Good thing it's called the "MathBike."
Anyway, there I was, staring at the Slipknot poster behind my computer screens, imagining what a bike with anti-dive would be like to ride. I kept trying to reconcile what the bike would do on corner-entry with what I had seen on the anti-dive plots I've generated, and realized it wasn't a simple interaction.
Anti-dive changes with front suspension position, and cornering forces change how high the bike rides. Therfore, anti-dive percentage changes with lean angle, but braking usually also changes with lean angle...
Would the front of the bike feel jacked-up, then plummet mid-corner when I relaxed off the trail braking? Would the anti-dive go weak because of the cornering forces, making the front pop back up when I was done trail braking? Also, the goddamn springs! They push back harder lower in the travel! Does that make most of this a moot point?
Trying to compare it in my head to telescopic forks, another thought occurred to me - knowing what the front suspension does on corner-entry is probably important, but what the hell happens to trail? Steering is trail!
Anti-dive or not, the rear of the bike is going to lift, making the rake steeper and reducing trail. But my Hossack linkages increase trail as I use up travel, does that counteract this behavior? More than counteract? Less? What happens when the rear suspension relaxes back down after braking in a corner?
And so I bit a bag of bullets and wrote, by far, my biggest piece of software ever.
My program eats up bike parameters like wheelbase, nonsuspended mass, CoG location and wheel radii; behaviors like anti-squat, wheelrate, anti-dive and rake change; and inputs like lean angle and accel/decel G, and spits out where both ends of the suspension are, and what the trail is.
Also, I have to gloat a bit about this - it solves these parameters iteratively, which eliminates a big source of error. You hit the brakes, and weight transfers according to the CoG height. But, this weight transfer lifts one end of the bike and lowers the other, changing the CoG height, and affecting the original weight transfer! My program solves this same situation again and again until the resulting suspension positions stop changing, signifying it's arrived at the correct answer. I think that's pretty neat.
Anyway, I took this program and fed it combinations of lean angle and braking that simulated different types of corner entry, and used that to compare the behavior of L3na (my gixxer track bike) to a particular Hossack setup I was playing with.
Let's explain this nonsense a little bit more -
Bold traces - Front suspension position
Faint traces - Trail
Red traces - L3na (my gixxer6)
Blue traces - Mathbike
*The bottom two plots are different, and show how the anti-dive behavior (left axis) and trail (right axis) changes with front suspension position (x-axis). Interestingly, a telescopic fork actually has negative anti-dive, because both load transfer and braking G compress the forks.
The other plots show the behavior of both bikes during different corner entry situations (with the exception of the "Brake grabs" plot, which literally just shows what the front does when you yank on the brakes in a straight line with increasing brutality).
I've normalized the two bikes by making the wheelrates the same (basically, the tires on both bikes feel the springs are identical), and the trail the same while coasting in a straight line. This just makes them easier to compare for now.
You can see that in most cases, the red bike (telescopic) dives hard, and relaxes upwards to a steady position mid-corner. The blue bike (hossack) sometimes relaxes upwards, sometimes downwards, and sometimes approaches gently in a flat line to this same mid-corner position.
As far as I can tell, the slower the front of the bike reaches the mid-corner "relaxed" position, the better the front suspension will feel on entry (meaning nothing sudden will happen when I let off the brakes). Interestingly, there is one situation (third plot on the left) where the telescopic bike (red) is already at steady-state for a bit before the hossack bike is, meaning it might feel better? In general, however, it looks like corner-entry suspension movement is better on the hossack.
Trail is an entirely different issue, and one I'm probably going to have to fight a bit on the hossack design.
You can see that, in all cases, there is a TON more trail on the hossack bike mid-corner (~15% more) which is probably going to make the thing a bear at the vertex. I need to adjust the linkage so that doesn't happen.
(Quick aside - people refer to the part of the corner where you are the closest to the inner curbing/shoulder as the 'apex'. However, the bike is not always supposed to be at the maximum lean angle at the apex. Sometimes maximum lean angle occurs out in a sea of pavement. I've taken to calling the max-lean-angle location the 'vertex' in an attempt to better describe a line through a corner.)
Also, the reduction in trail of a telescopic bike on the brakes helps it tip-in. Without that, will this bike suck to steer into a corner? I'm hoping not. I get the impression the regular trail change is a case of "If you can't fix it, feature it!" and that once I get used to the trail being more constant I'll be able to ride this bike just fine. In any event, I need to make this trail adjustable.
But wait, there's more!
I apologize in advance for how cerebral this is going to get...
Drawn above is something that approximates the classic "grip circle" of racecar lore. The 'circle' portion is drawn at 1.7G, which is ~60 degrees of lean angle on a bike. Inside the circle, I've drawn a box at 1G in each direction (the scale is a bit off, the squre should be one grid unit larger in every direction...whatever.)
On a sportbike, you wheelie/stoppie at about 1G because of how short the wheelbase is and how high up the CoG is. But, it gets weird...
When you lean a bike over, the CoG height gets closer to the ground. This means that you won't wheelie/stoppie until a greater longitudinal G. That's represented above by the "wheelie line" and "stoppie line" curving up/down as the lean angle increases. These lines cross this circle at about 45* of lean.
So, basically, this means that until you hit a certain lean angle, your driving/braking is not grip limited (limited by the tires sliding) but is tip limited (limited by looping out/faceplanting over the bars).
To make this sound even cooler - you can brake/throttle a modern sportbike on sticky tires HARDER when leaned over than you can in a straight line!
This region of extra braking/driving is represented by the shaded red area above.
The region most motorcyclists live in is represented by the non-shaded red area above - they brake until a stoppie, then let off the brakes as they tip in. Also, most 600cc bikes can't wheelie just on the power, so that's why I've included a "power limit" line above.
Now, this makes a big assumption - that the tires can support the same G when cornering as when driving/braking. This is hard to guess - normally, the harder you push on a tire, the less relative grip it has (like when all the weight is on one tire in a wheelie) BUT motorcycle tires behave like spheres (unlike car tires) and as you squish them the contact patch area grows rapidly. I wish I could show everyone motorcycle tire grip plots as a real answer, but EVERY TIRE MANUFACTURER HAS TOLD ME TO POUND SAND WHEN I ASKED FOR THEM. Dumb.
We know it's at least partially true, because a sportbike will flip over forwards/loop out before sliding the tires in good grip conditions. The ratio between longitudinal/lateral grip will change the size of the shaded red area above, but will not eliminate it totally.
I figured the above out when trying to describe in terms of lean angle + braking G what corner entry looks like. It's absurd. I can't wait to try it on track.
At some point in the last month, I got sick of staring at python interpreter errors and decided to CAD some frame stuff. Damn you Kawasaki for making this motor structurally useless. Anyway, here's a picture of some swingarm-mount frame bits that I hate and am 100% going to redesign.
I also ordered a gixxer rear brake setup, a front R6 caliper (with free brake-fluid soaked saran wrap!) a stock gixxer6 shock, some brake rotors, and these totally fugly disco-biscuit Katana wheels (that were delivered in a box filled with a sparkly white powder that I can only assume is anthrax):
And so the winter goes.
No comments:
Post a Comment
Don't be a dick!