Bicycle Safety - The Math of Speed

Discussion in 'General Bike Discussion' started by DrkAngel, Mar 28, 2010.

  1. 10 mph, or slower.

    2 vote(s)
    10.5%
  2. 15 mph.

    4 vote(s)
    21.1%
  3. 20 mph.

    3 vote(s)
    15.8%
  4. 25 mph, or faster.

    10 vote(s)
    52.6%
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  1. DrkAngel

    DrkAngel New Member

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    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!". ... [​IMG]

    I feel it necessary to prove that 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, 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, an additional, 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.
    [​IMG]

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Mar 29, 2010
  2. DrkAngel

    DrkAngel New Member

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    Math of Speed - The Open Road?

    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!". ... [​IMG]

    I feel it necessary to prove that faster is safer. Let me try a mathematical approach.

    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: Still "in progress" on the math, fairly accurate but will correct.

    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.
    [​IMG]

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Mar 29, 2010

  3. LawMan

    LawMan New Member

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    WOW! ... The Math of Speed ... WOW!

    I couldn't believe that your math could be accurate. Sooo ... I got out my calculator ... didn't help enough ... sooo ... got my Hot Wheels collection, Monopoly collection, couple yardsticks and created a movable representation.

    Result! Your good at math!

    Eliminate road hazards & mechanical failures for us and you'll get my nomination for ... anything!
     
  4. photosbymark

    photosbymark New Member

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    That is assuming that you consider getting passed as a danger. I don't. Sharing the road with a drunk is a danger. Drivers that are texting are a danger. Getting passed is a part of the game. IF that is that big of a concern, a motorcycle is the way to go for you. Then you can go just as fast as the cars and never be passed. Yet how do the number of fatal motorcycle accidents on the street compare to the number of road bike accidents??

    Even though I suspect there are far more cyclists, many of them children, on the roads that may not as trained as they should be (and adults too for that matter) the biggest difference is the speed.

    Gonna go see if I can find some stats somewhere. If you want to go fast, fine that's your business and your choice. If you feel safer though, that doesn't necessarily mean you are safer. Lot's of people FEEL safer in cars without seat belts too.
     
  5. photosbymark

    photosbymark New Member

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    The stats I found said in 2008 a little over 37000 people died in motorcycle accidents. That same year 714 died on a bike. Now there really isn't a way to compare miles or number of owners because bikes are not required to be registered and no way really to do much other than guess at the miles. Though motorcycles are licensed and the driver are too, a better guess can be made but unless you can get the data for both it makes a comparison tougher.

    One thing that I was surprised to see is the number of people getting hurt while drinking on a bike. Guess we have that in common with just about every other form of transportation.

    Yet there is one thing that bikes an motorcycles have in common. One the riders is unprotected outside of what they wear. Though motorcycles have engines and fuel to make burns and fire a possibility the vast majority seem to be things like broken bones and head trauma. The biggest difference between the two, speed.
     
  6. DrkAngel

    DrkAngel New Member

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    Drunks & Texters

    Please vote for your recommended speed!

    In a 30 mph enviornment:
    Biking at 10 mph vs 20mph.

    Per Mile - Biker at 10 mph will encounter 3 times as many drunks & texters as the Biker at 20 mph!

    10 mph Biker will be passed by 4 times as many (same direction) and will be passed by twice as many (opposite direction)!

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Apr 1, 2010
  7. BlazingPedals

    BlazingPedals Member

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    How about drunks and texters going the other way, or coming out of side streets or driveways? How will their decreased reaction time due to your higher speed affect safety? I suppose you could make the point that spending less time biking is safer, but there lies madness.
     
  8. DrkAngel

    DrkAngel New Member

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    Drunks vs Bikers

    Please vote for your recommended speed!

    For all listed - half the speed = twice the number of drunks & texters (per mile).

    As for their "reaction time", I would gladly rely on my speed - brakes - maneuvering ability over the efforts of a drunk or distracted driver!

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Apr 1, 2010
  9. photosbymark

    photosbymark New Member

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    No you won't. You will only encounter few drunks/texters approaching you from behind. That is the area where they are most likely to see you, but you don't need to rely just on that.

