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# Bicycle Safety - The Math of Speed

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# Bicycle Safety - The Math of Speed

07-13-13, 07:02 AM
#1
DrkAngel
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Bicycle Safety - The Math of Speed

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.

The Math of Speed! - Index

10mph vs 20mph - passed by 30mph traffic
In 60mph Traffic
Other traffic - Biker 10 mph vs 20 mph - 30 mph traffic
NPA's
The Solomon Curve
Cocky SOB
Bicycle Safety
Bicycle Accidents - Causes
150lb Biker vs 3000lb Car
Mach1 Bike
Rear Impact Solution!

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.

Last edited by DrkAngel; 07-30-14 at 12:42 PM.
07-13-13, 07:51 AM
#2
EBikeFL
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DrkAngel, I agree with you that going faster is safer. However, I've noticed cars don't like the idea of a bicycle either maintaining their same speed and/or catching up to them at the stop lights.

Imagine if you're in a car and see a cyclist maintaining speed with you. You probably start wondering why am I paying for gas, car payments, insurance, etc. when this cyclist is going to get to the same destination about the same time as me. It's like watching someone get a 50% discount when you just paid full price. It would make you upset and angry.

When you ride your bicycle at 30 mph you remind car drivers they just paid full price.

There is the other issue of reminding car drivers that gas prices are only going to go up and that they are stuck with being a forced consumer. Eventually, they will entertain the idea of riding a bicycle and that probably frightens them too.

The positive car drivers will actually see a light at the end of the tunnel witnessing you travel at 30 mph. I've always believed that traveling at 30 mph conveys to the driver that there are other transportation methods besides a car. They no longer see the bicycle as just a fun recreational activity but more of a legitimate form of transportation.

Many car drivers want to ditch their vehicles but they just don't know what other options are out there. When they see me carrying groceries and traveling at 30 mph it's like a light has come on in their head.
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07-13-13, 07:56 AM
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turbo1889
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Provided you don't wipe out - Yes, speed to keep up with traffic is good and helps earn you some respect. The same is true with a pedal only bike by the way. I can break above 20-mph for short spurts on my pedal only "bus bike" (ride the bus with the bike in the rack between towns and then ride the bike around town) and doing so really helps with safety and getting a little more respect when I ride around town in traffic riding "All In" technique center of lane and holding my position in the traffic cue like I was a motorcycle in stop and go 25-mph speed limit square grid traffic patterns.

Now when it comes to wiping out - speed is your enemy even more then weight since weight is linear to kinetic energy in a wreck where as velocity is exponential to the square. 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.
07-13-13, 08:06 AM
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Shimagnolo
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To be specific, energy in a moving object: 0.5 x mass x velocity^2

But I agree with the OP that I feel safer when my speed is closer to that of motor vehicles.
07-13-13, 08:22 AM
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turbo1889
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My point is the faster you go, the more carefully you need to ride because the harder you go down if you go down.

As to keeping up with traffic actually ticking off some drivers, that is usually only the case if you filter up, if you don't filter up at the reds and stops and instead hold your position in the traffic cue it won't make as many drivers mad and actually make a lot of them respect you more when they see that you can keep up with them and hold your own.

If you filter up and as a result you are either making better time then they are and getting further and further ahead of them at every light or worse yet they have to pass you over and over again (yes in the mental state of 99% of all car drivers when it comes to a bicycle in the road ahead of them they do have to pass even if it is in the middle of a block between stop lights and they know your just going to filter up again), now that is what gets them ticked off. They will blame you for constantly getting in their way and it just about makes them go critical mass nuclear with a lot of dirty fallout.

Long story short, if your moving fast enough to keep up with traffic, don't wipe out, and hold your position in the cue at the reds and stops rather then filter up because doing so can make some drivers go nuclear on you when they end up passing you multiple times and more then minus out any safety gains you may have made by keeping up with traffic better with more speed. Now if you can make good enough time to outrun them altogether, then it is worth considering filtering up but use some discretion on that as well.

Last edited by turbo1889; 07-13-13 at 08:32 AM.
07-13-13, 10:04 AM
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Jimi77
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Interesting way to think about it. Maybe I'll start looking at 2kw motor again.
07-13-13, 10:35 AM
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Watchdog
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Well I don't think you can assume that by going 30 mph no one is going to pass you. If you assume there are some a_hole's out there, then they'll certainly pass you at 30 mph. EBikeFL kind of touches on it. If someone is an a_hole and sees a bike going 30 mph they might be upset and pass you dangerously to prove a point.

