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Slope of Road on Front Wheel Formula

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Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability. Check FAQs

θ = a \cos (\frac{R F}{W \cdot \frac{b - x}{b + μ FW \cdot h}})

θ - Road Inclination Angle?R_F - Normal Reaction at Front Wheel?W - Vehicle Weight?b - Vehicle Wheelbase?x - Horizontal Distance of C.G. from Rear Axle?μ_FW - Friction Coefficient on Front Wheel?h - Height of C.G. of Vehicle?

Slope of Road on Front Wheel Example

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Here is how the Slope of Road on Front Wheel equation looks like with Values.

Here is how the Slope of Road on Front Wheel equation looks like with Units.

Here is how the Slope of Road on Front Wheel equation looks like.

10 = a \cos (\frac{7103}{13000 \cdot \frac{2.7 - 1.2}{2.7 + 0.456 \cdot 0.0079}})

10° = a \cos (\frac{7103N}{13000N \cdot \frac{2.7m - 1.2m}{2.7m + 0.456 \cdot 0.0079m}})

10 = a \cos (\frac{7103}{13000 \cdot \frac{2.7 - 1.2}{2.7 + 0.456 \cdot 0.0079}})

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Slope of Road on Front Wheel Solution

Follow our step by step solution on how to calculate Slope of Road on Front Wheel?

FIRST Step Consider the formula

θ = a \cos (\frac{R F}{W \cdot \frac{b - x}{b + μ FW \cdot h}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{7103N}{13000N \cdot \frac{2.7m - 1.2m}{2.7m + 0.456 \cdot 0.0079m}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{7103}{13000 \cdot \frac{2.7 - 1.2}{2.7 + 0.456 \cdot 0.0079}})

Next Step Evaluate

∴

θ = 0.174532924073972rad

Next Step Convert to Output's Unit

∴

θ = 9.99999993551774°

LAST Step Rounding Answer

∴

θ = 10°

Slope of Road on Front Wheel Formula Elements

Variables

Functions

Road Inclination Angle

Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Road Inclination Angle

Normal Reaction at Front Wheel

Normal Reaction at Front Wheel is the upward force exerted by the ground on the front wheel of a racing car during rear wheel braking.

Symbol: R_F

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Normal Reaction at Front Wheel

Vehicle Weight

Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Vehicle Weight

Vehicle Wheelbase

Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Vehicle Wheelbase

Horizontal Distance of C.G. from Rear Axle

Horizontal Distance of C.G. from Rear Axle is the distance from the center of gravity to the rear axle, affecting the racing car's stability during rear wheel braking.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance of C.G. from Rear Axle

Friction Coefficient on Front Wheel

Friction Coefficient on Front Wheel is a measure of the frictional force exerted by the front wheel on the road during rear wheel braking in a racing car.

Symbol: μ_FW

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Friction Coefficient on Front Wheel

Height of C.G. of Vehicle

Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a racing car during rear wheel braking.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of C.G. of Vehicle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: acos(Number)

Other formulas in Effects on Front Wheel (FW) category

Go Horizontal Distance of C.G from Rear Axle on Front Wheel

x = (b - μ FW \cdot h) - R F \cdot \frac{b - μ FW \cdot h}{W \cdot \cos (θ)}

Go Height of C.G. from Road Surface on Front Wheel

h = \frac{W \cdot (b - x) \cdot \frac{\cos (θ)}{R F} - b}{μ FW}

How to Evaluate Slope of Road on Front Wheel?

Slope of Road on Front Wheel evaluator uses Road Inclination Angle = acos(Normal Reaction at Front Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)/(Vehicle Wheelbase+Friction Coefficient on Front Wheel*Height of C.G. of Vehicle))) to evaluate the Road Inclination Angle, Slope of Road on Front Wheel formula is defined as a measure of the inclination of the road surface in front of the wheel, which affects the vehicle's stability and traction, and is influenced by factors such as the road's curvature, the vehicle's speed, and the frictional forces between the tires and the road. Road Inclination Angle is denoted by θ symbol.

How to evaluate Slope of Road on Front Wheel using this online evaluator? To use this online evaluator for Slope of Road on Front Wheel, enter Normal Reaction at Front Wheel (R_F), Vehicle Weight (W), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient on Front Wheel (μ_FW) & Height of C.G. of Vehicle (h) and hit the calculate button.

FAQs on Slope of Road on Front Wheel

What is the formula to find Slope of Road on Front Wheel?

The formula of Slope of Road on Front Wheel is expressed as Road Inclination Angle = acos(Normal Reaction at Front Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)/(Vehicle Wheelbase+Friction Coefficient on Front Wheel*Height of C.G. of Vehicle))). Here is an example- 571.6493 = acos(7103/(13000*(2.7-1.2)/(2.7+0.456032*0.007919))).

How to calculate Slope of Road on Front Wheel?

With Normal Reaction at Front Wheel (R_F), Vehicle Weight (W), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient on Front Wheel (μ_FW) & Height of C.G. of Vehicle (h) we can find Slope of Road on Front Wheel using the formula - Road Inclination Angle = acos(Normal Reaction at Front Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)/(Vehicle Wheelbase+Friction Coefficient on Front Wheel*Height of C.G. of Vehicle))). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

Can the Slope of Road on Front Wheel be negative?

No, the Slope of Road on Front Wheel, measured in Angle cannot be negative.

Which unit is used to measure Slope of Road on Front Wheel?

Slope of Road on Front Wheel is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Slope of Road on Front Wheel can be measured.

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Slope of Road on Front Wheel Formula

Slope of Road on Front Wheel Example

Slope of Road on Front Wheel Solution

Slope of Road on Front Wheel Formula Elements

Other formulas in Effects on Front Wheel (FW) category

How to Evaluate Slope of Road on Front Wheel?

FAQs on Slope of Road on Front Wheel

Variable Name