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

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Race Car Vehicle Dynamics

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✖Loaded radius of front wheels is height of front axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal.ⓘ Loaded radius of front wheels [R_LF]			+10% -10%
✖Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form rear axle measured along wheelbase of vehicle.ⓘ Horizontal distance of C.G. From rear axle [c]			+10% -10%
✖Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.ⓘ Wheelbase of Vehicle [b]			+10% -10%
✖Loaded radius of rear wheels is height of rear axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal.ⓘ Loaded radius of rear wheels [R_LR]			+10% -10%
✖Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle.ⓘ Horizontal distance of C.G. From rear axle [a]			+10% -10%
✖Weight of front wheels with rear elevated is the weight on front wheels measured when rear axle of vehicle is elevated/raised through some distance.ⓘ Weight of front wheels with rear elevated [W_F]			+10% -10%
✖Mass of vehicle is a quantitative measure of inertia, a fundamental property of all matter.ⓘ Mass of vehicle [m]			+10% -10%
✖Angle through which rear axle of vehicle raised is the angle made by front to rear wheel centerline (along wheelbase) with respect to horizontal.ⓘ Angle through which rear axle of vehicle raised [θ]			+10% -10%

✖Height of Center of gravity (C.G.) of vehicle is the theoretical point where the sum of all of the masses of each of its individual components effectively act.ⓘ Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear [h]

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Formula

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

Formula

`"h" = ("R"_{"LF"}*("c"/"b"))+("R"_{"LR"}*("a"/"b"))+((("W"_{"F"}*"b")-("m"*"c"))/("m"*tan("θ")))`

Example

`"1480.92in"=("11in"*("30in"/"2.7m"))+("15in"*("27in"/"2.7m"))+((("150kg"*"2.7m")-("55kg"*"30in"))/("55kg"*tan("10°")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
h = (R_LF*(c/b))+(R_LR*(a/b))+(((W_F*b)-(m*c))/(m*tan(θ)))
This formula uses 1 Functions, 9 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Height of Center of gravity (C.G.) of vehicle - (Measured in Meter) - Height of Center of gravity (C.G.) of vehicle is the theoretical point where the sum of all of the masses of each of its individual components effectively act.
Loaded radius of front wheels - (Measured in Meter) - Loaded radius of front wheels is height of front axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal.
Horizontal distance of C.G. From rear axle - (Measured in Meter) - Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form rear axle measured along wheelbase of vehicle.
Wheelbase of Vehicle - (Measured in Meter) - Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
Loaded radius of rear wheels - (Measured in Meter) - Loaded radius of rear wheels is height of rear axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal.
Horizontal distance of C.G. From rear axle - (Measured in Meter) - Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle.
Weight of front wheels with rear elevated - (Measured in Kilogram) - Weight of front wheels with rear elevated is the weight on front wheels measured when rear axle of vehicle is elevated/raised through some distance.
Mass of vehicle - (Measured in Kilogram) - Mass of vehicle is a quantitative measure of inertia, a fundamental property of all matter.
Angle through which rear axle of vehicle raised - (Measured in Radian) - Angle through which rear axle of vehicle raised is the angle made by front to rear wheel centerline (along wheelbase) with respect to horizontal.

STEP 1: Convert Input(s) to Base Unit

Loaded radius of front wheels: 11 Inch --> 0.279400000001118 Meter (Check conversion here)
Horizontal distance of C.G. From rear axle: 30 Inch --> 0.762000000003048 Meter (Check conversion here)
Wheelbase of Vehicle: 2.7 Meter --> 2.7 Meter No Conversion Required
Loaded radius of rear wheels: 15 Inch --> 0.381000000001524 Meter (Check conversion here)
Horizontal distance of C.G. From rear axle: 27 Inch --> 0.685800000002743 Meter (Check conversion here)
Weight of front wheels with rear elevated: 150 Kilogram --> 150 Kilogram No Conversion Required
Mass of vehicle: 55 Kilogram --> 55 Kilogram No Conversion Required
Angle through which rear axle of vehicle raised: 10 Degree --> 0.1745329251994 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (R_LF*(c/b))+(R_LR*(a/b))+(((W_F*b)-(m*c))/(m*tan(θ))) --> (0.279400000001118*(0.762000000003048/2.7))+(0.381000000001524*(0.685800000002743/2.7))+(((150*2.7)-(55*0.762000000003048))/(55*tan(0.1745329251994)))

