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# Bicycle Safety - The Math of Speed

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Advocacy & Safety Cyclists should expect and demand safe accommodation on every public road, just as do all other users. Discuss your bicycle advocacy and safety concerns here.

# Bicycle Safety - The Math of Speed

09-23-13, 02:29 PM
#76
GreatWhiteShark
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I just read this once, and I initially disagree, because driving faster means you would encounter more automobiles. Right? I cannot understand how it would be the same amount of automobiles, no matter how fast traveling.

I know for automobiles the law enforcement claims the faster someone drives the more dangerous it is to the people in the automobile, because it shrinks the reaction time the driver has. Why would this not also apply to any form of moving on a roadway? Now, I have to say, I only stopped speeding, when I drove, because of the cost of gas, because I strongly disagree, because there is another factor never considered and that is how used to and skilled the driver is at the speed.

Maybe, it has to do with the fact that I ride most in rural area and ride in mix environments.

With all that being said, I could not agree more with you, about driving besides automobiles makes for biggest danger!

Originally Posted by DrkAngel
Faster is Safer!
My Sister-in-Law just can't understand, why I feel that going faster, on a bicycle, is safer. "30 mph!" ... "You're gonna kill your self!". ...

I feel it necessary to prove that, up to the speed of surrounding traffic, faster is safer. Let me try a mathematical approach.

First, let me qualify;
1. My riding is in an urban area and 95% of the streets-roads are 30 mph limit.
2. I ride on the right side of the road, going "with traffic", as is the legal method.

For ease of math - Let's figure a 10 mile trip, w/traffic @ 10 cars per minute.

30 mph traffic:

At 10 mph -
60min x 10cars - 1/3 (for 1/3 speed of cars) = 400 cars passing you at 20mph.

At 15 mph -
40min x 10cars - 1/2 (for 1/2 speed of cars) = 200 cars passing you at 15mph.

At 20 mph -
30min x 10cars - 2/3 (for 2/3 speed of cars) = 100 cars passing you at 10mph.
AND, cars have twice the time to notice, and avoid, you! (vs 10 mph).

At 25 mph -
24min x 10 cars -5/6 (for 5/6 speed of cars) = 40 cars passing you at 5mph.

At 30 mph -
20min x 10cars - 3/3 (for 3/3 speed of cars) = 0 cars passing you!

(Math is simplified - but "sound")

When you consider that many bike accidents are directly related to passing cars, especially in a "road" environment, then 20 mph would be (4 times safer than 10 mph) x (2 - twice the time the, approaching, driver has to see biker) = 8 times safer @ 20 mph, compared to 10 mph!

Most impressive is that each speed increase of 5 mph reduces the volume of passing traffic by 50%!

A__hole factor! Everyone might agree that, possibly, 1 in 100 motorists are AHs toward bicyclists, (Conservative Estimate!), Going 10 mph you'll get passed by 4, only 1 @ 20 mph and at 30 mph you might never encounter 1.
09-23-13, 03:29 PM
#77
Keith99
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Originally Posted by skye
OP is making a common but utterly erroneous assumption. Most crashes do not occur as the result of unsafe overtakes; most collisions occur because of motorist inattentiveness (or cyclist error) at intersections, where the protective reduced speed differential favored by the OP can actually become an increased speed differential with deleterious consequences.

In any event, physics is the wrong discipline with which to solve automobile-bicycle safety problems, which are essentially social and psychological in nature.
I was never that fast a rider. But I was more than fast enough to see the problems with more speed than drivers expect at intersections, or for that matter driveways.

My biggest single problem was potential right hooks or pass and slow for the turn situations. Sometimes a total jerk driver, but often just one bad assumption, that I was going the speed they were used to seeing riders going. IF my speed was that of the more common slow rider on a near beach cruiser they would have passed me, slowed and turned without any interaction, as it was right hook or slam on the brakes. Similar for left crosses.
11-06-13, 07:26 AM
#78
DrkAngel
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One of the best, simplest, cheapest safety devices is a strobe headlight.
Less than \$10 can get you a 200-300lm+ LED light w/ wide to zoom focus ability.

