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View Full Version : What Makes A Safe Driver? Part 3 of 4


Saber
December 30th, 2007, 10:53 PM
Part 3 - Coefficient Of Friction


The what of Friction???

In the easiest of definitions is the resistance between two objects and everything has it. Rub your hands together, what happens? You generate heat, the harder you press them together the quicker you get that heat. By pressing you hands together harder you’re increasing the coefficient of friction and are generating heat quicker.

Every roadway has a coefficient of friction value known as mu (u) which is a level friction value. Now (u) is not the right symbol but it’s the closest I can come up with without a formula editor and that code probably wouldn’t post correctly.

All surfaces have a (u) value. Asphalt, concrete, grass, mud, gravel, dirt and on and on. When a vehicle slides across several surfaces like asphalt to grass back across asphalt it will have three different friction values during its skid. Every surface has a different (u) value as well. It can vary depending on many aspects from dry to wet, hot to cold, snow to ice and so on.

The basic speed formula is S = square root of (30)(d)(f) or Speed is equal to the square root of 30 times distance times friction. If a vehicle comes to a stop and the distance it took to stop and the surface friction value is know then you can determine how fast that vehicle was traveling with the above formula.

In Part 2 we reiterated that Newton tells us that a body moves with constant velocity unless acted upon by an external force. So why does my vehicle come to a stop if I let off the gas? Well, that is where gravity comes in. The friction (u) of a roadway is given a value and the value is the percentage of gravity in so many terms. The average coefficient of friction for a roadway is around (.75). That value is the percentage of gravity that is acting upon an object moving across it. The lower the friction values the less resistance and the longer it takes to stop and vise versa. A high friction value and the quicker you can stop. Roadway friction can get quite complicated with the elevation and super elevation of the roadway but for the purpose of this article we are on a level surface.

The easiest way to translate the different friction values is to compare a dry road to a snow covered one. A snow covered or even ice covered road has a friction value of around .10 to .15 and you’re going to slide a long way on that. Why? Because with the lower friction value it takes much longer for the kinetic energy of your vehicle to be dissipated and come to a stop. Newton’s Second Law, the faster you go, the more energy you have, the more you have the more you have to loose, the more you have the loose, the longer it takes, the longer it takes the further you will travel before it is gone.

Ok, so why not just make the roadway friction really high and that will drop our deceleration distances and give us more of a chance when are not paying attention right?

Well, yes and no. That question brings us into Newton’s Third and final Law. ~ To every action there is an equal and opposite reaction. This is defined as Impulse. (F1) = (-F2)

Now impulse is widely used in Vector Analysis and Occupant Kinematics. When two vehicles crash into one another, a speed can be determined by the impact and separation angles of those two vehicles if the approach and departure angles are known and how far they traveled at separation upon post impact.

But for the purpose of this section we are interested in Occupant Kinematics. The reason roadways are not given a high friction value is because of this third law. There are three impacts in every collision. The vehicle hitting something, the occupant then hitting something inside the vehicle and then finally the internal organs of the occupant hitting the internal walls of body. Remember, once in motion you will remain in motion until you are stopped by something, this is why there are seatbelt laws. An unrestrained person in a vehicle will keep traveling until it is stopped by something E.G. the dashboard or windshield. Seatbelts remove a great deal of that second impact by keeping you in your seat. This is known as the Delta V or Delta Velocity. It is the sudden and rapid change in your velocity during a collision. I will go into much more detail of this in Part 4 and the effects of the Principle Direction of Force which is also part of Newton’s Third Law.

*break due to size*

Saber
December 30th, 2007, 10:55 PM
*break due to size*

Back to roadway friction, if roadway frictions are too high say around 1.5 for example then yes you would be able to stop very very quickly but that results in an externally high Delta V to the occupants even if they don’t hit anything. There isn’t much difference in hitting another vehicle verse stopping very rapidly due to roadway friction; Delta V does not care how it is generated.

Back to our deer; we have already traveled 362.83 feet and we are getting on our brakes. How long will it take us to stop? Let’s say we are on an average friction value of (.75) and we were going 55 mph remember? The distance it would take us to stop is 134.44 feet. D = S^ \ (30)(f) or Distance is equal to Speed squared divided by (30) times the friction of the roadway. Now you keep seeing 30 a lot and it is a mathematical constant calculated from the work-energy theorem (your just going to have to trust me on that).

So from the point we took your eyes off the road to coming to a complete stop you traveled a total distance of 497.27 feet. Did we hit it? Well that depends on how far away it was when we saw it. Could we have swerved to avoid it? That depends on distance as well and there is a formula to determine that as well, D = (.366)(S)( SQ RT of DL\fS) ~ Distance from the object needed is equal to (.366) times your speed times the square root of the lateral distance divided by the lateral friction value of the roadway.

The point being is this, your vehicle is traveling a lot further than you realize as you are going down the road. How long it takes to stop is effected greatly on the road and the driving conditions not the performance of your vehicle. The 2003 Correvett has a reported lateral friction value of 1.5 G’s. That’s sounds cool and all but you will not find a roadway anywhere in this country with a curve that has a critical speed value of 1.5 G’s except at a race track. Will it take a curve faster than a VW Jetta? Absolutely, but it will only take that curve as fast as the critical speed of that curve, regardless of what the car is rated at. Now I am not going to give you the critical speed formula to determine the speed you can take a curve if you know its radius, because I guarantee someone will go test it and crash themselves.

Part 4 will discuss the elements and dynamics of a crash. It will bring all of the information from the past 3 parts together and explain the dynamics and forces involved in a crash. Hopefully some of this information will make some of us better drivers; I know it did me when I completed reconstruction school.