RogerFVila

Bicycle braking

As I am a complete Wiki newbie, please excuse any excessive stupidity on my part. Please also feel free to email me at rv@simulations.plus.com....

I was wondering whether the section on braking would benefit from some additional text and illustrations, both to illustrate the equations and to expand on their implications.

It might -AndrewDressel (talk) 21:28, 24 October 2012 (UTC)

The images that I would add are enclosed...

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These are nice, but I would recommend a couple of changes:

1. Place the head of the force arrow at the point of application of the force. Otherwise it appears that the forces Nr and Nf are acting at the hub of the front and rear wheels.

2. Use a thicker line to represent forces than that of dimensions

3. Label all force arrows -AndrewDressel (talk) 21:28, 24 October 2012 (UTC)

The text that I would add is that

Different ground surfaces have differing coefficients of friction.

When a ground surface is 'poor' and the coefficient of friction is low, both Fh and Bh are small. The weight of the rider is relatively evenly distributed and both brakes can contribute towards the reduction in speed.

When a ground surface is 'good', the brakes can give large horizontal forces Fh and Bh. When Fh and Bh are large, Mh is large. This increases Fv onto the front wheel and Fh becomes much larger than Bh, helping much more towards speed reduction. This means that it is essential that the front brake is in good working order. (Ultimately in good road conditions there is no force Bv at all and hence no Bh.)

What are "Fh", "Bh", and "Mh". I do not see them on any diagram. -AndrewDressel (talk) 21:28, 24 October 2012 (UTC)

In all cases both front and rear brakes should initially be applied at the same time, to maximise the time available for braking.

This contribution was initially prompted by a discussion with friends as to whether or not it is best to brake first with the rear brake - there is a long-standing theory to this effect which I believe to be incorrect.

That is fine, but to be included in Wikipedia, any detail must be backed up by a reliable external source. -AndrewDressel (talk) 21:28, 24 October 2012 (UTC)

Looking forward to your comments!

Roger Vila

Revised images 28/10/12:

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Braking according to ground conditions

Different ground surfaces have differing coefficients of friction. When a ground surface is 'poor' and the coefficient of friction is low, both Ff and Fr are small. The weight of the rider is relatively evenly distributed and both brakes can contribute towards the reduction in speed. When a ground surface is 'good', the brakes can give large horizontal forces Ff and Fr. When Ff and Fr are large, this creates a moment which increases Nf onto the front wheel and Ff becomes much larger than Fr, helping much more towards speed reduction. This means that it is essential that the front brake is in good working order. Ultimately in good road conditions there is no force Nr at all and hence no Fr. Any further braking initiates a stoppie. In all cases both front and rear brakes should initially be applied at the same time, to maximise the time available for braking (braking is acceleration to a lower or to a zero speed; the more time available the greater the acceleration).

RogerFVila (talk) 19:42, 28 October 2012 (UTC)

Here goes - a mock-up of my first Wiki entry

Braking according to ground conditions

When braking, the rider in motion is seeking to change the speed of the combined mass m of rider plus bike. This is a negative acceleration a in the line of travel. F=ma, the acceleration a causes a forward force F in mass m.

Add caption here

The braking a is from an initial speed u to a final speed v, over a length of time t. The equation u - v = at implies that the greater the acceleration the shorter the time needed to change speed. The stopping distance s is also shortest when acceleration a is at the highest possible value compatible with road conditions: the equation s = ut + 1/2 at^2 makes s low when a is high and t is low.

How much braking force to apply to each wheel depends both on ground conditions and on the balance of weight on the wheels at each instant in time. The total braking force cannot exceed the gravity force on the rider and bike times the coefficient of friction µ of the tyre on the ground. mgµ >= Ff+Fr or the rider will skid. A skid also occurs if the ratio of either Ff to Nf or of Fr to Nr is greater than µ, with the effects of the skid being less severe if it is a back wheel (Fr) skid.

When braking, the force ma in the line of travel, not being co-linear with f, tends to rotate m about f. This tendency to rotate, an overturning moment, is resisted by a moment from mg.

