The Effect of Bicycle Geometry, Rider Posture and Rider Anthropometrics

The Effect of Bicycle Geometry, Rider Posture and Rider

Anthropometrics on Pitch-Over Dynamics

Alex Moorhead

B.S., University of Colorado at Colorado Springs, 2013

A thesis submitted to the Graduate Faculty of the

University of Colorado at Colorado Springs

in partial fulfillment of the

requirements for the degree of

Master of Science

Department of Biology

2015

The thesis for the Master of Science degree by Alex Moorhead has been approved for the Department of Biology by

Jeffrey Broker, Chair

Jacqueline Berning

Andrew Subudhi

Jay Dawes

26 August, 2015 ii

ABSTRACT

Cycling is a popular activity that has been extensively studied. Unfortunately, within the research, there are sparse insights regarding pitch-over accidents. A pitch-over accident occurs when a bicycle is introduced to an abrupt deceleration, often from a front wheel impact or excessive front wheel braking. Pitch-overs due to front braking are avoided if deceleration levels do not exceed the longitudinal stability of the rider/bicycle system, which is defined by the location of the combined center of mass (COM) relative to the front tire contact point. The purpose of this study was to determine how bicycle designs and geometries, plus rider postures, effect rider/bicycle stability, and pitch-over propensity.

This study began by presenting and validating the use of a new force plate method (FPM) for locating rider and bicycle COM locations, as an alternative to a traditional anthropometric method (AM) used by Winter et. al. (2009). COM location estimates developed from the FPM were then compared to estimates derived using the AM. Finally, the FPM was used to evaluate the effects of bicycle types and rider postures on COM locations, and thus deceleration thresholds at pitch-over. The FPM was found to be much faster and more accurate than the AM. Resultant error with the FPM was less than 1cm

(7.8mm). Errors in the AM approached 135 mm. The FPM then exposed how both bicycle geometry and rider posture play large roles in effecting the deceleration thresholds of bicycles. Deceleration threshold differences between bicycles with similar rider positions were as large as .20 Gs, and these thresholds approached .21 Gs across different rider positions of the same rider on the same bicycle. The results derived from this study expose the effects of bicycle types and rider postures on pitch-over propensity, and provide an accurate method for examining these effects.

iii

TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION……………………………………………………………………..……….1

II. LITERATURE REVIEW……………………………………………………………..…...…4

Mechanisms of Pitch-Over Accidents………………………………….…….4

Pitch-Over Trajectories across Deceleration Mechanisms…….….….5

Pitch-Overs Involving Fork Failure…………………………………….……..5

Pitch-Over Dynamics………………………………………………………………6

Optimal Braking……………………………………………………………………..7

III. MATERIALS AND METHODS……………………………………………………………9

Subjects…………………………………………………………………………………9

Materials……………………………………………………………………………….9

Protocols………………………………………………………………………………10

Analysis………………………………………………………………………………..17

IV. RESULTS……………………………………………………………………………………….24

V. DISCUSSION………………………………………………………………………….……...29

VI. CONCLUSIONS………………………………………………………………………………33

REFERENCES…………………………………………………………………………………………………..….35

TABLES

Table

1. Comparison of FPM and AM locations………………….….……………………………....25

2. COM Position change due to saddle height changes….…………………………….….27

3. COM location differences due to posture and bicycle type………………………..…28

4. Average deceleration thresholds across bicycles, subjects and postures…….…28

FIGURES

Figure

1. Force plate validation; inclined position……………………………………….……………11

2. Rider with markers; “Hoods” position, flat and inclined……………………………..14

3. FBD of forces acting on system………………………..……………………………………….18

4. FBD with relevant dimensions………………………………………………………………….19

5. FBD, inclined positon………………………………………………………………………………19

6. Comparison of COM……………………………………………………………………………….20

7. Calculated COM vs. Measured COM………………………………………………………….24

8. Graphic representation of difference between FPM and AM……………………….26

CHAPTER 1

INTRODUCTION

Bicycling is an activity enjoyed by many people for transportation, recreation and competition. Unfortunately, although bicycling is generally beneficial, it also carries inherent risks for its participants. According to Werner et al. (2001), there are hundreds of thousands of bicycling accidents every year. With such high occurrences, further investigation related to the possible causes of these accidents is valuable to all types of riders.

Bicycle crashes can be initiated by many different factors. Collisions, component failures, rider error, hazardous terrain and loss of control are some of the most commonly identified factors associated with bicycling accidents (Broker, 2006). All of these factors can potentially result in a specific cycling accident known as a pitch-over.

A pitch-over is characterized by a rider and his bicycle encountering a rapid deceleration, resulting in a forward somersault about the front wheel. Pitch-over accidents have been studied in situations where the event is unavoidable, such as front wheel impacts and simulated component failures (Werner 2001). However, very little research has focused on pitch-overs resulting from over-application of the front brake.

According to the Consumer Product Safety Commission’s (CPSC) requirements for bicycles with hand brakes (front and rear), application of both brakes must effectively stop the bicycle from a velocity of 15 mph in 15 feet. The corresponding deceleration rate is equivalent to approximately 0.5 Gs (one G force is the acceleration due to earth’s gravity); a lower braking value than most bicycles are capable of achieving. Unfortunately, bicycle deceleration rates leading to pitch-over are often just slightly higher than the CPSC requirement in many bicycle type/rider posture combinations (Broker, 2006).