But I do agree with you that keeping up with traffic makes an aspect of riding safer. On my route to work I often take a different route in one section than the route I take coming home. The reason? Going to work the one street that's a more direct route is uphill (about 3% to 4% grade) on a narrow road and I don't want to be going 15 to 20 km/hr up this road with traffic stuck behind me getting pissed off. But going home it's downhill and with the slight downhill I can easily go over 40 km/hr and I find traffic doesn't mind being behind me for the one block stretch the road is narrow. No one ever honks or tries to pass, and I move over as soon as the road widens.
07-13-13, 12:15 PM
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Jimi77
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Originally Posted by Watchdog
Well I don't think you can assume that by going 30 mph no one is going to pass you. If you assume there are some a_hole's out there, then they'll certainly pass you at 30 mph. EBikeFL kind of touches on it. If someone is an a_hole and sees a bike going 30 mph they might be upset and pass you dangerously to prove a point.
For some reason, I suspect that a_hole is going to pass dangerously whether you're doing 10mph or 30mph.
07-13-13, 12:28 PM
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EBikeFL
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Originally Posted by Watchdog
Well I don't think you can assume that by going 30 mph no one is going to pass you. If you assume there are some a_hole's out there, then they'll certainly pass you at 30 mph. EBikeFL kind of touches on it. If someone is an a_hole and sees a bike going 30 mph they might be upset and pass you dangerously to prove a point.
I've had this happen on more than one occasion. Drivers become fascinated with my e-bike and slow down to get a closer look but piss off the drivers behind them in doing so. Then when they finally pass me, all the drivers behind them decide to take their frustration out on me.

I had one driver nearly run me off the road, then pointed to the sidewalk when I caught up to him.
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07-13-13, 12:36 PM
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EBikeFL
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Originally Posted by turbo1889
Long story short, if your moving fast enough to keep up with traffic, don't wipe out, and hold your position in the cue at the reds and stops rather then filter up because doing so can make some drivers go nuclear on you when they end up passing you multiple times and more then minus out any safety gains you may have made by keeping up with traffic better with more speed. Now if you can make good enough time to outrun them altogether, then it is worth considering filtering up but use some discretion on that as well.
You make a good point turbo1889. I don't filter when I stop at stoplights. I do take the center lane and hold it until I get across the intersection. I had a motorcycle filter up and pass me and several cars to make a right hand turn once. I couldn't believe what I was seeing, there was very little room for him to navigate but he did it anyway.
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07-13-13, 12:36 PM
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wphamilton
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Originally Posted by turbo1889
My point is the faster you go, the more carefully you need to ride because the harder you go down if you go down....
It may sound picky, but not necessarily. mass x g x height is the same at any speed. That's not just snarky because I'd rather fall with a moderate forward speed than a dead stop - easier for either a shoulder roll or forward roll. Hitting an obstruction or another vehicle you (and the other comments) would be right.

Which is all to say that travelling 30 as opposed to 15 isn't all that much more dangerous with respects to falls. Control, cornering and collisions is another story.
07-13-13, 02:51 PM
#12
turbo1889
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Originally Posted by wphamilton
It may sound picky, but not necessarily. mass x g x height is the same at any speed. That's not just snarky because I'd rather fall with a moderate forward speed than a dead stop - easier for either a shoulder roll or forward roll. Hitting an obstruction or another vehicle you (and the other comments) would be right.

Which is all to say that travelling 30 as opposed to 15 isn't all that much more dangerous with respects to falls. Control, cornering and collisions is another story.
The worst (single vehicle) bicycle wipe out I've had so far was when I lost it going down-hill on a pedal only mountain bike at about 40-mph on a gravel back-road (I was a lot younger and stupider back then) and I absolutely guarantee you that it was far worse at speed and I would have much preferred to be going a lot slower when I took that spill (hindsight being a lot clearer and wiser).
07-13-13, 04:03 PM
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You didn't hit the ground any harder for the speed. You'll get more road rash at the higher speed if you're sliding, and probably more impacts if you're bouncing. I've hit the ground at 60 without a scratch or bruise, and at 10 with some pretty serious contusions. Snapped my collarbone on impact with a curb at 25 mph (last year ). That's where the higher speed hurts you - anything vertical in your path - and sliding against a rough surface of course. But the energy equation (or momentum also) is not a good representation of how hard you're hitting.
07-14-13, 12:25 AM
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DrkAngel
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I've demonstrated how faster is safer, in a 30 mph traffic environment. But "On the road", with higher speed traffic, is where the most concern about passing vehicles exists. How does speed effect your risk in a 60 mph traffic situation.
First, let me qualify;
1. Riding is in an rural area and 95% of the roads are 55 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.