    Hearing is a much a part of situational awareness as vision. Yes I have been known to ride with an Ipod or radio, but only with an earbud in my right ear. Riding on road without curbs helps a lot too as the ditch is just a lean a way. Mirrors are something I am trying to find the right combo and for me its a bit tougher. I have a significant loss of vision in my left eye making some mirrors difficult to use. The mirror that clips on the glasses for me is useless. Trying a helmet mirror but it may have the same problem and also testing a modified bar mirror. Knowing what is coming puts some of the control back to me.

    Yet if you are going to cycle, there is some level of trust you must have to ride on the roads. Yes you have to assume every car out there is out to get you, but most are responsible. Yes bikes get hit from behind, but just how high is that risk?? We do know something about the fatals. We know that percentage of fatals compared to other areas of riding. What we don't know is how many times a bike is bumped and the rider just tossed into a ditch with a bent rear wheel and mad as h e double toothpicks. We really don't know how many bent fenders, doors ect in other areas where damage is done but riders are basically unhurt.

    You are apparently an engineer and engineers think in numbers. I taught a bunch of them and am married to one. The natural tendency is to try to make things fit a calculation and see what the numbers do. Trouble is the data isn't always there to do that and when it isn't, there are problems. Your calculation is correct as far as it goes, but there are so many other areas it does not even remotely consider that would affect the actual risks. The data you need to make those calculations are an engineers worst nightmare because they likely don't exist.

    Now speed in an of itself adds risks to almost any method of transportation. A number of years ago a driver in the Indy 500 was in a first lap crash. The field ran into the turn 3 wide as is the customary start for that race. A big crash sent one driver into the wall at over 200 with an impact so violent it broke the front of the car off leaving the drivers feet totally exposed and totally unprotected. Being clearly already knocked out he hit the wall again head on with unprotected feet first at somewhere around 170. He survived only to lose his life later in a car crash on the streets. Sad thing is he wasn't wearing a seat belt, and likely felt safe because he wasn't doing 200. It was a an accident he likely would have been able to survive had the belts been on.

    Now see if there are any 500 fans that have been around long enough to know the drivers name.
     
  10. DrkAngel

    DrkAngel New Member

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    Drunks/texters/NPAs (Not Paying Attention) etc.

    Please have your wife look over my calculations and try to explain them to you.
    Per mile, the Biker at 10mph will be passed by 4 times as many Drunks, texters etc. as the biker at 20 mph! Additionally, the number from oncoming traffic is double!

    Also, please vote in the poll and let us know what you consider to be the "safe" speed.

    [​IMG] EZip Engineering 101 [​IMG]
     
  11. DrkAngel

    DrkAngel New Member

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    The Math of Speed!

    "The Math of Speed" demonstrates the reduction of risk, from the application of higher speed, in many situations.

    For me, faster is much safer, most of my "traffic" riding is on arterial bypasses, around the outskirts of the city, (very few driveways, side streets etc.)

    "In city" I ride legally (reducing my risk of accident 50%, from the statistics) and make sure that I am seen, (the major contributing factor in all other bike-vehicle encounters.) I have tail-turn-brake light with strobe headlight and helmet with additional rear red flashy light and strobe headlight. Being able to direct a strobe light at a menacing vehicle is a real attention getter.

    [​IMG]

    Having reduced the probability of all other vehicular encounters I rely on speed to help alleviate the danger of the, now, greatest danger, passing vehicles. A 90% reduction in danger, simply by increasing speed from 10 mph, to 20 mph is well worth the effort, in my book!

    However, to assume that higher speed is, always, safer, is foolish, and not what I proposed. For example, residential areas might be "chock full" of driveways, or infested with playing children, or bikers etc., possibly, entering the roadway from between parked cars.

    Sadly, no one has attacked the factor where speed is a true detriment, the ability to stop. ... ??? Personally, I keep my bikes, (brakes), tuned and capable of going from 20 mph to zero in, not much more than 1 car length, it takes about 5 car lengths to get up to near 20 mph. I, personally, would much rather have the maneuvering-escape speed at my disposal, and be able to lose it, when necessary.

