Distribution of Weight and Vehicle Dynamics


The first part discussed tires, their performance curves and how tire vertical loads effected traction or lateral load. We used Figure 1 as an example of a tires performance curve. Knowing these things can also tell us some of the handling characteristics such as understeer and oversteer.

Figure 1

NOTE: This figure contains purely hypothetical data and does not represent the characteristics of those tires manufactured for use in RC cars. However if this information is known by the manufacturers, it would be appreciated.

Understeer & Oversteer

What is understeer and oversteer? Putting it simply, understeer or push means that the front end of your car is sliding through the turn and if you don't slow down you are going to hit that wall you see in front of you. Oversteer or loose means that the rear of your car is sliding through the turn and your not going to see that wall behind you when you hit it.

Weight Distribution

We learned that weight distribution is determined by the amount of weight each tire has to support. We also learned that these loads change continuiously in a race due to load transfer and are the result of forces acting on the car. Let's do some examples using our tire performance curve (FIGURE 1).

Example One (Neutral Weight)

In the first example we will calculate the traction available to our car and the total cornering force.

Car Weight:

30 lbs.

Front End Weight:

50 %

Left Side Weight Bias:

0

Load Transfer From Cornering:

0


Tire Location

Static Weight On Tire

Traction Available

Left Front

7.5 lbs.

8.2 lbs.

Right Front

7.5 lbs.

8.2 lbs.

Left Rear

7.5 lbs.

8.2 lbs.

Right Rear

7.5 lbs.

8.2 lbs.

Total

30 lbs.

32.8 lbs.

Knowing this we can now calculate the Total Cornering Force:

Total Cornering Force = Traction / Weight

= 32.8 / 30

= 1.093 g's

Not bad huh? Well If you said yes, then you haven't taken into consideration that some of this weight is going to shift from the inside to the outside in a turn. This leads us to the next example.

Example Two (Lateral Weight Transfer)

Tire Location

Static Weight

Lateral Weight Transfer

Weight On Tire During Cornering

Traction Available

Left Front

7.5

-5.625

1.875

2.25

Right Front

7.5

+5.625

13.125

11.5

Left Rear

7.5

-5.625

1.875

2.25

Right Rear

7.5

-5.625

13.125

11.5

Total

30

N/A

30

27.5

Our cars vertical loading will change as soon as our car begins to make a turn, usually at turn one. The vertical load will shift from the inside tires to the outside tires depending on the cars cornering force (g's), track width (T), center of gravity height (H), and the overall weight of the car (W). This can be expressed as:

Lateral Weight Transfer = (W x G's x H) / (Gravity x T)

If we assume and factor in a 1.0 g cornering force we can reduce the equation to:

Lateral Weight Transfer = (W x H) / T

Note: Some santioning body rules base the cars track width on outside-of-tire to outside-of-tire measurement. In the world of real cars, track is from center to center of the tires.

So let's say our car has a cg height of 6 inches and a true track of 16 inches. Our weight transfer for a 30 lb. car would be:

Lateral Weight Transfer = (W x H) / T

= (30 lbs x 6 inches) / 16 inches

= 180 / 16 = 11.25 lbs.

This means 11.25 lbs. will be transfered from the inside tires to the outside tires during cornering. With equal front-to-rear or 50/50 weight distribution, 5.625 lbs. will be transfered from each inside tire to each outside tire. So how much total traction would be avalable to us in the turn? Well our inside tires would have 1.875 lbs. of vertical loading and our outside tires will have 13.125 lbs. If we look at Figure 1 we will see that the inside front and rear tire will have 2.25 lbs. of available traction and the outside front and rear will have approximately 11.5 lbs. of available traction. for a total of 27.5 lbs.

How much cornering force do we have?

Total Cornering Force = 27.5 / 30 = 0.92 g's

Our cornering power was decreased from 1.093 g's to 0.92 g's, a difference of .173 g's due to lateral weight transfer. A pretty significant difference in that Static and Dynamic force I would say. One way to decrease the effect of this shifting lateral weight is with preloading. Preloading is the deliberate movement of predetermined weight to a predetermined location, such as moving existing weight from the outside tires to the inside tires for us "Circle Jerks". Which brings us to our third example.

Example Three (Preload)

If we maintain our 50/50 front-to-rear weight ratio and bias the left side by 10 lbs., 5lbs on the front and 5 lbs. on the rear and assuming our same 11.25 lbs. load transfer from cornering at 1 g. What is our Total Cornering Force now? Figure it out and we will talk more about it later.

This shows how, by increasing or positive biasing the left side weight of the car by negatively biasing the right side weight we can improve our cornering force. So far we have maitained a 50/50 weight ratio front-to-back. What happens when we bias the front end?

Example Four (Front End Bias)

To see this effect we are going to bias the front end of our car 10 %. This means we have a 60/40 front-to-back ratio. It really is important to point out that we have not added any weight to our car so far, only moved around the existing weight. So our front end weighs 18 lbs. and the rear weighs 12 lbs.

