One use of Xtracycles is to help riders of unequal speed ride together happily. The faster rider rides the Xtracycle, loaded up with kid, camping gear, food and water, tools, pig iron, parachute: whatever it takes to slow the rider down (except downhill of course). The slower rider rides an unladen bike. Think thoroughbred and drafthorse heading down a road together at their own naturally equalized pace (that of the drafthorse). Now, I ask you, do thoroughbreds really enjoy being hobbled to drafthorse speed? Suppose you might not undertake the journey at all if that’s the only choice?

landboatdrumStokemonkey makes this equalization work in reverse; the slower rider carries all the stuff and has assistance to make it easy to keep up with or speed ahead of the unladen rider. As a bonus, the unladen rider can draft the X/SM and get sucked along nicely whenever s/he tires. (I submit that Stokemonkey turns an Xtracycle into a fine sag wagon, with the capacity to haul a rider and his or her bike together. I know which kind of vehicle I’d rather have shadowing a “supported tour.” If one’s not enough, take three?)

This is how our overnight family trip to Sauvie Island worked. Wife rode Xtravois hauling child in trailer and all our stuff; I rode plain bike as fast as I wanted, and we stayed together without either of us even thinking about the pace. It was only 25 miles, so when we arrived at our Bed & Breakfast, she wanted to keep going, and we did. We visited a nursery and picked up four exotic potted plants, relishing the astonishment of the management as we loaded them onto the bike to haul back to Portland. The plants fluttering in the wind made a nice zinger as we overtook a couple of roadies on the way back.

We topped off the batteries as we slept. The next morning’s ride home, right after crossing the St. John’s Bridge, we saw an empty 55-gallon drum on the sidewalk with a sign taped to it: “FREE. CLEAN.” This is why we carry an extra-long compression strap. We had been looking for such a barrel to serve as a rain catchment. Lashed on tight, she said she couldn’t tell it was there.

Continuing home through North Portland, we attracted lots of stares, some unfavorable. Even I was feeling a bit nutty with that drum strapped on. We pulled up alongside an SUV at a light. I took a picture of the scene, but my camera settings were wrong so you have to use your imagination. I planned to annotate the photo of the two travelers under the heading “Who’s the Nut?” Over the SUV would be:

  • Fun?
  • Caged
  • Single occupant, fast food wrappers, cell phone
  • Approximately 3,000 pounds
  • In-town average speed: 20MPH (less after factoring in parking)
  • Expends ~6,600 calories per mile (petrocarbon, mostly imported)
  • ~$30,000 finance cost. Gas is what? Insurance? Parking?
  • Spews toxic fumes; makes noise; cars are the leading cause of death of children 2-14 in the US
  • Drives to gym?

Over the bike:

  • Fun
  • Free range
  • Double occupancy, plants, 55-gallon drum, changes of clothes, food, cell phone
  • Approximately 75 pounds
  • In-town average speed: 18MPH
  • Expends ~300 calories per mile (largely from rider’s metabolism)
  • ~$3500 initial cost. 20 miles strongly assisted for the cost of running a 100W lightbulb about 6 hours. Maybe $200 a year in maintenance, accessorization. Free parking at door.
  • No emissions, virtually silent, about as safe to operator as driving or walking per hour of exposure to cars; incomparably safer to other street users
  • Exercise=mobility.

It’s easy to pick on SUVs. So substitute a Prius: same difference.

42 thoughts on “Equalizer”

  • Erik Sandblom

    I love Stokemonkey and website and business, but I’m not sure about the “safety to other street users” part. It says in the newspapers that a car with a round shape, like a Prius but not like an SUV, can crash into a person at 30 km/h without fatally injuring that person. Now compare that to getting handlebars coming at you at 30 km/h. They probably dig deeper into your body before coming to a stop.

  • Todd

    I’m surprised you make this argument. Where to start? I submit that the situational awareness and agility of a bicyclist is so far superior to that of a car that the relative difference in likelihood of a collision makes the rest of the analysis nearly moot. I don’t think it’s quite fair to compare collisions at the same speed, because obviously the car has a much greater mean speed while moving unimpeded by other cars and traffic controls. The bicycle keeps up in human-scale built environments by means of riding past car queues and parking delays, not by having nearly as high a terminal speed. Even accepting equal speeds, the kinetic energy difference is enormous, even adjusted per unit of frontal area (a car has the width of several bikes). Finally, by “other street users” I wasn’t thinking solely of pedestrians. I was thinking first of motorists, who dominate in number presently. I acknowledge that in a high speed collision with a car, I will likely end up dead, while there is very little chance that my bike will kill a motorist. If we were both driving, the likelihood of 2 dead bodies is considerable. I find repugnant the reasoning that larger cars are safer than small, or small cars than bicycles, or freight trains than baby carriages; it’s the same with, say, nuclear proliferation or preemptive defense: safer for whom? Does anybody or anything else matter? Within the context of civilization, the safest vehicle or policy is the one with the least capacity to cause harm.

  • Erik Sandblom

    A fair amount of research and testing has gone into making cars collision-friendly for pedestrians at low speeds, ie 30 km/h. A low, rounded car like a Prius will hit a pedestrian in the legs, and then the pedestrian falls on the hood. You can see many cars built like this nowadays, the Mini Cooper for another example. Low, rounded and swept back. It’s not just for aerodynamics or looks.

    This has led the Swedish authorities to strive for 30 km/h being max wherever there are “unprotected road users”, ie pedestrians. Unfortunately this has not been fully implemented. If it were, more people would be bicycling!

    Bicycle handlebars, on the other hand, would probably hit a pedestrian in the stomach. The stomach is not going to absorb any kinetic energy from handlebars moving at 30 km/h without first being badly damaged. Given a choice, I’d rather be hit by the Mini or Prius at 30 km/h than a bicycle.

