globals [ sample-cyclist;; one cyclist whose movement can be tracked ] turtles-own [ cyclists nearest-neighbor ;; closest one of cyclists power ] ;; set initial random powers within a given range to setup clear-all crt peloton-size [ setxy random-xcor min-pxcor + 40 setxy random-xcor + 1 max-pxcor - 40 setxy random-ycor min-pycor + 8 setxy random-ycor max-pycor - 3 set heading 90 ] crt peloton-size [ setxy random-xcor min-pxcor + 40 setxy random-xcor max-pxcor - 40 setxy random-ycor min-pycor + 8 setxy random-ycor max-pycor - 4 set heading 90 ] crt peloton-size [ setxy random-xcor min-pxcor + 40 setxy random-xcor max-pxcor - 40 setxy random-ycor min-pycor + 8 setxy random-ycor max-pycor - 5 set heading 90 ] crt peloton-size [ setxy random-xcor min-pxcor + 40 setxy random-xcor max-pxcor - 40 setxy random-ycor min-pycor + 8 setxy random-ycor max-pycor - 6 set heading 90 ] ; Creates the population of cyclists. ; Slider adjusts the number of cyclists in random positions on each of four horizontal lines, ; facing directly to the right. set sample-cyclist one-of turtles ask sample-cyclist [ set color red ] follow sample-cyclist reset-ticks end ; This selects the cyclist whose movement can be tracked, indicated by a circle on the interface screen to setup-road if (pycor < 9) and (pycor > -9) [ set pcolor black ] end ; Sets the width of the roadway. to go ask turtles [ set shape "bike"] ask turtles [ peloton ] repeat 5 [ ask turtles [ fd power ] ] display ; Setup for basic forward power display/animation rules. ;ifelse trace? ; [ ask turtles [ pen-down ] ; every .15 [ clear-drawing] ] ; [ask turtles [pen-erase]] tick ;shows trajectory lines (which can be turned off) end to peloton ; Sets the main dynamics of the peloton. find-cyclists if any? cyclists [ find-nearest-neighbor ifelse distance nearest-neighbor >= drafting-zone [ separate ] [ align cohere ]] ; Allows for the Wilenski flocking rules to take effect ; Align and cohere allow cyclists to gravitate toward each other; ; Separate allows them to move away from each other. ; The "find-cyclists" rule is connected to the 'in-radius vision' rule, ; which allows cyclists to scan in the radius set by the slider let cyclist-ahead one-of cyclists in-cone 1 180; patch-ahead 1 ifelse cyclist-ahead != nobody; and count turtles-here > 1 [set heading [heading] of cyclist-ahead ] [fd power] ; Collision avoidance rule - if there are riders ahead, match their heading, and the proceed according to the rules below if peloton-convergence-ratio <= 2 [ set power [power] of self * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio)) set max-align-turn (0.01 + abs max-align-turn) * (peloton-convergence-ratio) * (sqrt distance-farthest-neighbor) set max-separate-turn .1 - (abs max-separate-turn) * (peloton-convergence-ratio) set max-cohere-turn .1 - (abs max-cohere-turn) * ( peloton-convergence-ratio) fd power ] ; This is the key peloton routine. The power ratio reflects the power of the cyclist "in the wind" relative ; to cyclists behind and in drafting positions. It is based on the equation PCR = [ Pqdraft - (Pqdraft * (D/100)) ] / Pmaxdraft ; In this simulation, where the power ratio is less than 1 the cyclists farthest behind can go proportionately faster than those closer ; to the front. As this ration increases, it becomes "harder" to pass, and passing behavior diminishes. if patch-at 8 dy = nobody [ set heading (90 - random-float .1 + .01) ] if patch-at -8 dy = nobody [ set heading (90 + random-float .1 + .01) ] ; If cyclists bump into the edge of the world, they move toward centre at random degree. set power .1 + random-float .1 end to find-cyclists set cyclists other turtles in-radius vision end ; Scans for cyclists within the radius set by the slider "vision" to find-nearest-neighbor set nearest-neighbor min-one-of cyclists [distance myself] end ; Scans for nearest neighbors to-report distance-farthest-neighbor let farthest-neighbor max-one-of turtles in-cone 10 180 [distance self] report distance farthest-neighbor end ; This is a critical peloton rule that computes the distance from each cyclist to their farthest neighbor ahead up to 10 patches to-report distance-farthest-neighbor2 let farthest-neighbor2 max-one-of turtles