    Please vote for your "Optimum bike speed in 30 mph traffic"

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Apr 14, 2010
  12. photosbymark

    photosbymark New Member

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    I don't need the wife to check your math. I openly admit the calculations are correct for the number of cars passed. They just don't hold the entire key to safety. First of all on the surface, just because you are passed by more cars is not necessarily proportional to the number of high risk drivers. Going for a midnight ride by a bar is going to have a lot higher percentage of drunks on the road, and that risk is much higher. Ride during rush hour and you are going to see more texters, but the key is that just because you passed by more cars doesn't mean that there is a direct proportion that you will be passed by an equal number of high risk drivers.

    The poll has an interesting twist to it that you seemed to miss. Safe speed is not a constant. It's a highly variable, just as it is in any other mode of transport. Would you ride the same speed on pothole filled stretch of pavement that you would a silk smooth stretch of new pavement? Are you going to ride the same speed on a gravel road or track as you would pavement? Will you ride just as fast in fog as you would on a clear day? How bout worn tires or any of a host of mechanical conditions that could affect your bike, would you slow down if your brakes were to be replaced by the bike wrench the next day?

    Now factor the skill level and experience of the rider. Are they a new rider? Do they have experience, but haven't been on a bike in 30 years? Did they just get back from finishing the Tour on the podium?? No way the new rider should or would feel comfortable at the speed the racer thinks is just having fun, nor should they.

    Your calculations factor in none of these things. What is a safe speed? One where you can keep track of your surrounds and keep a situational awarenes of what is going on around you, one where the bike is in total control, and one where one could expect to miss the unexpected by either dodging or stopping. It would be perfectly reasonable to go faster on a road with no driveways along the road or no parked cars along side.

    Remember "ALWAYS leave yourself an out".
     
  13. DrkAngel

    DrkAngel New Member

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    Bars @ Midnight?

    You seem to miss the point!
    I never even hinted that faster speed is "the entire key to safety."

    But! Faster speed will greatly reduce:
    The number of passing vehicles. (Reduced by 75%) *
    The passing speed of vehicles. (Reduced by 50%) *
    The quantity of oncoming traffic. (Reduced by 50%) *
    The severity, of impact, if stuck, or being "swiped", from behind. (Reduced by 50%+++) **

    * Based on, per mile. Biker speed of 10 mph vs. 20 mph.
    ** Some estimate that a 20 mph impact might be 4 times as severe as a 10 mph.!

    Any time, or any location ... that safety increase, is a constant!


    Once again:
    30 mph traffic situation.
    Riding same direction as traffic.
    10 mph vs 20 mph.

    Per mile, riding at any time, or in any location, (even past bars at midnight), at 20 mph, you will encounter many fewer passing vehicles, most notably the drunks. 25% traveling in the same direction and only 50% in the opposing direction, compared to the 10 mph biker.

    Also ... No, I am not recommending spending less time biking, at a higher speed. Traveling twice the distance, you will, still, encounter less passing traffic. Half the number as the 10 mph biker!

    [​IMG] EZip Engineering 101 [​IMG]
     
    Last edited: Apr 3, 2010
  14. photosbymark

    photosbymark New Member

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    Your post are leaving the impression that just because you are faster and maybe reducing the risk in one area that you are safer overall. That calculation can not support that conclusion. IF you think so we can agree to disagree.

    Now several errors do appear in your previous post. Riding faster will NOT reduce the speed of any car. It WILL only reduce the closure rate. You are still going speed X and no matter how fast the car catches you its still doing 30. Even if it takes an hour for them to bump you, the car is still doing 30 and you are doing about the same speed. The hit you will take will be a 30 mph one not a 5 mph one. Yet if you want to go test it, leave me out. Watch the old stock car boys doing 190 (they have a 200mph speed limit due to insurance) at Daytona. It usually just a little tap that sends a car out of control because they are all running about the same speed. The impact is a 190mph impact.

