Z

03-20-2014, 09:53 PM

WHY A SOFT TWIST-MODE???

==========================

It has been suggested (on another thread) that while a soft Twist-mode might be advantageous on bumpy roads, it might offer NO such advantages on smooth, sealed roads, such as those typical in circuit racing.

Those of you who prefer to "follow the numbers", rather than the unquantified opinions of experts, please read on...

~~~o0o~~~

Milliken's RCVD, Chapter 18 "Wheel Loads" starts with,

"The [vertical] loads at each wheel are extremely important in determining a car's maximum steady-state cornering capability." (my emphasis).

The chapter goes on to give examples of how to calculate these vertical wheel loads. Quite reasonably, these calculations are simplified by assumptions such as,

"...steady-state operating conditions - that is, smooth roadway, constant speed cornering, constant longitudinal acceleration, constant grade, etc.

... roll rates, spring rates ... are linear,

... chassis of the car ... is [torsionally] rigid.", and so on.

In fact, there are about 5 pages discussing the importance of a torsionally stiff chassis, because,

"... if the chassis torsional spring is weak, attempts to control the lateral load transfer distribution (and "balance" the car's handling by resisting more of the rolling moment on one track than the other) will be confusing at best and impossible at worst." (my emphasis again).

Equations for calculating the variations to wheel loads from a large number of different factors are then given, including,

* CG position,

* lateral and longitudinal load transfer from horizontal Gs,

* banking,

* crests and dips in the road (albeit in a 2-D vertical-longitudinal plane only),

* aero loads,

* engine torque reaction (for front-engine -> live-rear-axle drivetrain).

It is quite clear, however, from the seven-plus pages devoted to it, that the Millikens believe that Lateral Load Transfer Distribution is the most important factor to be considered when "adjusting handling balance" (which, in this particular area, I agree with). I repeat this for emphasis, if the wheel loads do NOT change as per your intended LLTD (or Claude's "Magic Number"), then the car will not handle the way you expect it to.

At the end of the chapter is "18.11 Summary Example". This works through some of the above calculations for what might be a "sportscar", or perhaps a fairly softly sprung racecar (the corner-spring and ARB rates are a lot less than the tyre rates, so the car is not a very stiffly-sprung aero-car). Right at the very end of the chapter, on page 708 (my older version), is Table 18.1 summarising the changes in wheel loads due to the various factors. For this particular example the "Banking" effect is quite large (ie. oval track racing), the "Aero" effect quite small (ie. no big wings), and, quite clearly, the LLTD is by far the most important effect.

Please go through the RCVD example in more detail, but for now take it that the car is slightly front heavy, but roughly with about 900 lbs weight per wheel. There is a Total LLT of about 800 lbs (from the two inside wheels, to the two outside wheels). This is distributed by the "springs, bars, and RC heights" as +/-430 lbs front, and +/-370 lbs rear, giving LLTD = 54%F, 46%R.

~~~o0o~~~

Now the twist in the story. :) Nowhere in this 40 page chapter is any mention made of any TWIST in the road! All four wheelprints are ALWAYS considered to be lying in a PERFECTLY FLAT plane!

Fortunately, there was a large blank space at the end of the chapter, so I added some more calculations. I imagined that the road is very "smooth", but it is also cambered in the usual manner so that the road surface has a cylindrical shape, which in "end-view" has a radius of about 40 metres. So, if the two edges of the road are 10 metres (30 ft) apart, then the centreline of the road is 0.3 metres (1 ft) higher than the edges (quite typical of real roads).

Driving parallel to the centreline of this road introduces no Twist into the suspension, even if the road curves around a bend. But a car with ~3 metre wheelbase and ~1.5 metre track, driving diagonally across this road at an angle of about 15 degrees to the centreline, has about 7 mm (1/4") of Twist-mode between its four wheelprints (ie. one diagonal pair of wheelprints are up 7 mm, and the other diagonal pair down 7 mm, wrt car-body). Please do the calcs to assure yourselves of this.

Furthermore, if the car is doing 100 mph (~45 m/s) while following this diagonal line from the outside of the road towards the inside "apex", then it will spend almost a full second with its suspension constantly "Twisted" by 7 mm. So the Twist is effectively "steady-state". But when exiting the corner, from inner apex to outside of road, the Twist will be in the opposite direction!

