Development of a Bicycle Dynamic Model and Riding Environment for - - PowerPoint PPT Presentation

Development of a Bicycle Dynamic Model and Riding Environment for Evaluating Roadway Features for Safe Cycling

Department of Civil & Construction Engineering

Mitchel Keil, Ph.D., P.E.

Professor

Abul Mazumder, M.Sc.

Graduate Research Assistant

Upul Attanayake, Ph.D., P.E.

Associate Professor Department of Civil & Construction Engineering Department of Engineering Design, Manufacturing and Management Systems

Introduction Objective and scope Bikeway geometric design parameters Simulation model Centripetal acceleration and jerk Conclusions and recommendations Acknowledgement

Cycling is promoted with new policies and guidelines. Facilities are provided within and outside of existing roadways to enhance

safety and comfort.

Classes of bikeway Bike path Bike lane Bike route Shared roadway Conventional Buffered Contra-flow Left side

Complete street policy

Verbal/written survey, video recording, tracking cycle using GPS

devices and smartphones, instrumented bicycle, and virtual reality are commonly used for evaluating interaction of motorists and cyclists with the cycling environment.

These methods are indispensable to evaluate human response. However, simulation models can be used to evaluate the impact

• f several bikeway design parameters on bicycle stability

(safety) and rider comfort.

Objective The primary objective is to develop a bicycle dynamic model and riding environment for evaluating the impact of bikeway design parameters on stability and rider comfort. Scope

Perform a state-of-the-art and practice review on bikeway

design, bicycle models and simulation efforts, along with stability and rider comfort evaluation.

Develop and validate a simulation model in the ADAMS

environment.

Evaluate the impact of bikeway design parameters on stability

and rider comfort.

Develop recommendations and deliverables.

• Separation width between path and roadway
• Design speed
• Horizontal curvature
• Superelevation
• Grade
• Sight-distance
• Stopping sight-distance
• Sight distance at horizontal curve
• Width of bikeway
• Horizontal and vertical clearance
• Friction

Transition curve is considered for simulation

Forces acting on a point mass

Assumption:

• Total mass (m) of the vehicle is acting on the center of

gravity.

𝜾=​𝒖𝒃𝒐↑ 𝒐↑−𝟐 ​​𝑾↑ 𝑾↑𝟑 /𝑺 =​𝟏.𝟏𝟕𝟖 𝟏𝟕𝟖​𝑾↑ 𝑾↑𝟑 / 𝑺

Considering equilibrium,

V - speed (mph) R - radius (ft) 𝜄 – lean angle (degree) – lean angle (degree)

Horizontal curve and lean angle

Forces acting on a point mass

Horizontal curve, superelevation, and friction

Assumptions:

• Total mass (m) of the vehicle is acting on the center of gravity.
• This centrifugal force is balanced by
• side friction,
• component of vehicles' weight acting parallel to road due to

superelevation, or

• combination of both.

Considering equilibrium,

𝐒=​𝐖↑𝟑 /𝐡(𝐠+​𝐟/𝟐𝟏𝟏 𝟐𝟏𝟏 ) =​𝑾↑ 𝑾↑𝟑 / 𝟐𝟔 𝟐𝟔(𝐠+​𝒇/ 𝒇/𝟐𝟏𝟏 𝟐𝟏𝟏 )

V - speed (mph) R - radius (ft)

f – frictional coefficient

e – superelevation rate (%) α – banking angle

To study the bicycle response when travelling along a

horizontal curve, the following parameters are considered:

• Radius
• Velocity
• Transition curve

Length of the transition curve for highway is determined based on

a) ​𝐌↓𝐭𝟐

𝐭𝟐 =​𝟒.𝟐𝟔 𝟐𝟔 ​𝐖↑𝟒 /𝐃𝐒 𝐃𝐒 , where 𝐃=​𝟗𝟏 𝟗𝟏/𝟖𝟔 𝟖𝟔+𝟐.𝟕𝟐 𝟕𝟐×𝐖

(AASHTO (2011) and IRC (2010))

b) ​𝐌↓𝐭𝟑

𝐭𝟑 =(𝐗+​𝐗↓𝐟 ) 𝐟 𝐎

(The Constructor (2017))

c) ​𝐌↓𝐭𝟒

𝐭𝟒 =​𝟖𝟓 𝟖𝟓.𝟓𝟏 𝟓𝟏 ​𝐖↑𝟑 /𝐒 (IRC

(2010))