    If this were considered a problem in practice, it could be solved by putting a 15cm high fairing on the handlebars. That way a bike would just knock a pedestrian over, not jam a steel bar in their stomach.

    I would like to see bikes given more space and priority. I’m a little irritated with dinky bike paths which seem to assume that a bike doesn’t top 15 km/h, or doesn’t take any energy to stop and restart. Maybe the designers of these paths are intentially trying to keep the speed down. Were the paths made for 20-30 km/h or so, and cars limited to 30 km/h, more people would ride and fewer would drive. And that’s when the bicycle-pedestrian-collision issue might crop up.

    Does that clear it up? Do you see where I’m coming from?

  • miketually

    “Given a choice, Iââ?¬â?¢d rather be hit by the Mini or Prius at 30 km/h than a bicycle”

    Really? I don’t believe that for a second.

  • Erik Sandblom

    Yes, Miketually, if the bike and Prius are both going to hit me at 30 km/h, I choose the Prius. The bike will probably hit with half-inch tubing in the stomach, torso, groin. I don’t think the impact will be lessened because the bike has less momentum; my body is taking all the impact anyway.

    The Prius has no protruding parts or tubes. I’m going to be hit in the legs first, then my hip or bum.

    Think of it this way: would you rather be hit by an ordinary Prius at 30 km/h, or a Prius with half-inch tubing sticking forward at stomach height, also at 30 km/h? To me it seems clear that a flat round Prius will hurt me less than one with tubing sticking out in front.

    If this seems counter-intuitive, it’s probably because, as Todd says, a bike is less likely to hit you anyway, since bikes can swerve and usually go slower than 30 km/h. But forget all that and think of when the impact is a certainty: what then? That’s what I’m talking about.

  • Todd

    OK I’ll play. The leading edge of a bicycle is not a length of tubing, but the rounded profile of a pneumatic tire, softer than most car bumpers, and with a mass driving it that’s negligible compared to that of a car. Moreover it will easily be deflected off to one side at the steering axis. Remember that the bike weighs far less than what its rider does, and the rider in the event of a collision will quickly become a projectile uncoupled from the bike itself. It goes without saying that a full-on bicycle-pedestrian collision will result in the bicycle coming nearly to a stop from the impact, while a car-ped collision often makes stopping a matter of discretion for the driver. “What was that bump?”

    If the bike-pedestrian collision is off-center, such that the tire isn’t the first bit to strike, then indeed the bars may strike first. But again thanks to the steering axis, the impact will have all the force of running through a revolving door, with the bars immediately yielding to one side.

    A car bumper, however rounded, will hit a small child in the head, chest, or waist.

    I don’t dispute that pedestrian-bicycle collisions can be very nasty, even fatal. And I’m glad that some cars are designed to mitigate collision damage to people outside the cage. But to talk about fitting bikes with fairings to address the supposed threat to pedestrians is, well, silly. See Velorution’s excerpt from recent debate at the House of Commons: http://www.velorution.biz/?p=1173 . Walking helmets will be next.

  • Erik Sandblom

    I’m impressed with your reply, Todd. The steering axis acts as a crumple zone, and the rider comes off, reducing momentum. Very elegant, never thought of that.

    That assumes the rider lets go of the handlebar and is not holding on for dear life in panic, using his/her arms to steer straight. If s/he holds on, the handlebars and wheel will not turn as much, and the rider will push the bike along with his own weight.

    I imagine holding on and trying to go straight is better for the cyclist, while letting go is best for the pedestrian being hit. I’m still not convinced the fairing wouldn’t do any good in a situation like that. But no, I’m not putting any fairings on my bikes.

  • Dad

    Not to put too fine a point on it, but what if the bike had a wire basket attached with a potted plant inside?

  • patrick

    My one experience in this subject agrees with Todd’s analysis.

    My worst bicycle accident to date was when I struck a jogger. It was raining, dark, January, Seattle. I was cycling at full clip (15 mph?), he was starting off from a standstill, crossing my path from my right. I saw him at the very last second, too late to even brake. I believe that I “let go” rather than hang on for dear life. In any event, the jogger didn’t see me. He started off and in doing so passed in front of me just as my bicycle’s front wheel made contact with his leg.

    I don’t have any memory of the next few seconds — my next memory is sliding along the pavement on my helmet — but from witnesses’ accounts I gather that he brushed my front wheel, my wheel turned to the left, the bicycle stopped, I flew off the bike and over it, and I landed hard on my right wrist, crushing my wrist beneath my torso.

    The jogger seemed vaguely annoyed to find this crumpled person beneath him. He helped me drag myself out of the roadway, and jogged off, seemingly without a scratch. I’m guessing his would have been a different experience had I been operating a Prius.

  • uroburro

    Todd, you’re being too kind to the SUV–average weight of these vehicles is well over 4,000 lbs now. Heck, average weight of all car/SUV’s is over 4,000 lbs now (EPA stats).

    Re: bike or car collision–Force = mass x acceleration. We’re talking order of magnitudes difference here.

  • Todd

    my caloric cost estimates are probably way off too. disclaimer: this is not a rigorously researched post.

  • Andrew

    As Patrick says, “I flew off the bike and over it”. I think this is what happens the vast majority of the time. The bike stops, the person keeps going. Thinking you can stay on the bike is dreaming.
    In the earlier case of a bike vs Prius , I suggest that the pedestrian would essentially have only the weight of a bike hitting them at 30km/h, since the rider would be thrown.
    There is simply far, far more energy being transferred to the pedestrian if hit by a car than a bike.
    Ultimately, I’d rather have handlebars to the midsection than a windshield to the head, especially if there was a nice wicker basket on the handlebars.

