Curb to Curb Diameter and Ackerman 1 and 2

Branch ID: 290 Request Number: 50000290

Table 1.
Component Unit Comment
1 (X): Curb to Curb Diameter (Method 1) m The first method of calculating the approximate diameter of the circle the vehicle would move around at the current steer angles assuming no rear wheel steer.
When the Vehicle is Steering Right

outer = abs((left toe-in)/rtod)

inner = abs((right toe-in)/rtod)

turn radius = (wheel base)/tan((inner+outer)/2)

ctoc diam = 2*sqrt(((turn radius)+track/2)^2+ (wheel base)^2)/1000

When the Vehicle is Steering Left

inner = -(left toe-in)/rtod

turn radius = (wheel base)/tan((inner+outer)/2)

ctoc diam = 2*sqrt(((turn radius)+track/2)^2+ (wheel base)^2)/1000
2 (Y): Percent Ackerman (Method 1) % The first method of calculating percent Ackerman. Ackerman is used to quantify the amount of scrubbing occurring on the front of the vehicle during a turn assuming no rear wheel steer. A vehicle whose front wheels are parallel (the same steer angle) has 0% Ackerman. Conversely a vehicle is said to be 100% Ackerman when the lines through the left and right spindle axes intersect in the top view at a lateral line passing through the rear wheel centers. The following equation is used to calculate percent Ackerman with Method 1. See Component 1 above for intermediate term calculations.
When the Vehicle is Steering Right

percent Ackerman = 100*((wheel base)/tan(outer)-(turn radius))/ (right spindle at kingpin y)

When the Vehicle is Steering Left

percent Ackerman = 100*((wheel base)/tan(outer)-(turn radius))/-(left spindle at kingpin y)
3 (Z): Ackerman Deviation (Method 1) deg The first method of calculating Ackerman deviation. Ackerman deviation, like percent Ackerman, is used to quantify the amount of scrubbing occurring on the front of the vehicle during a turn assuming no rear wheel steer. Zero Ackerman deviation means that lines through the left and right spindle axes intersect in the top view at a lateral line passing through the rear wheel centers. The following equation is used to calculate Ackerman deviation with Method 1. See Component 1 above for intermediate term calculations.

alpha = atan((wheel base)/((turn radius)+track/2))

deviation = (outer-alpha)*rtod

4 (RX): Curb to Curb Diameter (Method 2) m The second method of calculating the approximate diameter of the circle the vehicle would move around at the current steer angles assuming no rear wheel steer.
When the Vehicle is Steering Right

outer = abs((left toe-in)/rtod)

inner = abs((right toe-in)/rtod)

turn radius = track/2+(wheel base)/tan(inner)

ctoc diam = 2*sqrt(((turn radius)+track/2)^2+ (wheel base)^2)/1000

When the Vehicle is Steering Left

inner = -(left toe-in)/rtod

turn radius = track/2+(wheel base)/tan(inner)

ctoc diam = 2*sqrt(((turn radius)+track/2)^2+ (wheel base)^2)/1000
5 (RY): Percent Ackerman (Method 2) %

The second method of calculating percent Ackerman. See Component 2 above for an explanation of Percent Ackerman. See Component 4 above for intermediate term calculations.

alpha = atan((wheel base)/((turn radius)+track/2))

percent Ackerman = (inner-outer)/(inner-alpha)*100
6 (RZ): Ackerman Deviation (Method 2) deg The second method of calculating Ackerman deviation. See Component 3 above for an explanation of Ackerman deviation. See Components 4 and 5 above for intermediate term calculations.

deviation = (outer-alpha)*rtod