## 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 = Wcs*g/(M.R.*W.T.*cos(θ))
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 a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
Corner sprung mass of vehicle - (Measured in Kilogram) - Corner sprung mass of vehicle is the amount of weight supported by spring at one particular corner of vehicle with driver inside vehicle.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Motion ratio in suspension - Motion ratio in suspension is ratio of shock travel to the corresponding wheel travel.
Wheel travel - (Measured in Meter) - Wheel travel is the amount by which wheel moves vertically over the bump/droop.
Angle of spring/shock absorber from vertical - (Measured in Radian) - Angle of spring/shock absorber from vertical when viewed from front view of car.
STEP 1: Convert Input(s) to Base Unit
Corner sprung mass of vehicle: 50 Kilogram --> 50 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 = Wcs*g/(M.R.*W.T.*cos(θ)) --> 50*9.8/(0.85*0.1*cos(0.5235987755982))
Evaluating ... ...
k = 6656.50898595098
STEP 3: Convert Result to Output's Unit
6656.50898595098 Newton per Meter --> No Conversion Required
6656.50898595098 6656.509 Newton per Meter <-- Stiffness of Spring
(Calculation completed in 00.020 seconds)
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## <Race Car Vehicle Dynamics Calculators

Spring rate provided Wheel rate
​ Go Stiffness of Spring = Wheel rate of vehicle/(((Motion ratio in suspension)^2)*(cos(Angle of spring/shock absorber from vertical)))
Wheel rate in vehicle
​ Go Wheel rate of vehicle = Stiffness of Spring*((Motion ratio in suspension)^2)*(Spring angle correction factor)
Spring angle correction factor
​ Go Spring angle correction factor = cos(Angle of spring/shock absorber from vertical)
Roll rate or Roll stiffness
​ Go Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2

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

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 = Wcs*g/(M.R.*W.T.*cos(θ))

## 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, The Spring rate required for coilover given desired droop and motion ratio is the amount of force required to cause unit deflection of spring at one particular corner of the vehicle. 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 (Wcs), Acceleration due to Gravity (g), Motion ratio in suspension (M.R.), Wheel travel (W.T.) & Angle of spring/shock absorber from vertical (θ) 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 -> 6656.509 = 50*9.8/(0.85*0.1*cos(0.5235987755982)).

### FAQ

What is Spring rate required for coilover given desired droop and motion ratio?
The Spring rate required for coilover given desired droop and motion ratio is the amount of force required to cause unit deflection of spring at one particular corner of the vehicle and is represented as k = Wcs*g/(M.R.*W.T.*cos(θ)) 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 amount of weight supported by spring at one particular corner of vehicle with driver inside vehicle, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Motion ratio in suspension is ratio of shock travel to the corresponding wheel travel, Wheel travel is the amount by which wheel moves vertically over the bump/droop & Angle of spring/shock absorber from vertical when viewed from front view of car.
How to calculate Spring rate required for coilover given desired droop and motion ratio?
The Spring rate required for coilover given desired droop and motion ratio is the amount of force required to cause unit deflection of spring at one particular corner of the vehicle 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 (Wcs), Acceleration due to Gravity (g), Motion ratio in suspension (M.R.), Wheel travel (W.T.) & Angle of spring/shock absorber from vertical (θ). 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)*(cos(Angle of spring/shock absorber from vertical)))
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