What's this page for?
A lot of people argue the advantages of a hanging off riding style, claiming that it:
Whilst these two claims are, as we shall see, demonstrably correct, I think the first one misses the point a little -
particularly in respect of the Sprint ST, so let me restate it to provide the main focus of this article:
- Allows the bike to be leaned less for a given cornering speed, making the tyre contact patch bigger, and enabling more
power to be transmitted to the road.
- Enables the rider to rest his knee on the road, thus providing excellent awareness of the degree of lean of the
With the bike at its maximum lean (i.e. scraping the foot-pegs), hanging off enables you to corner at a significantly
higher speed than if you were to stay in line with the bike.
The aim of this article is therefore to substantiate this claim from both the theoretical and empirical points of view, and
to quantify the benefit in real terms, i.e. cornering speed.
The majority of this article is based on a photograph of me and my Triumph Sprint ST ('Wolfram') at Quarry Bend, Castle
Combe, UK in June 2002. This photo is particularly suitable for the analysis as it's a low shot
taken in line with the wheels - which makes measurements about as real as possible. Furthermore, it's one of me hanging off
about as far as I can get (I'm perhaps not the most agile of riders), and one of the ST at the limit of lean, dragging the
foot pegs. (In passing, ST riders might care to note that the foot pegs are the first thing to hit the deck -
on both sides.).
I'll use this bend as a case study for the rest of the article. As I take Quarry at about 100+ km/h, I've made the
assumption that it has a radius of 100 m.
In order to substantiate the main posit, we'll have to identify a few other features about cornering along the way:
- The difference between centripetal and centrifugal force.
- The three forces acting on a bike in a steady-state corner.
- The reason for the difference between the bike lean angle and the effective lean
- The reasons why tyre width affects lean angle.
- The reasons why hanging off increases the effective lean angle
When I first started getting interested in biking, no-one was hanging off, period. Then, somewhere in the early 1970s, the
Flying Finn, Jarno Saarinen took the world by stylistic storm and was an overnight sensation when he brought this ice-racing
style to the road. Since then every man and his dog has been doing it, whilst the old stalwarts casting scorn and doubt as to
the benefits of the new style (Geoff Duke springs readily to mind as one such voice).
One aspect of the style that I would impress on you from the outset is that it's one that requires you to commit heavily
to your line through a corner, and as such, leaves you in a poor position to cope with any unexpected hazards. For this
reason - if for no other - I believe it has no place on the road.
Let's get one thing straight about the ST from the start: it's not a sports bike. It's no slouch either, but
if you're trying to out-corner your neighbourhood Ducati or Gixer, the best you can hope for is to out-smart them with a bit
of good track-craft.
Regarding the mathematics... Any bike chassis maths is complex. A bike moves in three dimensions, and you can spend
an awful lot of time manipulating the algebra if you want to get things spot on. All of the books on the subject that I've
ever read, and this article included, make a lot of assumptions. But these are made selectively to simplify the approach and
keep the analysis on track. I'll try to identify mine as I go along, but the basic one is that the bike's going round a
constant-radius circle - but beware: this does not mean that it's in equilibrium!
The difference between centripetal and centrifugal forces.
One of my pet hates in this area of theory is the misuse of the word centrifugal; so a couple of definitions
to make sure we're all singing from the same hymn-sheet:
||is the force that makes a bike (or anything else for that matter) go round a bend. In this case it is supplied by
the road, and acts on the bike to accelerate it away from a straight line and towards the centre of the bend.
||is the force acting on the provider of the centripetal force; in the bike's case, it's the force the bike imparts
on the road surface. This works away from the centre of the bend but does not act on the
bike. If this is a difficult concept, consider the ripples that form in the tarmac on a bend. Something pushes
the tarmac away form the centre of the bend - this is the centrifugal force.
The three forces acting on a bike in a steady-state corner.
There are three and only three forces acting on a bike when it's cornering (in a steady state). These are:
- The weight [mg] - this acts through the bike's centre of Gravity [CG]
- The reaction [R] of the road against the point of contact (i.e. the tyre).