V - speed (mph) R - radius (ft) C - jerk (rate of change of centripetal acceleration) (ft/s3), and Ls - length of transition curve (ft)

a) Rate of change of centripetal acceleration b) Rate of change of superelevation and extra

widening

c) Indian Road Congress (IRC) empirical

formula

Transition curves are used at the entrance and exit of a horizontal curve to

introduce gradual change in centripetal force.

Dynamic behavior of a bicycle movement is studied over 140

years.

In 1899, Whipple developed the basic model with four parts of

a bicycle

• Front wheel, F
• Rear wheel, R

w – wheel base c – trail λ – steering axis tilt

Whipple model

• Front handlebar and fork assembly, H
• Rear frame including rider body, B

In 1987, Papadopoulos developed the following equation by

incorporating 25 parameters to describe the Whipple model.

𝐍​𝐫 +𝐰​𝐃↓𝟐 ​𝐫 +[𝐡​𝐋↓𝐩 +​𝐰↑𝟑 ​𝐋↓𝟑 ]𝐫=𝐠

q - vector of time-varying quantities M - symmetric mass matrix C - damping-like matrix K0 - a stiffness matrix (proportional to gravitational acceleration) K2 - a stiffness matrix (due to gyroscopic and centrifugal effects) v - velocity of bicycle f - generalized force matrix

Whipple model

Parameters used in Papadopoulos model

Linear stability:

Linear stability is evaluated by assuming exponential solution, q = q0 e(λt), and calculating the eigenvalues.

𝐞𝐟 𝐞𝐟𝐮(𝐍​𝛍↑𝟑 +𝐰​𝐃↓𝟐 𝛍+𝐡​𝐋↓𝐩 +​𝐰↑𝟑 ​𝐋↓𝟑 )=𝟏 Eigenvalues vs velocity plot Self-stable velocity range:

4.29 ~ 6.02 m/s

Velocity (m/s) Unstable mode < 4.29 Weave > 6.02 Capsize

Similar to Whipple mode, ADAMS bicycle model consists of four

parts.

• Front wheel
• Rear wheel
• Front handlebar and fork assembly
• Rear frame including rider body

ADAMS bicycle model Joints and contacts Coordinates (m)

Parameters of ADAMS bicycle model Eigenvalues vs velocity plot (MATLAB output) Self-stable velocity range is 5.50 ~ 8.53 m/s (12.30 ~ 19.09 mph)

Model validation

Force equilibrium Centripetal acceleration Instrumented probe bicycle (IPB)

Instrumented probe bicycle (IPB) Acceleration in 3 axes Magnitude of velocity GPS location Gyroscopic angles

Forces acting at wheel contact points

1.02 m

Rfront = (94×9.81×0.343)/1.02 = 310.09 N Rrear = 612.05 N

ADAMS output Rzfront = 309.98 N Rzrear = 612.34 N

• C. G. (0.343, 0.860)

Curve no. Centripetal acceleration (m/s2) Theoretical (V2/R) ADAMS 1 0.39 0.44 2 0.58 0.54 3 0.19 0.19

Model validation Instrumented probe bicycle (IPB)

Model validation Instrumented probe bicycle (IPB)

ADAMS road Simulating velocity is 7.03 m/s

Simulation is performed along a route that has a conventional

bicycle lane and shared roadway. Road is considered flat.

AutoCAD drawing Degree of curvature and radius

Velocity (mph) ADAMS velocity (m/s) 12.5 5.59 14.0 6.26 15.5 6.93 17.0 7.60 18.5 8.27 ADAMS velocity input ADAMS Road

Bicycle simulation is performed over a range of velocity within

self-stable velocity region (12.30 ~ 19.09 mph).

Bicycle responses along the route is analyzed.

