Dynamics: Toe
- Mackenzie Lui
What is Toe?
Toe is how much the wheels of a vehicle are turned in or out from a straight-ahead position. The amount of toe can be expressed as: the difference between the track widths measured from the leading and trailing edges of the tires, degrees, or fractions of an inch.
Effects of Toe-in and Toe-out
The effects of different types of toe on the front and rear wheels are different depending on whether a car is front, rear or four wheel drive. Since our solar car is very likely not going to be four wheel drive, we will focus on the effects on the front and rear wheels of front and rear wheel drive cars.
Front Wheel Drive
Front Wheel Drive: Front Wheels - Toe Out
Running toe out on the front wheels of a front wheel drive car will increase the grip within the front tires due to the increased slip angle in the tire. This will increase the acceleration of the car due to the increased grip from the driven tires. The tire will also heat up faster due to the slip angle, meaning that the tire will get to its most grippy point faster than if no toe was installed. However, running toe out will decrease the life of the tire due to the increased stress on the rubber.
The dynamic effects of toe out will give the car faster steering, meaning that the car turns in faster with less steering input from the driver. This is ideal for a tight, winding course with multiple direction changes. The increased response means that the high speed stability of the car is reduced and can feel twitchy in long fast corners.
Front Wheel Drive: Front Wheels - Toe In
Running toe in on the front wheels of a front wheel drive car has the same effects on grip, acceleration, and tire wear as toe out. The dynamic effect of toe in reduces the responsiveness of the steering. This means that the car requires a larger steering input from the driver for the car to change direction. This makes the car more stable at high speeds and makes the car feel planted through long fast corners. This set up is good for new drivers within motorsport or for drivers who do not have fast reaction times.
Front Wheel Drive: Front Wheels - Zero Toe
Running zero toe on the front wheels will increase the life of the tire. Therefore, this set up is commonly seen within road cars where tire life is important. That said, tire life can be of great importance within long races such as endurance racing, so running a set up close to zero toe can be beneficial. Furthermore, the top speed of the car is increased due to having less drag to overcome. The dynamic effect of running zero toe on the front wheels is that the car is no less or more stable in different corners and will respond evenly in short or fast corners. The behaviour of the car will be more dependent on other aspects of set up and geometry.
Front Wheel Drive: Rear Wheels - Toe Out
Running toe out on the rear wheels of a front wheel drive car will reduce the acceleration and the top speed of the car. This is because these wheels are not driven and are being pulled around the track. Any extra grip in the rear tires translates into increased drag, which slows the car down in a straight line. However, the slip angle does generate heat within the tire faster. This generates maximum grip faster, which is ideal for short races.
The dynamic effect of running toe out on the rear wheels effectively shortens the wheel base of the car. This happens due to the toe out rotating the car on corner entry allowing the car to turn in faster and tighter. This effect feels similar to oversteer, without the loss of grip, and makes the car more nimble. This is ideal for tracks with multiple quick direction changes. However, this does make the car feel more unstable through high speed corners.
Front Wheel Drive: Rear Wheels - Toe In
Running toe in on the rear wheels of a front wheel drive car has the same effects on acceleration, top speed, and grip as running toe out on the rear wheels. Running toe in on the rear wheels lengthens the effective wheel base of the car. This is because the loaded rear wheel during cornering is already pointing in the direction of the corner, causing it to work against the steering input. This makes the car rotate more slowly. This increases control and makes the car more stable through long high speed corners. It is especially effective when used on a short wheel base car.
Front Wheel Drive: Rear Wheels - Zero Toe
Running zero toe on the rear wheels of a front wheel drive car will increase the acceleration and the top speed of the car. This is because the tire is rolling in its most efficient direction and generating minimum drag. This reduction in drag force makes the car faster in a straight line. The tire life will be increased due to the reduced stress. However, the tire will take longer to heat up, so will not generate as much grip early on in the race. The dynamic effects of zero toe are that the car will feel neutral to control through tight and long fast corners meaning that the driver does not have to alter their driving style.