    Yes you MIGHT, but MIGHT NOT get a safety advantage. That advantage is NOT constant. Why? Because of the people and the attitudes they have on the road you share. It would only be a constant if you road 24 7 in all kinds of weather. One just does not ride long enough for the law of large numbers to apply. Where you ride, also would have a big impact on how drivers would treat a passing cyclist. Some cycle friend locations are very careful around other cyclists. In many cases they might give a bit of extra room while hollering "Hey Lance Armstrong" out the window at you. Others would crowd you and tell you that you are number 1. The attitude of the motorist is something beyond anyone's control, but its hardly constant. Id rather be passed by a 1000 careful motorist, than one drunk. Lots of factors come into play in calculating just how likely that driver behind the wheel will be a jerk, but I won't try biking after midnight on New Years eve/day. Regardless its not a constant. Since it isn't this calculation has very limited value if any IMHO.

    That advantage is also affected by how busy the street happens to be at any given time. If the street only has a few cars on it, the gain is reduced. Yet the other risks associated with the speed are still there. Your calculation does nothing to compare the risk of the increased speed. IF there were only a few cars on the road to begin with, its possible if not likely the increased speed would add more risk than it would reduce from the reduction in the number of cars that pass you.

    Closure rate has nothing to do with safety in many places. I ride on one stretch of road where I get passed by 100 percent of the cars all the time. You would too in that the speed limit is 60. Yet with a wide shoulder there for emergency parking, its perfectly safe for a bike and riders are there all the time. Is there a risk there? Sure if a car spins out of control, a biker is toast but that risk is every where. Big car and unprotected cyclist, the cyclist loses every time every where.

    Rarely if ever is risk management a one calculation operation. What's the old saying. There are lies, d#@* lies, and statistics. A good stats man can often make the numbers say what ever they want. But if everyone will question with boldness, then common sense usually leads to the correct conclusion.
     
  15. CTD50

    CTD50 DX's Biggest Member

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    photosbymark has you by the short hairs, drkangel.......

    You cannot reduce on-road risk to a simple equation; there are too many variables. You cannot, for instance, assume:

    1. regular rate of traffic;
    2. constant flow from time of day to time of day or evening;
    3. constancy of threatening/impaired drivers over the course of the day.

    PBM has already told you that being passed is not a hazard or a safety threat; being passed TOO CLOSELY is. And there isn't an equation out there to account for random stupidity. AND, regardless of the speed you are going, if you are struck by a 30mph vehicle, the speed of your immediate fall will be 30mph.

    Your math appears sound; your premise, however, is flawed. So, NO -- I'm not voting in your poll.
     
  16. DrkAngel

    DrkAngel New Member

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    Physics Major ....... NOT!

    I'm sorry, hopefully I just misunderstand what you wrote. But you seem to be saying that a car (going 30 mph) hitting a bicyclist (going 29 mph), from behind would be an impact as damaging as hitting a bicyclist sitting in the road!???

    That is totally foolish and might even be grounds for a criminal indictment of the educational system.

    Will the biker, somehow, (magically?), be accelerated to 59 mph?

    As an example, you note stock cars (doing 190 mph) bumping, and that bump being the equivalent of a 190 mph impact! ... In case you never watched a stock car race, most every car is bumped, several times, every race. And guess what ... they are not all completely crushed from repeated 190 mph impacts. 1 - 190 mph impact will totally crush & mangle any stock car!

    With logic like that, a child, on a jet plane could push a penny through a brick, sitting on the seat ahead of him, with his 600 mph speed.

    Even better ... since the Earth is moving at 1000 mph, don't touch anything! You will be crushed by a 1000 mph impact!!!

    Please talk with someone who has a basic understanding of physics.
     
    Last edited: Apr 3, 2010
  17. photosbymark

    photosbymark New Member

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    Well I apparently didn't make myself clear. What I did say that because a car approaches at a lower closure rate, it does not lessen the impact to that of the closure rate. It is still at least a 30 mph impact when person hits ground. It isn't the impact of the 5 mph closure rate. I don't know many cyclists that can have a rear wheel hit by a car, have the momentum of that spinning disk altered and still maintain control.