  • Bill Manewal

    On authority of an forensic engineer in a lawsuit I was involved in: in almost no instances can a rider of a bicycle or motorcycle stay on board if hitting something at a speed greater than 10 mph. That’s how it was proved that I did not hit a car, but that the front fork crown failed and released the front fork and wheel: the bones in my hands fractured when caught between the grips and the pavement as evidenced by my dried blood on both grips. And happy Mother’s Day!

  • Erik Sandblom

    I don’t think the greater weight of the car makes any difference, since the pedestrian is either being thrown to the side of the bike, or up over the car. The amount of force is the same since the weight of the pedestrian is the same. The greater weight of the car would only be relevant if the pedestrian is being sandwiched against a wall, or falls under the wheels.

    If the pedestrian survives the 30 km/h collision with the car, it will be because of the way the impact happens. He is being bumped in the legs, then the hip or bum, over the car. The car could keep going and that would be fine (as long as the pedestrian doesn’t impact again from falling off the car). It wouldn’t affect the way the impact happened.

    The reason the bike collision could be more dangerous at the same speed, is that the pedestrian is being hit once in the stomach, not the two-step legs and then hip collision. Even if the bike rider is sure to be thrown off, the mechanism causing this to happen is the pedestrian’s stomach. I assume the bones can heal, not sure about the stomach.

    Of course, this type of car design only helps people who are tall enough to be hit in the legs first.

  • Erik Sandblom

    Bill and Patrick, hope you have fully recovered.

  • Bill Manewal

    97.7%, thanks!

  • Todd

    Erik, the mass of the striking vehicle matters. Think of a battering ram or golf club. You don’t want a light one if you want to smash the gate or whack the ball far. Lighter striking masses decelerate more and more rapidly than heavier ones on impact.

  • miketually

    I think I’d choose the bike over the car. The mass of the (bike + person) is of the same order of magnitude as (person), whereas (car + person) is way more.

    Regardless of the design of the car, the impacts from a car will likely go:

    bumper (US: fender) against legs – legs against steel and plastic at 30km/h
    possibly hips against bonnet (US: hood?)
    head against windscreen (US: windshield?) – head against reinforced glass at 30km/h

    There are then various permutations of impacts as the pedestrian flies over the roof of the car. Ending with a fall from the back of the car to the tarmac below.

    During all this the velocity, and hence the energy, of the car remains virtually unchanged.

    When a bike hits a pedestrian, there are lots more variables, but the first point of impact is likely to be either the tyre, which would cause the handlebars to turn, of one end of the front face of the bars, which would also cause them to turn. These impacts are likely to be against the legs or the side of the body. The rider is also likely to hit the pedestrian. From here, all sorts could happen, but the bike will decelarate, so both parties “share” the energy of the impact.

    The masses and energies involved in a crash between a bike and pedestrian are all human-scale. Our bodies have evolved to cope with the sort of impacts we can receive when being hit with energies of this order of magnitude. Once a car is involved, we are talking energy above the level at which we are likely to survive.

    A good analogy just occured to me: Would you rather be hit in the legs and head with a sledgehammer, or in the stomach with a rubber mallet?

  • Bikeridingdonutguy

    You guys all have some good points of view, but most of us that ride (and I include present company) are still gonna ride because of one overriding factor………..

    It’s fun :-)

  • Mauricio Babilonia

    Heh, you’re right, donutguy, it is fun!

    Two things:

    1. An Xtracycle can carry two barrels if you have the wideloaders attached.

    2. Todd is correct. When you hit a pedestrian, the bike stops a whole lot faster than your body. Miketually is also correct that “both parties [assuming the pedestrian and cyclist are of roughly equal mass] ‘share’ the energy of the impact,” per Newton’s third law of motion. I can tell you from experience that cyclist vs. pedestrian sucks just about equally for both parties. Car vs. pedestrian almost always sucks a whole lot more for the pedestrian than for the driver of the car. Thus, I would argue that, if for no other reason than a cyclist’s normal interest in self-preservation, the bicycle is “incomparably safer to other street users” than the automobile.

  • Jim

    I was set to weigh in on this discussion yesterday, but changed my mind. But I guess I can’t resist.

    I’ve never heard of a pedestrian being killed in a collision with a cyclist. I’m not saying it never happens, just that I can’t recall hearing about it. I can’t say the same for car-pedestrian collisions resulting in dead pedestrian(s); I’ve heard of lots of those. Maybe having a round-fronted car reduces the damage to the pedestrian who gets hit, in theory, but that kinetic energy doesn’t just go into recharging the battery of the Prius. Depending on one’s traction on the pavement, I imagine some of the energy goes into breaking legs, and the subsequent skull cracking that happens when the pedestrian’s body slingshots into the hood/windshield.

    But far more important than kinetic energy and momentum transfer is the fact, which I think someone mentioned before, that it is much less likely for a bike to hit a pedestrian than for a car to do the same. The bike’s narrowness, not to mention the cycilst’s agility and awareness, conspire to make these collisions relatively unlikely.

  • @man

    This thread is crying out for some physics.

    Some of use remember that velocity is the derivative of position, and acceleration the derivative of velocity. Continuing this we have the intuitively named “jerk”, the change in acceleration with respect to time. It is jerk that causes injury; too much jerk to one part of the body will cause that part to strain or break, and jerk to the entire body just makes that happen in more places at once.

    Momentum is mass times velocity, and it is conserved; as mass is not transferred, it is entirely velocities that come into line. But read that carefully; it does NOT matter whether a vehicle is twice as massive or twice as fast, so being hit by a 2000 kilo SUV at 30km/h transfers the same amount of momentum as a 1000 kilo compact at 60km/h.

    As for our 200 kilo fully-laded SM/XC moving 30 km/h, it transfers as much velocity as that SUV at 3 km/h. That is to say, not much.

