Vehicle Weight Transfer in braking and acceleration - Why should the mass center get lower ?

What are your main concerns when you buy your car?

Style? Color? Fuel efficiency? Engine power?

The purpose of articles in this blog is to provide valuable tips helping you choose a perfect car and use those knowledge as your driving skill.

The information in the website give you various knowledge mostly about working principles of car components and systems, vehicle dynamics, electric vehicles, and etc., but, which are not the knowledge to choose a good car for you.

However, what I’m trying to show in my articles is about valuable tips to choose a good car.

Definition of perfect car

Good car is the car which has maximum performance with minimum weight and keep that performance for its lifetime. The outstanding ability of perfect car can be boiled down as minimizing the forces and moments during its all driving conditions and keep its remarkable performance for good compared to the non-perfect cars. You will know why it shows this features if you continue to visit my website.

1. Types of performance : safety, power train, ride, handling, drive ability, brake, durability, etc
2. Minimum weight  can be achieved by optimum design factors. 
• Weight distribution
• Structure optimization
3. Minimum cost of ownership
• low insurance premium
• low repairing fees
• low tax
• high fuel efficiency

You will get tons of valuable tips in my articles from now on.

Areas of car design 

1. packaging
2. styling
3. chassis
4. body - Interior & Exteria
5. power train
6. electric and electronics

Among them, the most important foundation of car design is package design because once it fixed so did the CG location and weight distribution.

More importantly, it should be fixed in the earliest stage of new car development cycle. Otherwise, it is difficult or impossible to change package design in the middle or final stage because it takes too much time and cost.

Packaging is a space design to allocate corresponding spaces to car components and systems in the total space of a car. It is deeply related to weight engineering

The most important area of car design is weight engineering.

Two main design factors in weight engineering

1. location of center of gravity(CG)
2. distribution of weight

Let’s get our journey start with weight engineering.

We have to remember! Weight tells majority of the car performance.

Simple terminologies about car coordinate system

Let’s call the location of center of gravity as simply CG.

CG is the origin of coordinate system.

z axis is vertical axis which goes vertically upward.

y axis is lateral axis which goes from right to left.

x axis is longitudinal axis which goes from rear to front.

You can make sure this by right hand law.

3 types of vehicle dynamics

1. Longitudinal dynamics
• Car movement when it moves in a straight line
• Corresponding areas : Acceleration, braking, and ride comfort. 
2. Lateral dynamics
• Planer car movement when it drives on the road surface like braking in a turn.
• Corresponding areas : handling, steering and ride comfort.
3. Vertical dynamics
• Vertical movements of a car
• Corresponding area : Ride comfort.

Terminologies related to car dimension

 We have some dimension terminologies here. The distance between front wheel center and rear wheel center is ‘Wheelbase’.

The distance between the center line of front left tire tread and the center line of front right tire tread is ‘Front Wheel Track’.

Similarly, the distance between the center line of rear left tire tread and that of rear right tire tread is ‘Rear Wheel Track’

Path of forces and moments

Every single force of the car passes through the contact patch existing between the tire and the road surface.

Traction force, braking force, cornering fore, vertical force, and even Aerodynamic force pass through the contact patch.

If we understand every force on the tire contact patch of each wheel, that will help you drive your car safely and efficiently and easily understand almost all of drive techniques of racing driver.

Role of friction coefficient µ of tire

Bottom figure shows the bottom view of the tire contact patch. Internal pressure of heading part of tire is higher than that of tail part in the direction of tire movement. In other words, tire shows compression in the heading part and expansion in the tail part. Therefore, tire contact patch-front is slightly wider than tire contact patch-rear. 

Let’s define Fz is vertical load on the tire, Fy is maximum acceleration force and µ is the friction coefficient of tire. Then, Maximum acceleration force Fy is determined by tire friction coefficient µ and Vertical Load Fz as the well-known equation here.

In other words, the larger tire friction coefficient and vertical load can make the bigger maximum braking or acceleration force.

If engine torque creates bigger force than this maximum force, wheel spin happens without making traction force and the engine inefficiently loses its power in the air. You can easily understand when you imagine a car on the black ice.

So, tire friction coefficient of perfect car should be larger as long as it can but high friction coefficient should not harm the other car performance(durability, fuel efficiency, etc). Actually, it's very difficult for tire to satisfy all the car performance.

Dimension for Weight Transfer Calculation

 ‘L’ is the wheelbase and ‘a’ is the distance from CG to front wheel center on the ‘x’ coordinate and ‘b’ is the distance from CG to rear wheel center on the ‘x’ coordinate.

Finally, ‘h’ is the height of CG which is the vertical distance from the road surface.

‘m’ is vehicle mass and ‘g’ is gravitational acceleration.

The Weight of car ‘W’ can be described as W = mg

Static Weight and Reaction Forces

Assuming that front weight is evenly distributed into two front wheels and rear weight is also evenly distributed into two rear wheels

Then, Fzf is the reaction force of front each wheel, and Fzr is the reaction force of rear each wheel.

