2. Handling & Stability

Question 1

what are the equations of motion in the x, y and z direction

Answer 1

• sum X = m(u_dot - vΩ)
• sum Y = m(v_dot + uΩ)
• sum N = I_z*Ω_dot - [sum(r) x (X + Y)]

Question 2

a car going at speed u has rear wheels and front wheels with its center of gravity in in between. The distance between the rear and the center is b and between the center and the front its a. the car is turning with angular velocity Ω and the front wheels have a yaw angle of δ. what are the front and rear slip angles α_f and α_r

Answer 2

• α_f = (v + aΩ / u) - δ
• α_r = (v - bΩ / u)

Question 3

if the car has side force coefficients for the front and rear axles C_f and C_r, what is the equation of motion Y

Answer 3

• Y = m(v_dot + uΩ) + C_fα_f + C_rα_r

Question 4

what is the equation of motion N

Answer 4

• N = IΩ_dot + aC_fα_f - bC_r*α_r

Question 5

what is total cornering stiffness c

Answer 5

• c = C_f + C_r

Question 6

what is the square of the yaw stiffness radius q^2

Answer 6

• q^2 = (a^2C_f + b^2C_r) / (C_f + C_r)

Question 7

what is the length of the vehicle l

Answer 7

l = a + b

Question 8

what is the yaw moment of inertia I

Answer 8

= I = mk^2

Question 9

what is the condition for the vehicle to always be stable

Answer 9

• bC_r > aC_f

Question 10

if the vehicle doesnt meet the condition to always be stable, what is the condition for it to be stable

Answer 10

• u^2 < (C_fC_rl^2) / m(aC_f - bC_r)

Question 11

the static margin is defined as -s/l, but what is the expression for s

Answer 11

• s = (aC_f - bC_r) / (C_f + C_r)

Question 12

what is the simple condition for the vehicle to reach steady state

Answer 12

• v_dot = Ω_dot = 0
• v_ss and Ω_ss are what satisfy this

Question 13

what is the formula for β

Answer 13

• β = v/u

Question 14

what are the neutral steer conditions

Answer 14

• s = 0
• Ω_ss = 0
• β > 0 for all speeds

Question 15

what are the understeer conditions

Answer 15

• s < 0
• Ω_ss > 0
• β > 0 for all speeds

Question 16

what are the oversteer conditions

Answer 16

• s > 0 for low speeds
• Ω_ss < 0
• β > 0 when U reaches sqrt(C_fC_rl^2 / csm) = U_c

Question 17

what is the neutral steer point

Answer 17

• the point on the vehicle for which a side force produces no steady state yaw

Question 18

what is the static margin SM = -s/l, measuring

Answer 18

• the static margin is a measure of handling behaviour
• its the distance that the neutral steer point lies behind G, normalized by l
• when NS is at G, SM = 0 so s = 0 so you get neutral steer
• when NS is behind G, SM > 0 so s < 0 so you get understeer
• when NS is forward of G, SM < 0 so s > 0 so you get oversteer

Question 19

in oversteer, what is the condition for the vehicle to become unstable and spin

Answer 19

• when U > sqrt(C_fC_rl^2 / csm) = U_c