    I did mention it’s not the velocity, it’s the jerk, which is how quickly you accellerate into that velocity. An SUV at 3km/h can’t transfer that velocity very quickly, so you accelerate with barely a jerk, while the bike and passenger crashing into you in a tumble at 30 km/h is going to jerk you various ways…here is where I’m going to start waving hands, but basically the jerk is determined by what percentage of the total velocity is transferred in any given time interval; if that percentage is low, the vehicle will accelerate less as the passenger accelerates more, like the difference between the speed of a baseball bat and the speed the ball jumps at. Thus, our Prius or SUV or whatever is going to cause considerably more jerk than our bicycle, moving at the same speed, possibly even greater than the difference in transfer of velocity. This is why the bicycle stops and the car doesn’t, in a collision with our 90 kilo test subject; a motorcycle would probably fall over and continue to skid a considerable distance, where the bike and test subject could be expected to collapse a few meters from the incident, probably 2ish.

    I hope this makes it clear why the only reason to worry about being hit by a bicycle as a pedestrian is that it might knock you into motor traffic.

  • Jim

    Crying out for physics is right!

    First, it is the fast transfer of kinetic energy which is responsible for doing the damage – specifically, the deformation regime of the front side of my skull at a speed of 30 kph (while the back side of my head is still at 0 kph) is brittle fracture, and, when that happens, my brains will fall out. Note that it isn’t the speed itself that kills – my skull travels at 30 kph every day – it is the quick acceleration to that speed, which is the result of a force imparted by the impact. It seems to me that the change in acceleration w.r.t. to time is irrelevant in this case, as are higher order derivatives. Consider that a steady acceleration (da/dt=0) of 0-30 kph in 1/100 of a second would probably be deadly, especially if the force is directed to a vital body part while the rest of the body is stationary, even though the change in acceleration is zilch. There would be a “jerk”, but you don’t need the third derivative of position w.r.t. time to be large to perceive a jerk. It’s the force that does the damage, not how fast that force is changing. At any rate, F=ma is the same as conservation of momentum. Since ma is really just the time rate of change of momentum of a body, and must be offset by forces on the system in question.

    It isn’t really meaningful, I don’t think, to talk about the mass of the impacting vehicle, particularly when the vehicle is large, in affecting momentum transfer. A large vehicle, like a SUV or a bus, barely notices the impact with a pedestrian. The only momentum that is transferred is that which is lost by the bigger vehicle, assuming the pedestrian is stationary. The SUV or bus hits the pedestrian, and the speed drops imperceptibly. If the pedestrian is Superman, and the car that hits him comes to a complete stop as a result, then the pedestrian will assume 100% of the momentum lost by the car (neglecting frictional and viscous losses). The only way to transfer the momentum of the car to the pedestrian in proportion to the car’s mass is if the impact resembles that of billiard balls, with the striking object (cue ball or car) coming to a total stop after imparting all of its momentum on the object it strikes. Think about bugs on the windshield. The fairings of fast recumbent bicycles get bugs splattered on them, as do the windshields of city buses. Every bug that splatters on the window increases the mass of the vehicle, and decreases the vehicle speed in proportion. It doesn’t really matter how big the vehicle is; beyond a certain speed, the bugs always splatter. If momentum transfer was relevant to the discussion, we would note that the bugs hit by a 1000 kg vehicle fly off at 1 million kph, while the bugs hit by a 2000 kg vehicle fly off at 2 million kph. But that’s not what happens. In fact, and I haven’t proven this, I’d wager that the size of the splatter is proportional to some power of the velocity, with mass hardly having an effect.

  • Todd

    The nice thing about our Sauvie Island trip were the flowers and the sheep. There were even a couple llamas. If a 126.4Kg llama were to wander into the road, how fast would a 1988 Lamborghini Countach need to be doing to sheer the llama off at the knees? I’m looking for a range here; obviously we can’t account for all the variables with precision.

  • Mike C

    There was a big discussion about this on the Brompton list a few months back. It was centered around whether it’s as bad for a cyclist to run a red light or stop sign as it is for a car. One factoid brought up during the discussion was a figure of 4 pedestrians killed by cyclists per year in the UK. Whether that’s the average over some period, or an actual figure from a recent year, I dunno. But the person citing it went on to compare (total car miles per year/car-pedestrian fatalities) to (total bike miles per year/bike-pedestrian fatalities) and the numbers came out about the same – i.e. (this person contended) that bikes are just as dangerous to peds per mile traveled as cars.

    It didn’t sound right to me at the time, and still doesn’t, but if it’s wrong, I’m not sure where or why. I do remember TransAlt in NYC saying that cars driving up on sidewalks kill ~20 people per year in the city, vs. 0 killed by bicycles; so anecdotally there’s a counterexample. But I’d be interested to see comparable figures for other countries.

  • miketually

    “If a 126.4Kg llama were to wander into the road, how fast would a 1988 Lamborghini Countach need to be doing to sheer the llama off at the knees?”

    Is that a North American or South American llama?

    Sorry, weak Monty Python-inspired joke.

  • Don Felix

    for Mike C.
    Further up in the thread there’s a reference to a debate in the House of Commons, where one MP notes “In 2004, one pedestrian was killed in a collision with a cyclist, but that is the only recent known death.” So I wonder if that 4 pedestrians per year number was just made up to make the pedestrian fatalities per miles travelled number come out equal. Though for all I know that MP may have been wrong.

  • Erik Sandblom

    It turns out the best car is not a Prius, it’s a Citroen C6; and the impact speed tested is 40 km/h, not 30.


    Jim, it’s impossible for your head to hit the car at 30 km/h if the crash happens as intended at 30, as your head will be the third impact your body makes. Your leg and hip are hard enough to accelerate you significantly, and the head hits the bonnet/hood downward, not horizontally.


    Anders Lie (pronounced lee-uh) at the Swedish road administration says that adult pedestrians survive a collision with a Citroen C6 at 40 km/h due to the way the car is designed. The hood pops up and becomes a crumple zone.


