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# motorcycle with offset wheels

motorcycle less likely to fall when skids? ... a 2-wheel steering bike, which as well as steering can also (somehow) angle the frame independently of the direction of movement, to aid in turns
 (+2, -2) [vote for, against]

motorcycle with horizontally offset wheels (imagine the two diagonal wheels of a car) might be less likely to fall over when one wheel looses traction? (because there is horizontal support)

key benefits + might make recovering from loss of traction in one wheel much easier. + braking and acceleration whilst cornering aid cornering ability of the bike + at speed the bike becomes 'a rudder' - providing additional cornering force. And even some downforce...

Here are some renders and drawings of the idea (which is quite tricky to describe) http://nicholaswhitworth.com/ halfbaked/motorbikewithoffsetwheels.html

problem - when you're racing a motorbike, and you loose traction on the front or rear - the bike, effectively 'falls over'. (lowsiding / high-siding or just spinning off). And though there is a small margin for recovery, it is small.

thinking behind this solution - cars don't have this problem - because there is a wheel on 'the other side' which makes it impossible for the car to fall over (obviously - cars don't have a side-stand....!)

So - if you could get some support 'on the inside' of the bike - then it wouldn't fall over so easily. However, a third wheel or whatever adds weight. So - how about a compromise?

The idea is that in a straight line - the front wheel is exactly in front of the back, as normal, when turning left, the front wheel goes more left than it normally would. (and visa versa). This would hopefully give it some 'dont fall over' protection. Imagine the 2 diagonally-opposed wheels of a 3-wheeler. That's the kind of layout i'm talking about.

How does it work? because the angle of the bike is now not 1:1 linked with the tyres - it's a vector. (if you imagine a cross-section of a car - the tyre angle doesn't change at all - but on the opposite extreme a motorcycle - the motorcycle shifts at 45 degrees. This would (/could) be half-way between the two. at 70 degrees the bike would be turning as hard as it could. This then 'buys' you 25 degress to 'fuck up' in. Allowing extra time for recovery and possibly other other benefits. (such as weird + beneficial wieght-shift and using the now-angled bike as an 'air-rudder' to increase turning + decrease bike angle still further (it is able to 'lean into the wind').

Possible downsides - with two wheels you can 'secure' 1 dimension of 'fall. On motorbikes, the 'secured' dimension is the wheelie/ stopie. Left and right is 'secured' with the centri-petal force of the wheel. Riding a motorbike in a straight line at 100mph is easy - riding at 2mph is NOT. Even experts find slow-riding Very Difficult. By offsetting the wheels - you are creating a 3rd dimension.

there is nothing stopping it falling over in this 'weird angle' that it's set up in ... other than the steering. Also - it's possible that this shape might be inherantly unstable ... ie - if it starts to fall - it might increase it's falling-ness.

It's also possible that it has no benefit whatsoever.

Though it might ... in the event of a slide actually pick itself up.

If it IS inheritantly unstable, BUT provides both safety and cornering performance gains - i would say that using computer control unstable shapes (such as that one- booster hovering jet) are now possible. But in that same vein computer control can probably provide good enough traction control to mitigate the problems of sliding.

RESPONSES TO FEEDBACK

thanks for your welcoming spirit guys! And i'm very interested in any links you think of interest!

The point on accelerating and braking are completely valid - and even IF the computer is able to control the angle of the bike to absorb the acceleration - you're putting (the angle of the bike) as a vector... amount of energy into the tyre (you'd have to turn-in) - which is wasted energy and tyre-grip. (assuming only one wheel is the drive wheel - and this is whist cornering also, where acceleration and braking potential are limited [potentially to zero] )

Thanks for the swing-bike links! they're amazing. I put a you-tube of people doing stunts.

I'm wondering about the super-bike version of this really. And - weather it would make sliding more controllable and less of an instant fall-off. I'll email the guy who posted the youtube...

@ Ian Tindale - you are going to have to explain that to me more... (before i understand it)

@mechE / post 1. kind of - in a straight line, the bike is configured straight so no problem, and when turning, the power or braking can Help it turn - which is good. Also, 2 wheel drive could make the effect disappear completely.

