body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 100%;
margin: 0;
padding: 0;
}
.calculator-wrapper {
max-width: 700px;
margin: 20px auto;
background: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-header {
text-align: center;
margin-bottom: 25px;
}
.calc-header h2 {
margin: 0 0 10px 0;
color: #2c3e50;
}
.input-group {
margin-bottom: 20px;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #495057;
}
.input-group input {
width: 100%;
padding: 12px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.input-group input:focus {
border-color: #4dabf7;
outline: none;
box-shadow: 0 0 0 3px rgba(77, 171, 247, 0.2);
}
.btn-calc {
width: 100%;
padding: 14px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
}
.btn-calc:hover {
background-color: #0056b3;
}
.result-box {
margin-top: 25px;
padding: 20px;
background-color: #fff;
border-left: 5px solid #007bff;
border-radius: 4px;
display: none;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
}
.result-row {
display: flex;
justify-content: space-between;
align-items: center;
padding: 10px 0;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #555;
}
.result-value {
font-size: 1.2em;
font-weight: 700;
color: #2c3e50;
}
.highlight-value {
color: #007bff;
font-size: 1.4em;
}
.unit-toggle {
display: flex;
gap: 15px;
margin-bottom: 20px;
justify-content: center;
}
.radio-label {
display: flex;
align-items: center;
cursor: pointer;
}
.radio-label input {
margin-right: 5px;
}
.article-content {
max-width: 800px;
margin: 40px auto;
padding: 0 20px;
}
.article-content h2 {
color: #2c3e50;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
margin-top: 40px;
}
.article-content h3 {
color: #34495e;
margin-top: 25px;
}
.article-content ul {
background: #f1f8ff;
padding: 20px 40px;
border-radius: 6px;
}
.formula-box {
background: #eef2f5;
padding: 15px;
border-left: 4px solid #6c757d;
font-family: monospace;
font-size: 1.1em;
margin: 20px 0;
}
.error-msg {
color: #dc3545;
text-align: center;
margin-top: 10px;
display: none;
}
@media (max-width: 600px) {
.calculator-wrapper {
padding: 20px;
}
}
function updateLabels() {
var unitRadios = document.getElementsByName('unit');
var selectedUnit = 'lbs';
for (var i = 0; i < unitRadios.length; i++) {
if (unitRadios[i].checked) {
selectedUnit = unitRadios[i].value;
break;
}
}
var mainLabel = document.getElementById('mainLabel');
var tenderLabel = document.getElementById('tenderLabel');
var unitText = selectedUnit === 'lbs' ? '(lbs/in)' : '(kg/mm)';
mainLabel.textContent = 'Main Spring Rate ' + unitText;
tenderLabel.textContent = 'Tender/Helper Spring Rate ' + unitText;
}
function calculateSpringRate() {
// Get input elements
var mainRateInput = document.getElementById('mainRate');
var tenderRateInput = document.getElementById('tenderRate');
var resultBox = document.getElementById('resultBox');
var errorDisplay = document.getElementById('errorDisplay');
// Parse values
var mainK = parseFloat(mainRateInput.value);
var tenderK = parseFloat(tenderRateInput.value);
// Validation
if (isNaN(mainK) || isNaN(tenderK) || mainK <= 0 || tenderK <= 0) {
errorDisplay.style.display = 'block';
resultBox.style.display = 'none';
return;
}
errorDisplay.style.display = 'none';
// Calculation: Combined Rate = (Main * Tender) / (Main + Tender)
// This is the formula for springs in series
var combinedK = (mainK * tenderK) / (mainK + tenderK);
// Calculate step up percentage (how much stiffer it gets when tender binds)
// Formula: ((Main – Combined) / Combined) * 100
var stepUp = ((mainK – combinedK) / combinedK) * 100;
// Determine units for display
var unitRadios = document.getElementsByName('unit');
var unitSuffix = ' lbs/in';
for (var i = 0; i < unitRadios.length; i++) {
if (unitRadios[i].checked) {
if (unitRadios[i].value === 'kg') unitSuffix = ' kg/mm';
break;
}
}
// Display results
document.getElementById('combinedResult').textContent = combinedK.toFixed(2) + unitSuffix;
document.getElementById('mainResult').textContent = mainK.toFixed(2) + unitSuffix;
document.getElementById('stepUpResult').textContent = stepUp.toFixed(1) + '% Increase';
resultBox.style.display = 'block';
}
Understanding Dual Coil Spring Rates
In the world of automotive suspension tuning, specifically with coilover setups, utilizing a dual spring configuration is a common technique to fine-tune handling characteristics and ride comfort. Our Dual Coil Spring Rate Calculator helps you determine the effective spring rate when two springs are stacked in series.
How Dual Rate Springs Work
A dual rate setup involves stacking two springs on top of each other, usually separated by a slider (a plastic or metal divider). The two springs are typically:
- Main Spring: The stiffer, longer spring that handles the majority of the suspension work during high loads.
- Tender (or Helper) Spring: A softer spring intended to compress first, providing a lower initial spring rate or keeping the main spring seated during droop.
When the vehicle is sitting on the ground or experiencing light bumps, both springs compress simultaneously. Physics dictates that springs stacked in series result in a softer combined rate than either individual spring. Once the suspension compresses enough to fully compress the tender spring (known as "coil bind"), the system transitions to the rate of the Main Spring only.
The Calculation Formula
To calculate the combined spring rate of two springs in series, we use the following harmonic mean formula:
Kcombined = (Kmain × Ktender) / (Kmain + Ktender)
Where:
- Kcombined is the effective initial spring rate.
- Kmain is the rate of the main spring.
- Ktender is the rate of the tender spring.
Example Calculation
Let's say you have a track car setup with the following springs:
- Main Spring: 600 lbs/in
- Tender Spring: 200 lbs/in
Using the formula:
(600 × 200) / (600 + 200) = 120,000 / 800 = 150 lbs/in
In this scenario, your suspension will have an initial softness of 150 lbs/in. Once the 200 lbs/in tender spring fully compresses (binds), the rate will instantly jump to 600 lbs/in. This allows for a compliant ride over small imperfections while maintaining high stiffness for cornering loads.
Tender Springs vs. Helper Springs
While often used interchangeably in conversation, they serve slightly different purposes in tuning:
Helper Springs
Helper springs are extremely soft (often 10-30 lbs/in) and have very flat wire profiles. Their primary purpose is not to influence handling, but to keep the main spring seated against the perches when the suspension is at full droop (e.g., when the car is jacked up). Because they are so soft, they are usually fully compressed by the car's static weight, meaning the car drives solely on the Main Spring rate.
Tender Springs
Tender springs are stiffer than helpers (often 150-300 lbs/in) and are designed to remain active during normal driving. They create a true dual-rate system where the car drives on the softer combined rate initially, and transitions to the main rate under heavier compression (braking or cornering).
Why Use a Dual Rate Setup?
- Traction over bumps: A softer initial rate allows the wheel to track uneven surfaces better, improving mechanical grip.
- Street Comfort: It absorbs small road irregularities, making a stiff race setup more tolerable on the street.
- Droop Travel: It increases the total travel of the suspension, allowing the wheel to extend further down into potholes or when cresting hills, maintaining tire contact with the road.
Use the calculator above to experiment with different spring combinations to find the perfect balance between initial compliance and ultimate support for your vehicle setup.