There was a thread over on F1 Technical earlier discussing the merits of a short versus a long wheelbase (incidentally one of many parameters I haven't nailed down). When I was thinking of how to reply it dawned on me that I had little objective or rigorous data to back up what my initial thoughts were. As a start, some might think that long wheelbase implies stability, whereas short wheelbase implies being nimble.
As a generality, I'm not really convinced that's true, at least thinking about it to a degree in 'derivative notation.' Milliken goes over this idea around page 149 of RCVD. In a nutshell it wraps some basic tire and basic vehicle concepts together into a fairly powerful but simple way of describing vehicle dynamics.
All other things being equal, a longer wheelbase should imply higher 'static' directional stability; if you split the axles apart further it should require more torque to 'dislodge' the car from a particular attitude. It should feel planted and secure.. but that's not to mean unresponsive. At the same time as you increase the distance from the front axle to the CG you bump up the control moment derivative; the front tires have a larger moment arm with which to act about the CG, and create higher yaw moment for a given steer angle.
Given that most of my regulars here have FSAE experience, the following example may be enlightening. If there's a series that needs sharp, fast, predictable response almost all the time.. FSAE is it. If you were to test the Goodyear D2692 and D2696 back to back on identical cars, you'd find some big differences in how they drive. The '96 generally should have higher response rates (cornering stiffness) overall, while in the same construction, size, etc. As such, the static directional stability is higher. The car can feel more settled and planted. At the same time it is much more precise and responsive to steering inputs, since the front response is also up! The '92 by comparison, with lower control and stability derivatives, can feel both vague and lazy. (The '96 also has higher ultimate grip, comes in faster, and has unbelievably good wear. Pretty good improvement.)
On the other hand, while the control moment derivative increases linearly with "a" (distance from CG to front axle), if you think of that front axle as a point mass it's contribution to vehicle yaw inertia increases with a^2. In theory then you'd think a car with a short wheelbase would offer higher yaw acceleration capacity. My question is - how much yaw acceleration do you fuckin need? "More" of anything is not always better, except for beer and scallops. I may have to see if I can dig up some old DAQ to see just how much you need. If you already have 2x the acceleration potential that you could realistically need.. why add more when there may be benefit elsewhere?
I'll let you marinate on that.
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6 comments:
That's pretty interesting as I've seen a couple of teams trying to absolutely maximise yaw acceleration and minimise the response time - obviously there are gains to be made here but, as you say, how far is too far?
The average FSAE/amateur driver perhaps isn't able to make the most of these gains as they've spent (relatively) only a small amount of time driving the car on the limit.
I guess that unlike professional drivers it's also more likely that "the limit" will be theirs rather than the cars. Which certainly begs the question - why spend so much effort doing this when there are plenty other areas to work on with such a tight timescale?
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Even with a professional driver there's a limit to how much yaw acceleration you really need.. which is dictated by track configuration. If at most you're using 10 deg/s/s on corner entry, how much benefit are you getting from having a car capable of 70? Why waste the development time?
Similarly let's say you have a really high speed track where at most you're pulling 1.5G lateral.. what's the benefit in having a tire with a mu of 2.5? You'll never use that extra G capacity.
Of course in FSAE the added benefit of a short car is the weight thing.. but there aren't many race series with no minimum.
No minimum, but nobody says you can't use ballast.
Moreover, somewhere in RCVD or in other books there is an equation which states a different things about wheelbase and stability.
For what i know, what really matters is J/l, with l eing wheelbase and j car yaw moment of inertia.
If you are able to increase l without changing too much J, you can actually have less understeer in corner entry and less oversteer in exit (talking always about a RWD car), so you have a more responsive car.
A lot of formula cars constructors are going to have longer and longer wheelbases changing control arm shapes rather than putting something between engine and gearbox..
How are you defining under- and over-steer.. and why do you say the trend would be as such?
My personal experience with short-wheelbase RWD racers is the tendency for trailbrake entry oversteer and exit understeer (up until the rear tires break free).. due to forward load transfer effects.
I had the same experienxe than you..but this is connected more to straigh line dynamic than to cornering. Then when you trail brake into the corner you have a very light rear end.
but if we talk of cornering without braking, for example, according to what i read, the problem you say is connected more to J than to l.
Normally cars with short wheelbase have also small yaw inertia.
But if you could have a car with low yaw inertia and long wheelbase you would have even faster response, so you would reduce its tendency to go on straight when you give a ramp steer for example...or it will reduce its tendecy to have power oversteer in exit.
If we are talking about increasing l without increasing J too, then the majority of FSAE cars has a potential to do just that with placing the front wheels further forward.
A car with 1600mm wheelbase could have 2000mm wheelbase without any serious increase in J.
And as far as I understand the whole thing, you always aim at as long wheelbase as possible to limit the load transfer.
But how far can you go on a tiny track? With a longer wheelbase, you would need more steering for the same radius, but does that mean you would be any slower? I can't yet calculate this, so for our first FSAE car, we are sticking at 1600 wheelbase. Don't have balls to increase it as I fear that the car won't be 'agile' on the tight track...
The other problem is weight distribution, as it would go quite a bit bacwards, but I saw many cars with 50:50, and something like 40:60 is in my view better (better for braking and still controllable throuhg roll center heigth and roll stifness to make it neutral in steady-state).
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