Physics question

[corksil]

Hey here's an interesting question. Not sure if anyone can answer it or not, but here we go.

Approximately how much downward force is applied to the surface of the tarmac through the front tire contact patch when braking hard in a straight line?

I'm sure there is a formula for calculating this and to most people it probably seems like trivial information but I'd still like to know.

Suppose a bike weighs 375lb, with a 150lb rider -- that would be 525lb riding on the front and rear tire contact patch if the bike was travelling in a straight line. If the rider was accelerating, more of the weight would be on the rear tire. If the rider was braking very hard with the front brake, all of the weight would shift onto the front tire and the rear would come up off the ground. That would mean 525lb on the front tire contact patch alone, which would be roughly 18in^3 or 18sq inches.

However, that still wouldn't account for the fact that the bike was in motion -- and actively slowing down (from 80mph to 25mph for example) which would exponentially increase the amount of downward force applied to the tarmac.

Is anyone handy with physics formulas? As with everything there are numerous variables involved like tire pressure which would affect the size of the front tire contact patch area, bike and rider weight, and speed the bike was travelling and decelerating from/to etc..

Anyone?

[corksil]

For the sake of discussion, let's assume that the bike had sticky race tires and the coefficient of friction was high enough between tire/track that the rider could routinely brake hard enough before a corner entry to lift the rear wheel off the surface of the track while travelling in a straight line before entering the corner and turning the bike.

[Triple Jim]

The downward force cannot exceed the combined weight of the motorcycle and the rider. Braking applies force to the road in the direction of the motorcycle's travel. Having a high coefficient of friction makes it possible to apply very high forces, but they will still be in the direction of travel.

As a check, the force applied by the motorcycle downward on the road must equal the force the road applied upward to the motorcycle, but the directions are opposite. If this force were to be greater than the weight of the motorcycle and rider, the motorcycle would have to accelerate upward, but if this were to happen, the tire would lose contact with the road!

[Flying]

https://theses.lib.vt.edu/theses/ava.../CHAP3_DOC.pdf

You're asking for a dynamic number that is suited for excel/matlab. A rough limiting number will be (friction coefficient) x (ground reaction force).

On ideal tires and dry asphalt, your downforce won't exceed about 0.8 x combined weight of rider and bike. This is a very very rough number that changes w/ the changes in suspension geometry and a whole load of other stuff.

[Motofool]

Originally Posted by corksil

However, that still wouldn't account for the fact that the bike was in motion -- and actively slowing down (from 80mph to 25mph for example) which would exponentially increase the amount of downward force applied to the tarmac.

The change of speed is irrelevant for the force you are trying to find out: the time in which the change happens is what is directly (rather than exponentially) proportional to the increment of that force.
Deceleration is that rate of change respect to time and it is translated into force when combined with the total mass of bike, fluids and rider.

Originally Posted by corksil

......... Is anyone handy with physics formulas? As with everything there are numerous variables involved like tire pressure which would affect the size of the front tire contact patch area, bike and rider weight, and speed the bike was travelling and decelerating from/to etc..

Anyone?

Please, study the content of these links:

http://www.dinamoto.it/dinamoto/index_eng.html

https://en.wikipedia.org/wiki/Equations_of_motion

In order to simplify the problem that you are questioning, forget all the parts of the bike, suspension, etc.
You have a spatially located center of mass, two points of support against the tarmac and the vectors related to gravity and deceleration.

Tire pressure has only a small influence on the rate of deformation of the front contact patch, and subsequent gripping, as the area can only grow a little more than what it is when there is no braking.

[Triple Jim]

Originally Posted by Flying

On ideal tires and dry asphalt, your downforce won't exceed about 0.8 x combined weight of rider and bike.

I think you mean that the stopping force won't exceed about 0.8 times the combined vehicle+rider weight. If the coefficient of friction is 0.8, then the stopping force would be

(vehicle weight)(0.8)

so if the combined weight is 500 lbs, in this case the maximum stopping force would be

500lbs x 0.8 = 400lbs, applied horizontally to the road, not downward.

The downforce is simply the combined vehicle and rider weight.

[Snake]

Wow this is way over my head! I love science though so I find it very interesting.

[SLOWn60]

Damn it Jim! I'm a Doctor, not a bricklayer!!!

[corksil]

Perhaps I was mistaken but I was under the impression that the downforce applied to the track would actually exceed the weight of the vehicle/driver.

Now that I think about it -- it seems understandable that the total downforce of the vehicle would not exceed the weight of that vehicle. Gravity only works in one direction.

I understand that equal upward force would be applied in proportion to downward force otherwise the earth would move or the road would collapse.

Anyways, interesting stuff. Thanks for the replies. I'll come back to this thread.

[Ducati999]

Please correct me if im wrong but there would have to be more weight pushed down into the track than the weight of the bike and rider. The energy from the forward momentum would be focused down as the vehicle decelerates and therefore would be over 1G. Bikes can accelerate at approx. .8G but they stop faster than they go (Some models at least).