The disastrous pitch-over sequence is initiated, or avoided, based solely on the interaction between two factors; rider/bicycle center of mass (COM) location relative to the front wheel contact point and rate of bicycle deceleration. To better understand pitch-over crashes, this study focuses on the location of the system (bike plus rider) COM, how it is altered by various bicycle and rider position factors, and how these factors influence maximum deceleration threshold before pitch-over occurs.

To determine the location of the COM of a rider and bicycle system, one must know the

COM locations of both the bicycle and the rider. Locating the COM for a bicycle is easy, straight-forward and results in very low error. This is most easily performed using a double suspension method. The bicycle is suspended sequentially from two different sites (e.g., the handlebars and the seat), and the intersection of plumb bobs hung through the bicycle from the suspension locations establishes the location of the bicycle’s COM.

Determining the location of a rider’s COM on a bicycle is not as simple. Suspending a bicycle and rider from two locations is impractical, dangerous, and replication of rider position in the suspended state is difficult. As such, the most popular method of determining COM for a rider seated on a bicycle incorporates an anthropometric method

(Winter, 2009). This method, which derives an estimate of the rider’s COM based on the summation of estimated body segment COMs, is time intensive and subject to error.

Although the anthropometric method has been used for many years, greater accuracy can be achieved with less computation time using a novel force plate-based method.

The purpose of this study was to offer a new approach to determining bicycle rider COM, using force plates. After validation of such a method, its derivation of rider COM is compared to the anthropometric method and then applied to multiple bicycle/rider position combinations to quantify the effects of bicycle geometry, rider position and rider anthropometrics on the location of the rider/bicycle system COM.

Our hypotheses are, first, that the force plate method is more accurate than the anthropometric method, and the differences between the methods are relevant to accurate quantification of deceleration thresholds. Additionally, we hypothesize that COM location variations across rider positions, bicycle designs and rider anthropomorphics are large, and thus have a critical effect on the maximum deceleration rate a bicycle can achieve before pitch-over. Finally, it will be shown that some rider/bicycle combinations exhibit deceleration thresholds that are dangerously close to the braking requirements outlined in the CSPC guidelines.

CHAPTER 2

LITERATURE REVIEW

Mechanisms of Pitch-Over Accidents

Pitch-over accidents are highly common occurrences in bicycling and often result in disastrous injuries (Bretting, 2010). There are a multitude of commonly misunderstood or disregarded variables that contribute to pitch-over accidents. Pitch-over accidents are essentially caused, or avoided by, the combination of two factors; bicycle deceleration and rider/bicycle center of mass position.

Broker (2006) outlined many of the events that cause rapid bicycle deceleration – potentially leading to pitch-over. These events include the bicycle striking an object, such as a curb, the bicycle encountering a rapid elevation change, such as the uphill side of a deep gully or ditch, objects (including bicycle components) entering the front wheel spokes or locking up the front wheel, and excessive front wheel braking. Broker explained how the relationships between rider/bicycle COM location and deceleration rates affect the propensity for pitch-over accidents.

Additionally, Broker (2006) explained how deceleration rates in relation to rider/bicycle

COM locations fundamentally influence the development of torque about the front wheel contact point, and how in front wheel braking, this torque can translate into forward rider/bicycle rotation about the front wheel ground contact point. Broker takes into account friction between the tire and pavement, the effect of hills, rider biomechanics and rider trajectory in his construct of pitch-over threshold determination. Broker’s work is helpful to the understanding of pitch-over accidents and serves as a firm foundation for continued investigation of pitch-overs.

Pitch-Over Trajectories across Deceleration Mechanisms

As previously stated, pitch-over accidents may be caused by multiple factors. The consequences of a pitch-over accident can be terrible. Bretting et al. (2010) studied pitch- over trajectories, or motions of the rider through space in the course of a pitch-over, with an interest in understanding the associated mechanisms of head and neck injuries. Their study investigated rider trajectories resulting from front barrier impacts, an object inserted in the spokes and over-application of the brakes. This study took into consideration the rider’s COM location. They used the anthropometric method to calculate the rider’s COM location, and assumed this location remained fixed during initial bicycle deceleration. These authors reported that with the exception of bicycle damage, rider trajectories across the pitch-over circumstances were very similar. The pitch-overs all resulted in the riders landing on their heads, with their body COM in a position to load the cervical spine.

Another interesting observation in the Bretting et al. (2010) study was that rider rotation and time in the air was effected by rider movement on the bicycle (i.e., sliding forward) as the bicycle was decelerating. It appears that these researchers may have exposed a significant contributor to bicycle pitch-overs, i.e., rider posture and rider coupling to the bicycle, but unfortunately they did not explore these findings further in their study. The

Bretting et al. study, along with the work of Broker (2006), highlights how rider/bicycle

COM locations affect pitch-over dynamics. Bretting’s study was focused on what occurs during a pitch-over incident, rather than before.

Pitch-Overs Involving Fork Failure

Werner et al. (2001) studied pitch-over bicycle accidents resulting from bicycle impacts to fixed objects. These impacts were at speeds associated with front fork failure. In their study they developed a mathematical model to analyze and simulate the kinematics of a

bicycle and rider during frontal collisions. Experimental data involving actual rider/bicycle barrier crash tests were also collected to test the accuracy of the mathematical model. This data was found useful, not only in furthering bicycle crash analysis, but also for designing performance bicycles.