in-cone 100 180 [distance self] report distance farthest-neighbor2 end ; Allows for graph to show "peloton length" - scans for all cyclists with a max range of 100 ;;; THE THREE FLOCKING RULES AND CODE BELOW ARE ADAPTED FROM WILENSKI'S FLOCKING MODEL ;;; to separate turn-away ([heading] of nearest-neighbor) max-separate-turn end ; "Max-separate-turn" is a slider that adjusts in proprotion to the power ratio. ;;; ALIGN to align turn-towards average-cyclists-heading max-align-turn end ; Allows for side-by-side or single-file alignment. "Max-align-turn" is a slider ; that adjusts in proportion to the power-ratio. to-report average-cyclists-heading ; We can't just average the heading variables here. ; For example, the average of 1 and 359 should be 0, ; not 180. So we have to use trigonometry. let x-component sum [dx] of cyclists let y-component sum [dy] of cyclists ifelse x-component <= 0 and y-component <= 0 [ report heading] [ report atan x-component y-component ] end ;;; COHERE to cohere turn-towards average-heading-towards-cyclists max-cohere-turn end ; Allows cyclists to move toward each other. to-report average-heading-towards-cyclists ; "towards myself" gives us the heading from the other turtle ; to me, but we want the heading from me to the other turtle, ; so we add 180 let x-component mean [sin (towards myself + 180)] of cyclists let y-component mean [cos (towards myself + 180)] of cyclists ifelse x-component > 0 and y-component > 0 [ report heading ] [ report atan x-component y-component] end ; Computes the mean heading of other cyclists back to me. ; Note the difference between the rule above, which computes angles from x and y coordinates "0". ; Here the angles are from other cyclists to me ;;; HELPER PROCEDURES to turn-towards [new-heading max-turn] turn-at-most (subtract-headings new-heading heading ) max-turn end ; Computes difference between the existing heading and the new-heading given by the "max-turn" function, and enables ; movement towards each other. to turn-away [new-heading max-turn] turn-at-most (subtract-headings heading new-heading ) max-turn end ; Computes difference between the existing heading and the new-heading given by the "max-turn" function, and enables ; movement away from each other. to turn-at-most [turn max-turn] ifelse abs turn >= max-turn [ ifelse turn >= 0 [ rt max-turn ] [ lt max-turn ]] [ fd power ] end ; Turn right by "turn" degrees (or left if "turn" is negative), ; but never turn more than "max-turn" degrees to-report heading-to-angle [ h ] report (90 - h) mod 360 end ; Converts the atan value to angles in degrees @#$#@#$#@ GRAPHICS-WINDOW 249 10 1495 341 51 12 12.0 1 10 1 1 1 0 1 0 1 -51 51 -12 12 1 1 1 time 50.0 BUTTON 29 51 106 84 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 124 52 205 85 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 4 10 227 43 peloton-size peloton-size 1.0 1000.0 20 1.0 1 NIL HORIZONTAL SLIDER 9 178 242 211 max-align-turn max-align-turn 0.0 2 395.3456549313881 .001 1 NIL HORIZONTAL SLIDER 4 270 237 303 max-separate-turn max-separate-turn 0.0 5 0.09993394874796183 0.01 1 NIL HORIZONTAL SLIDER 7 91 230 124 vision vision 0.0 10.0 5 0.5 1 radius bike-lengths HORIZONTAL SLIDER 8 128 231 161 drafting-zone drafting-zone 1 5 3 .1 1 bike-lengths HORIZONTAL SLIDER 423 355 754 388 peloton-convergence-ratio peloton-convergence-ratio .1 2 1.05 .01 1 NIL HORIZONTAL PLOT 445 417 972 575 Peloton Dynamics NIL NIL 0.0 10.0 0.0 0.02 true true "" "" PENS "Peloton dynamics #" 1.0 0 -14730904 true "" "plot sum [ (power * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100 ) / (peloton-convergence-ratio))) / count turtles ] of turtles * 100" "Peloton length" 1.0 0 -5298144 true "" "plot sum [ distance-farthest-neighbor2 / count turtles] of turtles" BUTTON 14 400 161 433 watch one of cyclists watch one-of turtles NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 16 476 162 509 follow one of cyclists follow one-of turtles NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 24 438 153 471 NIL reset-perspective NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 978 391 1128 531 Peloton Dynamics number is a combined function of speed, peloton density and PCR. It has been multiplied by 100 to scale with peloton length. Peloton length is simply a measure of the distance between the front cyclist and the rear cyclist to a max of 100. 