They claim 1.6G in Moto GP. I know they are not "regular" bikes but I think the same principals apply. I tried to copy the link but it would not work. Just Google "Max stopping G forces on a motorcycle.

1.6G would = 1.6X vehicle weight-----now I am not sure how much of that is directly applied to the track.

[Triple Jim]

Originally Posted by Ducati999

Please correct me if im wrong but there would have to be more weight pushed down into the track than the weight of the bike and rider.

Maybe there's confusion about what you mean by "pushed down into the track". The force straight down can't exceed the bike+rider weight, but the total force of weight plus braking will exceed the weight.

In your example of 1.6 for the coefficient of friction, if you assume the combined weight is 500 lbs, the motorcycle will apply 500 lbs directly downward, and 1.6x500=800 lbs in the forward direction. These forces can be combined into a singe vector with

Sum of forces = √ (500² + 800²) = 943
Angle = arctan (500/800) = 32 degrees

So the result can be thought of as a single force of 943 lbs, applied to the road at an angle of 32 degrees down from the forward (horizontal) direction.

[Brother Michigan]

I really wanted to chip in on this thread, but Jim has nailed.

[adouglas]

Since all the science-y answers have already been given, I'll just leave this here....

How much force?

All of it.

[SLOWn60]

Curious: how can you have a coefficient of friction greater than 1? Isn't 1=100%? If there is100% friction; there is no slip/maximum grip which is maximum force which would equal and be a product of the size of contact patch and coefficient of friction between the two materials (in this case: rubber and road surface).

[Brother Michigan]

A coefficient greater than one simply means that the force require to cause slipping between the surfaces is greater than the force "creating" that friction (in this case, the weight of the bike and rider). It's not an unusual thing to come across.

[corksil]

Originally Posted by Triple Jim

The downward force cannot exceed the combined weight of the motorcycle and the rider. Braking applies force to the road in the direction of the motorcycle's travel. Having a high coefficient of friction makes it possible to apply very high forces, but they will still be in the direction of travel.

As a check, the force applied by the motorcycle downward on the road must equal the force the road applied upward to the motorcycle, but the directions are opposite. If this force were to be greater than the weight of the motorcycle and rider, the motorcycle would have to accelerate upward, but if this were to happen, the tire would lose contact with the road!

After coming back to this thread -- all of it makes perfect sense. Some of it required a bit of thought but it's all very clear now.

What I didn't seem to understand in the initial post is law of motion etc.. every action/equal opposite reaction. Gravity is a constant, and the angle of force would change dependent on rate and direction of deceleration.

For some reason I was thinking that during maximum braking, a vehicle would actually exert more than it's own weight in downward force against the surface on which it was travelling. After the matlab examples, I see that is absolutely not the case.

The reason I made this thread is to gain a better understanding of roadway and track construction. All race tracks show their first surface imperfections on the most common entry lines into turns. Now I understand that it is because each and every vehicle braking before entering the turn (if braking to the maximum capability of the vehicle) is exerting close to it's own weight on the surface of the track in an area as small as the front tire contact patch.

[Triple Jim]

Not to mention the large braking force on the track in the direction of travel, which is probably worse than the down force, since it tends to tear the track surface.

["A"]

The contact patch of the tire could constantly changing, difficult to determine a specific number for the forces acting on all aspects of the bike slowing down... negating air resistance, possibility of lift effects from rider's aerodynamics at particular speed of travel, among other forces that are constantly acting on the bike/rider as a whole..

Personally, in real world operations, I use the brake as little as possible; they only slow you down and limit your options for escape route.

[dcj13]

Friction and traction are not the same thing.

[subxero]

.... a duck.

[Brother Michigan]

Originally Posted by subxero

.... a duck.

So... if the bike and rider weigh the same as a duck...?

[Triple Jim]

Yup, you have a witch!

[Motofool]

Originally Posted by dcj13

Friction and traction are not the same thing.

[corksil]

Originally Posted by Triple Jim

Not to mention the large braking force on the track in the direction of travel, which is probably worse than the down force, since it tends to tear the track surface.

Yeah this is exactly what I misunderstood. Deceleration is a vector and it's more along the horizontal axis than the vertical. I was thinking that heavy braking would cause more downward force than horizontal force. Horizontal force is what tears the track or road surface, which leaves potholes for smaller vehicles of lesser weight.

Originally Posted by Motofool

Friction is a fraction of available traction.

[Motofool]

Originally Posted by corksil

........Friction is a fraction of available traction.

What in your opinion are the rest of the fractions that complete available traction?

[SLOWn60]

Originally Posted by Motofool

What in your opinion are the rest of the fractions that complete available traction?

Fear!

[Brother Michigan]

Friction is the only force providing traction. Without friction, the tire would simply slide across the pavement.