The Werner et al. (2001) study was primarily aimed at understanding the difference in rider trajectories between frontal collisions in which minimal front fork damage versus major fork deformation occur. Their interest was in how fork deformation at time of impact (full failure or collapse) influences rider pitch-over trajectory. Although the majority of the study was not directly related to our study, because the pitch-over mode involved barrier impacts, it was relevant in the fact that the authors mentioned, “subtle variations in post bike-separation kinematics were… the result of slight differences in initial rider posture.” According to Werner et al., by standing, the rider’s COM was repositioned, which enhanced the pitching of the cyclist’s body. Of note, Werner et al. used the anthropometric method to estimate the location of the rider’s COM.

The Werner et al. (2001) study is helpful in demonstrating that a rider’s trajectory during pitch-over accidents is highly affected by the location of the rider’s COM. Although this study begins to recognize that rider COM location effects pitch-over dynamics, it does not accurately measure rider COM, or begin to attempt any understanding of how the COM specifically alters pitch-over thresholds.

Pitch-Over Dynamics

With the majority of studies concentrating on causes, trajectories, results, injuries and bicycle damage from pitch-over accidents, a study by Metz (2010) is a welcomed change.

His study looked at what conditions were achievable on a road bicycle without causing a pitch-over. Metz considered road asperities, cycling speed and braking performance in an attempt to explain this phenomenon. This approach was valuable because it identified and

assessed real-world cycling conditions in relation to one another, and their likeliness of generating a pitch-over. Metz explained that a bicycle/rider’s angular momentum about the front axle is directly related to the bicycle/rider’s inertia, which Metz’s states, “will depend on the position and physique of the rider and dimensions and mass distributions of the bicycle.” This is valuable information because Metz’s study takes into consideration how a rider’s posture can directly affect the rider/bicycle’s propensity for a pitch-over accident. Unfortunately, Metz does not continue on this topic. He uses one rider in one position, and only derives what the minimal speed for a pitch-over is for this single condition. He uses the anthropometric method to estimate the rider’s COM on the bicycle.

He reported that the rider/bicycle in a decelerating (braking) situation can induce a pitch- over accident at only 1.82 m/s (4.1 mph)! Although this data point is only applicable to the single rider and bicycle condition studied, it is insightful because it underscores how easily a pitch-over accident can happen, and invokes the need to find what variables can help avoid these disastrous accidents.

Optimal Braking

It is often believed that bicycles are able to stop quicker than motor vehicles and motorcycles, but this is a misconception. As outlined by Broker (2006), deceleration rates of 0.7 to 0.9 Gs are achievable for motor vehicles and motorcycles, due to their low center of gravity and its rearward position relative to the front wheel(s). Maximal bicycle deceleration rates are less (typically below 0.7 Gs), because the high and forward position of the rider/bicycle center of mass limits longitudinal stability.

The studies outlined above have shown the detrimental results of a pitch-over and how it may be caused from over application of the front brake. This may seem to indicate that front-wheel braking is dangerous and should be avoided, but such is actually not the case.

Front-wheel braking, when applied correctly, is actually safer and mandatory for

expedient braking. Rear-wheel braking is incapable of causing a pitch-over (Broker , 2006) but when used apart from front-wheel braking it may be incapable of stopping a bicycle and rider in a safe amount of time and distance in an emergency situation.

Broker (2006) reports that with rear-wheel-only braking, a bicycle rider may only be able to decelerate their bicycle at .30 Gs or less; much less than that of front- and rear-wheel braking. He reports that a rider utilizing both front and rear-wheel braking can achieve deceleration rates of .5 Gs up to .8 Gs without inducing a pitch-over, depending on bicycle, rider poster, terrain grade and friction coefficient. So, although front-wheel braking involves the risk of a pitch-over accident, the rear-wheel only braking alternative is inherently much more dangerous.

The key to safe deceleration is appropriate placement of a rider’s COM about the bicycle so that one can stop as quickly as possible while also avoiding a pitch-over. This study explores how bicycle geometry/design, rider posture and rider anthropometrics effect the rider/bicycle system COM location, and subsequently their combined pitch-over threshold deceleration rate.

CHAPTER 3

MATERIALS AND METHODS

Subjects

This study involved 5 volunteer subjects, two female and three male. The subjects, selected from the local community, were only required to be over 18 and competent at riding a bicycle. Subject demographics were recorded including age (avg. 26.66 ± 10.58 yrs), height

(avg. 171.70 ± 8.35 cm) and weight (avg. 67.10 ± 13.52 kgs); however, these demographics were not utilized in the data analysis. Because the study required no action from the participants other than sitting still on bicycles, there were no controls for time of day, training, dietary intake, sleep or any other physiological influence. Testing was performed at various times throughout the day, as early as 8:00 am and as late as 9:00 pm. Subjects signed an informed consent form including the study’s purpose, methods, benefits and risks. This study was approved by the University of Colorado, Colorado Springs IRB code of practice for investigations with human subjects.

Materials

All testing and data collection were performed in the human performance lab at the

University of Colorado at Colorado Springs. To perform the tests, four bicycles were used: a Giant TCR Advanced road bicycle, Novara Bonita hard-tail mountain bicycle, a

Specialized Epic Elite full suspension mountain bicycle, and a Schwinn Point beach cruiser bicycle.

Bicycle centers of mass were determined using a double suspension method as previously explained.

