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 Upul Attanayake, Ph.D., P.E. Associate Professor Department of Civil & Construction Engineering Mitchel Keil, Ph.D., P.E. Professor Department of Engineering Design, Manufacturing and Management Systems Abul Mazumder, M.Sc. Graduate Research Assistant Department of Civil & Construction Engineering

� 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. Complete street policy Classes of bikeway Bike route Shared roadway Bike path Bike lane Conventional Buffered Contra-flow Left side

� 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 of 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.

o Separation width between path and roadway o Design speed o Horizontal curvature o Superelevation o Grade o Sight-distance o Stopping sight-distance o Sight distance at horizontal curve o Width of bikeway o Horizontal and vertical clearance o Friction � Transition curve is considered for simulation

Horizontal curve and lean angle Forces acting on a point mass Assumption: o Total mass ( m ) of the vehicle is acting on the center of gravity. Considering equilibrium, 𝜾 = ​𝒖𝒃𝒐↑ 𝒐↑ −𝟐 ​​𝑾↑ 𝑾↑ 𝟑 /𝑺 = ​ 𝟏.𝟏𝟕𝟖 𝟏𝟕𝟖 ​𝑾↑ 𝑾↑ 𝟑 / V - speed (mph) 𝑺 R - radius (ft) 𝜄 – lean angle (degree) – lean angle (degree)

Horizontal curve, superelevation, and friction Considering equilibrium, 𝐒= ​ 𝐖 ↑ 𝟑 / 𝐡 ( 𝐠+ ​ 𝐟 / 𝟐𝟏𝟏 𝟐𝟏𝟏 ) = ​𝑾↑ 𝑾↑ 𝟑 / 𝟐𝟏𝟏 ) 𝟐𝟔 ( 𝐠+ ​𝒇/ 𝟐𝟔 𝒇/ 𝟐𝟏𝟏 V - speed (mph) R - radius (ft) Forces acting on a f – frictional coefficient point mass e – superelevation rate (%) α – banking angle Assumptions: o Total mass ( m ) of the vehicle is acting on the center of gravity. o This centrifugal force is balanced by o side friction, o component of vehicles' weight acting parallel to road due to superelevation, or o combination of both.

� To study the bicycle response when travelling along a horizontal curve, the following parameters are considered: o Radius o Velocity o Transition curve

� Transition curves are used at the entrance and exit of a horizontal curve to introduce gradual change in centripetal force. � Length of the transition curve for highway is determined based on a) ​ 𝐌 ↓ 𝐭𝟐 𝐭𝟐 = ​ 𝟒.𝟐𝟔 𝟐𝟔 ​ 𝐖 ↑ 𝟒 / 𝐃𝐒 𝐃𝐒 , where a) Rate of change of centripetal acceleration 𝐃= ​ 𝟗𝟏 𝟗𝟏 / 𝟖𝟔 𝟖𝟔+𝟐.𝟕𝟐 𝟕𝟐×𝐖 (AASHTO (2011) and IRC (2010)) b) Rate of change of superelevation and extra b) ​ 𝐌 ↓ 𝐭𝟑 𝐭𝟑 = ( 𝐗+ ​ 𝐗 ↓ 𝐟 ) 𝐟 𝐎 widening (The Constructor (2017)) c) Indian Road Congress (IRC) empirical c) ​ 𝐌 ↓ 𝐭𝟒 𝐭𝟒 = ​ 𝟖𝟓 𝟖𝟓.𝟓𝟏 𝟓𝟏 ​ 𝐖 ↑ 𝟑 / 𝐒 (IRC formula (2010)) V - speed (mph) R - radius (ft) C - jerk (rate of change of centripetal acceleration) (ft/s 3 ), and L s - length of transition curve (ft)

� Dynamic behavior of a bicycle movement is studied over 140 years. � In 1899, Whipple developed the basic model with four parts of a bicycle o Front handlebar and fork assembly, H o Front wheel, F o Rear frame including rider body, B o Rear wheel, R w – wheel base c – trail λ – steering axis tilt Whipple model

