Problem Set-1b Week 11Challenge : Basic Handling parameters

1
ackermann steer angle
=(L/R) * (180/pi)

for 500 ft = (100.6*180)/(500*12*pi) =0.96 deg
for 200 ft = (100.6*180)/(200*12*pi) =2.40 deg
for 50 ft = (100.6*180)/(50*12*pi) =9.60 deg

2
wf = 950lb
wr = 776lb
Caf = 225 + (950-900)(225-171)/(1125-900) =232.1
Car= 171 + (776-675)(225-171)/(900-675) =195.24

K=wf/Caf + wr/Car = 0.118

3
V characterstic = sqrt (57.3Lg/K)= 362 ft/sec

4
60 mph = 88ft/sec
=V^2/57.3Lg / (1 + (KV^2/57.3Lg))
0.473 g/deg

5
V/L / (1+ KV^2/57.3Lg)
9.91

6-
beta =(57.3c/R ) - WrV^2/Car Rg = -1.04 deg

c=Wf L/Wtotal

7- the calculated value of understeer gradient is lower than the actual value as for calculations we assume the system to be 2DOF and only tire stiffness comes into picture
but in real life application
steering stiffness , suspension system , compliance also comes into play which contributes to its value