For rider center of mass (COM) determination, each bicycle was mounted to a fixed cycling trainer set atop two hand-built platforms which were firmly fixed to 60 cm by 60 cm Bertec

Corporation force plates (see Figure 1). Signals from these force plates were directed to a data acquisition computer at a sample rate of 500 Hz. During tests that required the bicycles to be inclined, a 21.5 cm tall front wheel raiser was hand-built from lumber and inserted beneath the front wheel support (Figure 1). For postural measurements, a standard goniometer and measuring tape were used. In every phase, it can be assumed that all aforementioned equipment was used unless otherwise noted. Additional equipment used for each phase of this study will be noted where appropriate.

Protocols

Before beginning any testing, attributes of all riders and bikes were measured and recorded for bicycle modeling and later calculation of COM. Bicycle attributes included: the seat tube angle (STA), head tube angle (HTA), wheel base (WB), distance from the bottom bracket to the front axle (BFA), bottom bracket to the rear axle (BRA), bottom bracket height (BBH), rear axle height (RAH), front axle height in flat condition (FA1), front axle height in the inclined position (FA2), distance from ground to handlebar clamp center (GCL), seat length (SL) and bicycle weight (BW).

This study was conducted in three phases. Phase 1 involved the validation of the force plate method (FPM) in locating the location of a rider’s COM atop a bicycle. Phase 2 involved comparing the FPM to the traditional, anthropometric method (AM) of locating the COM of a rider. Phase 3 implemented the FPM in an evaluation of the effects of bicycle type and rider posture on COM locations, with an emphasis of how these locations influence ptich0over thresholds. The methods involved in each of these phases will be outlined separately.

Phase 1: Force Plate Method Validation. For this phase an Iron Grip 45 pound weight was fixed to a Giant TCR Advanced road bicycle and both were mounted to

Bertec Corp. force plates to measure ground reaction forces (GRFs) of the bicycle plus the weight (Figure 1). A general purpose measuring tape was used to measure the approximate location of 45 pound weight’s COM. To achieve an inclined position of the front wheel, the hand-built raiser was used. Standard electrical tape was used to mark the position of the weight on the saddle, to ensure it did not move along the saddle during bicycle positioning.

Figure 1: Force plate method validation; inclined position

In essence, this phase involved fixing a heavy weight to a bicycle, in a known and measurable position, and then determining the location of this weight using the FPM. The

FPM relies on measurements characterizing the weight distribution between the front and

rear wheels of the bicycle with the bicycle in level and inclined positions. The weight distribution in the level condition establishes the fore-aft position of the bicycle and rider system COM. When the bicycle is inclined (for example, when the front wheel is raised), the weight distribution on the wheels changes (the force is increased on the rear wheel in the raised front wheel condition). How the weight distribution changes when the bicycle is inclined is directly related to the applied inclination, as well as the height of the system

COM. If the inclination of the bicycle is known (set by the researcher in this case, using a platform placed beneath the front wheel), the height of the system COM can be calculated directly.

In this phase of the study, a 45 pound weight plate was secured to the saddle of a road bicycle, almost vertically (Figure 1). After the weight was securely fixed to the seat, electrical tape was put on the seat to mark the exact position of the weight. The location of the weight’s COM referenced to the bicycle’s BB was then measured (horizontal and vertical dimensions), independently by two investigators, using a tape measure. This measured COM location, when compared later to the COM location derived from the FPM, served to quantify the accuracy of the FPM.

Once the 45 pound weight’s location on the bicycle was measured, it was then removed and the bicycle was mounted to the cycling trainer atop the dual force plates. The force plates were then zeroed in this condition, so that during subsequent data collection with the weight applied to the bicycle, only the front and rear wheel ground reaction forces

(GRFs) associated with the 45 pound weight would be measured.

The weight was then replaced on the bike seat where it was previously marked, and data were then collected from the two force plates, for a period of five seconds, characterizing the front and rear wheel weight distribution in the level condition. The weight was then removed once more from the bicycle and the front wheel platform was inserted - to incline

the bike. The force plates were again zeroed with the now added mass of the front wheel raiser, the 45 pound weight was replaced on the bike’s saddle, with the bike in the inclined position, and 5 seconds of data were again collected. Weight distributions across the two trials and bicycle attributes were then used to calculate COM of the weight.

The calculations required to determine the location of the 45 pound weight’s COM, which are identical to the calculations used to locate a rider’s COM location, are developed and presented in the analysis section that follows. Comparison of the COM locations measured directly, with the tape measure, and calculated as part of the FPM characterized the accuracy of this method.

Phase 2: Force Plate Method vs. Anthropometric Method. To compare the accuracy of the anthropometric method (AM) to the FPM, five subjects with varying body types were tested in the same riding position. Four out of five riders were tested on the

Giant TCR Advanced road bicycle and the fifth was tested on the Specialized Epic Elite full-suspension mountain bike. Riders wore a standard bicycle helmet and were fitted with

8 reflective markers (Figure 2). Each rider was fit to the bicycles to a rider-preferred saddle height. Once the accuracy of the FPM was established, this method was used to quantify the errors introduced in using the traditional, anthropometric method (AM). The AM of determining rider COM location involves the estimation of body segment COMs based on the identification of joint centers (e.g., shoulder, hip, knee, etc.) and regression equations describing segment weights and segment COM locations (Winter, 2009).

Figure 2: Rider with arkers; Hoods positio, flat ad iclied.