\$6.89
Using rechargeable 18650 Li-ion battery recommended

Lighted ring shows side traffic my location.
Red preferred unless I put tape over the rings light from my point of view, too bright!

At dusk I go high with a slight zoom.
Often I go wide, but Velcro a zoomed 2nd light on my helmet, scanning further ahead for potholes or beaming potential cross-traffic.

I run wide angle strobe during daylight, it gets me seen-respected.
Door kickers see a flashing light directly at RR mirror level.
Cross traffic gives a 2nd look-thought.

If I accidentally forget to light-on, I quickly notice by how traffic treats me!

I also mounted a red flasher on the back of my helmet!

Mirror is a bar end type, mounted on visor.
Attached Images
Helmet.JPG (70.4 KB, 14 views)

Last edited by DrkAngel; 11-06-13 at 04:06 PM.
11-06-13, 10:19 AM
#79
spare_wheel
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Originally Posted by turbo1889
Wipe out at 20-mph instead of 10-mph and you hit with four times the kinetic energy, wipe out at 30-mph instead of 10-mph and you hit with nine times the kinetic energy.
Except that most cyclists do not run into brick walls. Observing a few Cat 4/5 crits is a very good antidote to safety-nanny false-concern.
11-06-13, 10:27 AM
#80
spare_wheel
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Originally Posted by DrkAngel
I ride on the right side of the road, going "with traffic", as is the legal method.
I want to add that riding at 25-30 on a 30 mph road on the right side is a very bad idea. Get thee into the lane, speed racer. Preferably on the left side (lane splitting has saved my arse on multiple occasions).

Also, I highly recommend this book:
https://www.powells.com/biblio/1-9780762743162-1

Last edited by spare_wheel; 11-06-13 at 10:59 AM.
11-06-13, 10:44 AM
#81
Cyclosaurus
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11-06-13, 02:30 PM
#82
Bacciagalupe
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I'm afraid there is a major flaw in the premise. To wit:

In a dense urban environment, mid-block collisions are rare. Most collisions happen at intersections.

If you get hit at a 90º angle, the speed at which you are traveling isn't likely to make a difference. (The speed of the motor vehicle is more important.)

If you get run over, it doesn't matter if you were traveling at 10 or 30mph. What will harm you is the weight of the car, crushing you.

There is a small chance that a motor vehicle is less likely to notice a bicycle traveling at 30mph compared to one that is traveling at 10mph. It's also possible that traveling faster will mean you avoid a potential collision. I for one view it as a wash.

So, I for one don't think your absolute speed matters. What matters is knowing that intersections are dangerous; remembering that drivers do not always expect you; and being able to control your bicycle.
11-06-13, 02:46 PM
#83
Keith99
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Originally Posted by Looigi
Are you suggesting that study and practice doesn't improve performance?
No, he is saying practicing in a nice controlled environment where you expect to stop is hugely different from an emergency stop without warning. That even held for cars before recent improvements to braking systems.

A typical rider gains far more by just making sure their hands are on the brake levers and their eyes looking forward going into an intersection than they will by parking lot practice.
11-06-13, 02:58 PM
#84
Keith99
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Originally Posted by Bacciagalupe
I'm afraid there is a major flaw in the premise. To wit:

In a dense urban environment, mid-block collisions are rare. Most collisions happen at intersections.

If you get hit at a 90º angle, the speed at which you are traveling isn't likely to make a difference. (The speed of the motor vehicle is more important.)

If you get run over, it doesn't matter if you were traveling at 10 or 30mph. What will harm you is the weight of the car, crushing you.

There is a small chance that a motor vehicle is less likely to notice a bicycle traveling at 30mph compared to one that is traveling at 10mph. It's also possible that traveling faster will mean you avoid a potential collision. I for one view it as a wash.

So, I for one don't think your absolute speed matters. What matters is knowing that intersections are dangerous; remembering that drivers do not always expect you; and being able to control your bicycle.
Going at a slower speed (10 vrs 30) in say a 45 zone makes it much more likely that a car will not see you in time to react when it comes to overtaking cars. Unless one is hugging the curb or staying in the door zone I don't think there is a significant difference in visibility fro crossing drivers.

