# 1 essential law of physics every slot-racer should master

There is one  law of physics every slot-racer should master. Screw it up and you will be spending much of your time putting your car back on the track. But when you get it right, you can race for the win.

So what is this magical formula that separates the pro’s from the nono’s? How can I use it to my advantage? Don’t worry, you’ve been using it all your life and it is one of the simplest formulas around:
Coulomb’s law of friction.

It is friction that allows the electric motor to propel the slot car forward. It also is friction that allows the car to accelerate through a corner or brake. In order to win, you need to be as close to the limit of friction as possible. If you’re not on the limit, you’re too slow. If you overdo it, you’ll skid off the track…

## So, how does it work?

Coulomb’s law of friction states that the maximum available friction (also known as traction) between two bodies (the tire and the road) is the product of a friction coefficient and the normal force exerted between the bodies. In symbols that is:

Ft = μ * Fn         [1]

Here Ft is the traction, μ is the friction coefficient and Fn is the normal force between the tires and the road. This normal force is the result of gravity acting on the slot car. It can be calculated by multiplying the mass of the slot car with the gravity constant (9.81)

Fn = m * G = m * 9.81           [2]

## What happens if you go too far?

To understand what happens if you exceed the traction, we need to discriminate between two types of friction:

• Static friction: There is no speed difference between the contacting bodies (rolling tire)
• Dynamic friction: There is a speed difference between the contacting bodies (spinning or skidding tire)

Experiments have shown that the friction coefficient of rubber with concrete (a tire on a concrete road) is about 1.0 for static friction, but it is reduced to 0.6 to 0.85 in case of dynamic friction. This means effectively that a spinning tire can not produce as much propulsive force as a rolling tire. Once a tire spins or skids, you will have to reduce the applied force (by releasing the throttle or brake) below the maximum dynamic friction in order to recover from spinning/skidding.

This is the complete game of slot-racing in a nutshell: Stay as close to the limit of static friction as possible, but NOT go over it!

## No how can we use this?

Let’s assume that more friction is better. For example, the traction is equal to the maximum accelerating (or braking) force the tires can apply to the road. As Newton figured out, the acceleration is calculated by dividing the propelling force by the mass. Which yields in this case:

a = Ft/m        [3]

Where Ft is the traction and ‘a’ is the maximum acceleration. From the first formula it can be concluded that you can increase the maximum friction by either increasing the friction coefficient or the normal force.

The friction coefficient is the result of the properties of the tires and track surface and will be a value between 0 and 1. The lower the value, the more slippery the track will be. As the track is a given in most cases, one is left with the possibility to try different tire materials. Another major factor that messes up the amount of friction is contamination of the track and/or the tires. Especially for carpet racers this is an issue. It is therefore advisable to regularly clean your track and tires.

When we leave the tires for what they are, there is still the option to increase the normal force. This could be done as per formula 2 by increasing the mass of the vehicle. So just add a few blocks of lead to the car and make it faster right? Wrong! If we look at the third formula, increasing the mass reduces the acceleration. If we substitute formal 1 in formula 3 we get:

a = (μ * m * G) / m    => a = μ * G    [4]

What I did here is cross out the mass, since it exists on both sides of the equation, which basically means we are multiplying everything else by 1. So the equation that remains does not contain the vehicle mass any more. That means the vehicle mass has no effect on the maximum acceleration from a friction point of view.

So if we can’t add weight, what can we do?

There are two options:

• Create downforce
• Change the weight distribution

### Creating downforce

The most common way to increase the normal force and thus the friction is by adding magnets to the car. These magnets pull the car down to the track and therefore increase the available friction. Stronger magnets mean more downforce and more friction. This however does have the drawback that the ride characteristics of the slot car will arguably not be realistic enough.

## Change the weight distribution

The front-rear weight distribution defines how much of the total vehicle weight is leaning on the front wheels and how much on the rear wheels. Let’s assume 60% of the weight is at the rear wheels and our slot car weighs exactly 100 grams. Using equation 2 tells us that the normal force at the combined rear wheels is 0.59 Newton (N) (Fn = m * G * 0.6) and at the front wheels it is 0.39 N (Fn = m * G * 0.4). So by moving the weight to the back wheels, we can actually increase the maximum propulsive force!!!

Wrapup

So recapturing what we have discussed:

1. Keep your track as clean as possible, dust is disastrous for your friction coefficient
2. Keep your tires clean. When driving your tires will pick up dust and particles, so make sure you run your tires along a piece of clear tape regularly