Riders were fitted with 8 markers in accordance with the methods outlined by Winter et al. (2009). Markers were placed on the left side of the rider’s body so they could be captured by a camera for later anthropometric analysis. Markers were located over the left styloid process of the ulna, the lateral epicondyle of the elbow, the head of humerus, the greater trochanter, the lateral condyle of the knee, the lateral malleolus of the ankle and the 5th metatarsal-phalangeal joint in the foot. After marker placement and zeroing of the force plates beneath the test bicycle, subjects were instructed to carefully mount the road bike and adopt the “hoods” position. This position has the rider place their hands on the hoods of the brake lever assemblies (Figure 2). Riders were instructed to always adopt a posture with the cranks in a bicycle-level condition.

Once the rider was set, they were instructed to stay completely still. A photograph of the rider and bicycle was then taken (perpendicular to the plane of the bicycle, 15 feet away),

while the force plates collected force data for 5 seconds. Select measurements describing the rider’s posture and position on the bicycle were then taken and recorded. These measurements included joint angles (left hip, knee, ankle, shoulder and ankle angles), as well as the distances between the bicycle handlebar clamp center and the rider’s chin and left greater trochanter.

Following the joint angle and chin/greater trochanter to handlebar clamp measurements, the rider was then asked to dismount the bike, the front wheel raiser was inserted under the front wheel, and the force plates were re-zeroed with the additional raiser weight. With the bike now in the inclined position, riders were instructed to remount the bike and adopt the same position they held in the flat condition. To confirm consistency between the two conditions, joint angles and chin/greater trochanter to handlebar clamp measures were compared to the previous measurements and adjustments were made until identical positioning was achieved. Once riding posture was replicated, the rider was again instructed to stay completely still while force plate data was collected and another photograph was taken. The photographs taken in the flat condition were later analyzed in assessing the accuracy of the AM. Force plate data collected in both the level and inclined conditions was used to determine rider COM as described in phase 1, above. FPM and AM

COMs for the same rider in the same position were then compared to determine the error involved in using the AM.

Phase 3: Effect of Bicycle Geometry and Rider Posture. All equipment for this phase was the same as described for Phase 2 with the addition of using all four bicycles instead of just one road bicycle.

This phase implemented the FPM in an evaluation of the effects of bicycle type and rider posture on COM locations, with an emphasis of how these locations influence pitch-over thresholds. To observe how bicycle geometry and rider postures affect system COM, riders

were asked to adopt three different positions on each of the bikes on which they were tested. Since the testing was extensive and time consuming, riders were only asked to be tested on two or three of the four different bicycles, depending on time constraints.

Bicycles were randomly assigned to each rider. The three positions adopted were unique to each of the four bicycle types, but were the same across all riders. This resulted in twelve possible bicycle/posture combinations for this study: road bike hoods (RBH), road bike drops (RBD), road bike sprint (RBS), full suspension up (FSU), full suspension down

(FSD), full suspension emergency braking (FSE), hard tail up (HTU), hard tail down

(HTD), hard tail emergency braking (HTE), beach cruiser up (BCU), beach cruiser down

(BCD) and beach cruiser standing (BCS). Each of these postures were tested in a flat and an inclined position, permitting the calculation of COM locations.

During this phase, riders were fixed with joint markers as described for phase 2, and their postures/positions on each bike were controlled across the level and inclined conditions using goniometric and distance measures. The procedure for testing a given rider on a given bicycle was identical to that described for Phase 2, except that in this phase each bike incorporated three different cycling postures. Force plate data were collected for each posture on each bike, after which the bike was inclined, postures were duplicated and force plate data were recollected. As described for phase 2, riders were instructed to stay completely still in each posture for data collection and photographs were taken to check for consistent positioning. This procedure was repeated for the successive bikes. All data was later analyzed to determine the effect of bicycle geometry and rider posture.

Pitch-Over Deceleration Thresholds: Once COM locations were determined for each rider in each posture across the various bicycle types studied, the critical effect of these locations on bicycle deceleration thresholds were determined. Maximum deceleration rates for each rider/posture/bicycle combination were computed per the

method reported by Broker (2006). The equation to determine deceleration at pitch-over is explained in the analysis section that follows. Once pitch-over deceleration rates were computed, average values across the rider postures and bicycle types were calculated.

Analysis

Prior to expounding on the application of the FPM it is imperative to establish definitions of terms and calculations performed to locate rider/bicycle COM:

FFAX = vertical force on the front axle – general FRAX = vertical force on the rear axle – general FFAX1 = vertical force on the front axle – level FFRX1 = vertical force on the rear axle – level FFAX2 = vertical force on the front axle – inclined FFRX2 = vertical force on the rear axle – inclined

Xcg = distance in X direction to COM Ycg = distance in Y direction to COM

WB = wheel base W = weight of mass (rider plus bicycle or just rider if bicycle was zeroed)

α = Inclination Angle

Preface: Determination of rider/bicycle COM. To determine the location of the COM using the FPM, both the X and Y coordinates must be calculated. The X coordinate is easily determined by comparing the ground reaction forces (GRFs) between the front and rear wheels. Determining the Y coordinate is much more involved, and requires comparison of GRFs in the flat and inclined positions. When calculating COM locations, it is important to remember that all cases are done in a static position; thus, the

sum of the moments about the rear axle (RAX) is always zero. Both processes are explained below:

Step 1: Establish a Free Body Diagram (FBD) of forces acting on the system

A free body diagram of the rider and bicycle system is provided in Figure 3, with the rider COM (blue dot) indicated, as well as the forces acting on the system.

Figure 3- FBD of forces acting on system.

Step 2: Add relevant dimensions, locating COM relative to rear axle.

Figure 4 - FBD with relevant dimensions.