But I have found a significant difference in right hooks, if going faster drivers often incorrectly think they have time to pass and turn right when they do not. Or for that matter drivers coming out of driveways think they have time to turn and merge when they do not.
11-06-13, 03:03 PM
#85
spare_wheel
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Originally Posted by Keith99
No, he is saying practicing in a nice controlled environment where you expect to stop is hugely different from an emergency stop without warning. That even held for cars before recent improvements to braking systems.

A typical rider gains far more by just making sure their hands are on the brake levers and their eyes looking forward going into an intersection than they will by parking lot practice.
Practising hard braking in a parking lot develops muscle memory (e.g. balance and position) as well as knowledge about which brake to use (the front).

Last edited by spare_wheel; 11-06-13 at 08:13 PM.
11-07-13, 06:24 PM
#86
achoo
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Originally Posted by spare_wheel
Except that most cyclists do not run into brick walls. Observing a few Cat 4/5 crits is a very good antidote to safety-nanny false-concern.
Unless it turns into a crash fest....

I still can't get over the idea that the OP sustains 30 mph constantly.
11-07-13, 06:45 PM
#87
spare_wheel
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Originally Posted by achoo
I still can't get over the idea that the OP sustains 30 mph constantly.
ebiker.
02-20-14, 06:36 AM
#88
DrkAngel
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Originally Posted by achoo
I still can't get over the idea that the OP sustains 30 mph constantly.
Never claimed I sustain 30mph!
I merely stated that cycling 30mph in 30mph traffic would be ideal.

Ideally, I could fine tune a bike for motor only 20mph (legal) but that supplies substantial pedal assist to 30mph.

With the proper voltage and amperage "fine tuning" this is possible.
Using the ebike.ca simulator I "built" this example ...

Overvolting, while reducing amps, provides less assist below 20mph but gives substantial assist past 30mph.
Ideal for the cyclist looking for a sustainable "keep up with traffic" speed.
Even moderate drafting should greatly reduce required assist effort.

Higher efficiency, especially at lower speeds
Less overheat potential in spite of the higher voltage
A perfect alternative as an eaBike as opposed to an eBike
Find a truck or van for substantial drafting
Find a car of proper height for good overall visibility, use it for moderate drafting, and as a "blocker"
(Drafting, especially with larger vehicles, does not require being dangerously close)

Graph is for a Mountain Bike, Road or Race bike should benefit even more!

3 shunt 35A Controller "switchable" by cutting and adding switch to one or more shunts?
1 shunt - 11.7Amp - 350w - 20mph motor only = legal
+ shunt - 23.4Amp - 620w - 28mph motor only
+ shunt - 35.0Amp - 820w - 28mph motor only = full power! (Substantial acceleration increase)

Adding a front geared hub motor to either would be a minimal weight disadvantage.
A geared hub freewheels when not powered, so there is no additional drag.
Simply apply the amount of throttle necessary to help sustain higher speed or for cruising up them ball-busting hills.
02-20-14, 09:57 AM
#89
JoeyBike
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Originally Posted by DrkAngel
Ideally, I could fine tune a bike for motor only 20mph (legal) but that supplies substantial pedal assist to 30mph.
I test rode a Specialized electric assist bicycle and hit 40.0mph with a lot of effort. The bike itself wants to do 25mph no matter what - up hill and/or against the wind. It was really easy to sustain 30 mph on that bike.

Allow me to add my experience cycling on the outskirts of my city at rush hour either direction. If I maintain 20 mph on a main arterial road that is posted at 30 mph - and run some red lights if that allows me to cycle in a traffic gap - I can frequently cycle 6 miles with ZERO cars passing me. It is a RARE day when everything is out of sync and maybe ten to twenty cars pass me. If I were to bike at 10mph I would bet (just a theory) that more than 100 cars would overtake me.

Every time I start out on certain streets like this I pick out a "pace car" or truck that is unique and easily recognized so I can keep track of how I am doing. Sometimes that pace car and I will leap-frog several times for those 5 or 6 miles (depending on how we hit the traffic signals) but mostly I just keep up. Then we hit the border of the inner city grid (Central Business District) and I leave them eating my dust. They have no chance.