@ mechE - lead tyre on the outside not inside ... i haven't thought that far - at the moment i am saying 'either or'. [i guess both front and rear are able to turn, so there is no lead]

@pocmloc 1- that looks brilliant. + I think 'slamming on the brakes' would be Ok. The bike would re-configure itself linear-ly again quickly. And (because in theory the danger of sliding is reduced) this might actually be the best bike to do that on... in fact, because the front wheel is on the 'inside' of the corner - braking would increase the turning effective-ness of the bike (under braking) over a normal bike! Buy one today.

@8th of 7 - good name, i updated this post after you posted this - you weren't to know!

@Skrewloose - sure, but only 'crab' around corners... benefits (may) = better slide control. (and even increased cornering speed)

@pocmloc 2 - i _think_ i understand what you're saying, but i would say - "i'm not adding more wheels". Also, i like your 4D motorway - 3D is 'left right + time' but 4D would include up and down (i assume!), besides, there _are_ benefits to 4 wheels - else they wouldn't be so popular... 5 wheels is getting useless though. Unless wheeling is a problem...

@RayfordSteele - congratulations on riding a wobble bike - please tell us more ! However, you're saying that it's Power that is going to keep the thing upright (hence the tire wear = uneven power distrobution = failure comment), though i believe that because it's only 45 degrees - steering still has an effect [see the animations i made after you posted] (possibly on whatever this '3rd arm' is). 2 wheel drive is going to help - definitely... but steering will be able to stabilise the bike. Though if it's a human steering (only) there may well be A Nack to it...

@baconbrain, cheers, i recon i agree, though if it was mechanical, and slight you might get some benefits at no cost. As you noted - it was easy to turn Into the 3 wheeler - this bike would be like that in both directions. And proposed advantage is more manageable slide control. I'd need some more renders to show this properly though...

My Conclusion - - - - - - - - - - - - Having thought about this All Evening & modelling it in 3D etc... the Real world problem is that : motorcyles are Very Simple machines. You've got 2 wheels, an engine, a steering column and a seat. This idea requires computer actuated (hydralic? servo?) control of two wheels. Also - the drive needs to go to at least one wheel. Yes, hub motors could do it... but they're not super-bike yet. Real motorbikes require large petrol engines, which connect to the wheels (exactly in front of the rear wheel) via chain or drive-shaft. This idea MAY WELL provide a benefit When Sliding... however, the technical cost might well be Too Large To Bear.

I'd love to know if it did provide a benefit. I can't help the feeling it might.

Update - ok.

Having rendered loads of animations, and thought about the angles quite a bit... i have decided. This WOULD actually help a motorcycle WHEN it starts to slide. It may even provide greater turning ability to race motorcycles. I would go as far as to say... in theory, either the back Or Front could Lock - whilst the bike is going around a corner (nearly) as fast as it could - ... the bike might be able to stay upright. quite a claim. ` Simply put - the greater the offset angle the more stable it is - but the less effect the steering has to be able to alter the bike's angle. If you have wheels at 45 degrees, you've bought yourself probably twice the time.

This idea could work quite subtly - say an offset of 3 degrees. This might be enough to 1) be mechanically achievable 2) provide enough of a benefit to make it worth-while.

This investigation is getting beyond my brain - but, There are factors with weight shift. Not least because - as this machine turns a corner, the front is 'raised' by what ever degree you make the offset. This is extra weight-shift.

I suspect this could provide an extra 2% stability or something in corners - which would be significant... But i am unable to take this any further. I am very interested in what you have to say on the matter.

 — nicholaswhitworth, Mar 31 2010

Swing bike or Wobble bike http://www.instruct...com/id/wobble-bike/
pedal version, steers at both ends, can be ridden along in your diagonal configuration. [pocmloc, Mar 31 2010]

This is what i mean - loads of diagrams with 3d renders... http://nicholaswhit...thoffsetwheels.html
go and see this - it's much easier to understand in pictures... [nicholaswhitworth, Mar 31 2010]

(?) You tube of stunts done on a swing-bike motorcycle with hor...or looses traction?
[nicholaswhitworth, Mar 31 2010]

OK, several cars have 4 wheel steer, not just the Skyline. http://en.wikipedia...four_wheel_steering
[Ling, Apr 01 2010]

wikipedia on bicycle dynamics. Results in pages of maths. I've not read it. http://en.wikipedia...motorcycle_dynamics
Shows that bikes display the effect i'm talking about here anyway in a small way. There are some good diagrams in here, and, lots of maths... [nicholaswhitworth, Apr 01 2010]

Wolsey - Schilovsky Gyrocar http://www.dself.ds...rocars/schilovs.htm
a 2 wheel vehicle, balanced by a fiendish gyroscopic contraption [pocmloc, Apr 02 2010]

Rather than having the center of gravity in-line with the thrust axis, this puts it to one side. This is a bad thing.
 — MechE, Mar 31 2010

This sounds novel and interesting, but I wonder how it would affect turning? Welcome to the HB, NW.

