Hypocycloid Gravity Train

gravitytrain.py

# -*- coding: utf-8 -*-

from math import *
import wolframalpha

client = wolframalpha.Client("YHQ3GK-PT45KT9AHG")
radius = 6367500
circumference = 2*pi*radius
gravitational_constant = 9.8 # m/s2

def cycloid_length(surface_distance):
    ''' Returns kilometer length of hypocycloid over surface_distance'''
    length = 2*surface_distance*(2*pi*radius-surface_distance)/(pi**2*radius)
    return int(length//1000)

def cycloid_time(surface_distance, humanize=True):
    ''' Returns seconds of travel time, or humanized representation of time'''
    travel_time = sqrt(surface_distance*(2*pi*radius-surface_distance)/(radius*gravitational_constant))
    if humanize:
        return humanize_time(travel_time)
    return travel_time

def cycloid_maximum_velocity(surface_distance):
    ''' Returns the maximum velocity that will be attained
        This velocity is reached at the bottom of the hypocycloid
    '''
    return sqrt(gravitational_constant*surface_distance*(2*pi*radius-surface_distance)/radius)/pi

def humanize_time(inseconds):
    hours = inseconds//3600
    minutes = (inseconds//60)%60
    seconds = inseconds%60
    hours, minutes, seconds = map(lambda x: str(int(x)).zfill(2), (hours, minutes, seconds))
    return "%s:%s.%s"%(hours, minutes, seconds)

def determine_city_transit(cityA, cityB):
    query = "distance between city {0} and city {1} in km".format(cityA, cityB)
    result = client.query(query).results
    for r in result:
        surface_distance = float(r.text.split(" ")[0])*1000
        print "Surface distance between %s and %s: %s" %(cityA, cityB, r.text)

        if surface_distance:
            print "Cycloid length between cities: %.2f km" %(cycloid_length(surface_distance))
            print "Travel time between cities: %s" %(cycloid_time(surface_distance))
            print "Maximum velocity: %.2f m/s" %(cycloid_maximum_velocity(surface_distance))
            
def determine_transit(surface_distance):
    surface_distance = surface_distance
    print "Cycloid length for %s km of surface: %.2f km" %(surface_distance, cycloid_length(surface_distance))
    print "Travel time: %s" %(cycloid_time(surface_distance))
    print "Maximum velocity: %.2f m/s" %(cycloid_maximum_velocity(surface_distance))


cityA = "London"
cityB = "New York"
determine_city_transit(cityA, cityB)

#determine_transit(pi*radius)