Tire Location

Static Weight

Lateral Weight Transfer

Weight On Tire During Cornering

Traction Available

Left Front

9

-6.75

2.25

1.75

Right Front

9

+6.75

15.75

12.5

Left Rear

6

-4.5

1.5

2

Right Rear

6

+4.5

10.5

9.5

Total

30

N/A

30

25.75

Now lets calculate our Total Cornering Force.

Total Cornering Force = Traction / Weight

= 25.75 / 30

= .86 g's

This is average, remember that. Also note that this total is misleading because if you look at just the front end weights and traction forces you see, that there is 14.25 lbs. for pulling a front end weight of 18 lbs. and 11.5 lbs of rear end traction to pull 12 lbs. around the corner. This means that the front has .79 g's of cornering force and the rear has 0.96 g's. What does this really mean? Well number one, it will corner slightly slower and two we will get a push in the turn. Why a push? The front end lhas less available traction than the rear, so the front will let lose before the rear. Because of this understeer, the car will only corner at 0.79 g's vice the calculated 0.86 g's. Pretty interesting, huh? Are you still with me?

Example Three Revisited (Preload)

Did you get the answers?

Tire Location

Static Weight

Lateral Weight Transfer

Weight On Tire During Cornering

Traction Available

Left Front

12.5

-5.625

6.875

7.5

Right Front

2.5

+5.625

8.125

8

Left Rear

12.5

-5.625

6.875

7.5

Right Rear

2.5

+5.625

8.125

8

Total

30

N/A

30

31

What did we know?
Weight front-to-rear was 50/50
Left Bias was 10 lbs.
Load transfer was 11.25 lbs.

Static Weight on each right tire is 2.5 lbs.
Static Weight on each left tire is 12.5 lbs
Lateral Weight transfer on each right tire is +5.625 lbs.
Lateral Weight transfer from each left tire is -5.625 lbs.
Weight on each right tire during cornering is 8.125 lbs.
Weight on each left tire during cornering is 6.875 lbs.
Traction Available on each right tire is 8 lbs.
Traction Available on each left tire is 7.5 lbs.
Total Cornering Force = Traction/ Weight = 31 lbs. / 30 lbs. = 1.03 g's

So now you see how preloading can enhance cornering ability. Simply by preloading the left side by 10 lbs. we have gone from 0.83 g's to 1.03 g's. Now with a little playing around with the weights we could get the car absolutely perfectly balanced.

Example Five (Left Side Bias)

In Example Five we are combining Examples 2, 3 and 4 to see if the use of left side bias will improve the cornering of a front-heavy car and solve the understeer problem.

Tire Location

Static Weight

Lateral Weight Transfer

Weight On Tire During Cornering

Traction Available

Left Front

14

-6.75

7.25

8

Right Front

4

6.75

10.75

9

Left Rear

11

-4.5

6.5

7.5

Right Rear

1

4.5

5.5

7

Total

30

N/A

30

31.5

The Cornering Force = Traction / Weight = 31.5 / 30 = 1.05 g's when compared to Example Three's 1.07 is almost as good.

Did we fix the understeer problem?

Front cornering force = Traction / Weight = 17 / 18 = 1.06 g's

Rear cornering Force = Traction / Weight = 14.5 / 12 = 1.17 g's

In this case no. Our front cornering force is still less than our rear, so we didn't fix the problem.

Example Six (Wedge)

A good use for the wedge is correcting understeer. We accomplish this wedging by preloading the left front OR right rear spring, but remember when we add the 2 lbs. to the right rear the weight on the left front also increases by 2 lbs. with a reduction of equal weight on the right front and left rear.

In this last example we are going to see the effects of wedge. Keeping all other parameters the same as Example Five, we are going to add 2 lbs. of weight to the right rear tire.

Assume our 30 lb. car has the following after adjusting to neutral static condition:

Wedge Weight: 2 lbs.
Front End Weight: 60%
Left Side Weight Bias: 10 lbs
Load Transfer from Cornering: 11.25

Tire Location

Static Weight

Lateral Weight Transfer

Weight On Tire During Cornering

Traction Available

Left Front

16

-6.75

9.25

9.25

Right Front

2

6.75

8.75

8.75

Left Rear

9

-4.5

4.5

6

Right Rear

3

4.5

7.5

8

Total

30

0

30

32

Now work the formula for the total cornering force, then just for the front and rear.

Total Cornering Force = Tcf = 32 / 30 = 1.07 g's

Front Cornering Force = Fcf = 18 / 30 = 0.60 g's

Rear Cornering Force = Rcf = 14 / 30 = 0.47 g's

This is what I am going to do, just to see how much interest there is or isn't in these articles, you figure these out for yourself, email me your answers, stevestevens@verizonmail.com, and if there is enough interest (at least 10 different people) I will continue the articles.

In Summary

Let's sum up what we have discussed:

1) Assuming the tire sizes are equal at all four corners, the best cornering power is achieved when front-to-back weight distribution is equal.
2) Left side bias increases cornering power for oval tracks (also assuming a counter-clockwise direction)
3) Cars with only front end bias will tend to understeer while cornering.
4) Wedging can reduce understeer in the corners and produce faster cornering.
5) The best cornering power will be when all four tires have equal weight during cornering, generally speaking.

I hope you are enjoying these articles. Until next time, keep the shinny side up.