Slope of Road on Rear Wheel Calculator

✖Normal Reaction at Rear Wheel is the upward force exerted by the ground on the rear wheel of a racing car during braking, affecting its stability and control.ⓘ Normal Reaction at Rear Wheel [R_R]			+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%
✖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 Rear Wheel is a measure of the resistance to motion between the rear wheel and the road surface during racing car braking.ⓘ Friction Coefficient on Rear Wheel [μ_RW]			+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%
✖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%

✖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 Rear Wheel [θ]

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Slope of Road on Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Road Inclination Angle = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Horizontal Distance of C.G. from Rear Axle+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle)/(Vehicle Wheelbase+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle)))
θ = acos(R_R/(W*(x+μ_RW*h)/(b+μ_RW*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 Rear Wheel - (Measured in Newton) - Normal Reaction at Rear Wheel is the upward force exerted by the ground on the rear wheel of a racing car during braking, affecting its stability and control.
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.
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 Rear Wheel - Friction Coefficient on Rear Wheel is a measure of the resistance to motion between the rear wheel and the road surface during racing car braking.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Normal Reaction at Rear Wheel: 5700 Newton --> 5700 Newton No Conversion Required
Vehicle Weight: 13000 Newton --> 13000 Newton No Conversion Required
Horizontal Distance of C.G. from Rear Axle: 1.2 Meter --> 1.2 Meter No Conversion Required
Friction Coefficient on Rear Wheel: 0.48 --> No Conversion Required
Height of C.G. of Vehicle: 0.007919 Meter --> 0.007919 Meter No Conversion Required
Vehicle Wheelbase: 2.7 Meter --> 2.7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_R/(W*(x+μ_RW*h)/(b+μ_RW*h))) --> acos(5700/(13000*(1.2+0.48*0.007919)/(2.7+0.48*0.007919)))

Evaluating ... ...

θ = 0.174532338183046

STEP 3: Convert Result to Output's Unit

0.174532338183046 Radian -->9.9999663664404 Degree (Check conversion here)

FINAL ANSWER

9.9999663664404 ≈ 9.999966 Degree <-- Road Inclination Angle

(Calculation completed in 00.020 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 Rear Wheel (RW) » Slope of Road on Rear 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 Rear Wheel (RW) Calculators

Friction Coefficient using Retardation on Rear Wheel

LaTeX Go Friction Coefficient on Rear Wheel = ((Braking Retardation/[g]+sin(Road Inclination Angle))*Vehicle Wheelbase)/((Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle)-((Braking Retardation/[g]+sin(Road Inclination Angle))*Height of C.G. of Vehicle))

Friction Coefficient between Wheel and Road Surface on Rear Wheel

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

Weight of Vehicle on Rear Wheel

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

Normal Reaction Force at Rear Wheel

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

Slope of Road on Rear Wheel Formula

LaTeX Go

Define Road Inclination Angel?

The road inclination angle is the angle at which a road surface is tilted or inclined relative to the horizontal. It measures the degree of slope or gradient of the road. This angle affects vehicle handling, stability, and traction. A steeper road inclination can make driving more challenging, impacting braking distances and the ability to maintain control, especially on inclines or declines.

How to Calculate Slope of Road on Rear Wheel?

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

How to calculate Slope of Road on Rear Wheel using this online calculator? To use this online calculator for Slope of Road on Rear Wheel, enter Normal Reaction at Rear Wheel (R_R), Vehicle Weight (W), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient on Rear Wheel (μ_RW), Height of C.G. of Vehicle (h) & Vehicle Wheelbase (b) and hit the calculate button. Here is how the Slope of Road on Rear Wheel calculation can be explained with given input values -> 572.9559 = acos(5700/(13000*(1.2+0.48*0.007919)/(2.7+0.48*0.007919))).

FAQ

What is Slope of Road on Rear Wheel?

Slope of Road on Rear Wheel formula is defined as a measure of the inclination of the road surface at the rear wheel of a vehicle, which affects the vehicle's stability and traction, and is influenced by factors such as the road's curvature, the vehicle's weight distribution, and the frictional forces acting on the rear wheel and is represented as θ = acos(R_R/(W*(x+μ_RW*h)/(b+μ_RW*h))) or Road Inclination Angle = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Horizontal Distance of C.G. from Rear Axle+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle)/(Vehicle Wheelbase+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle))). Normal Reaction at Rear Wheel is the upward force exerted by the ground on the rear wheel of a racing car during braking, affecting its stability and control, Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance, 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 Rear Wheel is a measure of the resistance to motion between the rear wheel and the road surface during racing car braking, 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 & Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.

How to calculate Slope of Road on Rear Wheel?

Slope of Road on Rear Wheel formula is defined as a measure of the inclination of the road surface at the rear wheel of a vehicle, which affects the vehicle's stability and traction, and is influenced by factors such as the road's curvature, the vehicle's weight distribution, and the frictional forces acting on the rear wheel is calculated using Road Inclination Angle = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Horizontal Distance of C.G. from Rear Axle+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle)/(Vehicle Wheelbase+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle))). To calculate Slope of Road on Rear Wheel, you need Normal Reaction at Rear Wheel (R_R), Vehicle Weight (W), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient on Rear Wheel (μ_RW), Height of C.G. of Vehicle (h) & Vehicle Wheelbase (b). With our tool, you need to enter the respective value for Normal Reaction at Rear Wheel, Vehicle Weight, Horizontal Distance of C.G. from Rear Axle, Friction Coefficient on Rear Wheel, Height of C.G. of Vehicle & Vehicle Wheelbase 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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