I have been told that thinking is a bad thing for me to do, and bad things come from it. But someone sent me a link to a rack and pinion steering system that was supposed to replace a Vega steering box and I got started thinking, did it really? From the initial blurb it certainly fit in place of a Vega box, but did it function like a Vega box?
Note to Siouxy, this can be used for advanced adult education in math.
First to get apples to apples we needed to get common units to determine functionality. The Vega box is spec’ed in box ratio and turns lock-to-lock, the rack and pinion is spec’ed in turns lock to lock and throw. So we have to figure out the throw of the Vega box, which boils down to the chord of the arc swept by the Pittman arm going from lock to lock. But first we have to “cipher” the angle of that arc, or convert ratio and turns lock to lock into the angle swept by the steering arm.
The Vega box has a ratio of 20:1 or 20 turns of the input shaft equal one turn of the steering output shaft, and 5 turns lock to lock for the input shaft. Reducing the fraction gives us 1:4 or the steering output shaft has turned ¼ of the way around, or 90°.
The formula for the length of a chord when you know the angle it sweeps is 2(sin(½Θ)*r) or in English 2 times the quantity the sine of half the angle times the radius of the circle. In this example we already knew the radius of the circle as the center to center distance of the Pittman arm, is 6.25″, and the angle as 90°, so half the angle is 45° and the sine of 45° I know as 0.707 from our friend Pythagoras and his theorem as 1/√2. So throwing all the numbers and functions together in the right order and rounding to the most significant digit we get a throw of 8.84″ for the Vega box and the Pittman arm that comes in the kit.
So now we have common units with which to compare the rack and pinion to the Vega box it’s supposed to replace. From the web page we know 3.75 turns lock-to-lock and total stroke of 5.25”. Right away we can see that while there aren’t as many turns lock to lock, it doesn’t move the front wheels as far as the Vega box, and comparing the throws and the turns lock to lock as a ratio we find the Vega box is 26% quicker than the rack and pinion in a head to head apples to apples contest, and gets 68% more steering angle at full lock. Now which one wins depends on what your criteria for the system in the car are, but for the Sprint-T application where the idea is to get the wheels changing direction as quickly as possible so the car can go fast on a slalom or get around a single pylon turn as quickly as possible having a greater steering angle at the wheels is better. Corollary to that is getting to that angle faster is also better. Conclusion : I’m not buying the rack and pinion kit, even if it was cheaper instead of about $80 more. I get more steering angle quicker for less money, and adding the steering quickener and the electric power steering assist just builds on that.