    New Jaguar does the same. Scroll for instructive picture.


    The GP article states that there are 50 pedestrian deaths in Sweden each year, not sure if they are all (maybe most) due to being run over. I do know that car crashes cause 500 deaths per year in Sweden. Year after year…


    Still don’t want handlebars in my stomach, and I don’t want to use my stomach as a deceleration or acceleration device :-(

  • @man

    Jim, you went and complimified my simplific answer.

    It is true, acceleration alone can in fact kill…but acceleration applied slowly kills slowly, and only at up above say 5 Gs or so in a healthy adult. That’s a lot. Small amounts of jerk, by contrast, are quite damaging; the british word for jerk is “jolt” and the intuitive feeling they describe is correct. Let us say you were pedalling along on your bicycle attached to a safety harness; you reach the end of the tether, your bike goes on, you drop to the ground. The “jerk” you feel is in fact the change in acceleration with respect to time, aka jerk in physics. You go from none (cruising speed) to a lot (whatever it takes to bring you rapidly to a stop) in a short period of time. It’s a well-named concept. It is always associated with the action of forces to transfer kinetic energy.

    This means you are not incorrect, per se, in your first paragraph. The fact that you don’t see the equivalence of our explanations proves you’re more comfortable working with force and acceleration in your thinking and less so with momentum and jerk. That’s okay! Some time with wikipedia will straighten that out.

    When you say “It isnââ?¬â?¢t really meaningful, I donââ?¬â?¢t think, to talk about the mass of the impacting vehicle, particularly when the vehicle is large, in affecting momentum transfer.” you are of course correct, but when you remove the “I don’t think” phrase the statement is straightforwardly wrong. The amount of momentum transferred is significant to both the vehicle and the test subject, and will increase linearly with both the mass and velocity of the vehicle assuming a still test subject. Hitting a deer typically triggers airbags; that’s significant transfer of momentum right there. Since you are comfortable thinking in terms of force, surely it’s clear that a more Massive vehicle departs more Acceleration to our test subject, making a more Forceful impact? I’m really not trying to be a Jerk here…I’m just shedding light and speaking as clearly as I can.

    Talking about bugs, which have essentially no mass, is a good way to isolate the energy variable in your system, but not relevant to the significant mass of our test subject, which is only one order of magnitude removed from that of our vehicles.

  • Andrew

    Oh no, someone brought out the physics! It’s like a broken bottle in a bar fight!

    Curiously, in four years of undergraduate physics I never once heard the term “jerk” to describe a change in acceleration. What the hell was I paying for?! Or maybe I missed that class…

    Llamas are cute. Sheep too. See any ducks?

  • derek

    That bike is so great. Im just a little north of you, it would be cool to see that beauty in person sometime :)


  • Jim

    I missed “jerk” also Andrew, and to think I wasted 11 years of college and grad school studying geophysics and fluid mechanics when I could have just read wikipedia. If I understand it correctly, jerk is just a really large acceleration, either positive or negative.

    @man: momentum conservation and the familiar definition of force (F=ma) are equivalent (i.e. Newton’s Second Law). It isn’t a matter of “force and acceleration” vs “momentum and jerk” as you state. I hate to do it, but darn it, I seem to be powerless over my desire to clear this up! For a constant mass object, the only way to change momentum is to change the speed, so the rate of change of momentum is proportional to the rate of change in velocity dv/dt – i.e the rate of change of momentum is equal to m*dv/dt, which is just ma, which we all know is equal to F. Newton’s Second Law in words: the rate of change of momentum of a body is equal to the sum of the forces on the body. In equations, F=ma=m*dv/dt. But you seem intent on squeezing something out of the second derivative of velocity, so try this. A body at rest or at constant speed has an acceleration of zero. As I sit here, I’m a body at rest. If I suddenly get up and walk across the room, I don’t accelerate slowly to my walking speed, I get to that speed almost instantly. My change in acceleration might be only a few m/s2, but the change in time during which I get up to that acceleration is almost negligible. So that small denominator makes my change in accleration w.r.t. time almost infinite! And yet, I’m still alive, miraculously, after a lifetime of nearly infinite accleration rates of change. Conversely, if I was riding my bike at a constant high speed of, say, 20 mph, and I crash into a brick wall head on, I’ll probably die at the scene, even though my change in acceleration throughout the process is zero. At the instant I hit the wall, I will negatively accelerate rapidly to zero velocity. It is this huge acceleration/force/momentum transfer rate that does the damage. But if I have just taken my first pedal stroke, and I’m accelerating rapidly, but only traveling at 3 mph when I hit that wall, I probably won’t get hurt at all. And one more example. If I’m sitting in the driver’s seat of a sports car, and I peg the accelerator, the car will accelerate rapidly, such that my body will be driven back into the seat. This force acts during any acceleration, regardless of whether the acceleration is changing or constant. If I reach a constant speed (zero acceleration), my body will no longer be driven back into the seat, except by normal gravity forces. If I then press the gas pedal closer to the floor, or press the brake, my acceleration rate will change almost instantly, again a near infinite time-derivative, but we do this all the time (though most of us don’t do it in a high performance sports car) and we generally live through it.

    Next, I’ll address this llama problem…

  • @man

    “If I understand it correctly, jerk is just a really large acceleration, either positive or negative.”

    You don’t understand it correctly. Check http://en.wikipedia.org/wiki/Jerk. I don’t know how you missed it, since you’re claiming an advanced degree in the field. A little embarassing, don’t you think? I even told you where you could look it up, if your textbooks weren’t handy.

