## Installation Ratio given Wheel Rate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical)))
IR = sqrt(Kt/(K*cos(Φ)))
This formula uses 2 Functions, 4 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Installation ratio - Installation ratio is the ratio between how much the spring and damper move in relation to how far the wheel and tyre move.
Wheel rate of vehicle - (Measured in Newton per Meter) - Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring.
Spring rate - (Measured in Newton per Meter) - Spring rate is the amount of weight in newtons that is needed to compress a spring by one metre.
Damper angle from vertical - (Measured in Radian) - Damper angle from vertical is the angle made by the damper with the vertical.
STEP 1: Convert Input(s) to Base Unit
Wheel rate of vehicle: 100 Newton per Meter --> 100 Newton per Meter No Conversion Required
Spring rate: 61484 Newton per Meter --> 61484 Newton per Meter No Conversion Required
Damper angle from vertical: 10 Degree --> 0.1745329251994 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
IR = sqrt(Kt/(K*cos(Φ))) --> sqrt(100/(61484*cos(0.1745329251994)))
Evaluating ... ...
IR = 0.0406390187901973
STEP 3: Convert Result to Output's Unit
0.0406390187901973 --> No Conversion Required
0.0406390187901973 0.040639 <-- Installation ratio
(Calculation completed in 00.004 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

## Installation Ratio given Wheel Rate Formula

Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical)))
IR = sqrt(Kt/(K*cos(Φ)))

Wheel rate is a measure of the effective stiffness of the suspension system measured at the wheel center. The wheel rate is the slope of a graph plotting wheel force vs wheel travel. It is expressed in Newtons per metre or N/m.

The primary contributor to the wheel rate is the suspension spring. If the suspension system has rubber bushes at the joints, the torsional stiffness of the bushes also contributes to the wheel rate of the suspension. Wheel rate in roll also includes the contribution of the anti-roll bar. The wheel rate of a suspension system can be used to calculate the ride frequency of a vehicle if the sprung mass is known.

## How to Calculate Installation Ratio given Wheel Rate?

Installation Ratio given Wheel Rate calculator uses Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical))) to calculate the Installation ratio, The Installation Ratio given Wheel Rate formula is used to find the ratio between how much the spring and damper move in relation to how far the wheel and tire move. Installation ratio is denoted by IR symbol.

How to calculate Installation Ratio given Wheel Rate using this online calculator? To use this online calculator for Installation Ratio given Wheel Rate, enter Wheel rate of vehicle (Kt), Spring rate (K) & Damper angle from vertical (Φ) and hit the calculate button. Here is how the Installation Ratio given Wheel Rate calculation can be explained with given input values -> 0.040639 = sqrt(100/(61484*cos(0.1745329251994))).

### FAQ

What is Installation Ratio given Wheel Rate?
The Installation Ratio given Wheel Rate formula is used to find the ratio between how much the spring and damper move in relation to how far the wheel and tire move and is represented as IR = sqrt(Kt/(K*cos(Φ))) or Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical))). Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring, Spring rate is the amount of weight in newtons that is needed to compress a spring by one metre & Damper angle from vertical is the angle made by the damper with the vertical.
How to calculate Installation Ratio given Wheel Rate?
The Installation Ratio given Wheel Rate formula is used to find the ratio between how much the spring and damper move in relation to how far the wheel and tire move is calculated using Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical))). To calculate Installation Ratio given Wheel Rate, you need Wheel rate of vehicle (Kt), Spring rate (K) & Damper angle from vertical (Φ). With our tool, you need to enter the respective value for Wheel rate of vehicle, Spring rate & Damper angle from vertical and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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