method-paper.Rmd

---
title: '"Propensity to cycle": a general method to estimate mode-specific flows between
  origin-destination pairs'
author: "Robin Lovelace"
output: pdf_document
bibliography: ~/Documents/Transport.bib
---

# Introduction

```{r, echo=FALSE}
# This research has many motivations: methodological, empirical and applied.
# Recent research suggests that less than half of economically viable reserves
# of fossil fuels can be burned to avoid dangerous
# climate change []. Given the various shortcomings of biofuels
# [], this provides an obvious imperative to transition away
# from reliance on energy converters that burns carbon-based matter,
# including thermal power stations, fossil-fueled heaters and the internal
# combustion engine (ICE) [].
# 
# In parallel to evidence that we are using *too much* energy in our technological
# systems, a recent spate of evidence has highlighted that humans are using
# *too little* energy in our bodies. The mechanisation of everyday tasks, from
# transport to food preparation, has led to sedentary lifestyles becoming the
# norm. A host of noncommunicable diseases has followed, including depression, cardiovascular
# diseases, diabetes and cancer [@Lee2012]. This paradox of energy overuse in
# technical systems coupled with energy underuse in human behaviour suggests
# a single solution: replace machines with muscles in appropriate sectors of the
# economy. There are many reasons With its requirements for low and variable power inputs, the benefits
# the weight savings of not transporting a motor and the user skill and enjoyment
# of navigating a complex urban environment, transport stands out as the
# obvious sector where muscles can replace machines.
# 
# As the most energy efficient mode of transport known to man (measured in
# MJ kinetic energy input per passenger kilometer --- MJ/pkm~kinetic~) [@Komanoff2004],
# cycling provides an obvious win-win solution from health and environmental
# perspectives.
```

## Definitions

- **The rate of cycling** is the measure of cycling activity. It can be measured
  in terms of the number of regular cyclists ($NC$) --- such as the number who regularly
  cycle to work ($NC~commute~$) or the number who would classify themselves as
  leisure cyclists ($NC~leisure~$) --- or in terms of the number of trips per year
  or week ($NT~yr~$ or $NT~wk~$)
- **Propensity to cycle** ($PC$) is the *expected* rate of cycling in given area or between
  origin-destination pairs. This propensity is calculated using a model and can
  incorporate the impact of socio-demographic variables on willingness to cycle
  long distances (i.e. see *distance decay*, below), the predicted influence of
  the transport network (e.g. *circuity* and the presence of dedicated cycle paths)
  and other place-specific variables.
- **Extra cycling potential** ($ECP$) is the number of additional trips or cyclists
  that can be expected in a given scenario of the future.
- **Distance decay** ($DD$) is function that relates the distance of a trip
  the probability of it being made by a specific mode of travel (e.g. by bicycle):
  
$$
DD = f(d, X)
$$

  - **Circuity**:

  


# Theory

## Flows over geographical space

Geographical space is usually divided into mutually exclusive irregular
tesselations for the purposes of administrative data (Figure 1).
The set of origin points ($O$).

## Distance decay

## Mode-specific rates of flow

From the previous section it is clear that flows between origin-destination
pairs will tend to be greater the closer they are together. However,
this rate of flow is clearly mode-dependent: in many instances flows
that are possible by wheeled vehicles are deemed impossible to walk, at least
in a reasonably short period of time. Thus the distance decay function
has a mode dependency. Clearly this mode-dependency will depend on many characteristics
of the mode related case-specific circumstances: how
frequently is the given mode *available*? is the local travel infracture suitable?
what are the abilities of the users of each mode (i.e. how fit are they for
walking and cycling)? To simplify, we can reduce these characteristics down
to a single continuous variable: average speed by mode ($v_m$). Clearly this
will also be context-specific ($v_m = f(Z, I)$, where $Z$ and $I$ are the
characteristics of the zones and individuals in the study area), but it
it a useful simplifying assumption nonetheless:

$$
DD_m = f(d, v_m)
$$


# Data

# Method