Spring rate required for coilover given desired droop and motion ratio Calculator

✖Corner sprung mass of vehicle is the mass of the vehicle's sprung components, including the chassis, engine, and transmission, affecting tire behavior in racing.ⓘ Corner Sprung Mass of Vehicle [W_cs]			+10% -10%
✖Acceleration due to Gravity is the downward force exerted on a racing car's tires, affecting its speed, handling, and overall performance on a track.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Motion ratio in suspension is the ratio of the motion of the suspension to the motion of the wheel in a racing car, affecting its overall performance.ⓘ Motion Ratio in Suspension [M.R.]			+10% -10%
✖Wheel travel is the maximum distance that a tire moves upward and downward while maintaining contact with the racing track, affecting the car's overall performance.ⓘ Wheel Travel [W.T.]			+10% -10%
✖Angle of spring/shock absorber from vertical is the inclination of the spring or shock absorber from the vertical axis in a racing car's tire behavior.ⓘ Angle of Spring/Shock Absorber from Vertical [θ_s]			+10% -10%

✖Stiffness of Spring is the measure of a spring's resistance to deformation in a racing car's tire behavior, affecting its overall performance and handling.ⓘ Spring rate required for coilover given desired droop and motion ratio [k]

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Formula

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Spring rate required for coilover given desired droop and motion ratio

Formula

k = W cs \cdot \frac{g}{M.R. \cdot W.T. \cdot \cos (θ s)}

Example

160.8213 N/m = 1.208 kg \cdot \frac{9.8 m/s²}{0.85 \cdot 100.0 mm \cdot \cos (30.0 °)}

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Spring rate required for coilover given desired droop and motion ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stiffness of Spring = Corner Sprung Mass of Vehicle*Acceleration due to Gravity/(Motion Ratio in Suspension*Wheel Travel*cos(Angle of Spring/Shock Absorber from Vertical))
k = W_cs*g/(M.R.*W.T.*cos(θ_s))
This formula uses 1 Functions, 6 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is the measure of a spring's resistance to deformation in a racing car's tire behavior, affecting its overall performance and handling.
Corner Sprung Mass of Vehicle - (Measured in Kilogram) - Corner sprung mass of vehicle is the mass of the vehicle's sprung components, including the chassis, engine, and transmission, affecting tire behavior in racing.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is the downward force exerted on a racing car's tires, affecting its speed, handling, and overall performance on a track.
Motion Ratio in Suspension - Motion ratio in suspension is the ratio of the motion of the suspension to the motion of the wheel in a racing car, affecting its overall performance.
Wheel Travel - (Measured in Meter) - Wheel travel is the maximum distance that a tire moves upward and downward while maintaining contact with the racing track, affecting the car's overall performance.
Angle of Spring/Shock Absorber from Vertical - (Measured in Radian) - Angle of spring/shock absorber from vertical is the inclination of the spring or shock absorber from the vertical axis in a racing car's tire behavior.

STEP 1: Convert Input(s) to Base Unit

Corner Sprung Mass of Vehicle: 1.208 Kilogram --> 1.208 Kilogram No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Motion Ratio in Suspension: 0.85 --> No Conversion Required
Wheel Travel: 100 Millimeter --> 0.1 Meter (Check conversion here)
Angle of Spring/Shock Absorber from Vertical: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = W_cs*g/(M.R.*W.T.*cos(θ_s)) --> 1.208*9.8/(0.85*0.1*cos(0.5235987755982))

Evaluating ... ...

k = 160.821257100576

STEP 3: Convert Result to Output's Unit

160.821257100576 Newton per Meter --> No Conversion Required

FINAL ANSWER

160.821257100576 ≈ 160.8213 Newton per Meter <-- Stiffness of Spring

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Tire Behavior in Racing Car » Mechanical » Wheel Parameters » Spring rate required for coilover given desired droop and motion ratio

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Created by Vivek Gaikwad

AISSMS College of Engineering, Pune (AISSMSCOE, Pune), Pune

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< Wheel Parameters Calculators

Contact Point of Wheel and Curb Distance from Wheel Center Axis

Go Contact Point Distance from Wheel Center Axis = sqrt(2*Effective Radius of Wheel*(Height of Curb-Height of Curb^2))

Angle between Traction Force and Horizontal Axis

Go Angle between Traction Force and Horizontal Axis = asin(1-Curb Height/Effective Radius of Wheel)

Tire Side Wall Height

Go Tire Side Wall Height = (Aspect Ratio of Tire*Tire Width)/100

Aspect Ratio of Tire

Go Aspect Ratio of Tire = Tire Side Wall Height/Tire Width*100

Spring rate required for coilover given desired droop and motion ratio Formula

More details about various terms used in this calculator.

1) spring rate- It is basically amount of force required to cause unit deflection of spring. More precisely in vehicle dynamics, it is simply amount of weight a spring is designed to carry at a certain ride height of vehicle.
2) motion ratio- It is ratio of spring travel(deflection) to the wheel travel. The “motion ratio” is mechanical advantage (lever ratio) that the wheel has over the spring in compressing it.
3)Bump and Droop is the amount of wheel travel in vertically upward(say on speed breaker) and downward direction respectively.
4) Spring angle correction factor- If your spring is mounted at an angle you will need to consider that in your spring calculations. Measure the angle of your spring from vertical in degrees. The greater the installed angle, the stiffer the spring rate must be to support the same weight. It is cosine of the angle of the spring/shock absorber with vertical when viewed from front view of car.
5) sprung mass of vehicle- The mass of vehicle supported by suspension.