    Check it:

    “Jerk is used at times in engineering, especially when building roller coasters. Some precision or fragile objectsââ?¬â??such as passengers, who need time to sense stress changes and adjust their muscle tension, or suffer, e.g., whiplashââ?¬â??can be safely subjected not only to a maximum acceleration, but also to a maximum jerk. Jerk may be considered when the excitation of vibrations is a concern. A device which measures jerk is called a “jerkmeter.”"

    Thing is, my jerkmeter is TOTALLY MAXED OUT for this conversation.

    You ask me to consider the case of a bicyclist riding at 20 mph crashing into a brick wall. This causes the acceleration of the bicyclist to go from 0, constant cruising speed, to extremely high, whatever it takes to bring the test subject to a halt while displacing the brick wall essentially none. Get that? A change from no acceleration to a large amount, over a small period of time, aka jerk, the third derivative of position with respect to time.

    “It is this huge acceleration/force/momentum transfer rate that does the damage” great. It’s called jerk. Now you know, and don’t have to wave your hands around the concept because you have a name for it. No. Big. Deal. “transfer rate” aka “change in respect to time”. The amount of momentum or force which is transferred over a given time period is represented as jerk, a vector quantity. It’s the difference between shoving someone and punching them in the face; the latter is more of a jerk move, even when equally forceful.

    I can demonstrate, suggestively, that it is jerk and not acceleration that causes damage in the typical case. Lets say you freefall for five seconds, at earth gravity. You agree that it would take five seconds of freefall at one G in the other direction to stop you? How about one second at 5 g? half a second at 10 g? The human body can take 10 gs of acceleration for two minutes or more, and you take at least that half a second to fully impact with the ground. But jumping from 0 change in acceleration to “a lot” in such a short time is enough jerk to kill you dead. The sensation of acceleration is smooth; the sensation of change in acceleration is, well, it’s a jerk.

    I encountered jerk in Resnick and Halliday but you can read about it on wikipedia, which is an excellent resource which I wouldn’t have to lend you. You picked the wrong bloke to patronize; your suggestive bloviation about getting up out of a chair and pressing the gas pedal would evaporate under hard numeric analysis, as it is for instance jerk which causes whiplash. That little jerk you feel when you go from resting comfortably in your seat to pressed back into it: that little jerk, magnified, is what kills you in a crash.

    This sentence represents a joke about llamas, showing how I’m way cool and above all this physics stuff.

  • Ian Hopper

    Who knew you could get so many miles from just a couple of jerks? smirk

    The writers have been sacked� and the sackers have been sacked as well�

    Blue…no yellowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

  • Ted Howard

    Hi folks
    Interesting topic, and sadly we’ve had a fatality here in NZ that made it into today’s
    local paper :

    “Cyclist Charged Over Death
    A cyclist involved in a collision with a jogger in a Hamilton underpass in February will be
    charged with careless use of a vehicle causing death. Police have been investigating the
    accident for the past three months.
    Momoe Sugiyama, 52, was jogging out of the eatern side of the tunnel at the corner of
    Wairere Drive and River Rd on February 9 when she was knocked down by a man on a bicycle
    and later died in hospital. The cyclist stayed with her after the accident”

    So I’m with Eric, and wouldn’t want a set of handlebars in my guts at 30kph!
    Shit happens, and it’s sad to see it be fatal.

    Have fun and be careful out there!

    Ted Howard
    Nelson, New Zealand

  • Josh Larios

    According to the Waikato Times: Mrs Sugiyama, the wife of a senior Japanese diplomat who was living in Hamilton while her daughter attended Waikato University, suffered severe head injuries and died a week later in Auckland Hospital.

    I don’t doubt that cyclists can and do kill pedestrians, as the unfortunate Mrs Sugiyama proves. But absent any evidence that handlebars to the torso cause organ trauma leading to death, I’m still not convinced that being hit by a well-designed car is better (for the victim) than being hit by a bicycle. I’m with you on not wanting to find out what it feels like to be hit by a cyclist in the absolute worst-case scenario. But I’m willing to bet that, on average, a head-on impact from a bicycle causes less damage than a glancing impact from a car.

    (Insert something clever about llamas here.)

  • Jess Austin


    Jim may have been unclear in his description of this situation, but what you write is simply wrong. I normally wouldn’t enter the fray after more capable physicists have already withdrawn in disgust, but in this case the forces of ignorance threaten real harm to the cause of bicycling, so if I didn’t step in my own degree would be worth a bit less.

    First, let’s back away from oddball physical terms that few engineers and even fewer physicists use. Let’s talk about energy, because in this case as in most others it’s much more instructive. We all know that the overall energy of a given system is conserved, but that it may be transferred among various components of the system. We know that the total kinetic energy of our two-component system is the sum of the respective mv^2 quantities. We know that as the pedestrian and vehicle tend more toward being two billiard balls, their collision will tend toward being more perfectly elastic. In the perfectly elastic case, the pedestrian would fly away at a velocity determined by the ratio of her mass to that of the vehicle, the vehicle would effectively stop, and we could say that the vehicle had transferred all of its energy to the pedestrian. We don’t live in that world, so much of the energy goes somewhere else. While the elastic modulus of billiard balls implies strains far below their elastic limit at the stresses associated with customary billiards energy levels, the elastic moduli of mammalian tissues make no such implication for the energy of a speeding automobile.

    As one of the other posters said, some airbags are triggered by collisions with deer. The mass of a typical deer approximates that of a typical human, so we’ll take this as proof that the vehicle transfers some kinetic energy to the pedestrian even in the real world case where the vehicle is a car. If you believed Newton you wouldn’t need that proof. As an aside, what do you think an airbag sensor measures? Acceleration or jerk?

