Fishtailing a pickup truck

Question: A magistrate and a police officer both testify that it is impossible for a pickup truck to fishtail on wet roadways. I thought that everyone knew that pickups are known to fishtail on wet or slippery roads. How can I prove the principle of friction or lack of it. I know that the more weight the more friction is applied.

I know that coefficient of friction is the ratio of the weight of the truck moving along the pavement. Pickup trucks have very little weight in the rear so the contact in rain is not as much as in dry weather. The police officer and the magistrate (judge wanna be) stated that it was physically impossible to fishtail a pickup truck. Rear wheel drive vehicles do fishtail in the rain. Front wheel drive cars have more weight over the drive wheels and therefore have more friction. How can I prove this to the cops? My son got a ticket for fishtailing around a corner when it was slippery out. He had borrowed a rear wheel pickup truck and was not familiar with how it drove.

Answer:

Lets think of the driving force of the wheels.

There is no doubt that if the truck is going in a straight line it will carry on in that line even if it brakes as long as the brakes on both sides of the truck all act at the same time and with the same force. It may skid but it will skid in a straight line in the direction its was going before.

However when it corners it matters if the drive is on the rear or on the front!

I have worked out a mathematical proof here that shows that in fact when the pickup is cornering there is a greater tendency to fishtail if the truck has a front wheel drive.

It will occur with rear wheel drive as well but the turning effect is not so great.

With front wheel drive the angled front wheels pulls the lightweight rear after them and this will give it a tendency to swing sideways. You could think of the driving force producing an acceleration which makes the back of the truck behave like a pendulum in a gravitational field. (All getting a bit involved).

I am very happy to send this proof as an email attachment if you would like. Let me know.

Not sure if this will help your son or not.

The loading over the wheels is important as you say but since wet roads have such a low friction I don't think that this is quite so important as the effects that I have just described.

Pickup truck first set of diagrams

Some notes about these first two diagrams:
Q – angle of lock (turning) of the front wheels
G =- centre of gravity of the pickup. (Red disc) Notice that it is nearer the front because of the heavier cabin and engine
P – centre point of front axle
Q – centre point of rear axle
Blue disc – drive point
d - PG

Pickup truck diagrams 2

         Torque = T_f = Fdsinθ        Torque = T_r = Fdsinθcosθ

Therefore: Tr/T_f = cosθ     but this is less than 1 for 0<θ<90
Therefore T_f > T_r
This means that fishtailing will be greatest with a front wheel drive vehicle