Add caption here

Taking moments about f at a point in time:

• When there is no braking, mass m is typically above the crankshaft, about 2/3 of the way back between f and r, with Nr greater than Nf. (1)
• In constant light braking, whether because an emergency stop is not required or because poor ground conditions prevent heavy braking, much weight still rests on the back wheel, meaning that Nr is still large and Fr can contribute towards a.
• As braking a increases, Nr and Fr decrease as ma increases because the moment ma h replaces the moment Nr L proportionately to the increase in a. At maximum constant a, clockwise and anti-clockwise moments are equal, at which point Nr=0. Any greater Ff initiates a stoppie.

  

  Add caption here

Other factors:

• Downhill it is much easier to topple over the front wheel because the incline moves the line of mg closer to f. To try to reduce this tendency the rider commonly 'stands back' on the pedals to try to keep the m as far back as possible.

  

  Add caption here

• When braking is increasing the centre of mass m tends to to move forward relative to F, both because the rider can move relative to the bike and because, if the bike has suspension on the front wheel, the front forks compress under load, changing the bike geometry. This puts extra N on the front wheel.
• At the end of a brake manoeuvre as the rider comes to a halt, the suspension decompresses and pushes the rider back. There is then extra N on the back wheel and less on the front wheel.

Values for µ vary greatly depending on a number of factors:

• The material that the ground or road surface is made of.
• Whether the ground is wet or dry.
• The smoothness or roughness of the ground.
• The firmness or looseness of the ground.
• The speed of the vehicle, with friction reducing above 30mph (50kph).
• Whether friction is rolling or sliding, with sliding friction at least 10% below peak rolling friction (2).

In response to your feedback

Images should be uploaded to Wikimedia Commons so they can be used on any language version of Wikipedia.

Charles (talk) 22:04, 25 October 2012 (UTC)

 

	DRY		DRY		WET		WET
ROAD SURFACE	below	30 mph	above	30 mph	below	30 mph	above	30 mph
PORTLAND CEMENT	From	To	From	To	From	To	From	To
New, Sharp	0.80	1.20	0.70	1.00	0.50	0.80	0.40	0.75
Travelled	0.60	0.80	0.60	0.75	0.45	0.70	0.45	0.65
Traffic polished	0.55	0.75	0.50	0.65	0.45	0.65	0.45	0.80
ASPHALT or TAR
New, Sharp	0.80	1.20	0.65	1.00	0.50	0.80	0.45	0.75
Travelled	0.60	0.80	0.55	0.70	0.45	0.70	0.40	0.65
Traffic Polished	0.55	0.75	0.45	0.65	0.45	0.65	0.40	0.60
Excess Tar	0.50	0.60	0.35	0.60	0.30	0.60	0.25	0.55
GRAVEL Packed, Oiled	0.55	0.85	0.50	0.80	0.40	0.80	0.40	0.60
Loose	0.40	0.70	0.40	0.70	0.45	0.75	0.45	0.75
CINDERS Packed	0.50	0.70	0.50	0.70	0.65	0.75	0.45	0.75
ROCK Crushed	0.55	0.75	0.55	0.75	0.55	0.75	0.55	0.75
ICE Smooth	0.10	0.25	0.07	0.20	0.05	0.10	0.05	0.10
SNOW Packed	0.30	0.55	0.35	0.55	0.30	0.60	0.30	0.60
Loose	0.10	0.25	0.10	0.20	0.30	0.60	0.30	0.60
FOR PASSENGER CAR TYRES				Sliding	Friction		Peak	Friction
Meadow, dry, firm, short grass					0.35			0.45
Off-road shoulder, firm dry					0.35			0.45
Soil, loose, moist, tyres sink 50mm					0.60			0.70
Asphalt, wet leaves					0.60			0.70
				Sliding	Friction		Peak	Friction
				From	To		From	To
Gravel, some grass				0.35	0.40		0.40	0.60
Grass meadow, wet				0.15	0.20		0.20	0.25
SLIDING FRICTION ONLY
Gravel, loose to packed				0.40	0.70
Mud on wet pavement				0.20	0.30
Diesel fuel on wet asphalt				0.25	0.30
Diesel fuel on wet, polished asphalt				0.05	0.12