� = = so ∗ − ∗ =

= ∗ / Step 3: FBD in inclined position, showing change in position of COM.

Figure 5- FBD, inclined position.

� = = ∗ so − ∗ ∗ cos =

= ∗ ∗ cos/ Step 4: Comparison of COM location in flat and inclined position.

Figure 6 - Comparison of COM.

Assuming the COM of the system is fixed above and forward of the rear axle as shown, imagine right triangle with Xcg1 and Ycg representing the positions of COM relative to the rear axle in the level and inclined conditions, respectively. The inclination angle β is indicated. This triangle stays intact when bicycle is rotated/inclined.

Step 5: Derivation. The triangle’s hypotenuse (R) in both the level and flat conditions is the same. The triangle’s angle β is also the same in both conditions.

For the level condition:

= = cos

For the inclined condition:

= + = cos + Setting R = R:

= cos cos +

Since:

cos + = cos ∗ cos − sin ∗ sin

cos = cos ∗ cos − sin ∗ sin Rearranging:

∗ cos ∗ cos − sin ∗ sin = ∗ cos Isolating Angle β:

∗ cos ∗ cos − ∗ sin ∗ sin = ∗ cos

∗ cos − ∗ cos = ∗ sin ∗ sin

sin ∗ cos − = cos ∗ sin

And since:

sin = tan cos

∗ cos − tan = ∗ sin So:

∗ cos − = atan ∗ sin Therefore:

= And finally: cos

= ∗ sin Note that Xcg1 and Xcg2 are known from the first set of equations, and α represents the inclination of the bicycle - which is determined from the wheelbase (WB) and the known height of the platform riser. The only changing variable is the location of the COM relative to the bottom bracket spindle of each bicycle.

Phase 1: Force Plate Method Validation. To validate the FPM, the FPM calculations returned X and Y coordinates which were then compared to the physically measured coordinates, and a resultant error was found using the following equation:

2 2 = √ � − � + � − � Phase 2: Force Plate Method vs. Anthropometric Method. To compare the accuracy of the FPM to the AM, coordinates of both methods were determined and then a resultant error between the two points was found using the following equation:

2 2 ℎ� = √ � − � + � − � Phase 3: Effect of Bicycle Geometry and Rider Posture. Each rider’s chosen saddle height affected the bicycle COM location alone (due to elevation of the saddle and its supporting seat tube). As such, the effect of saddle height on bicycle COM location was established. This was done by measuring the COM location of each bike, using the double suspension method described earlier, with three dramatically different saddle heights, and then deriving a linear regression to predict bicycle COM for each saddle height. Rider COM was then found using the FPM as the previously described. Once the

COM locations were determined for the bicycle and the rider, the system COM was determined using the following equations:

= � ∗ � + � ∗ � /� + �

= � ∗ � + � ∗ � /� + � After determining the system COM location, maximum sustainable bicycle deceleration rate (in Gs) was determined, unique to the bicycle being studied, as follows:

�� = � � � � �

CHAPTER 4

RESULTS

Phase 1: Force Plate Validation In-depth analysis of the FPM validated that the FPM calculation of an added weight’s COM location was accurate within 1cm (7.9mm), when compared to that of the actual measured weight’s COM. The COM locations derived using the FPM and the direct measurement are displayed graphically in Figure 7. The large circle on forward aspect of the saddle and the small diamond within this circle are the FPM-derived and directly measured COM locations, respectively. The large, light purple circle above the bicycle crank axis, inside the frame triangle, is the bicycle’s COM location.

Figure 7- Calculated COM vs. Measured COM.

Phase 2: Force Plate Method vs. Anthropometric Method. Assuming the

FPM yields the best estimate of the true rider COM location, a comparison of COM locations derived using the AM and FPM characterize errors introduced by the AM. The

AM-derived COM location was within 1cm (8.1mm) of the FPM value for only one of the five measured subjects. On average, the AM-derived COM locations were 7.46cm from the

FPM-derived location, and for one subject the discrepancy was 13.43cm. The data for all five subjects are provided in Table 1. These data are also provided graphically in Figure 8.

As can be seen in both the table and graphic, the AM consistently located the rider’s COM location forward and below its actual, FPM-based position.

Rider X Anthro Y Anthro X FPM Y FPM X Diff Y Diff Resultant Error 1 0.00 71.57936954 -9.907787383 80.64847044 9.906281077 9.069100899 13.43067369 2 -1.59 82.74505719 -2.360635242 82.96244781 0.773279414 0.217390623 0.80325571 3 -4.05 87.54838958 -8.575769049 98.08353882 4.528927249 10.53514924 11.46736899 4 -0.51 71.2192026 -6.409726421 75.96931982 5.904376832 4.750117218 7.577946909 5 2.29 80.39834307 -0.378794334 83.96099189 1.909058406 3.56264882 4.041901856 Average 4.604384596 5.626881361 7.464229432

Table 1 - Comparison of FPM and AM COM locations.

Figure 8 - Graphic representation of differences between FPM and AM. Squares and triangles of the same color represent COM locations for the same rider, derived using the FPM and AM, respectively.

Phase 3: Effect of Bicycle Geometry and Rider Posture. It was observed that a bicycle/rider system COM location changes across different bicycle types and is dramatically affected by the posture/riding position of its rider. Consequently, the maximum deceleration rate the rider plus bicycle system can sustain without pitching over is also greatly influenced by rider posture and position.

