Kart Steering, Physical Forces and Setup - Theory and Practice
Steering, Physical Forces and Setup - Theory and Practice
by James Hughes
Often when asking questions about chassis and steering settings, the usual answer is simply to say changing some setting or other causes an increase or decrease in grip. There is never an explanation of the physical principles involved in causing these changes. I hope in this article to explain the physical forces involved in driving a kart, along with how those forces are generated by the steering, and what the effect is on the track of changing the various parameters available as setup.
Although a kart may seem to be rather simple device, it is perhaps a more difficult subject to explain than an equivalent car. Both vehicles have many parts and principles in common but there two major differences, which account for a large divergence in design and in setting up. These differences are the karts lack of differential, and also its lack of any suspension components.
A good knowledge of the forces involved can help greatly when setting up a kart - giving the mechanic some knowledge as to what should happen when a parameter is changed. This should result in considerably less time spent on the track testing.
The steering geometry can be regarded at the movement and displacement of the front wheels as the steering wheel is turned. This movement is quite complex, and involves a number of different settings. There is one thing in common though, and that is the reason why we need a complicated geometry - We MUST lift the inside wheel while cornering.
The inside wheel lift is what enables a kart to go round a corner without using a differential.
Because of this lack of a differential, a karts natural direction of travel, forwards, is very difficult to change. This is down to the differing radii of turn experienced by the inner and outer rear wheels while turning a corner. The inside wheel is actually travelling a shorter distance than the outside, so therefor is needs to take fewer revolutions to go round the corner. However, the two rear wheels are attached by a solid axle, and must therefor move together, so in order to turn, one of the wheels need to skid over the track surface. In a car, the differential will allow the wheels to turn at different rates, without this skidding action.
This skidding action, or indeed the lack of it, is what make a stationary kart so difficult to turn round - you have to overcome the grip of one of the tyres, and with the sticky tyres used in many kart classes this can expend a lot of energy.
This is the reason for lifting the inside wheel and it effectively turns the kart into a tricycle during the cornering process! The steering geometry causes the inner rear wheel to lift off the ground while cornering, which means the wheel can rotate faster than it is passing over the ground. The rear inner wheel is no longer touching the track, and we therefor no longer need to overcome the grip from that tyre in order to turn.
In fact, depending on the power of the engine, we may be able to allow some scrub. For example, while a Prokart may need to entirely lift the inner wheel, because it does not have enough power to overcome the scrub, a more powerful kart may have power to spare in the corner, meaning that the power loss to scrub can be overcome. However, any scrub will start to cause understeer when entering a corner, so even though the engine may be powerful, it may still be necessary to completely lift the inner rear to maintain decent handling.
However, we haven't yet explained how the front geometry can affect the rear wheel lift, and in order to do this, lets define a few terms used when describing front end geometry.
To help explain how the front geometries affect the rear inside wheel, lets assume that the chassis is completely rigid - it is so stiff that it cannot bend in any direction. This assumption makes things a little easier to understand. Kart chassis are not actually this stiff - they flex in a number of areas. However, the differing effects caused by differing stiffness' in various parts of the chassis are beyond the scope of this article.
When we turn a corner, the steering geometry (but mainly the caster setting and scrub radius) causes the inside wheel to move down in relationship to the chassis, and the outside wheel to move up. As this happen, because our chassis is rigid, it pivots around a line from the inside front and outside rear, causing the inside rear to lift!
OK, so we have now explained how the front geometry is used to raise the inner rear wheel during cornering. There a quite a few other forces that come in to effect one a corner has been initiated, and that is what we will talk about next
|These are the most
obvious forces, and are a caused by the tyres exerting a force on the
track, either forwards or backwards, with the result being to brake or
Its is important to remember that this force is in the same plane as the track, that is, it is below the karts centre of inertia. For this reason, the force exerts a turning moment (or torque) on the entire kart. During acceleration this torque causes a weight transfer to the rear of the kart, and during braking it causes a weight transfer to the front of the kart. There is no actual movement of any mass, but the torque effectively forces the appropriate part of the kart 'harder' down on the track. It is possible to calculate the amount of weight transfer if we know the acceleration and the distance from the centre of inertia to the rear wheels, but that is beyond the scope of this article. Figure 4 shows the rotational torque while accelerating.