ADAMS Road ADAMS bicycle simulation (with two contact points)

ADAMS bicycle simulation at Velocity: 18.5 mph (8.27 m/s) (one contact point)

Simulation velocity is 6.93 m/s. Two points contact Simulation within the curve

Jerk is higher at the beginning and end of horizontal curve. Limit of jerk for highways is 0.3 – 0.9 m/s3 (1 – 3 ft/s3)

(AASHTO 2011)).

Length of a transition curve for curve 1, LS1 is calculated as follows:

​L↓s1 =​3.15 ​V↑3 /CR =​3.15 ​× 15.5↑3 /1.97×66.81 =89.12 ≈90 ft

Parameters: Velocity, V = 15.5 mph Radius, R = 66.81 ft Jerk, C = 0.60 m/s3 = 1.97 ft/s3

Without transition curve With transition curve

Variation of centripetal acceleration (ac) and jerk (C) with degree of curvature and velocity

Degree of curvature Velocity 12.5 mph (5.59 m/s) 15.5 mph (6.93 m/s) 18.5 mph (8.27 m/s) Entrance End Entrance End Entrance End

2 C 10.17 0.002 13.15 0.17 40.98 0.45 ac A 0.19 0.26 0.38 T 0.17 0.23 0.38 3 C 0.002 0.05 0.17 0.09 0.45 0.14 ac A 0.38 0.51 0.79 T 0.38 0.51 0.79 4 C 0.07 141.01 0.08 513.42 0.50 759.92 ac A 0.47 0.61 1.11 T 0.46 0.61 1.13 6 C 27.94 10.17 63.17 13.15 122.31 40.98 ac A 2.75 3.99 6.06 T 2.81 3.95 6.07 C - Jerk (m/s3) at entrance and end of the curve A – ADAMS average centripetal acceleration (m/s2) T – Theoretical centripetal acceleration (m/s2)

Average jerk vs. velocity

Find the velocity for a given degree of curvature and a desired threshold average

jerk.

Calculate the length of transition curve using following equation.

​𝐌↓𝐭𝟐 𝐭𝟐 =​𝟒.𝟐𝟔 𝟐𝟔 ​𝐖↑𝟒 /𝐃𝐒 𝐃𝐒

For a higher order curve, level of comfort and stability of a bicyclist is a concern.

Therefore, a “SLOW DOWN” caution sign or street marking is suggested to post.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 12.5 14.0 15.5 17.0 18.5 Average jerk, ft/s3 Velocity, mph 6th order 4th order 2nd order Upper bound Lower bound

V - speed (mph) R - radius (ft) C – average jerk (ft/s3) Ls - length of transition curve (ft)

Slip angle increases with the increase in velocity and degree

• f curvature of a horizontal curve.

ADAMS output shows variation of centripetal acceleration

within a horizontal curve that results in a jerk.

Jerk increases with the increase of degree of curvature and

bicycle velocity.

Jerk at the entrance and exit of a horizontal curve, in the

absence of properly designed transition curves, is the highest along a route.

A graph showing the variation of average jerk vs. velocity was

developed for different degree of curvature. This graph can be used as a design tool for calculating the required length of transition curves or to evaluate the impact of existing curves

• n stability and comfort of a cyclist.

When the available bicycle lane features cannot be altered to

accommodate the required length of transition curves, due to existing roadway and space constraints, a “SLOW DOWN” caution sign or street marking is suggested to post before the curve to warn cyclists to avoid or minimize stability and ride comfort concerns.

The simulation capabilities and the methodology presented in

this report can be used to evaluate the impact of horizontal curve, velocity, and transition curves on bicycle stability and rider comfort.

A graph is presented in this report that can be used as a

design tool. This tool was developed by considering only one bicycle model and a weight of a single cyclist. This tool needs to be further extended by incorporating various bicycle and rider characteristics to develop a tool that can be used to cover a wide range of such parameters during design of new bikeway and evaluation of existing bikeways or future implementations.

The simulation model needs to be further improved by

incorporating additional capabilities such as controlling lean and stability controls introduced by the cyclist.

Authors would like to thank TRC-LC at Western Michigan University for funding this study through a grant received from the United States Department of Transportation (USDOT) under the University Transportation Centers (UTC) program.