Slope of Road on Front Wheel Calculator

✖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.ⓘ Normal Reaction at Front Wheel [R_F]			+10% -10%
✖Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance.ⓘ Vehicle Weight [W]			+10% -10%
✖Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.ⓘ Vehicle Wheelbase [b]			+10% -10%
✖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.ⓘ Horizontal Distance of C.G. from Rear Axle [x]			+10% -10%
✖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.ⓘ Friction Coefficient on Front Wheel [μ_FW]			+10% -10%
✖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.ⓘ Height of C.G. of Vehicle [h]			+10% -10%

✖Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.ⓘ Slope of Road on Front Wheel [θ]

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Slope of Road on Front Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
θ = acos(R_F/(W*(b-x)/(b+μ_FW*h)))
This formula uses 2 Functions, 7 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

Road Inclination Angle - (Measured in Radian) - Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.
Normal Reaction at Front Wheel - (Measured in Newton) - 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.
Vehicle Weight - (Measured in Newton) - Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance.
Vehicle Wheelbase - (Measured in Meter) - Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.
Horizontal Distance of C.G. from Rear Axle - (Measured in Meter) - 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.
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.
Height of C.G. of Vehicle - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Normal Reaction at Front Wheel: 7103 Newton --> 7103 Newton No Conversion Required
Vehicle Weight: 13000 Newton --> 13000 Newton No Conversion Required
Vehicle Wheelbase: 2.7 Meter --> 2.7 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle: 1.2 Meter --> 1.2 Meter No Conversion Required
Friction Coefficient on Front Wheel: 0.456032 --> No Conversion Required
Height of C.G. of Vehicle: 0.007919 Meter --> 0.007919 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_F/(W*(b-x)/(b+μ_FW*h))) --> acos(7103/(13000*(2.7-1.2)/(2.7+0.456032*0.007919)))

Evaluating ... ...

θ = 0.174532924073972

STEP 3: Convert Result to Output's Unit

0.174532924073972 Radian -->9.99999993551774 Degree (Check conversion here)

FINAL ANSWER

9.99999993551774 ≈ 10 Degree <-- Road Inclination Angle

(Calculation completed in 00.011 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » Rear Wheel Braking for Racing Car » Mechanical » Effects on Front Wheel (FW) » Slope of Road on Front Wheel

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Created by Peri Krishna Karthik

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

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< Effects on Front Wheel (FW) Calculators

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

LaTeX Go Horizontal Distance of C.G. from Rear Axle = (Vehicle Wheelbase-Friction Coefficient on Front Wheel*Height of C.G. of Vehicle)-Normal Reaction at Front Wheel*(Vehicle Wheelbase-Friction Coefficient on Front Wheel*Height of C.G. of Vehicle)/(Vehicle Weight*cos(Road Inclination Angle))

Weight of Vehicle on Front Wheel

LaTeX Go Vehicle Weight = Normal Reaction at Front Wheel/((Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle)/(Vehicle Wheelbase+Friction Coefficient on Front Wheel*Height of C.G. of Vehicle))

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

LaTeX Go Height of C.G. of Vehicle = (Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle)/Normal Reaction at Front Wheel-Vehicle Wheelbase)/Friction Coefficient on Front Wheel

Normal Reaction Force at Front Wheel

LaTeX Go Normal Reaction at Front Wheel = Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle)/(Vehicle Wheelbase+Friction Coefficient on Front Wheel*Height of C.G. of Vehicle)

Slope of Road on Front Wheel Formula

LaTeX Go

Define Braking distribution?

Braking distribution refers to how the total braking force is divided between a vehicle's front and rear brakes. This distribution is usually biased toward the front brakes because the vehicle's weight shifts forward during braking, increasing the front tires' grip. Proper braking distribution ensures balanced stopping power, maintaining stability and preventing issues like skidding or loss of control. It's a key factor in safe and efficient braking performance.

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How to Calculate Slope of Road on Front Wheel?

Slope of Road on Front Wheel calculator 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 calculate 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 calculate Slope of Road on Front Wheel using this online calculator? To use this online calculator 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. Here is how the Slope of Road on Front Wheel calculation can be explained with given input values -> 571.6493 = acos(7103/(13000*(2.7-1.2)/(2.7+0.456032*0.007919))).

FAQ

What is Slope of Road on Front Wheel?

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 and is represented as θ = acos(R_F/(W*(b-x)/(b+μ_FW*h))) or 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))). 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, Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance, Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car, 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, 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 & 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.

How to calculate Slope of Road on Front Wheel?

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 is calculated using 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 calculate Slope of Road on Front Wheel, you need 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). With our tool, you need to enter the respective value for Normal Reaction at Front Wheel, Vehicle Weight, Vehicle Wheelbase, Horizontal Distance of C.G. from Rear Axle, Friction Coefficient on Front Wheel & Height of C.G. of Vehicle 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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