- The centripetal force [F] - i.e. the force making the bike go in a circle.
If you think that there's another one, do let me know... ~:)
These forces agree with Newton's Laws of Motion in so far as:
- The bike is not moving vertically - therefore the vertical components of all forces must add up to zero. Since, by
definition the reaction [R] is the same as the weight [mg], this is the case. (Note that F has no vertical
- If we resolve all forces horizontally, there is a net force F towards the centre of the bend. This means that in this
direction the bike is not in equilibrium - it is continuously accelerating away from a straight line in the
direction of the centre of the bend. F is the centripetal force, and has magnitude:
- For the bike to stay at a fixed lean angle, the forces rotating it around the centre of gravity [CG] must cancel out -
there must be no net moment around CG. In other words:
h is the height of CG above the ground (the line of the centripetal force)
a is the horizontal distance between the CG and the centre of the tyre contact patch.
This can be rewritten as:
It might not be obvious, but these last two equations tells us that the mass of the bike has no bearing on cornering angle.
However, as we shall see later on, there are other factors to be considered, which make this statement false.
The reason for the difference between the bike lean angle and the effective lean angle
Let us first define what we mean by bike lean angle and effective lean angle:
|Bike lean angle
||is purely and simply the angle between the bike centreline and the normal to the road (i.e. between the bike
centreline and the vertical, when the road surface is horizontal). This is not the same as the contact patch.
||Ignoring suspension compression and tyre deformation, the bike lean is important because it has a maximum value,
determined by the placing of protrusions on the bike, e.g. foot-pegs, exhaust, stands etc. This in turn dictates the
position of the bike CG, which is used to determine...
|Effective lean angle
||is the angle between the normal to the contact patch and a line drawn between the contact patch and the combined
centre of gravity (CG).
||The effective lean angle defines the centripetal force on the bike, and hence determines (using Newton's Laws) how
fast the bike will go round the corner.
The following diagram illustrates these two angles.
When we go round a bend, the contact patch moves round the tyre profile. This behaviour is well known by virtually all
bikers, as it is an intuitive indicator of the angle to which the bike has been leant. If we now look at an example of this
(by the way, the rear tyre is a 180/70 Avon Azaro AV36 at 2.9 bar), we can see that there is a considerable difference
between the centreline of the bike and the contact point. [For CG to be in a realistic position, you'll have to imagine that
the rider is not hanging off ...]
The consequence of this is that that we somehow don't get the full benefit of leaning over - in this example we somehow
lose 5 degrees of lean. We need to examine this in more detail...
The reasons why tyre width affects lean angle.
Firstly, if the rear tyre had no width, there would be no difference between the bike lean angle and the
effective lean angle. It is only because the tyre has a significant width that there is an effect. There are two consequences
of a wider tyre that we need to quantify to see if they produce a measurable effect:
Some simple geometry allows us to examine the effects of a wider tyre on the bike lean angle. As the width of the tyre is
increased, any fixed protrusions (e.g. foot-pegs) are now higher off the ground, and can therefore lean further. The
following exaggerated illustration shows this point:
- The effect on maximum bike lean angle
- The effect on effective lean angle
The yellow schematic (with the wider tyre) has a larger lean angle (θL) than the white schematic (smaller tyre
θS) We can calculate this effect, but the results are, in any case, clear to see:
A wider tyre increase the maximum bike lean angle.
Our next posit concerns the effect of the tyre on the effective bike lean angle. For this, we need to examine the position
of the CG with respect to the contact patch. The following diagram compares the effective lean angles of bikes with large and
small tyres. Both bikes have the same bike lean angle.
For the same bike lean angle (the two angled lines are parallel), the yellow schematic (wider tyre) has a smaller effective
lean angle (φL) than the white schematic with the narrower tyre (φS). Again, we can simply
A wider tyre reduces the effective lean angle
So here we have a classic scenario of two effects working against each other. On the one hand, the wider tyre gives us a
greater maximumbike lean angle, but on the other hand, for any given bike lean angle provides us with less
effective lean (and hence less cornering speed) than would a narrower tyre. Let's look at a graph of these effects to try to
identify what's happening.
