peloton fluid dynamics

;Peloton fluid dynamics, Hugh Trenchard 2014

to go
    
    clear-all
    
    crt mean-peloton-speed
    crt peloton-density
    crt max-width-peloton
    crt average-effective-pedal-force
       
    reset-ticks
end 

to start 
  
  set-current-plot "Dynamic Viscosity"; u = Fl/Av, 
  plot ((average-effective-pedal-force * lateral-distance-between-riders) / (peloton-side * passing))
  ;where:
    ;F is pedal force at given speed -- equivalent to force in standard viscosity equation;
    ;l is mean lateral distance between cyclists -- equivalent to distance between plates, or hard surfaces, in standard equation; 
    ;A is area of one side of peloton, or line of riders -- equivalent to area of upper plate in standard equation; 
    ;v is relative passing speed -- equivalent to the distance displacement (delta x) / second, 
                                    ;determined by cyclists' actual passing speed - mean peloton speed
       
   set-current-plot "Peloton Reynolds Number"
   plot ((peloton-density * mean-peloton-speed * max-width-peloton) / Dynamic-Viscosity)
end 

to-report Dynamic-Viscosity
  
  let viscosity ((average-effective-pedal-force * lateral-distance-between-riders) / (peloton-side * passing))
    report viscosity
end 

to-report Peloton-RN
  let RN (peloton-density * mean-peloton-speed * max-width-peloton) / Dynamic-Viscosity
  report RN
end 

to-report D
  let drafting-rate (((mean-peloton-speed / 1000) * 3600) * 0.621371); D as percentage equivalent to mph
  report drafting-rate
end 

to-report D2
  let drafting-rate (((mean-peloton-speed / 1000) * 3600) * 0.621371) / 100; D as decimal value percent equivalent to mph
  report drafting-rate
end 

to-report Peloton-convergence-ratio
  ; let MSO-following-rider average-effective-pedal-force / 1.78  
   ;1.78 m/s is standard pedal velocity given 100rpm, crank length of 170mm using equation vp=(cadence*crank-length * 2pi) / 60 / 1000
   let pcr (average-effective-pedal-force - (average-effective-pedal-force * D2)) / (MSO-following-rider) 
   ; PCR = (power-front-rider - (power-front-rider * D/100)) / MSO following rider
   report pcr
end 

to-report MSO-pedal-force
   let MSO-force MSO-following-rider / 1.78
   ;1.78 m/s is standard pedal velocity given 100rpm, crank length of 170mm using equation vp=(cadence*crank-length * 2pi) / 60 / 1000
   report MSO-force
end 

to-report power  ;parameters from analyticcycling.com
     let A 0.5; frontal area of cyclist in m^2
     let Cw 0.5 ; drag coefficient
     let Rho 1.226; air density kg m^3
     let GradHill 0
     let Crr .004 ; coefficient of rolling resistance
     let Wkg 75; weight of rider and bike in kg
     let fw 0.5 * A * Cw * Rho * (max-passing-speed ^ 2)
     let fsl Wkg * 9.8 * GradHill
     let frl Wkg * 9.8 * Crr
     let power-output (fw + fsl + frl) * max-passing-speed
     report power-output
end 

to-report average-effective-pedal-force
    let pedal-force power / 1.78 ; aepf = power / pedal veloctiy; 1.78m/s is a standard pedal velocity
    report pedal-force
end   

to-report passing
    let relative-pass-speed max-passing-speed - mean-peloton-speed
    report relative-pass-speed
end 

to-report lateral-distance-between-riders; equivalent to actual viscosity parameter "l", which is the distance between two plates
    let lateral-distance 9.5 - 9.5 * (Peloton-convergence-ratio); 10 is 10m, or the maximum width of the peloton and maximum density, in this illustration;
    ;since one rider at shoulder width is ~0.5, the minimum width of the peloton is one-rider wide, or 0.5, so this is set so when PCR = 1, peloton cannot 
    ;be less than 0.5m wide
    report lateral-distance
end 

to-report peloton-side; equivalent to actual viscosity parameter "A", which is the area of a solid surface that moves "right with velocity v"
   let peloton-side-area1 12.4 + 12.4 * (14 ^ peloton-convergence-ratio); 12.4 = 1.65m (bike length) x 1.5m (height of crouched cyclist) x 5; 
   ;where 5 is the approximate number of cyclists who can fit single-file in 10m, given by: 10m / (1.65+0.20), where 0.20 is the optimized wheelspacing 
   ;between rear wheel of rider ahead, and front wheel of following rider
   ; 14 is the number of cyclists laterally who can fit in a 10m space, given shoulder width of 0.50m, and 0.20 spacing between cyclists side-to-side, for 10m/0.7m
   report peloton-side-area1
end 

to load-chart
  ;loads an image as a background from the current directory the model was launched from
   import-drawing "peloton.jpg"
     reset-ticks
end