Review By John Forester Of:
Bicycle Accident Reconstruction:
A Guide For The Attorney and
Forensic Engineer, 3rd. Ed.
James M. Green, P.E.
Lawyers & Judges Publishing Co., Tucson AZ
Mr. Green is an active expert witness in bicycle accident cases. This book is intended to cover the scientific knowledge necessary to determine the causes of bicycle accidents by the methods of accident reconstruction, for a readership of both engineers and attorneys. Engineers would need only the particular engineering knowledge specific to bicycles, while most attorneys would also need a basic overview of the principles of physics that underlie Green's methods. Bicycle Accident Reconstruction (hereafter, BAR) fails for both types of readers because Green does not understand the principles of physics that he thinks that he is using. Engineers would discover this by reading BAR, while attorneys would be (have been, on the evidence) mislead because they have no greater understanding of the laws of physics than has Green.
Green misunderstands the standard procedures for evaluating scientific work. He writes that he has "asked for peer-review from other professional engineers on the engineering dynamics." Peer review is done by referees chosen by scientific journals or societies. Asking one's friends and associates is not peer review and is unlikely to be very stringent. In Green's case it has not worked very well; his book is full of errors in elementary physics and mathematics that any competent referee would have caught. A very few of the many errors in the two earlier editions have been corrected in this one. Several, perhaps most, of Green's corrections correspond to criticisms that I made of his work during court cases.
Rather than being the survey of scientific knowledge or engineering methods that would make a suitable book, BAR is merely a collection of papers that Green has written about particular cases in which he has been involved. Green fails to distinguish liability from reconstruction when he writes that agreements waiving liability change the method to be used in accident reconstruction. Experts have often been asked to express opinions about whether the conduct of people, as disclosed by the reconstruction process, has met some standard, but changes in the standard do not change the mechanism of the accident or the scientific facts. Green errs about accident statistics. He writes that most failures of bicycle components "are experienced by bicycle racers when the equipment is stressed during racing." He also writes that "my investigative work has shown that one of the most prevalent accidents that has occurred to bicyclists is the premature release of the front wheel." No general survey of accidents to determine those that have been caused by mechanical failure has shown any connection with racing. Insofar as we know, racing and training for racing has a somewhat lower accident rate than general cycling. No general survey of accidents to cyclists has shown any proportion of them caused by premature release of the front wheel. If there were any such accidents, they were so infrequent that they were classified in the catch- all category.
Mechanical drawings have a rigid format that takes some familiarity to understand. Green writes that forks with holes for the front axle instead of slots are one cure for quick-release hubs, asserting on the basis of a drawing in Sharp's Bicycles and Tricycles of 1895 that such forks have been available since then. In truth, the drawing shows that the fork end must have been slotted (Sharp's words assume that it was), because the axle's internal components are larger than its ends and couldn't fit through the space shown in the fork if it were a hole instead of a slot.
The attorneys who read this book, not being engineers, should pay particular attention to evaluating Green's understanding of the laws of physics. Green calculates the speed of a cyclist descending a hill by the formula for masses falling in a vacuum. He gives several versions of his formula, one including the rotational inertia of the wheels, the others expressing the descent in different ways. He states that "field testing reveals that V = [2gd sin(slope)]**0.5 to be the most accurate formula." Since this does not consider the rotational inertia of the wheels it must overstate the speed more than one that does consider it. Green admits that his formula already overstates the speed because it does not consider wind resistance. The effect of wind resistance is considerable; at 25 mph about 75% of the total resistance is wind resistance. Using Green's formula, a cyclist on an 8% descent would reach 30.7 mph after traveling for 394 feet. When air resistance is considered, the speed would be 25.5 mph at the same point.
The dynamics of inertia present problems that Green does not recognize. One error is his frequent references to "shifting weight." He believes that the cyclist shifts weight when pedaling and must shift his weight when shifting the front derailleur. This is because Green does not understand the distinction between applying muscle force between fixed elements and moving a mass.
A similar problem surfaces in his calculations of impact force. For reasons of space, I give only two examples of Green's handling of physical concepts. The first example is his method of calculating the speed of a car that hit a bicycle by the amount of damage that the collision caused the bicycle, specifically by the shearing of a rear axle "bolt" by a "glancing blow." Let's assume, charitably, that Green means the rear axle when he says rear axle bolt. It is practically impossible for a rear axle to be sheared by the glancing impact from a car (or, for that matter, any of the other items that Green mentions: "pedal bolts, seat post bolts, and head-set bolts.") Shear requires a force resisted by a support, both practically on opposite sides of a single plane. The bicycle provides no such support, while the motor vehicle has no such sharp-edged corner that could provide such force. Green starts with the following information: a cyclist weighing 150 lbs, a car weighing 3,500 lbs, and a rear axle made of low-carbon steel with a shear strength of 48,000 pounds per square inch. Green also assumes that the axle fails in shear when one part has moved 0.096 inch relative to the other part. Green's earlier edition had different errors than I discuss below. By a fortuitous concatenation of errors, the calculation in his second edition produced a speed for the car of 58 miles per hour, a speed that sounds plausible for a collision that shears an axle. Presumably Green adopted a different procedure for this edition because he was given a copy of my review of his first procedure. Green develops a formula for the speed of the car based on the idea that the energy required to shear the axle is the total energy of the moving car. The energy to shear the axle is the shear strength of the material per square inch, times the area, times the distance moved before failure. The energy of the car is the standard M(V**2)/2 for total energy, which is equivalent to saying that the collision with the end of the axle uses all the energy of the moving car and stops it in its tracks. Green does no intermediate calculations, but produces a formula that calculates V**2 directly.
v**2=(r*pi*(d**2)*2*D)4*m Where r = unit shear strength, d = diameter of the axle, D = movement required to shear, and m = mass of the car.