And even furthermore, if the road surface is smoothly cambered "concave up", as is common with banked corners, then the Twist introduced by a diagonal driving line is of the same magnitude as above, but of opposite sign.

~~~o0o~~~

So, the big question:

What does this twist-in-the-road do to your precisely calculated wheel loads?

Based on the (quite soft) corner-spring and ARB rates in the Milliken example, the 1/4" Twist changes the wheel loads by about +/-160 lbs! And depending on which way the Twist is, the LLTD ends up being either 74%F, 26%R (for corner entry of convex-up road), or 34%F, 66%R (corner exit, convex-up road). Put simply, the handling balance changes from massive understeer on corner entry, to massive oversteer on corner exit. Yippeeee!!!

Anyway, there are a whole lot of other effects which should also be considered, some of which lessen the above changes, others which exacerbate them. But the bottom line is that with conventional suspensions, all your precise "handling balance" calculations get tossed out the window as soon as you put the car on a real road. And THE STIFFER THE SPRINGS, especially the Roll and Twist-mode stiffening Lateral-U-Bars (= ARBs), THE WORSE! Please do the calcs.

~~~o0o~~~

Finally, it is worth noting that FSAE's short-wheelbase-small-track cars don't feel the above sort of twist-in-the-road as much as larger cars (because the further the wheelprints are apart, the further the road surface moves out of a flat-plane). But any "twist-in-the-road" will still change the wheel loads of your FSAE car.

How much? Easy to measure! Put your car on its four corner scales, on FLAT ground. Adjust your spring-mounts so that the corner-weights are symmetrical side-to-side. Now slip a 6 mm thick piece of plywood under two diagonally opposite wheels (or a single 12 mm piece under one wheel). This represents a Twist-mode of 3 mm (1/8"), which might represent some parts of some of the "wilder" FSAE tracks. Write down the changes in the four wheel loads.

Now ask yourselves why you bothered doing all those precise "handling balance" calculations in the first place. Because, with conventional suspensions, the road decides what the LLTD is, not you!

Z

==========================

It has been suggested (on another thread) that while a soft Twist-mode might be advantageous on bumpy roads, it might offer NO such advantages on smooth, sealed roads, such as those typical in circuit racing.

Those of you who prefer to "follow the numbers", rather than the unquantified opinions of experts, please read on...

~~~o0o~~~

Milliken's RCVD, Chapter 18 "Wheel Loads" starts with,

"The [vertical] loads at each wheel are extremely important in determining a car's maximum steady-state cornering capability." (my emphasis).

The chapter goes on to give examples of how to calculate these vertical wheel loads. Quite reasonably, these calculations are simplified by assumptions such as,

"...steady-state operating conditions - that is, smooth roadway, constant speed cornering, constant longitudinal acceleration, constant grade, etc.

... roll rates, spring rates ... are linear,

... chassis of the car ... is [torsionally] rigid.", and so on.

In fact, there are about 5 pages discussing the importance of a torsionally stiff chassis, because,

"... if the chassis torsional spring is weak, attempts to control the lateral load transfer distribution (and "balance" the car's handling by resisting more of the rolling moment on one track than the other) will be confusing at best and impossible at worst." (my emphasis again).

Equations for calculating the variations to wheel loads from a large number of different factors are then given, including,

* CG position,

* lateral and longitudinal load transfer from horizontal Gs,

* banking,

* crests and dips in the road (albeit in a 2-D vertical-longitudinal plane only),

* aero loads,

* engine torque reaction (for front-engine -> live-rear-axle drivetrain).

It is quite clear, however, from the seven-plus pages devoted to it, that the Millikens believe that Lateral Load Transfer Distribution is the most important factor to be considered when "adjusting handling balance" (which, in this particular area, I agree with). I repeat this for emphasis, if the wheel loads do NOT change as per your intended LLTD (or Claude's "Magic Number"), then the car will not handle the way you expect it to.

At the end of the chapter is "18.11 Summary Example". This works through some of the above calculations for what might be a "sportscar", or perhaps a fairly softly sprung racecar (the corner-spring and ARB rates are a lot less than the tyre rates, so the car is not a very stiffly-sprung aero-car). Right at the very end of the chapter, on page 708 (my older version), is Table 18.1 summarising the changes in wheel loads due to the various factors. For this particular example the "Banking" effect is quite large (ie. oval track racing), the "Aero" effect quite small (ie. no big wings), and, quite clearly, the LLTD is by far the most important effect.

Please go through the RCVD example in more detail, but for now take it that the car is slightly front heavy, but roughly with about 900 lbs weight per wheel. There is a Total LLT of about 800 lbs (from the two inside wheels, to the two outside wheels). This is distributed by the "springs, bars, and RC heights" as +/-430 lbs front, and +/-370 lbs rear, giving LLTD = 54%F, 46%R.