� 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 K 0 - a stiffness matrix (proportional to gravitational acceleration) K 2 - 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 = q 0 e ( λ t) , and calculating the eigenvalues. 𝐞𝐟𝐮 ( 𝐍 ​ 𝛍 ↑ 𝟑 +𝐰 ​ 𝐃 ↓ 𝟐 𝛍+𝐡 ​ 𝐋 ↓ 𝐩 + ​ 𝐰 ↑ 𝟑 ​ 𝐋 ↓ 𝟑 ) =𝟏 𝐞𝐟 � Self-stable velocity range: 4.29 ~ 6.02 m/s Velocity (m/s) Unstable mode < 4.29 Weave > 6.02 Capsize Eigenvalues vs velocity plot

� Similar to Whipple mode, ADAMS bicycle model consists of four parts. o Front wheel o Rear wheel o Front handlebar and fork assembly o Rear frame including rider body Joints and contacts Coordinates (m) ADAMS bicycle model

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

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

C. G. (0.343, 0.860) 1.02 m R rear = 612.05 N R front = (94 × 9.81 × 0.343)/1.02 = 310.09 N Curve Centripetal acceleration (m/s 2 ) ADAMS output no. Theoretical (V 2 /R) ADAMS Rz front = 309.98 N 1 0.39 0.44 Rz rear = 612.34 N 2 0.58 0.54 Forces acting at wheel contact points 3 0.19 0.19

Model validation Instrumented probe bicycle (IPB)

Model validation Instrumented probe bicycle (IPB) Simulating velocity is 7.03 m/s ADAMS road

� 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

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

ADAMS bicycle simulation (with two contact points) ADAMS Road

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/s 3 (1 – 3 ft/s 3 ) (AASHTO 2011)).

� Length of a transition curve for curve 1, L S1 is calculated as follows: Parameters: ​ L ↓ s1 = ​ 3.15 ​ V ↑ 3 / CR = ​ 3.15 ​ × 15.5 ↑ 3 / 1.97×66.81 Velocity, V = 15.5 mph =89.12 ≈90 ft Radius, R = 66.81 ft Jerk, C = 0.60 m/s 3 = 1.97 ft/s 3 Without transition curve With transition curve

Variation of centripetal acceleration ( a c ) and jerk ( C ) with degree of curvature and velocity Velocity Degree of 12.5 mph 15.5 mph 18.5 mph curvature (5.59 m/s) (6.93 m/s) (8.27 m/s) Entrance End Entrance End Entrance End C 10.17 0.002 13.15 0.17 40.98 0.45 2 A 0.19 0.26 0.38 a c T 0.17 0.23 0.38 C 0.002 0.05 0.17 0.09 0.45 0.14 3 A 0.38 0.51 0.79 a c T 0.38 0.51 0.79 C 0.07 141.01 0.08 513.42 0.50 759.92 4 A 0.47 0.61 1.11 a c T 0.46 0.61 1.13 C 27.94 10.17 63.17 13.15 122.31 40.98 6 A 2.75 3.99 6.06 a c T 2.81 3.95 6.07 C - Jerk (m/s 3 ) at entrance and end of the A – ADAMS average centripetal acceleration (m/s 2 ) curve T – Theoretical centripetal acceleration (m/s 2 )

3.5 3.0 Average jerk, ft/s 3 2.5 2.0 1.5 1.0 0.5 0.0 12.5 14.0 15.5 17.0 18.5 Velocity, mph 6th order 4th order 2nd order Upper bound Lower bound 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. V - speed (mph) ​ 𝐌 ↓ 𝐭𝟐 𝐭𝟐 = ​ 𝟒.𝟐𝟔 𝟐𝟔 ​ 𝐖 ↑ 𝟒 / 𝐃𝐒 𝐃𝐒 R - radius (ft) C – average jerk (ft/s 3 ) L s - length of transition curve (ft) � 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.