Welcome Nicholas. Have you tried riding a Swing Bike (link)? It may be a useful test-bed for this idea. Personally, I would be terrified to touch the brakes or the accellerator.
 — pocmloc, Mar 31 2010

 // how it would affect turning? //

It would no doubt turn rather better in one direction than the other, depending on the offset.
 — 8th of 7, Mar 31 2010

So you want an automated/rider controlled wobble motorbike set up most of the way to crab steering?
 — Skrewloose, Mar 31 2010

Consider the location of the centre of gravity of the bike with respect to the wheels. There is an important geometrical difference between a unicycle, a bicycle and a tricycle. More wheels than that does not develop this geometrical progression (unless you can find a 4-dimensional motorway)
 — pocmloc, Mar 31 2010

If this is feasible, I think you'd want the lead tire to be outside of the turn, not inside, but I retain my doubts on feasibility.
 — MechE, Mar 31 2010

 You'd quickly end up spinning out, with the non- centered center of gravity. Think moment arm of the non-centered force. If you were to have a "2- wheel drive" motorbike in which the front wheel is pulling at the same torque as the rear, you might be able to counteract most of the force, but the moment that one tire wears differently than the other or has a different traction coefficient, you'd wipe out under any sort of speed change.

I've ridden a 'wobble bike.' It was rather fun.
 — RayfordSteele, Apr 01 2010

 — 2 fries shy of a happy meal, Apr 01 2010

Monster Garage built a trike with a '72 Peterbilt engine in it... the engine was next to the driver; not too symmetrical.
 — FlyingToaster, Apr 01 2010

 I am not seeing any advantage to this.

 If you imagine a vehicle with two wheels progressively more and more offset, you will wind up with a dicycle (like a Segway) which wil promptly fall over forward or backward (like a Segway would without all the gyros). What you gain in side-to-side you lose in fore-and-aft.

 Any bike turning in a circle actually has some side-to-side stability, as the two wheels are turning in different arcs. But that doesn't get you much. Flat-track motorcycles often ride with the rear wheel 'way outside the front, which is an exaggeration of that, and the rider almost always has a foot down.

 I used to help build a three-wheeled vehicle with front-wheel drive. We would sometimes get into a sharp turn to lift the inside back wheel, then drive around on the front and one side/back wheel. I think that might count as an offset wheel, although the wheels weren't vertical. It was possible to ride straight ahead like that, and easy to turn into the raised wheel, but I don't think anyone ever completed a 360° turn away from the raised wheel.

 I like the renderings and all, but not so much the idea. It doesn't gain anything. Plus, if it has to be computer controlled, it might as well be completely automated and free in all directions, like a robot on roller skates.

Welcome to the HB.
 — baconbrain, Apr 01 2010

I see [Vernon] has some competition.
 — coprocephalous, Apr 01 2010

 I think that if it was viewed as rear wheel steering, much like - what was that car? - the Nissan Turbo Nutter Bastard Skyline or something*, then it might make it easier to understand.

 It steered the rear wheels in the opposite direction at slow speeds, and in the same direction at high speeds. It added manouverabiity and high speed stability. The latter is what is proposed here?

 I think the angles were small.

 — Ling, Apr 01 2010

 OK I'll be blunt, this idea will inevitably fail since any 3d vehicle running on a 2d road surface resting on 2 contact points will fall over, unless it is actively balanced (1).

 On a bicycle or motorbike, that balance is provided by a combination of gyroscopic precession and driver-input steering to keep the c/g over the line joining the contact points.

 On a Segway the balance is provided by complex computer control systems which run the wheels forwards and backwards to keep the c/g over the line joining the contact points.

