vehicle mass center effects on braking & acceleration - why do the braking and acceleration bring about the yawing motion of the vehicle?

CG effect on braking & acceleration

Summary

1.  Quiz : Which brake should keep its function for the entire braking process if you choose only one brake among 4?
2. Why does a car tend to rotate at braking and accelation?
3. What are the effects of CG location on braking and acceleration
• Effects of vertical location
• Effects of horizontal location
4. Where is the best CG location of perfect car

Figuring out the answer to this quiz, you will have a chance to think about the important effects of CG related to its height and horizontal location on braking and acceleration.

And we will have a discussion on why a car tend to rotate at braking and acceleration.

Then, I will explain what are the effects of CG location on braking and acceleration. Effects of vertical location, effects of horizontal location.

Finally, I will explain what is the best CG location of perfect car.

Review

I picked up this picture from my previous article.

As I explained, front tire braking force and vertical reaction force are bigger than those of rear tires because of weight transfer as we have discussed already.

By this reason, Front brake capacity is designed always bigger than rear one to endure the transferred weight.

It looks like no problem at all if we design the front brake capacity bigger than rear one.

But, ironically the real problem exists at the rear wheels.

Because vertical reaction force reduction due to weight transfer bring about brake force reduction at rear wheels. Weaker brake force at rear wheels can cause a serious safety problem. We will discuss this in detail in quiz.

Please, remember braking forces are produced differently at each wheel relying on individual friction coefficient multiplied by also individual vertical reaction force. Of course, we have no braking force at all, if either friction coefficient or vertical reaction force is equal to zero.

Quiz

Here we have a car on the road which has straight lane and there are large and deep swamps in both sides of the road and alligators are living in the swamp.

Assuming that the driver found a dear all of a sudden and smash down the brake pedal.

Unfortunately, only one brake is allowed to be available among 4. Which brake should keep its function during the entire braking process

There is a driver alone in the car 

Wow! Alligators are waiting for something!!! I hope I’m not on their menu.

Front Right Brake Alive

Let’s analyze our case one by one. Our first case is this. Front right brake with red color is alive only.

Then, what will happen at the panic brake? As you see, we have CG location on the longitudinal center line depicted as yellow fan. At the braking, front right wheel won’t move because its brake is alive.

Then, a car weight inertia(yellow arrow) produces the moment with moment arm length L1.

This moment turns the car about vertical pivot axis passing through the center of front right tire contact patch because CG is on the longitudinal center line placed moment arm length 𝑳𝟏 apart from the longitudinal tire center line.

This situation becomes catastrophic disaster. Car tail likely pass the car front end. As a result, the car gets unstable and could be roll over into the swamp.

Of course, alligator are very interested in this accident. Therefore, I don’t like this case.

Front Left Brake Alive

This is our second case. Front left brake with red color is only alive. Then, what will happen at the panic brake? As before, we have CG location on the longitudinal center line depicted as yellow fan. At the braking, front left wheel won’t move because its brake is alive.

A car weight produces the moment with moment arm length L1. This moment turns the car about vertical pivot axis passing through the center of front left tire contact patch because CG is on the longitudinal center line placed moment arm length 𝑳𝟏 apart from the longitudinal tire center line.

This situation also becomes catastrophic disaster. Car tail passes the car front end and roll over into the swamp. Of course, alligator are very interested in this accident. So, I don’t like this case either.

Rear Right Brake Alive

This is our third case. Rear right brake with red color is only alive. Then, what will happen at panic brake?

As before, we have CG location on the longitudinal center line depicted as yellow fan. At the braking, rear right wheel won’t move because its brake is alive. 

Then a car weight produces the moment with moment arm length L1. This moment turns the car about vertical pivot axis passing through the center of rear right tire contact patch because CG is on the longitudinal center line placed 𝑳𝟏 apart from the longitudinal tire center line. This situation will end up with safe stop because rear brake is alive. Car tail doesn’t pass the car front end and the direction of car heading doesn’t change too much. Alligator are not interested in this accident because nothing added in the swamp.

Rear Left Brake Alive

This is our fourth case. rear left brake with red color is only alive. Then, what will happen at panic brake? As before, we have CG location on the longitudinal center line depicted as yellow fan. At the braking, rear left wheel won’t move because its brake is alive. Then the car weight produces the moment with moment arm length L1. This moment turns the car about vertical pivot axis passing through the center of rear left tire contact patch because CG is on the longitudinal line placed 𝑳𝟏 apart from the longitudinal tire center line. This situation will also end up with safe stop. Car tail doesn’t pass the car front end and the direction of car heading doesn’t change too much. Alligator are not interested in this accident because again nothing added in the swamp.