However, Green gets his units wrong because he calculates partly in feet and partly in inches. Therefore, after multiplying his calculated value by what he thinks are the proper correction factors, he ends with a speed of 4.5 mph. The correct answer to this calculation is 0.8 mph.
Had Green computed intermediate values during his calculation, he would have learned that the force required to shear the axle is over 9,400 pounds. If a car moving at 0.8 mph, or even at Green's calculated 4.5 mph, hit a bicycle, it would have got the bicycle up to its own speed long before the impact had developed 9,400 pounds to shear the axle. If nothing else, before the axle sheared the wheel would have folded, and then the bicycle's frame, because both of these are much weaker than the axle. In any case, the car would have continued in motion, carrying the bicycle with it.
In theory, it is possible to calculate the initial velocity of one body involved in a collision if the following items are known: the mass of the body, the mass and initial velocity of the other body, the velocity of the combined mass after the collision, and the energy lost in the collision. In general, there is considerable uncertainty about the velocity of the other body, about the velocity after the collision, and about the amount of energy lost in the collision and its distribution among the various parts. These uncertainties render the method generally useless for calculating the unknown initial velocity. The standard method uses the conservation of momentum (speed times mass), which eliminates consideration of the energy lost during the collision (very hard to calculate), but which still requires both masses (generally obtainable) and two of the three velocities (may be available) to find the third velocity.
The second example of Green's handling of inertia is his methods of calculating both the speed of a cyclist and the instantaneous maximum force of impact, from the deformation of the bicycle when it hits an object. Green's first error is in adding the velocities of the bicycle and the other object. It is obvious that the impact velocity of the bodies is the difference between their velocities, not the sum of them. As a result, Green gives the following formula for the average force during impact (assuming that the deformation proceeds under constant force).
F = (M/g)*[(Vi**2) + (Vf**2))/(2*deltaL)
The correct formula should be:
F = (M/g)*[(Vi**2) - (Vf**2)]/(2*deltaL)
Green then applies his equation to the deformation of bicycle forks. He assumes that the deformation force is 3,500 pounds (a value that he says has been obtained by "numerous frontal impact tests in the laboratory"), the fork deforms 0.75 feet, the cyclist weighs 210 pounds, and the final velocity is zero. From this he calculates a velocity of 28.4. I participated in the law case for which Green made these calculations. In that case he gave the initial velocity as 28.4 mph instead of the arithmetically correct 28.4 fps. It is obvious that in such a collision the force on the front fork decelerates the mass of the bicycle; the question that remains is to what extent the front forks decelerate the cyclist. Since the cyclist is not connected to the bicycle by any significant mechanism, the cyclist continues on when the bicycle slows from the impact. Therefore, the mass of the cyclist should not be considered in the calculation. The 210 pounds Green uses for the weight of the cyclist consisted of 180 pounds of cyclist and 30 pounds of bicycle.
In the tests to which he referred, Green loaded three bicycles with 180 pounds of cast iron and crashed them into a steel barrier at measured speeds. The method of mounting the weights did not match the way that cyclists are connected to bicycles and therefore introduced great error. The 3,500 pounds that Green says he determined to be the typical strength of front forks was computed using his formula and his inaccurate tests. This method of calculation appears in Chapter 20. In Chapter 16, Green has already described actual tests of the front end crush strength of bicycle frames and forks, showing that the strengths of typical frames and forks run from 200 to 400 pounds. Green shows no awareness that the difference between the actual measurements of 200 to 400 pounds and his calculated strength of 3,500 pounds presents a serious conflict. He apparently suffers (and this is supported by his other writings) from the common misconception that inertial effects naturally produce enormous forces. They can do so, but only to the extent that the strength and rigidity of the structures that produce the acceleration allow.
Green then derives a formula for calculating the instantaneous maximum force developed in the collision. This turns out to be exactly the same formula that he used for calculating the speed. He uses the following data: impact speed = 51.5 fps; residual speed = 7.4 fps; fork deflection = 0.75 ft.; cyclist's mass = 210 pounds. Using Green's formula, the answer is 11,770 pounds. However, Green says that the answer is 11,289 pounds. He obtained that answer by subtracting the squares of the velocities instead of adding them, and by using 7.5 fps instead of 7.4 fps. Had he actually considered the velocities correctly, the answer would have been 8,417 pounds. Green writes that this comparison shows that the instantaneous maximum force is much greater than the average force. He shows no awareness of the fact that since he used exactly the same formula in each case, changing only the name of the force, the numerical result must be identical in both cases whenever the same data are used. That is a simple law of arithmetic.
Any attorney who wishes to rely on the methods given in any edition of Bicycle Accident Reconstruction should see that the method that he wishes to use is checked against the actual accident situation to see that it matches both the data that are available and the laws of physics that apply to that situation.
Review of Bicycle Accident Reconstruction page last changed: 25-Sep-08