Compute a plot speed as a function of cadence for different gear ratios

speed-vs-cadence.rkt

#lang racket/base

(require plot)

; gearing specifications
(define crings (list 36 48))
(define cassette (list 12 13 14 15 17 19 21 23 25))

; wheel circumference in km
(define wheelc (/ 2190 1e6))

(define crange (list 75 95))

; compute the distance traveled per one full rotation of pedals
; assumes non-accelerating motion
; Arguments:
;   - circ: wheel circumference
;   - front: number of teeth on front chainring
;   - rear: number of teeth on rear gear
(define (dist-per-turn circ front rear)
  (* circ (/ front rear)))

; speed
(define (calc-speed circ front rear cadence)
  (* 60 (* (dist-per-turn circ front rear)
           cadence)))

(plot-file (list (axes)
                 (map (λ (z)
                        (map (λ (y)
                               (function (λ (x)
                                           (calc-speed wheelc z y x))
                                         50 115
                                         #:alpha (- 1 (/ y 40))
                                         #:style (cond
                                                   [(eq? z (car crings)) 'long-dash]
                                                   [else 'solid])))
                             cassette))
                      crings)
                 (lines-interval (list (vector (car crange) 0) (vector (car (cdr crange)) 60))
                                 (list (vector (car crange) 0) (vector (car (cdr crange)) 60))
                                 #:alpha 0.3
                                 #:label "Typical Cadence"))
           #:title "Surly Cross-check gearing"
           #:x-label "Cadence (rpm)"
           #:y-label "Speed (kph)"
           #:y-min 15
           #:y-max 45
           "surly.png")