Motion Ratio Calculator

What Is Motion Ratio?

Motion ratio (MR) describes how much the spring moves compared to the wheel.

Simple definition:

Motion Ratio = Spring Travel ÷ Wheel Travel

In most control arm setups, motion ratio is calculated using distances:

• D1 = Pivot to spring mount
• D2 = Pivot to ball joint (wheel)

Formula:

MR = D1 ÷ D2

If the spring is mounted halfway along the control arm, the motion ratio will be less than 1.0. That means the spring moves less than the wheel.

Why Motion Ratio Matters

Motion ratio directly changes:

• Wheel rate
• Ride quality
• Suspension frequency
• Spring stiffness required
• Mechanical leverage

If your motion ratio is 0.70, the spring only moves 70% as much as the wheel.

Because force and travel both change, the wheel rate is affected by the square of the motion ratio.

That is where many people get it wrong.

Wheel Rate Formula (The Important Part)

The calculator uses this formula:

Wheel Rate = Spring Rate × (Motion Ratio)² × (Angle Correction)²

Let’s break that down.

1. Motion Ratio Squared

The motion ratio is squared because:

• The spring compresses less
• The force is also reduced by leverage

So if MR = 0.5:

Wheel Rate = Spring Rate × 0.25

A 400 lb/in spring becomes 100 lb/in at the wheel.

That is a huge difference.

2. Angle Correction Factor

If the shock is mounted at an angle, it becomes less effective.

Angle correction factor:

ACF = cos(angle)

The calculator squares it for precision:

Wheel Rate = Spring Rate × MR² × cos²(angle)

If your shock is tilted 20 degrees:

• cos(20°) ≈ 0.94
• cos²(20°) ≈ 0.88

You lose about 12% efficiency just from angle.

Mounting shocks more vertically improves performance.

Suspension Frequency Explained

The calculator also gives suspension frequency in Hertz (Hz).

Formula used:

Frequency = (1 / 2π) × √(Wheel Rate × 386.4 / Corner Weight)

Frequency tells you how stiff the car will feel.

General Guidelines

Street cars usually sit around 1.2–1.4 Hz.

Track cars often run 1.8–2.0 Hz.

Race cars can exceed 2.5 Hz.

Motion Ratio Types

The calculator classifies leverage type automatically.

1. Direct Acting (MR above 0.9)

• Common in strut setups
• Spring almost matches wheel movement
• Very efficient

2. Leveraged (MR 0.6–0.9)

• Common in double wishbone setups
• Moderate leverage
• Requires stiffer springs

3. Highly Leveraged (MR below 0.6)

• Inboard rocker systems
• Formula cars
• Requires very stiff springs

Lower motion ratio means higher mechanical leverage.

Example Calculation

Let’s use realistic numbers.

• D1 = 12 inches
• D2 = 18 inches
• Spring Rate = 500 lb/in
• Shock Angle = 10°
• Corner Weight = 800 lb

Step 1: Motion Ratio

MR = 12 ÷ 18 = 0.67

Step 2: Angle Correction

cos(10°) ≈ 0.984
cos²(10°) ≈ 0.97

Step 3: Wheel Rate

Wheel Rate = 500 × 0.67² × 0.97
Wheel Rate ≈ 217 lb/in

Your 500 lb/in spring is effectively 217 lb/in at the tire.

That means efficiency is around 43%.

This is why geometry matters.

How to Use the Motion Ratio Calculator

The calculator requires:

Geometry Inputs

• Pivot to spring distance (D1)
• Pivot to wheel distance (D2)
• Spring angle (optional but recommended)

Spring & Weight Inputs

• Spring rate
• Corner weight

After calculation, it shows:

• Motion ratio
• Wheel rate
• Efficiency loss
• Angle correction factor
• Suspension frequency
• Ride quality estimate
• Leverage type
• Tuning insight

It also visually shows efficiency versus leverage loss.

How to Choose the Right Spring Rate

Here is the correct workflow:

1. Decide your target frequency
2. Calculate required wheel rate
3. Use motion ratio formula backwards
4. Solve for spring rate

If you skip motion ratio, you will almost always choose the wrong spring.

Common Mistakes

Ignoring Motion Ratio

Many people assume 500 lb/in equals 500 lb/in at the wheel. It almost never does.

Ignoring Angle

Shock angle can reduce efficiency by 10–20%.

Using Total Vehicle Weight

Always use corner weight, not total weight.

Not Squaring Motion Ratio

Wheel rate depends on MR², not MR.

Practical Tuning Insight

If efficiency is below 50%:

• Your setup has high leverage
• You need much stiffer springs
• Expect faster damper shaft speeds

If frequency is below 1.0 Hz:

• Car will feel soft and floaty

If above 2.2 Hz:

• Car will feel harsh
• Excellent for aero grip
• Poor for street comfort

Why Engineers Care About Motion Ratio

Suspension geometry defines how the car behaves.

Motion ratio affects:

• Load transfer
• Tire grip
• Response time
• Ride comfort
• Body control

Professional race teams calculate this before choosing springs.

You should too.