    So now we have that the vehicle has transferred energy to the pedestrian, much of which does not end up in kinetic form. Where did the energy go? Recall that energy and work are the same quantity. Somehow, a force has acted over a distance. The distance isn’t far (although it’s farther than that for the billiard ball case, it’s shorter than that for an insect, splat), and the force is great. At car-on-highway energies, this force will certainly be great enough to strain and then break bones, ligaments, membranes, and other structural and vital tissue. Bicycle energies are lower, the distance in contact will be longer, the force applied in contact will be less, the stress to the vehicle (or at least the bike rider) will be more similar to that to the pedestrian and both stresses will be less, and, on average, the likelihood of exceeding the elastic limit of a fatal proportion of vital tissue will be less. The sad news from New Zealand is a reminder that that isn’t always the case. Human impact resistance is probably somewhat chaotic at the margin. It’s certainly possible for one human body to cause the death of another without the use of a bicycle or any other dangerous tool.

    Where does the energy go next? It breaks some chemical bonds and then meets its destiny as heat.

    In the foregoing I fudged a bit because I was talking about car-on-highway energies. If the hypothetical car and hypothetical bicycle strike the pedestrian with the same velocity, what can we predict? Since the car has much greater mass (thus, even at the same velocity, greater momentum and greater energy) than the bicycle and rider, the somewhat inelastic collision with the pedestrian is unlikely to stop the car, while the bicycle will cease movement entirely. Therefore in addition to the forces of impact, you must consider the forces applied by each tire in series, unless the driver of the car notices the collision and applies the brakes in a timely fashion. Even if we assume that a typical pedestrian will be thrown clear of continued peril (after all, the collision is somewhat elastic), the car will still cause more damage at the moment of collision. The steel front end of a typical automobile has a much higher elastic modulus than tissue, so over a shorter contact time and distance it will spring back and deliver all potential energy absorbed in deformation to the body of the pedestrian. This means more force will be applied, which is what actually strains and damages tissue. This is why punching a steel post hurts more than punching a jerk, and this is the advantage of the crumple effect that certain automobiles employ – the energy is dissipated in crumpling the vehicle rather than the pedestrian, which is certainly a positive development. Consider that because of elasticity the pedestrian will be travelling faster after the collision with the car than after that with the bicycle, and so will be more vulnerable to secondary injury upon “landing”. Also consider the fact that (in my experience) in most collisions the bicyclist continues in motion after the bicycle stops, so there is actually a lower percentage of the bicycle’s already lower energy transferred to the pedestrian. I would rather be hit by a bicycle than by a same-velocity car in every case short of mounting a trampoline on the front of the car and arranging another one down the road a bit to catch me (which could be somewhat thrilling actually).

    OK, enough real physics. You quote omnipotent wikipedia thus: “Jerk is used at times in engineering, especially when building roller coasters. Some precision or fragile objects such as passengers, who need time to sense stress changes and adjust their muscle tension, or suffer, e.g., whiplash can be safely subjected not only to a maximum acceleration, but also to a maximum jerk.”

    You’ll note that even in the entry for jerk, in which jerk is the concept under consideration, even in the context of this somewhat contrived example the writer mentions maximum acceleration first before describing maximum jerk. Acceleration and force govern tissue integrity as already described. If I had to guess what jerk and yank (I’m not making that up!) are doing in this situation, I’d hazard that they affect how quickly a passenger must adjust the forces applied by her muscles to changes in acceleration so that her head doesn’t bounce from side to side, which could certainly annoy a roller coaster passenger. You’ve mistaken something that must be measured only in particular physical contexts for a deep meaningful concept.

    The other examples you mention are identical to the vehicle striking the pedestrian, under a suitable change of inertial frame of reference, so I won’t address those, other than to say that there’s a reason they call the gas pedal the accelerator. I was trying to figure out how someone with such a superficial understanding of physics could lecture a postdoc in such a rude fashion, so I decided to examine “Resnick and Halliday”. I found the review by Lydia Joyce on this page: http://www.amazon.com/gp/product/0471232319 quite instructive. Wrote Ms. Joyce, “The moral of the story is that Halliday & Resnick is easy–and deceptive. For an extraordinarily superficial survey for someone with little to no background in physics or calculus, it is adequate. But if you want to understand at a deeper level what is happening and why–go somewhere else.” I guess I need wonder no longer.

    The take-home for the bicycle enthusiasts who have witnessed this unfortunate exchange is that bicycles travel with much lower energies than automobiles. For a variety of reasons, the dissipation of these energies in a collision with a pedestrian is thus less likely to deform tissue in a fatal fashion. Add to this the greater situational awareness of a bicyclist over a driver, and I firmly believe that every able-bodied person who bikes rather than drives makes our society safer.

    I just got my Free Radical, so I’ll be travelling with a bit more momentum from now on. b^)

  • fred


    That was great reading. I never took physics in college and I feel deprived for it, but I think I still have some
    understanding of the sciences involved. Your explanation and elaboration was just as I have pictured such things in my
    alleged mind. I took the terms “jerk” and “yank” to represent short duration accelerations in a direction not necessarily
    desired by the designers of a ride, and as such, they seemed to be simpler ways of saying so. I’ve found such experiences
    on a roller coaster to be unpleasant and the primary reason I don’t care to ride one. I do enjoy riding my bicycle, however
    and hope not to collide with a jerk. Here in Florida, there are plenty of northern visitors, so I could possibly collide
    with a yank.

    On a more realistic note, my wife and I had the unfortunate experience (back in the early 80s) of a drafting overlap,
    resulting in our combined mass on a tandem bike colliding with a tree. Very little elastic involved in the energy transfer,
    but plenty of heat in the form of bent tubing and damaged tissues. Luckily the damage to the tissues was mostly caused
    by scraping skin on the tree.

    I have no intent of causing a helmet war, but the same accident noted above happened when bike helmets were not a common
    sight. We were on a club ride and were the only riders with helmets. The tree was angled in such a way that my helmeted
    head impacted first. I was knocked out, but came about a moment later. On succeeding club rides, there were six more
    riders with helmets, and the one after that, a dozen or more. Now it’s unusual to see club rides without head protection.
    In the spirit of the topic, I’m sure there was beneficial energy transfer between the tree and my helmet!!


