Damper angle from Vertical given wheel rate Calculator

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Race Car Vehicle Dynamics

Driveline

Front Axle and Steering

Suspension Geometry

Vehicle Collision

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Rates for Axle Suspension in Race Car

Ride Rate and Ride Frequency for Race Cars

Tire Behavior in Racing Car

Vehicle Cornering in Race Cars

Weight Transfer during Braking

Wheel Centre Rates for Independent Suspension

✖Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring.ⓘ Wheel rate of vehicle [K_t]			+10% -10%
✖Spring rate is the amount of weight in newtons that is needed to compress a spring by one metre.ⓘ Spring rate [K]			+10% -10%
✖Installation ratio is the ratio between how much the spring and damper move in relation to how far the wheel and tyre move.ⓘ Installation ratio [IR]			+10% -10%

✖Damper angle from vertical is the angle made by the damper with the vertical.ⓘ Damper angle from Vertical given wheel rate [Φ]

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Formula

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Damper angle from Vertical given wheel rate

Formula

`"Φ" = acos("K"_{"t"}/("K"*("IR"^2)))`

Example

`"89.62724°"=acos("100N/m"/("61484N/m"*(("0.5")^2)))`

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Damper angle from Vertical given wheel rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2)))
Φ = acos(K_t/(K*(IR^2)))
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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Damper angle from vertical - (Measured in Radian) - Damper angle from vertical is the angle made by the damper with the vertical.
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.
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.

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
Installation ratio: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = acos(K_t/(K*(IR^2))) --> acos(100/(61484*(0.5^2)))

Evaluating ... ...

Φ = 1.56429052330598

STEP 3: Convert Result to Output's Unit

1.56429052330598 Radian -->89.6272449177605 Degree (Check conversion here)

FINAL ANSWER

89.6272449177605 ≈ 89.62724 Degree <-- Damper angle from vertical

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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< 12 Race Car Vehicle Dynamics Calculators

Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear

Go Height of Center of gravity (C.G.) of vehicle = (Loaded radius of front wheels*(Horizontal distance of C.G. From rear axle/Wheelbase of Vehicle))+(Loaded radius of rear wheels*(Horizontal distance of C.G. From rear axle/Wheelbase of Vehicle))+(((Weight of front wheels with rear elevated*Wheelbase of Vehicle)-(Mass of vehicle*Horizontal distance of C.G. From rear axle))/(Mass of vehicle*tan(Angle through which rear axle of vehicle raised)))

Spring rate required for coilover given desired droop and motion ratio

Go 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))

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)))

Installation Ratio given Wheel Rate

Go Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical)))

Damper angle from Vertical given wheel rate

Go Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2)))

Spring rate given wheel rate

Go Spring rate = Wheel rate of vehicle/((Installation ratio^2)*cos(Damper angle from vertical))

Wheel rate

Go Wheel rate of vehicle = Spring rate*(Installation ratio^2)*cos(Damper angle from vertical)

Wheel rate in vehicle

Go Wheel rate of vehicle = Stiffness of Spring*((Motion ratio in suspension)^2)*(Spring angle correction factor)

Track Width of Vehicle given Wheel rate and Roll rate

Go Track Width of Vehicle = sqrt((2*Roll rate/ Roll stiffness)/Wheel rate of vehicle)

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

Wheel rate given Roll rate

Go Wheel rate of vehicle = (2*Roll rate/ Roll stiffness)/Track Width of Vehicle^2

Damper angle from Vertical given wheel rate Formula

Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2)))
Φ = acos(K_t/(K*(IR^2)))

More about Wheel rate

Wheel rate is a measure of the effective stiffness of the suspension system measured at the wheel centre. 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 Damper angle from Vertical given wheel rate?

Damper angle from Vertical given wheel rate calculator uses Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2))) to calculate the Damper angle from vertical, The Damper angle from Vertical given wheel rate formula is used to find the angle made by the damper with the vertical. Damper angle from vertical is denoted by Φ symbol.

How to calculate Damper angle from Vertical given wheel rate using this online calculator? To use this online calculator for Damper angle from Vertical given wheel rate, enter Wheel rate of vehicle (K_t), Spring rate (K) & Installation ratio (IR) and hit the calculate button. Here is how the Damper angle from Vertical given wheel rate calculation can be explained with given input values -> 5135.263 = acos(100/(61484*(0.5^2))).

FAQ

What is Damper angle from Vertical given wheel rate?

The Damper angle from Vertical given wheel rate formula is used to find the angle made by the damper with the vertical and is represented as Φ = acos(K_t/(K*(IR^2))) or Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2))). 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 & Installation ratio is the ratio between how much the spring and damper move in relation to how far the wheel and tyre move.

How to calculate Damper angle from Vertical given wheel rate?

The Damper angle from Vertical given wheel rate formula is used to find the angle made by the damper with the vertical is calculated using Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2))). To calculate Damper angle from Vertical given wheel rate, you need Wheel rate of vehicle (K_t), Spring rate (K) & Installation ratio (IR). With our tool, you need to enter the respective value for Wheel rate of vehicle, Spring rate & Installation ratio 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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