60 mph traffic:

At 10 mph -
60min x 10cars - 1/6 (for 1/6 speed of cars) = 500 cars passing you at 50mph.
Driver has 7 seconds to notice & accommodate biker.

At 15 mph -
40min x 10cars - 1/4 (for 1/4 speed of cars) = 300 cars passing you at 45mph.

At 20 mph -
30min x 10cars - 1/3 (for 1/3 speed of cars) = 200 cars passing you at 40mph.
Driver has 9.5 seconds to notice & accommodate biker. Cars have approx. 1.4 times the time to notice, and avoid, you! (vs 10 mph).

At 25 mph -
24min x 10 cars - 5/12 (for 5/12 speed of cars) = 140 cars passing you at 35mph.

At 30 mph -
20min x 10cars - 1/2 (for 1/2 speed of cars) = 100 cars passing you at 30 mph!
Driver has 12 seconds to notice & accommodate biker.

(Math is simplified - but "sound")

When you consider that, in "open road" conditions, most bike collisions are directly related to passing cars, then 20 mph would be (2.5 times safer than 10 mph) x (1.4, the time the, approaching, driver has to see biker) = nearly 4 times safer @ 20 mph, compared to 10 mph!

30 mph would be (5 times safer than 10 mph) x (2, the time the, approaching, driver has to see biker) = 10 times safer @ 30 mph, compared to 10 mph!

Note: Some of the math is approximated, fairly accurate, but will modify if deemed necessary.

Most impressive is that every bit of speed increase greatly reduces the volume of passing traffic and therefore increases the safety factor!

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 5, only 1 @ 30 mph.
07-14-13, 12:44 AM
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turbo1889
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There is one additional "safer" factor you didn't calculate. Under the riding conditions you specify if someone does hit you the speed differential comes into play.

Namely if some knuckle head high speed heavy vehicle operator either runs right into the rear of you on your bike or passes so closely there is a sliding physical contact between the right side of their car and your left side and the protrusions such as the mirror, door handle, and trim make multiple impacts with your bike and body along with road rash like burns from the sliding contact with the main smooth body of the car. That kind of "accident" (in quotes for a reason, criminal negligence on the part of the passing vehicle would be more like it) is known as "getting sliced" up here where I live and is a common danger to avoid on the kind of roads you are talking about.

Anyway, long story short if we assume the car is going 60-mph.

----- If a car either rear-ends you or "slices" you on a too close pass and you are going 10-mph the speed of the impact is 50-mph
----- If a car either rear-ends you or "slices" you on a too close pass and you are going 20-mph the speed of the impact is 40-mph
----- If a car either rear-ends you or "slices" you on a too close pass and you are going 30-mph the speed of the impact is 30-mph

Providence-Forbid, if one of the drivers of those faster moving heavy vehicles on the road either plows into you from behind or "slices" you on a too close pass the faster you are going the lower the speed of that impact will be when they hit you and thus the better your chances of avoiding death and/or reducing injuries from the initial impact.

So, provided you are riding on the correct side of the road and not being a salmon (speed gets added rather then subtracted in that case, which is part of the reason you shouldn't ride like that) then you have an additional safety cushion if you are moving at higher speed if someone actually does hit you.

If you ride correctly with traffic the faster you ride and close the gap between the speed of other traffic on the road the better off you are if they hit you. The reverse is true as far as you hitting them (be careful when drafting cars, sometimes they can brake before you can and if you don't leave enough room you can rear-end them, the only at-fault collision I have been in on a bike was when I rear-ended a vehicle in front of me and split a foam bike helmet in half when my head hit the rear of their vehicle, and I was riding a pedal only bike !!!).

Last edited by turbo1889; 07-14-13 at 12:50 AM.
07-14-13, 02:24 AM
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009jim
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You're assuming there is only one type of accident scenario between cars and bikes. Wrong, there's at least 57 scenarios and for the other 56 you are safer if you go slower.
07-14-13, 04:29 AM
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DrkAngel
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Bicycle Safety - The Math of Speed - Other Traffic

Originally Posted by 009jim
You're assuming there is only one type of accident scenario between cars and bikes. Wrong, there's at least 57 scenarios and for the other 56 you are safer if you go slower.
Exaggerated ... but ... Good point!
Let's compare other traffic situations:

Biker at 10 mph vs 20 mph in a 30 mph traffic situation.

