2. Handling & Stability Flashcards

1
Q

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

A
  • sum X = m(u_dot - vΩ)
  • sum Y = m(v_dot + uΩ)
  • sum N = I_z*Ω_dot - [sum(r) x (X + Y)]
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2
Q

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

A
  • α_f = (v + aΩ / u) - δ
  • α_r = (v - bΩ / u)
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3
Q

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

A
  • Y = m(v_dot + uΩ) + C_fα_f + C_rα_r
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4
Q

what is the equation of motion N

A
  • N = IΩ_dot + aC_fα_f - bC_r*α_r
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5
Q

what is total cornering stiffness c

A
  • c = C_f + C_r
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6
Q

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

A
  • q^2 = (a^2C_f + b^2C_r) / (C_f + C_r)
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7
Q

what is the length of the vehicle l

A

l = a + b

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8
Q

what is the yaw moment of inertia I

A

= I = mk^2

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9
Q

what is the condition for the vehicle to always be stable

A
  • bC_r > aC_f
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10
Q

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

A
  • u^2 < (C_fC_rl^2) / m(aC_f - bC_r)
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11
Q

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

A
  • s = (aC_f - bC_r) / (C_f + C_r)
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12
Q

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

A
  • v_dot = Ω_dot = 0
  • v_ss and Ω_ss are what satisfy this
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13
Q

what is the formula for β

A
  • β = v/u
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14
Q

what are the neutral steer conditions

A
  • s = 0
  • Ω_ss = 0
  • β > 0 for all speeds
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15
Q

what are the understeer conditions

A
  • s < 0
  • Ω_ss > 0
  • β > 0 for all speeds
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16
Q

what are the oversteer conditions

A
  • s > 0 for low speeds
  • Ω_ss < 0
  • β > 0 when U reaches sqrt(C_fC_rl^2 / csm) = U_c
17
Q

what is the neutral steer point

A
  • the point on the vehicle for which a side force produces no steady state yaw
18
Q

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

A
  • 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
19
Q

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

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