Although seemingly minute, even a change in saddle height will result in a change to both the height and fore/aft position of the bicycle COM. The changes in bicycle COM location for each of the four bicycles tested, affected by alterations in saddle height alone, are provided in Table 2. As indicated, modest changes in saddle height (14 to 26 cm changes)

resulted in very small changes in bicycle COM locations (less than 1 cm in both the vertical and horizontal directions).

Hard Tail Full Suspension Seat Height (CM) COM Height from Ground COM Fore/Aft of BB Seat Height (CM) COM Height from Ground COM Fore/Aft of BB 72 47.4 11.9 87.2 48.4 11.9 82.4 47.7 11.7 95.5 49.9 11.4 97.1 47.9 11.5 105.9 50.6 11.2 Road Bike Beach Cruiser Seat Height (CM) COM Height from Ground COM Fore/Aft of BB Seat Height (CM) COM Height from Ground COM Fore/Aft of BB 84 47.2 6.8 96.3 49.3 -0.2 90.2 48 6.7 85.4 47.6 0 98.3 48.6 6.5 78.7 46.9 0.4

Table 2 - COM position change due to saddle height changes.

By contrast, rider COM locations are significantly influenced by bicycle type and rider posture/positioning on the bicycle. An example of one rider’s data set across all three bicycles tested, with three different riding positions, is provided in Table 3. Here, deceleration thresholds are provided as a meaningful, functional consequence of COM location movements. Deceleration threshold differences between two bikes using the same riding position were as high as .24 Gs. On the same bicycle, postural differences

(e.g., moving from a low riding position to a standing position on a beach cruiser) yielded deceleration threshold differences as high as .27 Gs (Table 3)! Although this is one of the more extreme cases, large COM location differences were observed, on average, across all subjects and bikes.

Deceleration thresholds for each bicycle/rider position combination, averaged across all five riders, are provided in Table 4. As indicated, deceleration threshold changes as high as .19 Gs arise due to posture modifications within each bicycle, and are as great as .21 Gs due to bicycle geometry, or bicycle style effects.

Table 3 - COM location differences due to posture and bicycle type.

Position Avg. Max SD Bike Avg.

Hoods 0.598546994 0.060213422 0.597129064 Road Bike Drops 0.595711135 0.038298226 Sprint 0.541144141 0.13215727

Up 0.662967574 0.042032295 0.648474968 Hard Tail Down 0.633982361 0.018525409 Emergency Brake 0.805887766 0.002371066

Up 0.669433922 0.097046897 0.659218302 Full Suspension Down 0.649002681 0.076536104 Emergency Brake 0.828103634 0.051154526

Up 0.834668714 0.021704758 0.835471994 Beach Cruiser Down 0.836275275 0.021129561 Standing 0.628421829 0.082197955

Table 4 - Average deceleration thresholds across bicycles, subjects and postures.

CHAPTER 5

DISCUSSION

This study yielded two primary findings. First, force plates can be utilized to accurately determine a rider/bicycle’s COM location, and second, rider and bicycle COM locations vary greatly depending on bicycle geometry, rider posture and rider anthropometrics. A single bicycle’s COM location changes slightly with alterations in saddle height, but it remains the rider’s posture and positioning on the bicycle, partially influenced by the bicycle’s style, that most influences rider plus bicycle COM location, and thus deceleration threshold before bicycle pitch-over.

Our theory prior to this investigation was that a new FPM could efficiently and accurately determine rider COM location on a bicycle. To validate this theory, the FPM was developed and tested using a rigid object (a steel plate) fixed to a bicycle at a known location. Using this approach, the FPM was validated to be accurate at locating a large mass’ location, within one cm (7.8 mm). Accordingly, the FPM was utilized to evaluate the accuracy of the

AM.

The use of force plates to determine a subject’s COM location is unique yet important, because it has long been assumed that the AM method of locating a rider’s COM is accurate. Data collected during this study establishes that the AM generates significant errors in locating a rider’s COM location. Errors introduced by the AM are likely related to the assumptions made in applying cadaver-based regression equations to live subjects, compounded by errors introduced by marker misplacement, body anthropomorphic variations and/or improper measurements during photographic image processing.

To our knowledge, the FPM has never been utilized for locating rider COM on a bicycle.

We discovered that the FPM provides a quick, efficient, accurate and thus promising

method of locating rider COM, and this method is much more precise than the AM.

Provided force plates are available, the FPM has tremendous utility, because it accounts for body anthropomorphics does not require marker placement, and is free of time- consuming subsequent video/kinematic processing.

One assumption of the FPM method is that the subject (rider) maintains the same posture on the bicycle in both flat and inclined positions. This can be checked and verified through multiple measurements, but does leave room for error in determining COM location.

However, if care is taken to ensure consistency of the subject’s position on the bicycle, using joint angle and chin/hip position checks for example, these errors can be controlled and minimized.

Provided steps are taken to duplicate rider position across the level and inclined positions, the collected data can be exported easily from the force plates to be rapidly processed.

Additionally, since the FPM can determine COM location of a rider/bicycle system as a whole, it allows for the assessment of many additional equipment variables that can influence COM location, such as bicycle baskets, backpacks, saddlebags or any other factor that may change COM location. While being more accurate, the FPM is more versatile for application to real-life scenarios.