 In either case, once one of the wheels starts to skid, the control input which keeps the centre of gravity above the line joining the contact points stops working, so the vehicle falls over.(2)

 In my opinion this idea fails because it combines the poor points of both bicycle (no support to lateral falling save steering) and segway (no support to fore-and-aft falling save computer control) without giving the strengths of either bicycle (cannot fall forwards or backwards because wheels are in the way) or segway (cannot fall sideways because wheels are in the way).

 footnote 1: There are also systems that use a massive spinning flywheel to keep the entire vehicle upright at all times but they are silly.

 footnote 2: Yes OK, if the rear wheel is skidding but the front not, a skilled rider can steer so as to keep the c/g over the contact points and stay upright

footnote 3: by 'over' or 'above' I mean on the line through which the sum of all centrifugal, centripetal, gravitational, static, dynamic and illusory forces acting on the vehicle plus passengers at any one time appears to act.
 — pocmloc, Apr 01 2010

 [Marked-for-tasteful- rearrangement-by-Moderator]

 Hi, [nw], welcome to the HalfBakery.

It's more usual to reply to annotations by appending them to the annotation list rather than the idea itself. There's a help that you might find informative which you can find in the [meta] section of the HB.
 — 8th of 7, Apr 01 2010

 Nice to meet you, [Nicholas].

 Not sure about the physics here but I'm not optimistic. My gut feeling is that by moving the chasis from the plane perpendicular to the motion, you end up with forces working against the natural balance (alluded to by [pocmloc]).

 With the chasis of the bike offset from the direction of travel, won't there be pressure/drag on the leading edge? Not to mention that the poor driver might be sitting squint. You'd need a little bit of clever mechanics to sort that out at the very least.

Also, with the drive wheel out of line with the front wheel, there will be a natural tendency for the bike to rotate (turning right if drive wheel is orientated left of chasis).
 — Jinbish, Apr 02 2010

Well, it might sell well to clowns...
 — 8th of 7, Apr 02 2010

If the tyres rotated (relative to the rims) around their toroidal axis, then the wheels could be parallel but still allow for this 'crabwise' motion
 — pocmloc, Apr 02 2010

Indeed; we have always considered that the internal-combustion pogo stick (q.v.) is a sadly neglected area of personal transportation.
 — 8th of 7, Apr 02 2010

 From the gyrocar link: //However, in what can only be described as a act of bestial philistinism, the car was broken up for scrap in 1948. //

 Idiots.

 pocmloc I don't understand, why is //footnote 1: There are also systems that use a massive spinning flywheel to keep the entire vehicle upright at all times but they are silly.//true?

That Honda prototype link is creepy. Very Wall.E-ish.
 — 2 fries shy of a happy meal, Apr 02 2010

 Thanks [morrison_rm], yes exactly like that.

{2fr], why is it true? That is an existential question that I am not philosopher enough to answer.
 — pocmloc, Apr 02 2010

I'm thinking that if Beanie and Vernon had a child...
 — MaxwellBuchanan, Apr 02 2010

My God, Honda's developed the Orb-It! They must have an HB lurker. RUN!!!
 — RayfordSteele, Apr 03 2010

 Also, as [8th] points out, it is local custom to address points raised in an annotation as another anno, keep the editing of the original post to a reasonable minimum, and/or mark where one has edited and in response to what/whom. This lets the development of the idea play out more like a conversation, with a visible history of its growth.

 Consider: as soon as you accelerate, you will topple backwards. As soon as you brake, you will topple forwards. The contact points of the tyres still form a line (one dimension) upon the road, and as long as any part of the force of engine or brakes has an angle to that line, the bike will tend to topple. I think. Not directly forward or backwards, but at right angles to the pivot line, which is the line between fore and aft contact patches.

 Cars avoid this problem, not by having a wheel to the side, but by having more than two wheels. Three or four wheels meet the ground in a plane, not a line, so there is no line about which to pivot. Provided the sum of CG and CP stays above the plane so marked out, the car remains anchored firmly the ground.

 Even the swingbike has the advantage of the CG (centre of gravity, or more precisely centre of mass) being mostly over one wheel (the rear), close to the CP (centre of pressure, where force is applied), which is (mostly) the rear tyre-to-road contact point. On a motorbike, the rider's weight is more in the center between the two wheels, and away from the CP, so this source of inherent stability is gone. At a a minimum, you'll need 2WD (and computer control) to correct for this.

