The Math Behind The Magic
We start by noting that the wheel speed sensors mounted at each wheel are integral components on all vehicles with Anti-Lock Brakes. At each wheel, the sensor has a variable frequency output of continuous pulse cycles. The frequency of each is directly proportional to the speed of the rotating wheel. Assume a given application where IntelliTurn is programmed to function using the signals from the left rear and right rear wheel sensors. One measure used is the instantaneous frequency output of each wheel speed sensor and are known as L and R. Another measure is the cumulative total pulse count from each wheel speed sensor. These values are known as P and S (for left total and right total, respectively) and are values that each start at zero when the driver moves the turn signal lever to signal a turn, then proceed to accumulate pulse counts. Pulse counts represent the distance traveled. Simple mathematics and computations yield a pinpoint accurate control scheme resulting in an intelligent turn signal.
Now, we’ll look at the computations that take place:
Steering System Position / Steering Wheel Rotation / Arc Turn / Lateral G’s
The diagram to the left illustrates the steering geometry with respect to the four tires and their position in a turn. As seen, all four tires make a turn radius about a common point, regardless of turn radius. The common point will change based on the position of the steering wheel. It will also always be in the axis of the rear wheels (for a two wheel steer vehicle).
For every steering wheel position, there is a corresponding steering system position.
For every steering system position, there is a corresponding convergent wheel arc center shared by all wheels.
For every wheel arc center, there is a corresponding arc radius differential, left rear to right rear.
For every arc radius differential, there is a corresponding speed sensor frequency differential, regardless of vehicle speed.
Therefore, at any vehicle speed, any concurrent L value divided by the R value yields a quotient that describes a unique steering system position, and therefore describes a given steering wheel position. L divided by R values for most vehicles range from about 0.700 to 1.400, with the straight ahead position equal to 1.000. The greater the steering wheel excursion or turn from straight ahead, the further the values from 1.000. This information not only provides real time steering wheel position, but also contributes to computing the arc turn radius and lateral G’s of the vehicle at any given time.
Although these are simple computations, the value of computing the exact steering system position at all times and at all vehicle speeds within the IntelliTurn computer is nothing short of amazing. This is especially amazing when one considers that there is no direct connection to the steering system. These computations therefore allow the elimination of the steering column mechanism, further allowing a variable shut off point that is appropriate for the situation. This compares to the current mechanism that must be designed with compromised fixed mechanical shut off points.
Yaw – Cumulative / Yaw Rate
Yaw is the lateral rotation of a vehicle as it makes a turn. In the world of vehicle turn signal control, it would be an understatement to say that knowledge of yaw is vital information that would be of extraordinarily high value. But as valuable as this information is, it is also the case that the current mechanical turn signal has never monitored vehicle yaw for turn signal shut off.
The IntelliTurn control system achieves this with, again, just two sensors. Recall that P and S values are cumulative pulse counts of left and right wheel speed sensors. P and S pulse count values are directly proportional to the total distance traveled by the left rear and right rear wheels. Knowing this and realizing that in a turn, the outside wheel travels a greater distance than the inside wheel, the subtraction of these values, “P minus S” is continuously computed and compiled. This yields a value that corresponds to vehicle yaw rotation, regardless of total distance. This value is both positively and negatively cumulative, and renders any given momentary steering wheel position irrelevant to the total yaw value. IntelliTurn, therefore, knows the yaw position within about 1 degree horizontal rotation of the vehicle at all times, based upon a “straight ahead” or zero degree reference at the point of the driver’s turn signal actuation.
The diagram to the left illustrates several different turns of the left rear and right rear tires, each eventually resulting in a 90 degree turn. The "start" point would represent the moment that the turn signal is actuated by the driver. Regardless of total distance or path traveled, “P minus S” values for each set shown are identical due to their identical resultant cumulative yaw rotation angles. The subtracted value would be the same for each pair for any turn, as long as the resultant turn angle is the same. Each angle turn position has its own unique "P minus S" value. Therefore, as seen, a real time running tally of vehicle yaw position throughout a turn is created. The yaw rate can then be determined by computing the time rate of change of the running “P minus S” value. Once again, simple calculations yield amazing information for IntelliTurn to decide on a situation-appropriate turn signal shut off.
Acceleration / Deceleration / Velocity / Distance / Time
These parameters are routine kinematic computations that can be made with the sensor data information presented. Using only left and right wheel speed signals will yield true vehicle dynamics from the moment the turn signal is actuated through the entire turn. These are indeed valuable pieces of data for IntelliTurn, and contribute to achieve high precision turn signal control characteristics over a wide range of turn signal situations. For example, IntelliTurn knows that a deceleration can be an anticipation of a pending turn. Conversely, vehicle acceleration is indicative of the completion of a turn. These can be contributing factors in determining proper turn signal shut off points.
“Turn-Signal-By-Wire” Has Arrived
As you read this, it has probably become evident to you that the IntelliTurn system is more advanced than the steering column mechanism method in common use today. Instead of fixed mechanical shut off points, programmed software can now be tailored to decide on a conditionally computed, situation-appropriate shut off. Additionally, even simple programming can result in very sophisticated algorithms that can instantly and continuously compensate for many conditions such as wheel slip or skid, one or both tires with low pressure, or a smaller diameter compact spare tire. This is a system that can even adapt to accommodate individual driver’s turn signal usage habits. IntelliTurn works on 2 or 4 wheel drive vehicles, as well as 2 or 4 wheel steering vehicles. It works equally well from the smallest economy car to the largest busses and semi’s. It has unsurpassed accuracy that faithfully tracks and maps the movement of the vehicle to within 2 inches of surface travel at all times.
There is not enough space in this forum to explore the limitless, yet simple programming code that can help realize IntelliTurn’s full potential. Engineers, Mathematicians, and Programmers can fine tune the system to ever more perfect levels. Suffice to say that in every situation, all “turn signal events” are vastly improved with IntelliTurn.
©2008 RLP Engineering