With the new FPM established, the next question to answer was how rider/bicycle COM locations are altered by the geometry of the bicycle, the posture of its rider and the anthropometrics of that rider. This was a concept widely overlooked by previous studies concerning pitch-over accidents. Some studies briefly considered the location of a rider’s

COM, but not the rider and bicycle COM together, and not how and in what direction each factor changes the overall COM location. This is an oversight considering that posture alone can alter a bicycle/rider COM location by 18.61 cm.

Consistent with our hypothesis, bicycle geometry was found to modify COM location to a lesser extent than rider position. There were, however, large differences in bicycle COM location between vastly different bicycles - such as the road bicycle and beach cruiser.

Regardless of bicycle COM location, however, the rider always had the greatest influence on rider/bicycle COM position.

These data establish that a beach cruiser, a very heavy bicycle with the saddle positioned more rearward in relation to the front wheel, would be very difficult to pitch-over in seated riding (average deceleration threshold of 0.83G). However, this threshold rises precipitously as soon as the rider stands (average deceleration threshold of 0.62G). Clearly what matters is the relationship between the bicycle geometry and the rider. Put another way, bicycle geometry resulted in a set COM location that did effect the rider/bicycle COM location, but what is most important is how the bicycle’s geometry influences the rider’s posture.

Each bicycle influenced the way the rider was positioned on the bicycle. So, although the rider’s position is what ultimately has the largest impact on pitch-over dynamics, the bicycle does essentially control how the rider is able to ride it. This shows that the two are both equally important to pitch-over deceleration thresholds.

A final observation from this study focuses on the ability of a rider to modify his/her position on a bicycle to facilitate rapid, emergency braking. Riders were tested on both full suspension and hard tail (front suspension only) mountain bicycles in both normal riding postures and emergency braking postures, in which the riders moved rearward atop the bicycle. This is a technique used by advanced riders to permit more rapid braking without risking pitch-over. The data indicate that average maximum deceleration rates

(pitch-over thresholds) for our five riders on the mountain bikes in normal riding positions was 0.66 Gs. The adoption of the emergency braking position on these mountain

bikes elevated the pitch-over threshold to just over 0.80Gs. Indeed, this advanced technique is highly effective in reducing the propensity for a given rider/bicycle system to pitch-over. Of note, this emergency braking posture is more easily accomplished on a mountain bicycle than a road bicycle or beach cruiser, due to saddle height and saddle design effects.

CHAPTER 6

CONCLUSIONS

Bicycling is an activity that has been thoroughly researched, but very few insights have been developed regarding pitch-over accidents. Pitch-over accidents are the result of abrupt decelerations combined with a compromised COM location. Rider plus bicycle

COM location is critical to the pitch-over phenomenon.

Locating the COM of a bicycle is quite easy. Accurately locating the COM of a human, and specifically a human seated on a bicycle, is more complicated. The current and oft- used AM of locating a rider’s COM atop a bicycle involves estimates of individual body segment mass locations in relation to estimated joint centers. This method has been valuable and heavily used, but is now challenged for bicycle applications by the alternative FPM developed and presented in this study.

The results from this study indicate that the FPM is much more accurate than the previously popular AM. Although this study did not involve a larger number of participants, such experimental lengths are not required to prove its value. Part of what makes the method so innovative is its ability to determine the COM location on any subject in any position. The one drawback to this method is that is cannot be performed without force plates, and cannot be used with dynamic movement. Of course, dynamic movements are not typical on a bicycle. A bicyclist’s posture is relatively static and can be easily replicated in a lab.

Altering the system’s COM location results in increased or decreased bicycle deceleration thresholds. A systematic assessment of the factors responsible for movement of the rider plus bicycle COM, and thus variations in pitch-over propensity have not been studied until now. Because pitch-over accidents are common and often result in serious injury

(Broker, 2006), the implications related to bicycle and bicycle/rider specific deceleration thresholds are critical.

When considering pitch-over thresholds due to front-wheel braking, COM location is crucial. For bicycling, COM location can now be determined using the FPM in place of the AM. The components that contribute to that location have not previously been studied, but this research proves that bicycle geometry, rider posture and rider anthropometrics all play a vital role. Most important is the rider’s distribution of mass about the bicycle. When a rider adopts different positions on a bicycle, he/she is able to dramatically modify the sustainable deceleration rate short of a pitch-over accident. For all subsequent studies pertaining to bicycle pitch-over accidents, these variables should be taken into consideration and, ideally, assessment of various bicycle and rider/bicycle effects should be studied using the validated FPM.

References

1. Broker, Jeffrey P., and Paul F. Hill. "Bicycle Operating Characteristics." Bicycle Accidents Biomechanical, Engineering, and Legal Aspects. Tucson, Arizona: Lawyers & Judges, 2006. 25-67. 2. Broker, Jeffrey P., and Paul F. Hill. "Principles of Bicycle Accident Reconstruction." Bicycle Accidents Biomechanical, Engineering, and Legal Aspects. Tucson, Arizona: Lawyers & Judges, 2006. 97-134. 3. Werner, Stephen, William Newberry, and Robert Fijan. "Modeling of Bicycle Rider Collision Kinematics." Society of Automotive Engineers 01.765 (2001). 4. Bretting, Gerald P., Henricus P. Jansen, and Michael Callahan. "Analysis of Bicycle Pitch-Over in a Controlled Environment." SAE International 3.1 (2010): 57-62. 5. Mertz, Daniel. "Road Bicycle Dynamics in the Presence of Idealized Roadway Irregularities." SAE International (2010). 6. Winter, David A. Biomechanics of Human Movement. Waterloo, Ontario, Canada: John Wiley & Sons, 2009.