~~~o0o~~~

Now the twist in the story. :) Nowhere in this 40 page chapter is any mention made of any TWIST in the road! All four wheelprints are ALWAYS considered to be lying in a PERFECTLY FLAT plane!

Fortunately, there was a large blank space at the end of the chapter, so I added some more calculations. I imagined that the road is very "smooth", but it is also cambered in the usual manner so that the road surface has a cylindrical shape, which in "end-view" has a radius of about 40 metres. So, if the two edges of the road are 10 metres (30 ft) apart, then the centreline of the road is 0.3 metres (1 ft) higher than the edges (quite typical of real roads).

Driving parallel to the centreline of this road introduces no Twist into the suspension, even if the road curves around a bend. But a car with ~3 metre wheelbase and ~1.5 metre track, driving diagonally across this road at an angle of about 15 degrees to the centreline, has about 7 mm (1/4") of Twist-mode between its four wheelprints (ie. one diagonal pair of wheelprints are up 7 mm, and the other diagonal pair down 7 mm, wrt car-body). Please do the calcs to assure yourselves of this.

Furthermore, if the car is doing 100 mph (~45 m/s) while following this diagonal line from the outside of the road towards the inside "apex", then it will spend almost a full second with its suspension constantly "Twisted" by 7 mm. So the Twist is effectively "steady-state". But when exiting the corner, from inner apex to outside of road, the Twist will be in the opposite direction!

And even furthermore, if the road surface is smoothly cambered "concave up", as is common with banked corners, then the Twist introduced by a diagonal driving line is of the same magnitude as above, but of opposite sign.

~~~o0o~~~

So, the big question:

What does this twist-in-the-road do to your precisely calculated wheel loads?

Based on the (quite soft) corner-spring and ARB rates in the Milliken example, the 1/4" Twist changes the wheel loads by about +/-160 lbs! And depending on which way the Twist is, the LLTD ends up being either 74%F, 26%R (for corner entry of convex-up road), or 34%F, 66%R (corner exit, convex-up road). Put simply, the handling balance changes from massive understeer on corner entry, to massive oversteer on corner exit. Yippeeee!!!

Anyway, there are a whole lot of other effects which should also be considered, some of which lessen the above changes, others which exacerbate them. But the bottom line is that with conventional suspensions, all your precise "handling balance" calculations get tossed out the window as soon as you put the car on a real road. And THE STIFFER THE SPRINGS, especially the Roll and Twist-mode stiffening Lateral-U-Bars (= ARBs), THE WORSE! Please do the calcs.

~~~o0o~~~

Finally, it is worth noting that FSAE's short-wheelbase-small-track cars don't feel the above sort of twist-in-the-road as much as larger cars (because the further the wheelprints are apart, the further the road surface moves out of a flat-plane). But any "twist-in-the-road" will still change the wheel loads of your FSAE car.

How much? Easy to measure! Put your car on its four corner scales, on FLAT ground. Adjust your spring-mounts so that the corner-weights are symmetrical side-to-side. Now slip a 6 mm thick piece of plywood under two diagonally opposite wheels (or a single 12 mm piece under one wheel). This represents a Twist-mode of 3 mm (1/8"), which might represent some parts of some of the "wilder" FSAE tracks. Write down the changes in the four wheel loads.

Now ask yourselves why you bothered doing all those precise "handling balance" calculations in the first place. Because, with conventional suspensions, the road decides what the LLTD is, not you!

Z