  • Jess Austin

    hi Fred,

    I’m glad you enjoyed the explanation. For precision, let me elaborate a bit. The key concepts, in this as in all mechanics scenarios, are force and energy. Since we’re considering it, however, the definition of “jerk” is “the rate of change of acceleration”, not “a short-term acceleration”. If you haven’t had calculus, think of this as how fast the quantity called “acceleration” is changing at any moment. Also, note that acceleration is thought of similarly as how fast the quantity called “velocity” is changing at any moment. Likewise, velocity is thought of as how fast the quantity called “position” is changing at any moment. You probably have an intuitive kinesthetic understanding of position, velocity, and acceleration. There’s a reason why evolution hasn’t equipped us for perceiving or thinking about jerk. Tempting as it is to keep differentiating ad infinitum, our universe isn’t constructed so as to care about jerk and higher derivatives.

    Some have defined “yank” to be mass multiplied by jerk (there’s probably a social commentary buried in that definition), so that these two quantities are related in the same way that force and acceleration (and for that matter, momentum and velocity) are related.

    Your mention of helmets is appropriate. You’ve probably seen “one-time”, bicycle-style helmets, as distinguished from “reusable”, skate-style helmets. I guess the intent is that the former are more appropriate for the rare catastrophic collision, and the latter are designed for frequent lower-energy collisions. In theory, while both should have a much lower elastic modulus and elastic limit than bone, the one-time helmets might have a lower elastic limit than the reusable, which could allow them both to increase the “crush distance” and to dissipate more energy by breaking chemical bonds, at the expense of having to buy another helmet. However, they all appear upon examination to be made of polystyrene. I suspect that any such helmet is damaged somewhat by all impacts, and damaged beyond usefulness only rarely.

    I too have been knocked unconcious while wearing a helmet. I fell from a horse while wearing a snowboarding helmet. That same helmet had earlier provided seemingly complete protection from a tree encountered at high velocity while snowboarding (helmet marketers would probably have something to say about this sequence of events, especially in contradiction to the last point of the previous paragraph). Maybe this winter I’ll buy a new helmet. If I knew I were going to have a terrible collision tomorrow, I’d probably buy a new helmet for the occasion.

    As it is, I bike every day, and only rarely (e.g., on official rides that for some reason have insurance) do I wear a helmet. Last year I had a bike wreck that bent my fork enough to require replacement. I wasn’t wearing a helmet, I flipped over the handlebars, I landed on my lower back on asphalt, and I was sore for a couple of days. My head never touched anything so I suppose a helmet wouldn’t have mattered for this incident.

    There is a set of collisions for which helmets increase the probability of survival. If we order all collisions by the energies involved, that set will fall in the middle of the continuum. If collision survival were my only value, I would wear a helmet all the time. Of course, in that case I probably wouldn’t ever operate any vehicle near any street. Some other, implicit values must be responsible both for my decision to bike and for my typical decision to do so helmetless. Those values are probably reinforced every time a driver realizes that I know she knows what a terribly unsafe maneuver she just made, and then rolls down the window and yells that I “ought to wear a helmet”. Possibly my value set isn’t consistent or rational, but I try to behave rationally in response to that value set.


  • lizardbiker

    All the physics talk is phascinating. Thank you!

    How long does it take to honk?

    One additional consideration in the dangerousness of cars versus bikes is the difference in the reaction time it takes for the operator of a car versus a bike to sound a warning. Depending on how habitual a honker one is, it may take more than a split second for a car driver to find and hit the car horn when about to bump a pedestrian.

    Contrast the reaction time it takes for a cyclist to open their mouth and yell “Look out!” or “Aaaah!” There is only instinct involved in yelling, versus the learned response of hitting a horn, which in my driving experience can be slowed down by the more powerful learned reaction to hit the brakes hard. That difference in audible warning timing might be enough to avert some accidents. I think it saved my skin and that of the old lady who stepped in front of me on the bike path the other day. She heard me, stopped just in time as I swerved just in time, and we brushed by inches apart. If she’d stepped out from between parked cars and I’d been driving one, she wouldn’t have been able to hear me yell, and I couldn’t have stopped or swerved as fast as I did on the bike. Neither one of us would be very happy llamas right now.

    I also survived a potential car collision on a bike once, because the dude cutting into my lane happened to be driving a convertible. If he’d had the windows up and the radio on, he wouln’t have heard my well-thought-out articulate warning of, “Hey, don’t cut over here!” which under duress came out as the aforesaid “Aaaah!!” Luckily that was sufficient, and I slipped by with a couple inches to spare.

    This is part of why I never, ever wear headphones while bicycling. And always wear a helmet on my North American coconut.

  • fred

    Geico rider: I agree with you that a shout is a good warning system. It’s so very often intuitive and instinctive and with
    the right motivation, it’s probably as loud as a good horn! I’ve been in situations not quite as harrowing as yours, but
    enough so that my “hey!” was a good deterrent to being part of a collision from an unwary motorist.

    This past week, I committed an unforgiveable act of bicycling while answering my cell phone, in the rain, approaching
    a green traffic light. Of course it turned to red before I noticed and I proceeded through the intersection. Timing was
    such that the cars had not started to move, so I was not killed. I never run lights in any kind of traffic and this
    has permanently modified my behavior very certainly. It’s easy to do things not commonly performed on a bicycle when
    one’s bicycle is a velomobile, but I’ve removed cell phone use from the list.

  • [...] it has been some years since we’ve camped or even put more than 25 miles in a day on bikes as a family, much less nearly 200 in mountain wilderness, heavily laden, beyond services including cell phone [...]

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