The only increase in danger from speed is the occasional failure of crossing traffic judging my speed and pulling out on me. This can be largely avoided by just merging in with the auto traffic and position myself in traffic same as a motorcyclist would.

FYI: I can easily sprint up to 20mph from a dead stop in 10 seconds flat, 25mph in 15 seconds, and 30mph in 25 seconds without too much effort. I can usually sustain 30 mph in the flow of traffic (and drafting vehicles here and there) for half a minute. I can hold 25ish for a couple of minutes, and I can do 20-22 all day.

All of these skills make me safer I believe.

Watch and learn...

Last edited by JoeyBike; 02-20-14 at 10:32 AM.
02-22-14, 03:42 PM
#90
j814wong
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Relative velocities.

If you are stationary and a car hits you, you received far more "force" than if you are moving 25 mph while the car is moving 30 mph and hits you from behind. But that still doesn't mean that the injuries are any better...

Also, if you are going faster while not zig zagging between traffic, drivers are less liely to see you as a slow moving nuisance.
07-23-14, 08:41 AM
#91
DrkAngel
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Prologue ...

The purpose of Bicycle Safety -The Math of Speed is to numerically illustrate the relationship of a cyclists speed vs the quantity and velocity of passing vehicles. Further, it proposes that it is safer for the cyclist to maintain a speed that is closer to the speed of the passing vehicles.

1. In any traffic environment, especially on the open road, cycling faster means that you are passed by fewer vehicles = less possibility of collision.

2. These fewer vehicles have much more time to notice and make adjustment for you = less probability of collision.

3. Due to the resultant reduction in relative velocity, any contact with you would be less severe = greatly reduced severity of injury or possibility of death.

WARNING !
Do not be misled into thinking this was supposed to be some type of 1 page Bible of bicycle safety!
Others have gone there, and seem to have suffered varying degrees of cognitive malfunction.

Last edited by DrkAngel; 07-23-14 at 03:56 PM.
07-23-14, 11:34 AM
#92
Keith99
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Originally Posted by DrkAngel
The purpose of Bicycle Safety -The Math of Speed is to numerically illustrate the relationship of a cyclists speed vs the quantity and velocity of passing vehicles. Further, it proposes that it is safer for the cyclist to maintain a speed that is closer to the speed of the passing vehicles.

1. In any traffic environment, especially on the open road, cycling faster means that you are passed by fewer vehicles = less possibility of collision.

2. These fewer vehicles have much more time to notice and make adjustment for you = less probability of collision.

3. Due to the resultant reduction in relative velocity, any contact with you would be less severe = greatly reduced severity of injury or possibility of death.

WARNING !
Do not be misled into thinking this was supposed to be some type of 1 page Bible of bicycle safety!
Others have gone there, and seem to have suffered varying degrees of cognitive malfunction.
Not sure 3 really makes that much difference. It is more the absolute speed of the car. Most of the time the major damage comes from hitting the pavement or getting run over after going down.

That said if you are only 10MPH slower than the car and the driver has hit the brakes just before impact that means there is a considerable smaller chance that you will get run over than if the difference if 20MPH.

EDIT: I've found that going at a speed different from what drivers assume for a bike creates issues. When I was fast enough to be significantly faster than expected right hooks was an issue. Drivers would think they had plenty of time to pass and make a right turn when they did not.

Last edited by Keith99; 07-23-14 at 11:37 AM.
07-23-14, 02:55 PM
#93
spare_wheel
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Originally Posted by Keith99
EDIT: I've found that going at a speed different from what drivers assume for a bike creates issues. When I was fast enough to be significantly faster than expected right hooks was an issue. Drivers would think they had plenty of time to pass and make a right turn when they did not.
Riding at high speeds on the right side (or in a bike lane) is like nominating yourself for a darwin award. See Joey's video for visual illustration of how to ride at higher speeds.
07-27-14, 08:01 AM
#94
hermanchauw
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Originally Posted by DrkAngel
Further, it proposes that it is safer for the cyclist to maintain a speed that is closer to the speed of the passing vehicles.
This is the exact reason why cycling on the road is not safe. You can't match the speed of cars or even the slowest moving vehicle most of the time. Unless you want to be tired. I'd rather ride relaxed on the sidewalk.
07-27-14, 03:10 PM
#95
wphamilton
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I think that drivers are as equally likely to right hook you independently of the bicycle's speed. The problem is their poor judgment of your speed, not the cyclist's actual speed that they misjudge.