Rear Wheel Drive
Rear Wheel Drive: Front Wheels - Toe Out
Running toe out on the front wheels of a rear wheel drive car will decrease the acceleration and top speed of the car in a straight line. Since the front wheels are not being driven any extra grip generated by toe will increase the drag on the system. The life of the tire will also be reduced which is not ideal for endurance racing. However, the tire will warm up faster and reach its temperature sooner in the race.
The dynamic effects of toe out will increase the agility of the car, making it turn in faster and sharper with less steering input from the driver. This makes the car more nimble and allows it to navigate through a tight, twisting course faster. Toe out also means that the car feels less stable at high speeds and though high speed corners due to the twitchy nature of the set up.
Rear Wheel Drive: Front Wheels - Toe In
Running toe in on the front wheels of a rear wheel drive car has the same effects on acceleration, top speed, tire life, and tire performance as running toe out on the front wheels of a rear wheel drive car. The dynamic effect of toe in is that the car feels more stable at high speeds and during high speed cornering. This is due to the car requiring larger steering inputs from the driver to turn, giving the car a more planted feel. This does reduce the agility through tight, slow corners but the trade-off is especially worth it for new or unconfident drivers.
Rear Wheel Drive: Front Wheels - Zero Toe
Running zero toe will increase the straight line acceleration and top speed of the car. It will also prolong the life of the tires out on track or on the road. The disadvantage to this set up means that the tire takes longer to warm up to operating temperature to generate maximum grip. Running zero toe will make the car feel relatively stable in a straight line at high speeds. It will also make the car feel more neutral when taking long sweeping corners and slower tight corners. It leaves the feeling of the steering and the responsiveness of the steering in the hands of the Ackermann geometry as well, which can be a good thing for a race car.
Rear Wheel Drive: Rear Wheels - Toe Out
Toe out on the rear wheels of a rear wheel drive car will improve the acceleration of the car but decrease the top speed due to the increased grip and drag force. It will also reduce the life of the tire due to the increased slip angle. The acceleration is increased as there is more grip available from the tire due to the toe putting a greater slip angle into the rubber. This allows more power to be transferred to the ground without spinning the wheels, allowing the car to accelerate faster. The tire will also heat up faster getting to its most effective level of grip faster.
Toe out on the rear wheels will make the car more nimble and faster through tight sections, making it feel as though it has a shorter wheel base. This effectively makes the car have a higher tendency to oversteer so is a set up used by smooth drivers who can be light on the throttle. Toe out will also make the car feel less stable through high speed corners due to the feeling of oversteer occurring at the rear wheels.
Rear Wheel Drive: Rear Wheels - Toe In
Toe in on the rear wheels improves the acceleration of the car due to the increased grip levels allowing more power to be put through the tire without spinning the wheels. However, the top speed of the car is reduced due to the increased drag from the tire. The tire heats up faster when running toe in as the rubber is stressed, generating heat, getting the tire to operating temperature much sooner in the race; this in turn reduces the lifetime of the tire.
Having toe in at the rear wheels will increase the high speed stability of the car round long fast corners and makes the car feel as though it has a longer wheel base. The increase in high speed stability is comforting for new drivers who are not used to a nimble car that is sensitive to steering inputs. Toe in does mean that more steering effort is required from the driver through tight corners which can slow the car down through tight sections. Toe in on the rear wheels can also give the car a tendency to understeer due to the increased rear-end grip.
Rear Wheel Drive: Rear Wheels - Zero Toe
Zero toe on the rear wheels will reduce the acceleration capabilities of the car but will increase top speed due to the tire rolling in its most efficient direction. This also means that the life time of the tire is increased but it takes longer to heat up to its operating temperature.
Zero toe makes the car more stable in a straight line at high speed and stops the rear end of the car from shifting around. It also gives the car a similar feel through fast and slow corners and leaves the dynamic feeling of the car down to other aspects of set up and geometry.
How is Toe Adjusted on a Car
Toe is adjusted by modifying the length of the tie rod. The tie rod is a linkage that connects the wheel hub to the steering rack. The body of the tie rod can be threaded or unthreaded to increase or decrease its length which adjusts the toe of the car.
Measuring Toe
A simple way to measure toe is by using a string and line kit. Two equal length poles are mounted parallel to the axles at either end of the car with string joining both ends. The string should be coincident with the centre point of the wheels. A ruler or tape measure is then used to measure the distance between the string and front and back of each wheel, giving a toe measurement in units of length.