Per mile - 10 mph biker will be:

1. passed by 4x (times) as many vehicles =
a. 4x the possibility of hit, or swipe x (2x impact speed)
b. 4x the possibility of "right cross" **

2. 2x the volume of oncoming traffic =
a. 2x the possibility of "left cross" **
b. 2x possibility of head on x (.8 impact speed)
(30 + 10 mph vs 30 + 20 mph = 80% impact speed)

3. 2x the volume of cross traffic, sidestreets, driveways etc. =
a. 2x the possibility of cross traffic collision **
Twice as long, being a target, in the intersections!

Note: Actual percentages listed where available. Other impacts are highly variable due to possible angle and bike into vehicle or vehicle into bike.

** Speed, or severity, of impact will vary, from 50% to 100% (possibly higher).

Best case is 50% impact speed of 10 mph biker into side of vehicle.

Worst case would be, side impact of biker by car, 100% impact speed. Possibility of being "run over" might be 2x, for the 10 mph biker. (Momentum of 20 mph biker is much more likely to carry him past the car = much greater chance of not being under car!)***

(Same direction impact already established at 4x possibility & 200% speed-severity.)

*** 20 mph Biker possibility of impact is approx. 25% to 50% that of the 10 mph Biker.
Additionally, 20 mph Biker is 2x as likely to strike the vehicle while the 10 mph Biker is 2x as likely to be struck by vehicle. (Applicable to all, except same direction & head-on!) Possibility of 10 mph Biker going under vehicle is MUCH greater!

The final, measurable, variable might be, "time to see", (tts), the biker. (10 mph biker) While following traffic only has .5x the tts, oncoming traffic has 1.25x the tts, and the cross traffic has 2x the tts.

The additional factor of faster motion being more noticeable, especially in the peripheral vision area, should be added, but, I'm afraid, assigning percentages would be sheer speculation.

(Peripheral vision is much more attuned to detecting motion, as well as light, especially flashing light. Another good reason for a "strobe" headlight, during the day.)

Personally, I believe, faster still looks a whole lot better-safer.

Last edited by DrkAngel; 07-14-13 at 08:36 AM.
07-14-13, 06:12 AM
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turbo1889
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Originally Posted by 009jim
You're assuming there is only one type of accident scenario between cars and bikes. Wrong, there's at least 57 scenarios and for the other 56 you are safer if you go slower.
I mainly was focusing on danger approaching from the rear where it is the least likely to be noticed in time by the cyclist to take action to avoid the situation. Even with a good mirror or two you spend less time looking in the mirror and for danger you don't have much say in - that is most likely to come from the rear in the form of getting rear-ended or a too close pass.

I focused on the highest potential of "surprises" for the cyclist and ASSumed the cyclist of sufficient skill and capabilities to make a difference in avoiding the others. I capitalized the first three letters of that word because you may be correct that you can't count on that and its a ill-advised assumption to make. The rider will be the one that makes the choice as to whether those first three letters should be capitalized or not on that one. I try to keep myself on the lower case level but I will admit there have been times where I've managed to turn myself into the capitalized version.
07-14-13, 07:24 AM
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DrkAngel
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Impact From Behind - Best Scenario & Solution!

Absolutely the best solution to a rear impact scenario requires good speed capability, constant awareness, and one piece of specialty equipment.

First you want to be traveling, as closely as possible, to the speed of the approaching vehicle.

Second you must have an awareness as to the velocity, angle, mass and surface composition of the vehicle. Sets of 4 mirrors, or more, recommended, if possible, arrange into a stereoscopic, full 3D configuration.

Thirdly, and most importantly, the one piece of specialty equipment! "Cyclists Downunder", (based, possibly, in Australia?), has begun marketing their "Octopi" line of cyclewear.

Just make sure that you are struck squarely from behind. If you are about to be hit, quickly swerve and position yourself directly towards the center of the vehicle, the car should knock the bicycle from under you and you should roll gracefully onto the hood and, or, windshield, where the Octopi suction cups should keep you safely secured. (Tip: As soon as you get stuck to the vehicle, rip off one, or both windshield wipers! Some drivers will use them to try to knock you off. You can also beat them on the roof to get the drivers attention, in case he is sleeping, or just doesn't notice you.) Hopefully the car will come to a gentle stop and you can then safely get off. Much safer than rolling down the road at 30 mph or bouncing over the roof and landing, "who knows where"! (Tip: Please do not anger, or insult, the driver! You will probably need their help getting unstuck from the car!)