So riding fast on the right side is not so much more dangerous than riding there slowly. And in my experience, considerably LESS dangerous than riding on the sidewalk. In our USA infrastructure that is. In Singapore as in the previous poster's case, I understand that traffic dynamics are somewhat different from ours.

If I'm at the speed of traffic, or even reasonably close to it, I'm away from the curb and firmly in the traffic lane. That's just common sense.
07-28-14, 07:37 AM
#96
DrkAngel
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Hut! Hut!

Keeping pace with traffic would be ideal!

Most of my eaBikes are capable of 20+mph-motor only, with some motor and pedal assist till near 30mph.
Perfect for "in city" traffic - .
"Blending" with traffic is possible ... and reasonably safe.
To be extra safe, I wait, and choose a good blocker before I start my run.

Blocker 101
Look for larger vehicle with modest height. You want a solid hefty vehicle that you can still see over.
Preferably a more expensive well cared for vehicle with no damage. I driver who takes care and cares about his vehicle!
Slide in behind them and use them as a blocker, let them run interference and help you stake a claim ... in traffic - ≤ 30mph.

Even on my non-motor assisted bike, I return from the post office at ~30mph. (Used to be ... governments built their buildings on higher ground, out of the reach of possible floods or to look more impressive?) Anyhow, I wait for an appropriate vehicle and jump in behind them on the downhill run, I easily push to 30+ ... on the slope. Takes some effort, but I can usually maintain near 30mph for the 5 blocks till my turn off.

No, even with a eaBike, I can't always pace traffic.
One of my most important safety devices is a wide angle strobe headlight.
Really helps me get noticed, I can tell when I forgot to turn it on ... by how traffic treats me!
Nice to have a strobe light at rear view mirror level when I get forced into the door kicker arena!
Cheap Qree Q5 LED light has High - Low -Strobe and wide-zoom functions.
I even mounted a 2nd on one of my helmets as a zoomed strobe for highbeaming inattentive drivers and zoomed High for scanning ahead for potholes at night.

Oh! eaBike?
Electric assist bike = motor is used to supplement, not replace, human power.
~500w motor and 34T rear sprocket jumps me ahead of traffic from the green light, shift to 24T about 10mph, then skip some gears on my way to 25mph+ ... usually traffic doesn't catch up till nearly a block.

Oh Oh! Sidewalks?
Statistically, riding a bicycle on sidewalks is as dangerous as on the street.
Numerically, just as bad, though severity is likely less.
Most drivers anticipate pedestrian speed sidewalk traffic!
If you include crosswalks with sidewalk cycling ... you are talking about the majority of all bicycle-traffic accidents!
Many urban areas ban bicycle-sidewalk traffic as a safety measure, for pedestrians and cyclists!
07-29-14, 02:44 PM
#97
spare_wheel
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Originally Posted by hermanchauw
You can't match the speed of cars or even the slowest moving vehicle most of the time.
It sounds to me like Singapore needs to dramatically decrease speed limits because I match or exceed the speed of cars for most of my commute.
07-29-14, 02:56 PM
#98
italktocats
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Originally Posted by spare_wheel
It sounds to me like Singapore needs to dramatically decrease speed limits because I match or exceed the speed of cars for most of my commute.
not the best place to ride a bike anyway
07-30-14, 12:20 AM
#99
hermanchauw
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Originally Posted by spare_wheel
It sounds to me like Singapore needs to dramatically decrease speed limits because I match or exceed the speed of cars for most of my commute.
That's nice. Here even in two lane roads with many pedestrians crossing, some drivers drive as if they are racing.
07-30-14, 12:47 AM
#100
kickstart
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As a cyclist, motorcyclist and professional driver, I can say these esoteric "faster is safer" theories are simply stuff and nonsense. Speed only changes what the threats and consequences are.

I can also see from some responses a willingness to accept the theory as a fact not on its merits, but because it allegedly justifies particular behaviors.