During cornering the driver feels like he is being pushed outwards from the kart. This is actually wrong, he is not being throw out but is simply trying to move in a straight line. The tyres of the kart are producing a grip which imparts an angular acceleration on the kart (and driver), forcing the kart to corner. It is this angular acceleration that the driver feels. The force which the ground imparts on the kart to make it corner is known as the Centripetal force, and it always acts at towards the centre of the imaginary circle we are cornering round. It important to remember that there is NO SUCH THING as centrifugal force.
|In figure 5, we see that the centripetal force is split into two components, a vertical and a horizontal. The horizontal force we have just described, but the vertical can be regarded as the cornering equivalent of the forward acceleration case. Because the centripetal force is acting on the kart, it imparts acceleration to it, and again, this acceleration is acting at ground level. Therefor a torque effect is again produced, but this time it is acting across the kart, and we get a weight shift to the outside of the kart (vertical component Y in our diagram). This weight shift also helps the inside wheel lift, as the weight shift reduces the weight on the inside wheel by an equivalent amount. This force has not been show on the diagram to aid clarity, but is simply in the opposite direction over the inside rear. In fact once cornering is initiated, this weight shift is more important to raising the inside wheel than the steering geometry.||
The distance between the rear wheels affects how the centripetal force is distributed over the horizontal and vertical components. In the diagram, F1 is the centripetal force spread over a wide track, F2 over a narrow track. In proportion to the Y components, X1 is higher than X2, meaning that as track is increased, more centripetal force is distributed as a sideways force in relation to the weight shift. This means a wider track produces less weight shift to the outside rear, and more sideways force. A narrow track increases the weight shift and decreases the sideways force. Therefor a narrow track is less likely to exceed the grip of the tyres when cornering than a wide track. Consequently, the grippier the tyres used, the wider the stance can be before the grip is exceeded.
|On final force to consider is a torque around the vertical axis experienced when accelerating during a corner. It is common knowledge that braking while cornering on a kart causes massive understeer (the kart attempts to continue in a straight line) while accelerating can improve cornering. This at first seems counterintuitive, since normally when accelerating there is a weight transfer to the rear, which you would expect to try to push the inside rear back onto the track. However, this weight transfer is dwarfed by the torque around this vertical axis caused by the fact that only one wheel rear wheel in on the track, and this wheel is offset from the centre of inertia.||
The further this wheel is from the centreline of the kart (and therefor the centre of inertia), the greater the turning moment, and the more likely the kart is the overcome the grip of the tyre on the track . This causes the back to break away - oversteer when accelerating and understeer when braking.
Handling Problems - Symptom and Cures.
Understeer at first, then a sudden grip of front which pulls you into the turn, and possibly going into oversteer.
This is usually explained by insufficient lifting on the inside wheel, causing the initial understeer. As the car starts to turn, weight transfer through centripetally caused torque on the chassis lifts the inside rear. Unfortunately, you now have so much steering lock on trying to initiate the turn, that once the inside rear lifts, the fronts are turned so far that massive oversteer usually results.
This can often be mistaken for a lack of rear end grip, since the final sensation is one of oversteer, but it in fact almost the opposite, since it's too much grip on the inside rear which is the main culprit.
We can use the steering geometry to cure this problem. As we showed above, increasing caster causes the inside front to move down further, thereby increasing inside rear lift. Also, moving the front wheels out on their stub axle (increasing the scrub radius) gives a greater effect, with the same result. Also, increasing the Ackerman effect can have an influence on this - making the inside wheel turn further and therefor move further down.
This is where on turning the wheel, the kart immediately and rapidly changes direction, the rear end breaks away, which results in a spin, or rear end slide.
This is down to insufficient rear end grip - as the turn is started, the inside wheel lifts, but the outside rear is unable to cope with the extra cornering forces involved, and breaks away. So we either have approached the corner too fast - and hence corner forces have overcome the grip of the tyre, or the tyre isn't producing the required grip level.
