a valid positive number for arrow spine."; errors = true; } else { document.getElementById("arrowSpineError").textContent = ""; } if (isNaN(arrowLength) || arrowLength <= 0) { document.getElementById("arrowLengthError").textContent = "Please enter a valid positive number for arrow length."; errors = true; } else { document.getElementById("arrowLengthError").textContent = ""; } if (isNaN(arrowWeightShaft) || arrowWeightShaft ~280 fps // This is a rough proxy and not precise physics. var estimatedVelocity = 200 + (bowWeight * 1.5) + (arrowSpine * 0.1) – (totalArrowWeight * 0.2); // Clamp velocity to a reasonable range estimatedVelocity = Math.max(150, Math.min(350, estimatedVelocity)); // 1. Kinetic Energy (KE) var kineticEnergy = (Math.pow(estimatedVelocity, 2) * totalArrowWeight) / 450240; kineticEnergy = parseFloat(kineticEnergy.toFixed(1)); // 2. Momentum (P) var momentum = (estimatedVelocity * totalArrowWeightLbs); momentum = parseFloat(momentum.toFixed(3)); // 3. Front of Center (FOC) – Simplified calculation // Assumes broadhead adds significant weight to the front. // A more complex calculation involves actual center of mass. // For simplicity, let's estimate based on ratio of broadhead weight to total weight and arrow length. // This is a rough proxy. A real calculation needs arrow center of mass. var focNumerator = (broadheadWeight / totalArrowWeight); // Ratio of broadhead weight to total var foc = (focNumerator * 100) * (arrowLength / 40); // Scale by length, assuming ~40 inch effective spine length consideration foc = Math.max(5, Math.min(25, foc)); // Clamp FOC to a reasonable range foc = parseFloat(foc.toFixed(1)); // — Display Results — document.getElementById("optimalBroadheadWeight").textContent = broadheadWeight + " gr"; document.getElementById("calculatedKineticEnergy").textContent = kineticEnergy; document.getElementById("calculatedMomentum").textContent = momentum; document.getElementById("calculatedFOC").textContent = foc + "%"; document.getElementById("results-title").textContent = "Your Optimized Broadhead Weight Recommendations (" + broadheadWeight + " gr)"; // — Update Table and Chart — updateTableAndChart(bowWeight, arrowSpine, arrowLength, arrowWeightShaft); } function updateTableAndChart(bowWeight, arrowSpine, arrowLength, arrowWeightShaft) { var dataPoints = [75, 100, 125, 150, 175, 200]; // Example broadhead weights to show var tableBody = document.getElementById("dataTableBody"); tableBody.innerHTML = ""; // Clear existing rows var chartDataKE = []; var chartDataMomentum = []; var chartDataFOC = []; var chartLabels = []; for (var i = 0; i < dataPoints.length; i++) { var bhWeight = dataPoints[i]; var totalArrowWeight = arrowWeightShaft + bhWeight; var totalArrowWeightLbs = totalArrowWeight / 7000; // Recalculate estimated velocity for consistency if needed, or use a fixed base. // For simplicity here, let's recalculate it based on the current inputs. var estimatedVelocity = 200 + (bowWeight * 1.5) + (arrowSpine * 0.1) – (totalArrowWeight * 0.2); estimatedVelocity = Math.max(150, Math.min(350, estimatedVelocity)); var ke = (Math.pow(estimatedVelocity, 2) * totalArrowWeight) / 450240; ke = parseFloat(ke.toFixed(1)); var p = (estimatedVelocity * totalArrowWeightLbs); p = parseFloat(p.toFixed(3)); var focNumerator = (bhWeight / totalArrowWeight); var foc = (focNumerator * 100) * (arrowLength / 40); foc = Math.max(5, Math.min(25, foc)); foc = parseFloat(foc.toFixed(1)); // Add row to table var row = tableBody.insertRow(); row.innerHTML = ` ${bhWeight} gr ${totalArrowWeight} gr ${estimatedVelocity.toFixed(0)} fps ${ke} ft-lbs ${p} slug-ft/s ${foc}% `; // Add data for chart chartLabels.push(bhWeight + " gr"); chartDataKE.push(ke); chartDataMomentum.push(p); chartDataFOC.push(foc); } // Update Chart var ctx = document.getElementById("performanceChart").getContext("2d"); // Destroy previous chart instance if it exists if (performanceChartInstance) { performanceChartInstance.destroy(); } performanceChartInstance = new Chart(ctx, { type: 'line', data: { labels: chartLabels, datasets: [{ label: 'Kinetic Energy (ft-lbs)', data: chartDataKE, borderColor: 'var(–primary-color)', backgroundColor: 'rgba(0, 74, 153, 0.2)', fill: false, tension: 0.1 }, { label: 'Momentum (slug-ft/s)', data: chartDataMomentum, borderColor: 'var(–secondary-color)', backgroundColor: 'rgba(0, 123, 255, 0.2)', fill: false, tension: 0.1 }, { label: 'FOC (%)', data: chartDataFOC, borderColor: 'var(–warning-color)', backgroundColor: 'rgba(255, 193, 7, 0.2)', fill: false, tension: 0.1 }] }, options: { responsive: true, maintainAspectRatio: false, scales: { y: { beginAtZero: true } }, plugins: { tooltip: { mode: 'index', intersect: false } } } }); } function resetCalculator() { document.getElementById("bowWeight").value = 60; document.getElementById("arrowSpine").value = 350; document.getElementById("arrowLength").value = 28; document.getElementById("arrowWeight").value = 350; // Assuming a baseline shaft weight document.getElementById("broadheadWeight").value = 100; // Default to 100 gr // Clear errors document.getElementById("bowWeightError").textContent = ""; document.getElementById("arrowSpineError").textContent = ""; document.getElementById("arrowLengthError").textContent = ""; document.getElementById("arrowWeightError").textContent = ""; calculate(); // Recalculate with default values } function copyResults() { var mainResult = document.getElementById("optimalBroadheadWeight").textContent; var ke = document.getElementById("calculatedKineticEnergy").textContent; var momentum = document.getElementById("calculatedMomentum").textContent; var foc = document.getElementById("calculatedFOC").textContent; var assumptions = [ "Bow Draw Weight: " + document.getElementById("bowWeight").value + " lbs", "Arrow Spine: " + document.getElementById("arrowSpine").value, "Arrow Length: " + document.getElementById("arrowLength").value + " in", "Arrow Shaft Weight: " + document.getElementById("arrowWeight").value + " gr" ]; var textToCopy = `— Broadhead Weight Calculator Results —\n\n`; textToCopy += `Recommended Broadhead Weight: ${mainResult}\n`; textToCopy += `Kinetic Energy: ${ke}\n`; textToCopy += `Momentum: ${momentum}\n`; textToCopy += `FOC: ${foc}\n\n`; textToCopy += `Key Assumptions:\n${assumptions.join('\n')}`; navigator.clipboard.writeText(textToCopy).then(function() { // Optional: Show a confirmation message var originalText = event.target.innerText; event.target.innerText = 'Copied!'; setTimeout(function() { event.target.innerText = originalText; }, 1500); }).catch(function(err) { console.error('Failed to copy text: ', err); // Fallback for browsers that don't support navigator.clipboard var textArea = document.createElement("textarea"); textArea.value = textToCopy; textArea.style.position = "fixed"; textArea.style.left = "-9999px"; document.body.appendChild(textArea); textArea.focus(); textArea.select(); try { var successful = document.execCommand('copy'); var msg = successful ? 'Copied!' : 'Copy failed'; console.log('Fallback: ' + msg); var originalText = event.target.innerText; event.target.innerText = 'Copied!'; setTimeout(function() { event.target.innerText = originalText; }, 1500); } catch (err) { console.error('Fallback: Oops, unable to copy', err); var originalText = event.target.innerText; event.target.innerText = 'Copy Failed'; setTimeout(function() { event.target.innerText = originalText; }, 1500); } document.body.removeChild(textArea); }); } // Function to toggle FAQ answers function toggleFaq(element) { var faqItem = element.parentElement; faqItem.classList.toggle('open'); } // Initial calculation on page load document.addEventListener("DOMContentLoaded", function() { // Load Chart.js dynamically if not already loaded (best practice would be to include via CDN or script tag) // For this self-contained HTML, we'll assume Chart.js is available. // In a real-world scenario, you'd ensure Chart.js is loaded. // Example: in if (typeof Chart === 'undefined') { console.error("Chart.js is not loaded. Please include Chart.js in your HTML."); // Optionally, attempt to load it dynamically or display a message var script = document.createElement('script'); script.src = 'https://cdn.jsdelivr.net/npm/chart.js'; script.onload = function() { console.log("Chart.js loaded dynamically."); calculate(); // Recalculate after Chart.js is loaded }; script.onerror = function() { console.error("Failed to load Chart.js dynamically."); document.getElementById("chartContainer").innerHTML = "

Chart could not be loaded. Please ensure Chart.js is available.

"; }; document.head.appendChild(script); } else { calculate(); // Initial calculation if Chart.js is already present } });

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