Sample Toe Values/Configurations
Solar Cars
MSXII: 0 toe
MSXIV: ?
Rutgers: 0 toe
UC Berkley: slightly negative
(credit to Min for the other teams' numbers)
Different statically (no Mercedes DAS) adjustable toe configurations could be useful for different phases of ASC/FSGP. For example: toe-out would be useful on track and for figure 8 and slalom tests, whereas toe-in would be useful for highway driving or straight line tests.
Motorsports
Most racecars will run toe out on the front wheels and toe in on the rear wheels. The front toe helps warm the tires faster and provide more grip and stability while cornering. The rear toe helps produce a larger footprint since the wheels tend to try to straighten under breaking. A general figure for toe in at the rear will be 2.5mm per wheel but at the front it can be as much as 5mm toe out per wheel.
Consumer Cars
The front tires of consumer cars are usually toe-in to improve straight line stability since cornering performance does not matter as much. Typical toe-in specs vary from 1/32” (0.79mm) to 1/8” (3.175mm) depending on the vehicle. Some manufacturers calibrate their cars with a slight degree of toe that goes to zero once the car is on the road.
Other Factors that Change Toe
Bump Steer
Bump steer is a change in the steering angle of the wheel when the wheel is in bump or droop without turning of the steering wheel or lateral movement in the steering rack. When a car drives over a bump, the wheels, control arms, and tie rods displace vertically (each by the same distance). Since the control arms and tie rods pivot around a fixed point, this displacement follows the path of an arc. The fixed point the linkages pivot around is called the instantaneous center (IC). If the tie rod is configured in such a way so that it does not rotate around the same IC, the control rods and tie rods travel about different arcs, and horizontal displacement occurs. This horizontal displacement causes unwanted steering, or bump steer. Bump steer can also occur if the tie rods are not the correct length. The tie rods should have a length that falls along an imaginary line passing through the control arm connection points on the chassis and the upright. If the tie rod is too short, it will have a more severe arc. If the tie rod is too long, it will not arc enough. If the tie rods pass through the same IC as the control arms and are the correct length, bump steer is minimized. If the steering rack is positioned behind the wheel spindle, the tire with toe out on bumps. If the steering rack is positioned in front of the spindle, the tire with toe in on bumps.
Bump steer is highly undesirable within racing especially on tracks or surfaces that contain bumps. If the suspension is constantly transitioning between bump and droop, then a car with bump steer will constantly be shifting the steering angle of the car and will make the front end very unstable at high speeds. The bump steer in the system will affect the steering geometry and will make steering more unpredictable for the driver.
Compliance Steer and Camber Compliance
Compliance steer is a metric to measure the amount of self steer generated by a suspension system when it is subject to a cornering (lateral) load at the contact patch. Compliance steer is measured as degrees of toe change per Kilo-Newton of force at the contact patch, Deg/kN. On all production cars compliance steer gives an understeer tendency from the suspension. Most mainstream production cars have lateral compliance steers somewhere between ~0.1 – 0.2 Deg/kN. Below ~0.05 Deg/kN would be considered a low level for a production car.
When designing a suspension system, it can be difficult to separate compliance steer from camber compliance. In the case of compliance steer, the system needs to be reasonably soft to deliver a level of understeer from the suspension, on the other hand, low camber compliance requires a stiff suspension system. In mainstream production cars, this compromise almost always favours compliance steer as it ensures that the car has a sufficient level of understeer to be safe for all potential customers. As a results camber compliance is very often compromised. The results is a safe car with lots of understeer but with compromised handling, steering feel and agility.
Like bump steer, lateral compliance steer is not something which should be eliminated completely from a suspension system. Some level of understeer is good in a suspension system. Cars people drive on a daily basis have inherent understeer designed in. This is a behaviour we are all familiar with and have become accustomed to. Therefore driving something with no understeer or inherent oversteer would feel unnatural, too agile and too responsive. Lateral compliance steer is also key to ensure the car feels stable and less nervous at high speed. This means that even high performance sports cars with >200mph top speeds have relatively high levels of lateral compliance steer.
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