 Unfortunately, it looks like you have designed a much more unstable motorcycle, not a more stable one. [baconbrain]'s point that this is half-way to being a Segway seems correct. With the amount of computer control this is going to need to stay upright - if even possible - you may as well just build a powered unicycle.

 It is however (apparently) wrong in an interesting and novel way, so I shall refrain from casting piscine skeletal remains your way. Also, you may be onto something that I've missed, but I remain unconvinced, for the reasons given. I invite your response.

Welcome.
 — BunsenHoneydew, Apr 07 2010

<pedant alert> 4 =/= 2 </pa>
 — pocmloc, Apr 07 2010

 Sorry [pocmloc], let me rephrase.

In what way is it silly to use a large gyroscope to keep a vehicle upright?
 — 2 fries shy of a happy meal, Apr 08 2010

because you might want to stay pointed in the same direction ?
 — FlyingToaster, Apr 08 2010

Well, [2 fries], as a regular bicyclist and occasional motorist, I am used to the behaviour of large and small two and more wheeled vehicles. The idea of a large, motorised vehicle, stationary yet thrumming away, with its large flywheel within, makes me giggle in a slightly indecent manner.
 — pocmloc, Apr 08 2010

 I see. Hmm, if this flywheel could be easily tilted so that a vehicle no longer had to fight precession in order to turn, and could perhaps even use precession to make turns which would cause another vehicle to lose traction, would it still be silly?

 You see, I think I have that bit figured out, and lately I've been dreaming up a vehicle using dual opposed flywheels as it's power scource. You would plug the car or motorcycle into a standard outlet and elctric motors would spin the flywheels up to speed while it is parked. With a centrifugal clutch for power take-off the vehicle would be almost soundless and have zero emissions.Making a flywheel obey a driver would be the easy part. How to keep that flywheel from ripping loose in an accident and going on tour is the part that has me stumped.

Make one flywheel fight the other maybe?
 — 2 fries shy of a happy meal, Apr 08 2010

 //use precession to make turns//I've a (semi)theoretical aircraft (electric flying pancake) that does that: precessing its huge tip-mounted propellers to supplement/replace control surface involvement. IIRC it worked on the theoretical-drawing-board slash barcolounger.

//which would cause another vehicle to lose traction//
Maybe... your tires would still have to grip in order to actually move in the desired direction.
 — FlyingToaster, Apr 08 2010

 //Maybe... your tires would still have to grip in order to actually move in the desired direction.//

 Which is where [nicholaswhitworth]'s off-set wheels come into play.

 — 2 fries shy of a happy meal, Apr 09 2010

 //pancake// yeah I did sorta dangle that out there, okay, you twisted my arm :)

 Start with a Zimmer Skimmer (very low aspect ratio and huge propellers on the tips of the wings (Wikipedia:V-173): the rotational element of the thrust neutralizes and even reverses tip vortices), change the drivetrain to diesel-electric (for simplicity's sake), add an electric-powered nosewheel (to keep from chopping up groundcrew, and to minimize facepalm landings), and finally (the part you're interested in) give the propeller assemblies a small amount of yaw and pitch movement, tied in to the attitude controls. The propeller assemblies are deliberately precessed to complement movement of the flight controls: 2 mechanisms come to mind: either hydraulics on the entire assembly (motor included) or use the propellers blades (the props are already articulating somewhat for the same reason helicopters do it)

 Pitch: up = both props inwards | down = opposite(both outwards); Yaw: left = left up & right down | right = opposite; Roll: clockwise = left inward, right outward | counterclockwise = opposite.

 This system can be used passively (ie: make normal control-surfaces usage both precession and vibration free) or actively: ramped up to actually move the airplane around (when control-surfaces are less than optimally effective). I'm not sure what the angles/force would be since I have no data on weight distribution of the original aircraft or propellers.

While I'm sure it would improve the handling characteristics of the machine in question, I'm not sure you'd be able to justify the extra weight and complexity of having moveable motor mounts on any other design.  roll won't work of course.
 — FlyingToaster, Apr 09 2010

 Hello (said nicholas)

 I'm using anotations as instructed.

 Intriguingly the gyro-car could use flip the car to 90 degress whenever required (by jamming on the brakes of the horizontal flywheel, and therefore applying its rotational force to the entire car)- good for rally-style sliding perhaps?