Warning! Speed is important! 20 mph bike speed is optimal to be hit by a 30 mph car.
Slower can result in fairly severe injuries.
Faster and you might not be bounced onto the top of the car, you might have to jump backwards, timing is critical! Warning! Be careful, some a__hole drivers will approach like they are going to hit you, then ... slow down, just before impact. If not aware you might jump, and miss, ... then where would you be? ... Embarrassed! ... ???

Large trucks can be very tricky. Most don't have a nice hood to get stuck to.
1. Ideally, you must be going 10 mph slower than the truck.
2. Timing is critical, you must jump straight up just as you are being run over.
3. You must hit the windshield squarely, with enough body, to stick. Grills-radiators don't work well with suction cups!

This is a skill! Like any skill it requires practice. You should have a friend try to run you down, a few times, just so you can get good at being safer.

Oh, ... Make sure you have a good supply of bikes handy.

P.S. Be prepared for being hit by the, proverbial, "Redneck Pickup". Keep an Armageddon bag handy, on your bike. Recommend couple bottles of water, sun screen, some granola bars, "Space blanket" ... anything you might need in case they drive around with you stuck to their hood, for a few days.

Disclaimer! You must read "Epitaphs of the Downunder Cyclists", before attempting this "solution"!!!
07-14-13, 09:46 AM
#20
Monsoon
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And the s**t eating grin they see on your face as you ride the same speed they are, increases the odds of them hating their lives, selling their cars and buying an e-bike.

win-win, bro.

07-14-13, 11:14 AM
#21
OYO
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As far as i am concerned nothing ive read here "demonstrates" a faster speed is safer. I run an ebike but i also run 2 trucks & several motorcycles & the single most important factor when assessing levels of safety on urban streets is how other road users assess what risk you are to them if they do something wrong..
for example pulling out of a side turning into your path. unfortunately if you are on a bicycle they tend to assume you are doing alot less that 30mph & after a quick glance at you they will look away & pull out. obviously flowing traffic at a similar speed is safer but not if you are on a small frontal area vehicle which people assume will be approaching at bicycle speeds.
I find the largest frontal area vehicle i drive (a truck) makes people decide not to risk entering my path far more often, even if I'm going extremely slow, however, they happily enter my path if I'm riding my ebike & its down to me to take avoiding action which is most certainly more dangerous at higher speeds..o

Last edited by OYO; 07-14-13 at 11:21 AM.
07-14-13, 11:45 AM
#22
Monsoon
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Originally Posted by OYO
As far as i am concerned nothing ive read here "demonstrates" a faster speed is safer. I run an ebike but i also run 2 trucks & several motorcycles & the single most important factor when assessing levels of safety on urban streets is how other road users assess what risk you are to them if they do something wrong..
for example pulling out of a side turning into your path. unfortunately if you are on a bicycle they tend to assume you are doing alot less that 30mph & after a quick glance at you they will look away & pull out. obviously flowing traffic at a similar speed is safer but not if you are on a small frontal area vehicle which people assume will be approaching at bicycle speeds.
I find the largest frontal area vehicle i drive (a truck) makes people decide not to risk entering my path far more often, even if I'm going extremely slow, however, they happily enter my path if I'm riding my ebike & its down to me to take avoiding action which is most certainly more dangerous at higher speeds..o
Many of these issues can be resolved by using the appropriate warning device.

07-14-13, 12:37 PM
#23
Shimagnolo
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Originally Posted by Monsoon
Many of these issues can be resolved by using the appropriate warning device.

In action: https://vimeo.com/44650294
07-14-13, 05:28 PM
#24
turbo1889
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Bikes: Too many to list, some I built myself including the frame. I "do" ~ Human-Only-Pedal-Powered-Cycles, Human-Electric-Hybrid-Cycles, Human-IC-Hybrid-Cycles, and one Human-IC-Electric-3way-Hybrid-Cycle

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Since we have gotten into the humor end of the discussion, I'll join into that as well:

If OYO is correct that in order for other drivers to respect you on the road you must represent sufficient threat to them ~ I believe that should do the trick. I was looking for a picture of a tadpole tandem I saw years ago on the net with hard mounted double forward gatling guns and the stoker sitting backwards with a single gatling gun on pivot mount for a tail gun but was unable to find that picture and those were the best I was able to come up with on short notice.

Last edited by turbo1889; 07-14-13 at 05:40 PM.
07-14-13, 07:46 PM
#25
OYO
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hahaha reminds me of this ... at first glance it has a good threat score.

Last edited by OYO; 07-14-13 at 07:50 PM.