11 0.0 1 SLIDER 8 224 180 257 max-cohere-turn max-cohere-turn 0 10 0.09993394874796183 .1 1 NIL HORIZONTAL MONITOR 7 170 240 215 Alignment angle mean [heading-to-angle max-align-turn] of turtles 6 1 11 MONITOR 3 219 251 264 Coherence angle mean [heading-to-angle max-cohere-turn] of turtles 6 1 11 MONITOR 4 269 240 314 Separation angle mean [heading-to-angle max-separate-turn] of turtles 6 1 11 TEXTBOX 759 343 909 413 Peloton convergence ratio (PCR)reflects the relative power output of a drafting cyclist to a non-drafting cyclist. 11 0.0 1 TEXTBOX 18 316 168 386 Alignment varies according to power and PCR; coherence and separation angles are set to adjust only according to PCR. 11 0.0 1 TEXTBOX 203 538 353 608 Power values shown in code are scaled here to reflect realistic cyclist power outputs. Black = sample cyclist (circle); Green = mean peloton output 11 0.0 1 PLOT 201 365 401 515 Power output NIL NIL 0.0 10.0 0.0 10.0 true false "" "" PENS "peloton" 1.0 0 -16777216 true "" "plot mean [((power) * peloton-convergence-ratio)] of turtles * 1500" "sample cyclist" 1.0 0 -13840069 true "" "plot [((power) * peloton-convergence-ratio)] of sample-cyclist * 1500" @#$#@#$#@ The applet requires Java 5 or higher. Java must be enabled in your browser settings. Mac users must have Mac OS X 10.4 or higher. Windows and Linux users may obtain the latest Java from Oracle's Java site. he applet requires Java 5 or higher. Java must be enabled in your browser settings. Mac users must have Mac OS X 10.4 or higher. Windows and Linux users may obtain the latest Java from Oracle's Java site. Peloton 3.0 By Hugh Trenchard March 2013 ________________________________________ WHAT IS IT? Cyclists well know that as they increase their power-output toward their maximums, it becomes harder to pass those ahead of them. When cycling at low power-outputs, riders can pass others frequently at comparatively fast speeds. As their collective power-output increases, riders pass others less frequently, they reduce their lateral movement, and the peloton begins to lengthen. At a certain output threshold, they cannot pass others at all, but by drafting they can keep up to those ahead, even if riders ahead are stronger. As cyclists adjust their power-outputs, interesting changes in their collective behavior occur, and peloton behavior shifts through observable phases. The peloton motion that appears in this model is not created or led in any way by special leader cyclists. There are no Lance Armstrongs here. Each cyclist follows the same set of rules, from which collective peloton motion emerges. This model contains a key improvement over previous versions for collision avoidance among the cyclists. The previous versions did not contain this. While the behavior is essentially the same, this fact has altered the phase transition thresolds a little. However, those alterations do not matter much, since the main achievement here is to show that realistic peloton behavior and phase dynamics can be demonstrated by introducing a basic passing/power-output algorithm into a flocking model. This model shows three main phases of peloton dynamics: ~ a low power-output phase in which behavior oscillates in density; ~ a high-power-output phase in which the peloton begins to lengthen into a stretched (single-file line); ~ disintegrated behavior (cyclists spread out without passing) HOW IT WORKS The model incorporates some rules from Uri Wilenski’s Flocking model with several important adaptations I have introduced. The following modifications represent principles specific to pelotons: • a random speed rule for cyclists; • a collision-avoidance rule; • a rule that causes cyclists in front or "in the wind" to slow down relative to those behind according to an adjustable ratio (“Peloton-Convergence-Ratio” or "PCR" (1)) such that when PCR is less than 1, cyclists in front slow down relative to those behind, and if PCR is 1 or more, cyclists in front move as fast or faster than those behind; • also, when PCR is less than one, cyclists behind can accelerate toward the front