How to find the best combination of angles for minimum turn radius

I am looking to find the best combination of a set of angles from 0 degrees to 68 degrees resulting in the minimum turning radius for a vehicle only turing with the front wheels. The goal is provide optimum ackermann steering and currently the wheel can roate a maximum of 68 degrees each way. I currently have this code however it doesn't seem correct and it isnt showing the best 2 angles for minimum radius. Any help would be appreciated. Wheelbase = 72 in. Track width = 54" want a radius of roughly 6-7ft I believe the equation for min radius at low speed is R = (track width/2) + (wheelbase/(Sin(average of outer + inner angle)) Thank you

radius = 72;
inner_angle = (0:68)
outer_angle = (0:68)
inner_angle_rad = inner_angle * pi /180
outer_angle_rad = outer_angle * pi /180
w = sin(outer_angle_rad+inner_angle_rad/2)
v = [72]
R= repelem (v,91)/w
if R < min_radius
    min_radius = R
end

[John D'Errico]

Do you think that computation performs all combinations of the two angles? It does not.

[Image Analyst]

I don't understand why a car making a turn has to make two turns of different angles. Can you provide a diagram of the situation?

[Gabe Mergenthaler]

For sure. Based upon ackermann steering criteria one wheel must turn sharper than the other for effective turning. hence why two angles. Here is a diagram where l is wheelbase, w is track width, and sigma o and sigma i are the steering angles:

Answer 1

[Walter Roberson]

radius = 72;
inner_angle = (0:68).';
outer_angle = (0:68);
inner_angle_rad = inner_angle * pi /180;
outer_angle_rad = outer_angle * pi /180;
w = sin(outer_angle_rad + inner_angle_rad/2);
v = [72]

v = 72

R = v./w;

[min_radius1, location1] = min(R, [], 'all', 'linear');
[r1, c1] = ind2sub(size(R), location1);
inner_angle1 = inner_angle(r1);
outer_angle1 = outer_angle(c1);

R(location1) = nan;

[min_radius2, location2] = min(R, [], 'all', 'linear');
[r2, c2] = ind2sub(size(R), location2);
inner_angle2 = inner_angle(r2);
outer_angle2 = outer_angle(c2);

result = table([min_radius1; min_radius2], [inner_angle1; inner_angle2], [outer_angle1; outer_angle2], 'VariableNames', {'Radius', 'Inner Angle', 'Outer Angle'});
result

result = 2x3 table
    Radius    Inner Angle    Outer Angle
    ______    ___________    ___________

      72          68             56     
      72          66             57     

[Gabe Mergenthaler]

Fantastic. So if I am reading this correctly to achieve a radius of 72 inches the inner vs outer steering angle must be 68 and 56 or 66 and 57 respectively. If i wanted a tighter or larger turning radius I would be ale to change the radius value to continue? Thanks