So, what’s the answer to the quiz?

We all know that front brake is not the answer, then the answer will be one of two rear brakes, which one?

Answer is that rear left brake(case2) should be alive during entire stop because the moment produced by car weight is smaller compared to case1.

Why? Here is a reason. L1 is equal to L2 in the absence of driver but if we add driver weight in the front left seat, total car CG location including driver weight moves more to the left side.

Therefore, moment arm length L1(case1) GETS BIGGER THAN L2(case2) As a result, the moment of case1 is greater than that of case2

Therefore, Case1 is more unstable than case2 because of bigger yawing moment

Front Two Brake Alive

Let’s investigate two more cases, This is our fifth case. Both of front 2 brakes with red color are all alive while both of rear 2 brakes are dead. We have to know that friction coefficient is different at each tire contact patch because friction coefficient is the function of tire and road surface properties having variety of spectrum. Therefore, brake forces are different at both sides even when vertical reaction forces are the same at both sides because friction coefficients are different each other. Then, let’s continue our question, what happens at panic brake? Assuming that right hand friction coefficient is larger than that of the other side, a car tends to rotate clockwise. As you see, we have CG location on the longitudinal center line depicted as yellow fan.

 At the braking, car weight produces the moment with moment arm length L1. This moment turns the car about vertical pivot axis passing through the center of front right tire contact patch because CG is on the longitudinal line placed distance 𝑳𝟏 apart from the longitudinal tire center line.

I hope you can find a small dot in the right hand tire marked by red. This is the center of rotation

This situation may become catastrophic disaster. Car tail passes the car front end and roll into the swamp. Of course, alligators are very interested in this accident.

This disaster always happens when the moment produced by the car inertia due to braking is larger than the moment produced by smaller braking force(the left in this case) among both sides. 

Rear Two Brake Alive

This is our sixth case. Both of rear 2 brakes with red color is all alive while both of front 2 brakes with blue color were dead. 

what happens at panic brake? Assuming that righthand friction coefficient is larger than that of the other side, a car tends to rotate clockwise. As you see, we have CG location on the longitudinal center line depicted as yellow fan.

At the braking, car weight produces the moment with moment arm length L1.

This moment will turn the car about vertical pivot axis passing through the center of front right tire contact patch because CG is on the longitudinal line placed distance 𝑳𝟏 apart from the longitudinal tire center line. This situation will end up with safe stop and the direction of car heading doesn’t change two much because rear brakes are all alive.

This result is much safer than that in the previous slide

Ride Height due to Braking Force

Weight transfer changes the car attitude. Pictures in the slide shows the vehicle attitude for various cases of the ride height according to the magnitude of brake forces.

Brake force is increasing to the left.

Ride heights at the rear wheels increase bit by bit while those at the front wheels decrease bit by bit in proportion to the magnitude of total brake force.

Brake forces at the rear wheels decrease bit by bit while those at the front wheels increase bit by bit in proportion to the quantity of transferred weight.

Let’s investigate what happened at the rear wheel in the braking. The higher CG height results in series of undesirable effects to make car performance deteriorating, the bigger weight transfer, the higher ride height and the weaker tire grip which cannot produce the stable brake forces at the rear wheels. The higher CG height makes both of braking time and distance longer because you have to relieve the brake pressure at relatively earlier time compared to the case of lower CG height. Otherwise, rear wheels lose their tire grip and a car may spin. Therefore, CG height should be as lower as it can.

CG location on the horizontal plane

There are two cases about CG location in horizontal road surface in the picture.

In the first picture, CG is located on the longitudinal center line of a car.

In the second picture, CG is located some distance apart from the longitudinal center line of a car.

Friction Coefficient 'µ' changes by factors of road surface(wet, snow, roughness) and tire(material properties, temperature, tread wear, internal pressure)

Those factors are not the same at each tire in the car

When braking is applied, a car has a tendency to rotate on the vertical pivot axis of tire contact patch  having largest friction force

Tendency to rotate gets larger if CG location has bigger offset from the longitudinal center line of a car.

A car start to rotate when the moment by inertia force gets bigger than the moment  by smaller longitudinal brake force between left and right side. Rotation center is the center of tire contact patch with the biggest brake force.

Perfect Car has a CG location on the longitudinal center line

Conclusion

1. CG location is important to prevent unwanted yawing motion
2. Rear brake force gets smaller when CG height gets higher.
3. CG location offset from the longitudinal center line of a car makes bigger yawing moment and a car gets unstable.
4. CG location should be on the longitudinal center line of a car.
5. CG location should be lower as far as it can

Next Article : Brake Slip, Brake Force Distribution