at speeds proportionate to the distance between themselves to the cyclist farthest ahead to a given maximum, and proportionate to PCR; i.e. at low power outputs (e.g. cycling slowly on a flat road), riders can pass from behind and move toward the front fairly quickly; • associated with the rule above, rules that constrain the directional angles of cyclists proportionately to PCR. PCR is adjustable by a "slider" on the interface screen. As PCR is increased through its range from PCR 0.1 to 1.0, the peloton shifts from higher density states to a stretched phase, or single-file line (lower density). This demonstrates an important effect in pelotons when riders synchronize their speeds at near sustainable maximum power outputs. Weaker riders can sustain the same speeds of stronger riders by taking advantage of the energy-savings benefits of drafting (2). As PCR is further increased, the synchronized (single-file) phase breaks down and riders separate and travel at their own intrinsic speeds (such as on steep ascents). At intermediate ranges of PCR, the peloton exhibits mixed phase dynamics as it oscillates between high density and single-file lines. The model is set to mimic a roadway on which all cyclists move to the right and, if isolated on their own, will drift randomly at shallow angles. As a roadway, the “world” has barriers at the top and bottom of the world view, and cyclists cannot “wrap” above or below these barriers. There are three rules incorporated from Wilenski’s Netlogo flocking model: “alignment”, “separation”, and “cohesion”. Here “alignment” means that a cyclists tend to turn so they move in the same orientation of nearby cyclists.“Separation” means that cyclists turn away from others. “Cohesion” means that cyclists move towards others. I refer to these as the “ASC” rules. For realistic peloton behavior, the ASC sliders must be initially set very low so that the degree of random lateral movement is low. You will see they remain at angles near 90 degrees (in Netlogo 90 degrees means you are facing directly to the right). This simulates cyclists’ forward movement along a roadway, compared with birds in the air which can move in any direction. HOW TO USE IT First, determine the number of cyclists you want in the simulation. Note there are four rows on which cyclists start in random positions, and the count for the "Peloton-riders-per-row" slider reflects the number in each row. So, multiply by 4 for the total. Press SETUP to create the cyclists, and press GO to get them moving. Delta icons will change to cyclist icons. The current settings for the sliders will produce reasonably good peloton behavior. The main slider to adjust is Peloton-Convergence-Ratio, which mimics the dynamics that correspond to a changing power outputs and to drafting magnitude. Adjusting this slider alters the density of the group and whether cyclists travel in lines or in clusters, or divide into groups. For the most interesting and realistic peloton behavior, keep the "vision" and "drafting-zone" in the mid to higher ranges while adjusting PCR 0.1 increments at a time and watching for a while. It may take one or two thousand ticks (a minute or two) to see the behavior change noticeably. THINGS TO NOTICE In the low PCR (~0.05 to ~0.25) where passing capacity is highest, behavior oscillates between high density clusters and the stretched state. At higher PCR ranges, behavior behavior oscillates less as groups split and peloton remains in a stretched state. Above PCR 1.0 see the peloton generally disintegrates. These PCR ranges where the behavior are stable represent the different phases of the peloton. In real pelotons there are of course different strategies and tactics and cyclists compete for top placings. For that purpose there are teams and team leaders and different roles within teams. This model demonstrates, however, that basic physical and physiological principles are the primary drivers of certain collective behaviors despite the influences of strategy and teamwork. RELATED MODELS • Flocking; Flocking vee formation • Basic Traffic by Uri Wilenski There is a cycling race simulation developed by Samuel Manier for the video game, "Pro-Cycling Manager". There is one