This graph plots the change in maximum bike lean angle (green) and maximum effective lean angle (yellow) against tyre width.
This demonstrates that a wider tyre will result in an increase in effective lean angle (and hence an increase in cornering
speed). It also shows that the bike lean angle will have to increase more and more to achieve this. This isn't an issue for
the Sprint ST, where the maximum bike lean angle is well within the tyre's limits, but will be an issue for bikes with
greater bike lean capabilities.
In short, we can say that:
A wider tyre increases our maximum effective lean angle - but the bike has to lean more and more to achieve
Which means that we can corner faster on a wider tyre. So now, after all that hype, we come to the realistic data.
Let's make a couple of assumptions, which, although not correct, are close enough to make comparisons meaningful:
The following data can be calculated:
- Assume that the tyre profile is circular
- Assume that the stated tyre width (e.g. 180) gives a 50 degree profile from the tyre centre. (This enables us to come
up with a figure for the radius of the profile.)
- Assume that the protrusion (foot peg) is 335 mm from the bike centre and 280 mm above the centre of the tyre
|Tyre width [mm]
||Max. bike lean angle [deg]
||Max. effective lean angle [deg]
||Maximum cornering speed [km/h]
What this says is that the difference is small 1.3 km/h. So perhaps there's another reason for fitting wide tyres! [By the
way, these calculated data are slightly different to the observed results. I'll use the observations for the rest of the
The reasons why hanging off increases the effective lean angle
Now let's consider the case of hanging off. What's really happening?
Well, with a bike like the ST, the maximum bike lean angle (empirically) is 42.5 degrees, which, with no hanging off and a
180-section tyre, equates to an effective lean angle of 37.5 degrees. The point of re-stating all of this is that with normal
tyres on a reasonably good quality road, maximum lean plus the 87 N m rear wheel max. torque of the ST isn't likely to cause
things to break away. (This is why I suggested at the outset that the objective of keeping the bike more upright wasn't the
If I hang off the bike however, the centre of gravity of me moves off to the inside of the bend, and with it the combined CG
of me and the bike.
Now with centres of gravity, we lay people have to go in for a lot of crystal ball/navel gazing, as they're nigh-on
impossible to evaluate or calculate in practice. However, using the fact that the all-up mass of the ST is in the order of
230 kg, and I'm heading for 105 kg in race trim, I've assumed the combined hang-off CG to be one third of the distance
between my CG and the bike CG. I've assumed the height of the bike CG from various other publications. What we have now is a
new combined CG, which is several degrees to the inside of the no-lean CG, and this increases the effective lean angle
considerably. The next picture illustrates the point.
This shows that the new effective lean angle is 5 degrees greater than that of the no-hang effective lean
angle (42.5 - 37.5 degrees). Remember that I said that weight does play a part in the cornering maths.
Well this is why: If you're a bulky rider, the combined CG will be higher than for a lighter person. When you lean out, this
moves the combined CG further out and increases the effective lean angle. However, the downside of this is that making the CG
higher makes the bike less flickable - either into or between corners.
Okay, so what does 5 degrees mean in real money, I hear you ask?
Well, again, let's consider the bend in question. Then, using the standard formula for circular motion the following results
||Bike Lean [deg]
||Effective Lean [deg]
That's a 9 km/h difference in cornering speed. Now we're really talking!
The simple conclusion of this article is that hanging off enables you to significantly increase your cornering speed. For
the Sprint ST, this also means increasing the maximum cornering speed, as the foot pegs hit the deck well before a
contemporary sport/touring tyre is likely to lose adhesion.
If you want to be in with even a chance of holding your head high at a track day, then it's a style that must be adopted.
(But at the same time, it's a style that significantly increases your risks if practised on the road, and one that
significantly increased your prominence to the authorities.)