Methodology and concept behind calculating spring rate.

It's obvious that greater the droop in vehicle more & more will be the ground contact maintained by wheels in drops. But at the same time it makes springs softer which affects handling of vehicle. So once you fix your desired droop value according to your track & preferences you can proceed to calculate corresponding spring rate required to maintain the ride height in static position of vehicle. Now we will talk about one corner(quarter car model) of vehicle. So if we assumed that vehicle is jacked up and slowly raised down, the amount of force on spring is equal to the corner sprung mass of vehicle. While doing so, the distance through which your wheel will move vertically upward with respect to chassis will be equal to your droop value. So to calculate corresponding spring deflection, you should know your spring installation ratio(motion ratio). Thus calculate spring travel by multiplying droop value with motion ratio and then just divide corner sprung mass by spring travel according to spring rate formula.

How to Calculate Spring rate required for coilover given desired droop and motion ratio?

Spring rate required for coilover given desired droop and motion ratio calculator uses Stiffness of Spring = Corner Sprung Mass of Vehicle*Acceleration due to Gravity/(Motion Ratio in Suspension*Wheel Travel*cos(Angle of Spring/Shock Absorber from Vertical)) to calculate the Stiffness of Spring, Spring rate required for coilover given desired droop and motion ratio formula is defined as a measure of the stiffness of a coilover suspension system, which is critical in determining the vehicle's ride quality, handling, and overall performance, taking into account the weight of the vehicle, motion ratio, and desired droop. Stiffness of Spring is denoted by k symbol.

How to calculate Spring rate required for coilover given desired droop and motion ratio using this online calculator? To use this online calculator for Spring rate required for coilover given desired droop and motion ratio, enter Corner Sprung Mass of Vehicle (W_cs), Acceleration due to Gravity (g), Motion Ratio in Suspension (M.R.), Wheel Travel (W.T.) & Angle of Spring/Shock Absorber from Vertical (θ_s) and hit the calculate button. Here is how the Spring rate required for coilover given desired droop and motion ratio calculation can be explained with given input values -> 160.8213 = 1.208*9.8/(0.85*0.1*cos(0.5235987755982)).

FAQ

What is Spring rate required for coilover given desired droop and motion ratio?

Spring rate required for coilover given desired droop and motion ratio formula is defined as a measure of the stiffness of a coilover suspension system, which is critical in determining the vehicle's ride quality, handling, and overall performance, taking into account the weight of the vehicle, motion ratio, and desired droop and is represented as k = W_cs*g/(M.R.*W.T.*cos(θ_s)) or Stiffness of Spring = Corner Sprung Mass of Vehicle*Acceleration due to Gravity/(Motion Ratio in Suspension*Wheel Travel*cos(Angle of Spring/Shock Absorber from Vertical)). Corner sprung mass of vehicle is the mass of the vehicle's sprung components, including the chassis, engine, and transmission, affecting tire behavior in racing, Acceleration due to Gravity is the downward force exerted on a racing car's tires, affecting its speed, handling, and overall performance on a track, Motion ratio in suspension is the ratio of the motion of the suspension to the motion of the wheel in a racing car, affecting its overall performance, Wheel travel is the maximum distance that a tire moves upward and downward while maintaining contact with the racing track, affecting the car's overall performance & Angle of spring/shock absorber from vertical is the inclination of the spring or shock absorber from the vertical axis in a racing car's tire behavior.

How to calculate Spring rate required for coilover given desired droop and motion ratio?

Spring rate required for coilover given desired droop and motion ratio formula is defined as a measure of the stiffness of a coilover suspension system, which is critical in determining the vehicle's ride quality, handling, and overall performance, taking into account the weight of the vehicle, motion ratio, and desired droop is calculated using Stiffness of Spring = Corner Sprung Mass of Vehicle*Acceleration due to Gravity/(Motion Ratio in Suspension*Wheel Travel*cos(Angle of Spring/Shock Absorber from Vertical)). To calculate Spring rate required for coilover given desired droop and motion ratio, you need Corner Sprung Mass of Vehicle (W_cs), Acceleration due to Gravity (g), Motion Ratio in Suspension (M.R.), Wheel Travel (W.T.) & Angle of Spring/Shock Absorber from Vertical (θ_s). With our tool, you need to enter the respective value for Corner Sprung Mass of Vehicle, Acceleration due to Gravity, Motion Ratio in Suspension, Wheel Travel & Angle of Spring/Shock Absorber from Vertical and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Stiffness of Spring?

In this formula, Stiffness of Spring uses Corner Sprung Mass of Vehicle, Acceleration due to Gravity, Motion Ratio in Suspension, Wheel Travel & Angle of Spring/Shock Absorber from Vertical. We can use 1 other way(s) to calculate the same, which is/are as follows -

Stiffness of Spring = Wheel Rate of Vehicle/(((Motion Ratio in Suspension)^2)*(Spring Angle Correction Factor))

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