published paper by Manier, S., and Sigaud, O. [year not given] "Compacting a Rule Base into an and/or Diagram for a Game ai". www.isir.upmc.fr/files/gameon_final.pdf, in which the authors refer to their Pro-Cycling Manager simulation. They indicate having incorporated physics equations into their simulation, but do not specify which ones, and they do not address complex dynamics or peloton phases. I am not aware of any other computer simulations of bicycle pelotons. CREDITS This model relies significantly on the work of Uri Wilenski, with important modifications that distinguish this peloton model from Wilenski’s model. Wilenski notes that his flocking model is inspired by the Boids simulation invented by Craig Reynolds. Information on Boids is available at http://www.red3d.com/cwr/boids/. • Wilensky, U. (1998). NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. • Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. REFERENCES (1) Trenchard, H. and Mayer-Kress, G. 2005.Self-organized coupling and synchronization in bicycle pelotons during mass-start bicycle racing. In Book of Abstracts of International Conference on Control and Synchronization in Dynamical Systems. Leon, Gto. Mx. (2) Hagberg, T. and McCole, S. 1990. The effect of drafting and aerodynamics equipment on energy expenditure during cycling. Cycling Science 2:20. NOTES PCR = ((Wa - Wb) / Wa) / (D/100) Where Wa is the maximum sustainable power output (watts) of cyclist A at any given moment; Wb is the maximum sustainable power of cyclist B at any given moment (assuming Wa>Wb); D/100 is the percent energy savings (correlating to reduced power output) due to drafting at the velocity travelled. Recently, I have derived the following version of PCR: PCR = [ Pqfront - (Pqfront * (D/100))] / Pmaxdraft Where Pqfront is the power output of the front rider at the given speed and equals the power output of the following, drafting rider, to maintain the speed set by the front rider if the following rider were not drafting. Pmaxdraft is the maximum sustainable output of the following rider. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 bike false 1 Line -7500403 false 137 183 72 184 Circle -7500403 false false 65 184 22 Circle -7500403 false false 128 187 16 Circle -16777216 false false 177 148 95 Circle -16777216 false false 174 145 102 Circle -16777216 false false 24 144 102 Circle -16777216 false false 30 150 90 Polygon -2674135 true true 226 194 211 89 203 91 204 106 109 121 94 82 86 84 99 122 90 132 76 194 136 194 137 187 87 187 99 132 207 115 219 194 Polygon -2674135 true true 92 83 136 193 129 196 83 85 Polygon -2674135 true true 135 188 209 120 210 131 136 196 Line -7500403 false 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75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 5.0.3 @#$#@#$#@ set population 200 setup repeat 200 [ go ] @#$#@#$#@ @#$#@#$#@ setup go density setup go density setup go density setup go density setup go density setup go count turtles setup go density setup go density setup go density setup go density setup go count turtles setup go density setup go density setup go density setup go density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles setup go count turtles setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density avg-speed setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go sum [(speed * (((distance-farthest-neighbor * distance-farthest-neighbor) / 100) / (peloton-convergence-ratio))) / count turtles] of turtles density setup go Mean [ (speed * ((( distance-farthest-neighbor * distance-farthest-neighbor) / 100 ) / (peloton-convergence-ratio))) ] of turtles * 100 mean [ distance-farthest-neighbor2 ] of turtles setup go mean [ (speed * ((( distance-farthest-neighbor * distance-farthest-neighbor) / 100 ) / (peloton-convergence-ratio))) ] of turtles * 100 mean [ distance-farthest-neighbor2 ] of turtles setup go Mean [ (speed * ((( distance-farthest-neighbor * distance-farthest-neighbor) / 100 ) / (peloton-convergence-ratio))) ] of turtles * 100 mean [ distance-farthest-neighbor2 ] of turtles @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 1.0 0.0 0.0 1 1.0 0.0 0.2 0 1.0 0.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@