The Beck 550 Spyder described below has manual hydraulic brakes with a singlemaster cylinder. The car is traveling on level ground at sea-level where g = 9.81 m/s².Find the values for the front and rear brake gains that will make this car decelerate at8.829 m/s², or 0.90g, on a road surface where the peak coefficient of friction is 0.90when the pedal force is F₂ = 250 N. Neglect the aerodynamic drag and the rollingresistance, but this time include the rotational inertia of the tires and wheels.Answer: G₁ =166.1 N-m/MPa for each front wheel and G, = 114.5 N-m/MPa for eachrear wheel.Pedal AssemblyThe diameter of the master cylinder is DMC = 19.05 mm.The pedal length is Lp = 225 mm.The pushrod for the master cylinder is located at LR = 50 mm.●●PushrodLRLpFpMasses, Tire Radius, Wheelbase and Location of the CGMass of the car with driver, passenger and some stuff: m = 780 kgInertia of each tire and wheel: I = 0.7 kg-m²Tire rolling radius: r = 0.31 mWheelbase: L = 2.16 mThe center of gravity is located at distance b=1.18 m behind the front axle andh = 0.34 m above the ground.

Answered: The Beck 550 Spyder described below has…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The Beck 550 Spyder described below has manual hydraulic brakes with a single
master cylinder. The car is traveling on level ground at sea-level where g = 9.81 m/s².
Find the values for the front and rear brake gains that will make this car decelerate at
8.829 m/s², or 0.90g, on a road surface where the peak coefficient of friction is 0.90
when the pedal force is F₂ = 250 N. Neglect the aerodynamic drag and the rolling
resistance, but this time include the rotational inertia of the tires and wheels.
Answer: G₁ =166.1 N-m/MPa for each front wheel and G, = 114.5 N-m/MPa for each
rear wheel.
Pedal Assembly
The diameter of the master cylinder is DMC = 19.05 mm.
The pedal length is Lp = 225 mm.
The pushrod for the master cylinder is located at LR = 50 mm.
●
●
Pushrod
LR
Lp
Fp
Masses, Tire Radius, Wheelbase and Location of the CG
Mass of the car with driver, passenger and some stuff: m = 780 kg
Inertia of each tire and wheel: I = 0.7 kg-m²
Tire rolling radius: r = 0.31 m
Wheelbase: L = 2.16 m
The center of gravity is located at distance b=1.18 m behind the front axle and
h = 0.34 m above the ground.

Expert Solution

Step 1

The front and rear brake gains can be calculated using the following formulas:

G_f = (2 $\times$ μ_f $\times$ (b / L) $\times$ m $\times$ g)/(D_m $\times$ A_f)
G_r = (2 $\times$ μ_r $\times$ ((L - b)/L) $\times$ m $\times$ g)/(D_m $\times$ A_r)

where:

μ_f and μ_r are the peak coefficients of friction for the front and rear wheels, respectively
b is the distance from the center of gravity to the front axle
L is the wheelbase
m is the mass of the car
g is the acceleration due to gravity
D_m is the diameter of the master cylinder
A_f and A_r are the effective piston areas for the front and rear brakes, respectively

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