Let's Feel Weight Transfer on Bicycle

I will give you a tip how to feel the weight transfer. You cannot feel the weight transfer in the car because a car weight is way higher than your own weight. But, you can easily feel the weight transfer on your bicycle.

Remember again every force pass through tire contact patch.

Suppose that you suddenly stop your bicycle by braking on the way of constant speed drive on the straight and flat lane.

Then, you can feel the longitudinal forces generated on your hands.

Also you can feel the vertical forces pressing down front tire.

Those forces are due to your weight only.

You can feel more force at front tire than that at rear tire and you will feel your body try to go forward continuously.

This is the way you can feel ‘weight transfer’ by yourself.

Reaction forces of two bicycle tires shown as red arrows are longitudinal reaction forces and shown as blue arrows are vertical reaction forces. Those forces are due to your weight plus bicycle weight. As you can see, and front ones are larger than rear ones due to weight transfer.

Now, you are ready to understand the weight transfer in a car

Weight Transfer at  Acceleration

Now, let’s think about accelerating a car with acceleration ‘a’. please remember every force pass through the tire contact patch.

As you can see in the picture, acceleration forces longitudinally act on the tire contact patches and CG location of a car is higher as much as distance ‘h’ than the road surface.

Therefore, acceleration forces from tire contact patches generate the moment with moment arm length ‘h’ at the CG location.

This moment decreases the reaction forces of front wheels as much as the quantity in the red circle and increases those of rear wheels as much as the same quantity. We call this effect as ‘weight transfer’.

So, we can see some portion of reaction force moved at front wheel have moved to rear wheel.

Parked Car in the upward slope

Weight transfer at acceleration has similar force and moment pattern to the parked car on the upward slope.

As you can see in the picture, weight transfer happens in the same pattern as shown in the previous picture.

Some portion of weight at the front wheel have moved to rear wheel. You can see just sine term added as multiplier. Sine term shows the slope of the road

Weight Transfer at  Acceleration

Once you understand weight transfer for accelerating a car, you can easily understand it for braking.

The principle is the same, but in the braking, the forces on the tire contact patches is opposite to those of acceleration.

Weight transfer happens from rear side to front side. As you can see in the picture, braking forces longitudinally act on the tire contact patches while CG location of a car is higher as much as distance ‘h’ than the road surface.

Therefore, acceleration forces from tire contact patches generate the moment with moment arm length ‘h’ at the CG location.

This moment decreases the reaction forces of rear wheels and increases those of front wheels.

Parked Car in the downward slope

Weight transfer at braking has similar force and moment pattern to the parked car on the downward slope.

As you can see in the picture, weight transfer happens in the same pattern as shown in the previous slide.

Some portion of weight at the rear wheel have moved to front wheel. You can see just sine term added as multiplier. Sine term shows the slope of the road

Other ways of weight transfer?

It also happens by steering your car even in constant speed or does by aerodynamic force. But, I will cover that issue later.

Sensitivity of Weight Transfer

Let’s define the weight transfer sensitivity(Sw)as the ratio of CG to Wheel base ‘h/L’.

At the constant acceleration, the bigger the weight transfer sensitivity causes the lager the weight transfer quantity.

In the extreme case, assuming that CG point is just on the road surface, weight transfer components go to zero because CG height ‘h’ is zero.

Then, there is no weight transfer at any level of acceleration. But, that is impossible for the car driving on the road. 

Weight Transfer Comparison for two sets of dimensions

Now, Let’s think about two cars having different dimensions.

There are two vehicles as you can see. The weight of each vehicle is the same. Car weight is ‘W=mg’. The car on the right has two times higher CG and two times smaller Wheelbase than those of the car on the left respectively. Weight transfer of the right car increases 4 times compared with that of the left car at the same braking deceleration as shown in the bottom of picture. That means the stability of the car on the right is worse than that of the car on the left.

Sensitivity of Weight Transfer

Green one shows the result when you accelerate the car with 14.7 m/sec. red one with 9.8 m/sec, and blue one with 4.9 m/sec.

You can make a car more stable by reducing CG height and increasing wheelbase.

As you can see, transfer weight ratio gets smaller when the weight transfer weight sensitivity gets smaller.

Unfortunately, You cannot increase wheelbase too much because you end up with other performance values deteriorating.

Examples of those performance values can be Turning radius, ground clearance, steering agility, etc.

Wheelbase is determined on the base of total length of a car. On the other hand, car designers can lower CG height by their own efforts any how.

Conclusion

Weight Design tells majority of the car performance.

Weight transfer in acceleration or braking is proportional to weight transfer sensitivity

The larger the Tire coefficient, the better the performance.

The lower the CG height, the better the performance.

Those conclude this article. Next article will explain why I insist the lowest CG height in longitudinal dynamics.

See you next article! Goodbye!