[choneofakind]

Let's also not forget that the convention for vehicle mathz says that "traction" is the force used to make the vehicle move; i.e. Tractive forces are the forces that propel the vehicle. "Traction" does not refer to cornering or braking.

For example, when you calculate a vehicle's maximum possible rate of acceleration, you look at two cases; case one assumes the vehicle is power limited and traction is never an issue, while case two assumes the vehicle is traction limited and power is never an issue. Which ever rate of acceleration is greater is the max theoretical rate of acceleration.

Seriously, there's some great books written on car physics. I know that we're talking motorcycles instead of cars, but many of the basic concepts are the same. Some of y'all need some help... Try Fundamentals of Vehicle Dynamics by Thomas D Gillespie. It's from the 90's and the example problems are horribly dated, but the concepts never change and it's written out so that it's very easy to follow.




To answer Hernan's question: the forces at the tires are generally broken into 3 types of forces. Tractive forces, cornering forces, and braking forces. That's it. The sum of any of these can be equal to or less than the maximum possible friction, which is F=mu*N, where N is the normal force on that tire contact patch and mu is the coefficient of friction between the tire and that road surface. Please note that N changes due to aero effects, as well as weight transfer during cornering, braking, acceleration, etc. This is easily calculated for steady state conditions, but is much more difficult during transitions.

[Flying]

[choneofakind]

Milliken is the man. He's really the go-to expert whenever vehicle dynamics are in question.

However, have you read through his books??? They're about racecar dynamics and F1 and very high level, specific cases. For the basic needs of the nerds here, Gillespie is more than sufficient for answering questions and grasping concepts. Milliken is an amazing 2nd step once you've got the basics.

The brutally detailed world of motor sport engineering is not needed for the basic conceptual work here. Gillespie's book is so well laid out and easy to follow. We have people here who don't even know what a free body diagram is or why it is needed.

[corksil]

If anyone would like to read those books, they can contact me.

Haven't had the time to read them yet but I've got 'fundamentals of vehicle dynamics' and 'race car dynamics' on the kindle now. Along with a whole bunch two stroke engine theory books which are quite interesting.

Anyways this thread has been very informative and interesting. I spend a lot of time behind the wheel of a f350 crew cab with a fully loaded bumper pull trailer attached to it. I weighed a typical load once and I'm in the ballpark of 20k pounds on eight tires when driving that rig.

The nice thing about understanding physics is that the knowledge is directly transferable to all other aspects of life. Also in the process of buying another motorcycle, but I don't want to jinx it so I won't spill the beans. I'll make a thread once I have it in my custody. Something truly wild.

Thanks guys. I'm gonna re-read all of this again to make sure it all clicks.

[Yakaru]

Heh, looks like the forum has this covered.

This kind of math is a huge part of my career as a game developer -- though my aim is feel over accuracy, so I frequently can approximate these things (though that comes up more when you start getting into calculus/PDEs, basic algebraic physics and trig is usually pretty close to reality in a reality-oriented simulation.

[tfkrocks]

Originally Posted by Triple Jim

Yup, you have a witch!

A witch! Burn her!

[choneofakind]

Corky, I think you'll like those books. Great way to get the basics and lots of application. Also do some reading into Bosch and their work with stability control/traction control. It's an interesting topic.

[corksil]

^ Any recommendations?

[Flying]

Ooooh, books! Here are a few to look out for:

Carroll Smith's Tune to Win - A good primer on the goals behind race car design/tuning. Book is definitely showing its age at this point and the author tends to ramble, but you get a good scratch at suspension and aero tuning. Everything is about the tires.

Gillspie's Fund. of Vehicle Dynamics - More focus on engineering vehicles in general, serves as a decent textbook, not quite the skin-tearing focused book that Doug Milliken's book is. Covers tires and vibrations well.

Milliken Racecar Vehicle Dynamics - Really, the only the first two chapters (tires) can probably suffice for most people. This is a dense book with a lot of fundamental info on aero and suspension physics, but it has remained the bible of anyone taking vehicle dynamics seriously since its first publication. You get to learn about cool stuff like how the traction circle is actually an ellipse, non-linear tire loading, and other spooky voodoo that affects the everyday motorcyclist without them knowing.

The Bosch Automotive Handbook - Quick reference on any and all auto technology and refinements made to systems.

John Heywood Internal Combustion Engine Fundamentals - Like Milliken, bare-bone physics surrounding engine performance. It will open one's eyes.

Ricardo, The High Speed Internal Combustion Engine - More of an interest book. The premise behind reading this is to learn that nearly everything has already been tried before to some degree. It was written in the late 20s-early 30s.

Gillespie and Milliken will give you the most value and will most definitely dispel a lot of the bullcrap that is thrown about in conversation and online.

[corksil]

Yay, new stuff to read!

Spoiler for topic:

If anyone wants to read these books plz pm me.

[allanoue]

Originally Posted by tfkrocks

A witch! Burn her!

Link to original page on YouTube.