If the inside wheel is lifting a long way, this can causes grip problem since the tyre is at a larger angle to the track. Kart tyres do not react well to large angles of attack (unlike road or car race tyres which are able to distort to a greater extent because of a lower profile ratio), and this reduces grip. Reducing caster may reduce initial lift, but may also detrimentally affect initial turn in. Since the centripetal force acting on the kart overrides the caster settings while corning, there is probably a problem with the chassis more than the front geometry. It is flexing too far and allowing the rear too far off the track. Moving the rear hubs outwards can improve this situation, since a wider stance makes it harder for the centripetal forces to lift the inside rear, thereby decreasing the amount it will lift in any given corner.
If the back breaks away under braking or acceleration, then its possible that our rears are too far apart, which increases the rotational torque under changes of speed. Since this is most noticeable in wet weather, its is more fully described in the next section.
It could be that our tyre is running at the wrong pressure - and is therefor not at the right temperature to produce the required grip level. Tyre pressures are an arcane science that also won't be explored here, so the best option is to try different pressures during testing, once initial handling has been sorted out.
This is where things get (even more) complicated. The ultimate aim is the same, but because of various changed factors, there are some alterations to make…
In the wet, we are cornering much more slowly, and we cannot accelerate as fast, or brake as heavily because of the lower grip levels available.
Lower corner speed means we do not get the same level of centripetal force during cornering, so the inside rear may not lift correctly. Moving the front wheels outwards emphasises the twisting effect induced by caster, improving initial turn in. In effect the front geometry has more of an effect throughout the corner in wet weather than in dry, where it is overshadowed by the centripetal forces.
Because we still have the same amount of power available, in low grip conditions the rotational torque caused on power application can exceed the grip levels more easily, causing rapid spin out. Moving the rear wheels in reduces this torque, so more power can be applied without breaking rear end grip. Some people refer to moving the rears inwards as increasing grip. This is not strictly true - the grip level remains the same, but the power can be applied more efficiently along the chassis, giving forward acceleration, rather than as a rotation torque which can cause spin out.
You are sure to encounter many other problems with handling, but there isn't the space to go into them all here. However, hopefully the information presented should now be enough to make an educated guess as to the causes of any problems.
You will have guessed by now that we have described an optimal set of parameters for the kart geometry and wheel setup. Of course this never happens - tyre grip level change according to the circuit, weather, and the whim of the manufacturer, some circuits are mostly large radius corners while other are very twisty. What we need is to get to a setup that sits in the mid range of acceptable parameters, and adjust along this range for a particular circuit. For example, on a low grip circuit (or in cold weather) we may want to increase the caster to improve initial turn in. In very cold weather we may want to increase toe in, forcing the tyres to scrub, and therefor warm up faster to the required grip level. However, this can cause other handling problems, which may need to be over come.
The most important thing is to ensure that the inner rear contributes little or no grip in order to improve handling and reduce scrub and hence power loss. This is so important to keeping up speed through the corner, and makes handling so much more manageable.
However, we can also see from the explanations above that changing some settings can affect more that one area. For example, changing the distance between the rear wheels affects both weight transfer across the kart, and the rotation torque caused by accelerating or braking while cornering. Setting the kart up, even with of good knowledge of why a particular change works, still requires a certain amount of track time, although hopefully with the additional knowledge presented here, this track time can be greatly reduced.
with the permission of Karting Magazine.
Thanks to James Hughes for supplying the article!
The Physics of Racing Brian Beckman http://www.getfaster.com/gftechtips.html
Thanks also to the following people who helped (usually via the UK Karting website, www.karting.co.uk)
Neil Dodson, Brian Kavanagh, Brian Pollard, Martin Capenhurst, Peter Holroyd
Copyright © 2000 by James Hughes.
All rights reserved. No part of the contents of this document may be reproduced or transmitted in any form or by any means without the written permission of the Author. All images were created using Satori from Spaceward Graphics Ltd, see www.satoripaint.com for a free demo.
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