    Well I say I have seen a few Nascar stock car races. I have been around long enough to see Richard Petty run in his prime. Yes they make contact all the time. Yes they can even bump draft of the straight, but IF that tap comes in a quarter panel, isn't perfectly straight or comes in a turn at just the wrong time, it takes very little to lose control and that impact with the wall is a 190 mph impact not the little tap it took to lose control of the car. The cars don't often crush because they are designed to crash, but I have seen it. The difference in the analogy is that a stock car is racing cars of equal mass and rough equal abilities in traction and tires. That's not the case with a car/bike impact.

    To take that to the bike, the perfect bump draft would still disturb that spinning rear wheel and foul up the gyroscopic affect helping one keep their balance. Any other is going to push the bike to one side or another. Regardless I take the wager that no matter how it hits, one isn't going to stay on the bike.

    Now your standing still vs car at 30. That is different but not the point I was trying to make. Still it would of course be a bigger hit, well actually two. Impact one would be car striking you. Lots of mass and speed to transfer energy, for impact two which is you hitting the ground if you are awake to feel it.

    Now if the earth were to stop moving, lets just hope its a gradual stop. If its not and we keep moving anyway it won't matter. grin
     
  18. DrkAngel

    DrkAngel New Member

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    Impact?

    I'm afraid that I consider the "impact" to be the collision with the vehicle. No matter what the initial speed, the biker will be almost instantly accelerated to the vehicles speed, within inches, similar to being hit with a gigantic baseball bat. The slower the biker is going, the more horrific is the blow from the "bat". After the initial "impact", the biker will go into some form of 30 mph slide or tumble, (stopping over, possibly, 30 - 50 feet.) Nasty, road rash, bruises etc. but not much that could be considered an "impact". Likely, nothing near so traumatic as a 20 mph blow from a vehicle.
     
    Last edited: Apr 4, 2010
  19. photosbymark

    photosbymark New Member

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    not necessarily. Not all the energy will be transferred to the biker. Will it cause a bike rider to accelerate? Maybe depending on the angle of impact. There are a lot of situations where the initial contact with the car may not be the immediate acceleration you envision. Though possible, it would take things to be just right. It may not even be with the front of a car. The last close call I had was when a car moved back over after passing me and forgot to remember that things are closer than they appear in a mirror. Part my fault because he gave me plenty of room and I got a bit complacent. It was a situation I could avoid, but more alertness on my part would not have made it as close as it turned out to be. It would have been his rear bumper that dumped me. It could just as easily have been a bump to a handlebar that puts you down from being crowded.

    You won't maintain control. As to the aftermath, again it depends. Yes you might slide and tumble and if you are lucky just get road rash. That impact with the ground isn't going to be under control either. Broken arms and legs are just as likely. A broken leg can be very serious depending on where it happens. You can bleed out very quickly if the artery is severed. Hit head or neck first and the scale of the injuries pile up. Bad news, and likely you will have no control over how you hit. Even if you miss the injury from impact with the ground, you are not out of the woods. Slide into a parked car, fire plug, hit a curb in the wrong way, or a light pole and its gonna hurt bad not to mention that you are counting on the person that just hit you not to run over you again.

    Yet these types of discussions are important to safe cycling. You can not manage a risk you either don't think about, don't recognize or don't understand. Risks you don't manage, manage you. One thing I am doing as a result of this discussion is to do more testing to find a better solution with mirrors. What ever the speed, being better aware is going to help me to take more control of what goes on around me. A helmet mirror might be a problem for me because my left eye has a fairly significant vision loss putting the mirror in my blind spot if its where everyone else puts one. The one on the handlebar may or may not be effective. Time will tell
     
  20. DrkAngel

    DrkAngel New Member

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    Actually, the "impact" with the ground is solely a result of the falling distance from the bike to the ground, 3 - 4 feet, very minor, and in itself not likely to produce injury. The initial vehicle impact is the major factor, followed by the possibility of sliding into stationary object, followed by the "slide", and leastly, the fall from the bike.
     
    Last edited: Apr 4, 2010
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