 As for my idea. I've thought about it for hours/ days now and am happy that it would work enough to be beneficial in the domain of controlling skids. I'd have to do loads more rendering (/ mathmatical modelling) if i wanted to convince the world, but frankly it's not worth it. Either the bike will surface in 20 years time (unlikely) or not. The benefits probably are outweighed by the costs, but i think remain true.

 I agree the device is inherently unstable, but the swing-bike shows that it's possible for humans to operate this device, and the segway shows that computer-controlled things are spookily good at balancing.

 Why people think this would not work: The A.ccelerating and B.raking is not applied in- line with the Center of Gravity.

 either A or B would apply a 'toppling' force on the bike.

 True.

 However it is easy to 'untopple' by turning either wheel. This bikes is held upright by constant steering input anyway.

 This would probably mean that the bike becomes more / less 'offset' under A or B. I don't think the path it takes would be effected, and the change might not be as bad as you'd think.

 However, this effect might actually aid turning.

 Take the example of the bike - at 45 degree offset, entering into a corner. If you brake more on the front wheel - this actually causes a rotation of the bike around it CG - helping it to turn. I admit that the rotation of the bike is not the largest cost in cornering, but it is a factor nonetheless. Also - you don't Have to brake more with the front - it's just an option.

 A.cceleration is much the same (a posative contribution towards cornering). I DO take the point that a percentage of the acceleration input is wasted (when one wheel drive) because it is pushing against the front tyre to rotate the bike, which in-turn is trying to rotate it back. What i'd say to this is - when you're in the middle of a corner you're using all the tyres available grip for cornering and not A ing or B ing (if you can help it). For a motorcycle to B in the middle of a corner it would have to sit-up and brake - this would effect its trajectory anyway.

 The advantage this bike has (in theory) over traditional motorcycles is flexibility in terms of slide-recovery and management.

 If you can turn the back wheel OR the front - you've got options that no normal bike has. This can buy you either the time to un-lock the wheel, or change your strategy WITHOUT falling over. POCMLOC was saying above that when the wheel skids it offers no support - which is not true, it offers Reduced support. This is how "a skilled rider" can recover from a rear-wheel slide. However I've never seen anybody recover from a front wheel-slide, which i think my bike could - quite easily.

 Because it is *in essence* only leaned over half-as- much as a normal bike would be at this point - so has "lean" .. "to spare".

 If anybody is modelling motorcycles or bicycles in software or anything - please get in contact. If you apply yourself you'll find a way to contact me.

Also, if somebody wants a wacky welding project I am curious weather a 'fixed' mechanical version could be made - where the front is linked to the back, but you'd also need another input (perhaps twist or lift) which was able to 'setup' the offset shape.
 — nicholaswhitworth, Apr 09 2010

 so to make a long story short, you want a 2-wheel steering bike, which as well as steering can also (somehow) angle the frame independently of the direction of movement, to aid in turns. Sounds like you got something there. [+] for the idea [-] for the amount of crap I had to wade through to understand it... [ ].

 "somehow" is easily(ish) achieved in motion by having the machine be dynamically asymetric 2-wheel drive as well as 2-wheel steering.
 — FlyingToaster, Apr 09 2010

 I'm on my third glass of wine, so I'm not going to go into the physics.

 However - the concept is interesting: [+]

 The 3D renderings show plenty of effort: [+]

 //It's also possible that it has no benefit whatsoever.//: [+]

Pull up a seat Nicholas, I think you'll fit right in.
 — wagster, Apr 09 2010

(mentioned above) gyroscope which holds bike upright -> this is used in radio-control model motorcycles.
 — nicholaswhitworth, Apr 10 2010

 Not if the flywheel/s are housed in an aerodynamic, and preferably evacuated chamber.

 I had never read the term Zimmer skimmer before, AND I have never thought about the effects of precession on flying objects before.

Very, very cool.
It's giving me the start of a headache, but a good one.
 — 2 fries shy of a happy meal, Apr 11 2010

@21 Quest - the aerodynamics - one of the extra benefits of this idea is that you can 'air steer'. Extra cornering power is generated by the body shape being like a rudder. You could also lean the bike "against" the wind - enabling the bike to stand even more upright, and be even more easy to control in a skid.
 — nicholaswhitworth, Apr 11 2010

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