Evaluating ... ...

h = 37.6153671776983

STEP 3: Convert Result to Output's Unit

37.6153671776983 Meter -->1480.91996761999 Inch (Check conversion here)

FINAL ANSWER

1480.91996761999 ≈ 1480.92 Inch <-- Height of Center of gravity (C.G.) of vehicle

(Calculation completed in 00.020 seconds)

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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

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

All about Height of Center of gravity of vehicle

Height of Center of gravity of the vehicle is the theoretical point where the sum of all of the masses of each of its individual components effectively acts. One method of determining the height of CG is to Jack the rear axle up so that the front to rear wheel centerlines are at an angle θ with horizontal. Conditions for this test are, suspension motion must be locked up. The standard way to do this is to replace the shock absorbers with rigid links that will keep the car at ride height. for example weld up an old set of shocks. The front wheels are choked on scales and rear axle is raised.

How to Calculate Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear?

Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear calculator uses 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))) to calculate the Height of Center of gravity (C.G.) of vehicle, The Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear is the theoretical point where the sum of all of the masses of each of its individual components effectively acts. Height of Center of gravity (C.G.) of vehicle is denoted by h symbol.

How to calculate Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear using this online calculator? To use this online calculator for Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear, enter Loaded radius of front wheels (R_LF), Horizontal distance of C.G. From rear axle (c), Wheelbase of Vehicle (b), Loaded radius of rear wheels (R_LR), Horizontal distance of C.G. From rear axle (a), Weight of front wheels with rear elevated (W_F), Mass of vehicle (m) & Angle through which rear axle of vehicle raised (θ) and hit the calculate button. Here is how the Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear calculation can be explained with given input values -> 58303.94 = (0.279400000001118*(0.762000000003048/2.7))+(0.381000000001524*(0.685800000002743/2.7))+(((150*2.7)-(55*0.762000000003048))/(55*tan(0.1745329251994))).

FAQ

What is Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear?

The Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear is the theoretical point where the sum of all of the masses of each of its individual components effectively acts and is represented as h = (R_LF*(c/b))+(R_LR*(a/b))+(((W_F*b)-(m*c))/(m*tan(θ))) or 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))). Loaded radius of front wheels is height of front axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal, Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form rear axle measured along wheelbase of vehicle, Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle, Loaded radius of rear wheels is height of rear axle above ground from side view when rear axle of vehicle is jacked so that front to rear wheel centerlines are at an angle θ from horizontal, Horizontal distance of C.G. From rear axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle, Weight of front wheels with rear elevated is the weight on front wheels measured when rear axle of vehicle is elevated/raised through some distance, Mass of vehicle is a quantitative measure of inertia, a fundamental property of all matter & Angle through which rear axle of vehicle raised is the angle made by front to rear wheel centerline (along wheelbase) with respect to horizontal.

How to calculate Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear?

The Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear is the theoretical point where the sum of all of the masses of each of its individual components effectively acts is calculated using 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))). To calculate Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear, you need Loaded radius of front wheels (R_LF), Horizontal distance of C.G. From rear axle (c), Wheelbase of Vehicle (b), Loaded radius of rear wheels (R_LR), Horizontal distance of C.G. From rear axle (a), Weight of front wheels with rear elevated (W_F), Mass of vehicle (m) & Angle through which rear axle of vehicle raised (θ). With our tool, you need to enter the respective value for 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, Weight of front wheels with rear elevated, Mass of vehicle & Angle through which rear axle of vehicle raised 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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