Calculate absolute and relative crash change with new NC equation

bicyclingplus / atp-bc-tool-analysis

Analyzing inputs/outputs from the CTC Active Transportation Benefits/Costs tool, to identify and investigate potential issues (analysis notebooks only - input/output data is not included)

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Calculate absolute and relative crash change with new NC equation #4

Open mRaffill opened 12 months ago

mRaffill commented 12 months ago

So new To-Do list:

[x] Calculate the total crash change with the new equation (for both model and user-input)
[x] Calculate the relative crash change with the new equation (for both model and user-input)
[x] Check if they are then mostly negative

Originally posted by @mRaffill in https://github.com/mRaffill/atp-bc-tool-analysis/issues/3#issuecomment-1722398509

mRaffill commented 12 months ago

To go from the new NC equation to crash change: $NC{cmojk}=EC{cmoj} (1 + \sum{i}\sum{F}E_{ik} \frac{Ni}{L} I_{F})^{p}CRF{mojk}$ $\Delta C{cmok} = \sum{j} NC{cmojk}-EC_{cmoj}$

So the code should look something like:

Add a new column for $NC{cmojk}-EC{cmoj}$ (crash change, separated by location type)in the existing table where NC and EC are calculated
Add a new column for $\sum{j} NC{cmojk}-EC_{cmoj}$ to the crash change table

mRaffill commented 12 months ago

Calculate the total crash change with the new equation (for both model and user-input)

Added in 925923b3f967fe36bd144b9080eaafd033e45dbc

mRaffill commented 12 months ago

To get the relative (per 1000 volume) before/after crashes: $BCO{cmo}=\sum{j}\frac{EC{cmoj}}{EV{cmj}} 1000$ $ACO{cmok}=\sum{j}\frac{NC{cmojk}}{PV{cmjk}} 1000$ And the relative crash change is not defined yet (since it is not displayed anywhere in the tool), but it should be: $\Delta CO{cmok} = ACO{cmok} - BCO_{cmo}$

mRaffill commented 12 months ago

Note that:

$PV{cmjk} = EV{cmj} (1 + \sum{i}\sum{F}E_{ik} \frac{Ni}{L} I{F})^{p})$ and $NC{cmojk}=EC_{cmoj} (1 + \sum{i}\sum{F}E{ik} \frac{Ni}{L} I{F})^{p}*CRF_{mojk}$ (based on manipulating the original equations - see the issue for the new NC equation)

so $BCO{cmo}=\sum{j}\frac{EC{cmoj}}{EV{cmj}} * 1000$

$ACO{cmok}=\sum{j}\frac{EC{cmoj} * (1 + \sum{i}\sum{F}E{ik} \frac{Ni}{L} I{F})^{p}*CRF{mojk}}{ EV{cmj} * (1 + \sum{i}\sum{F}E{ik} \frac{Ni}{L} I_{F})^{p})} * 1000$

$ACO{cmok}=\sum{j}\frac{EC{cmoj} * CRF{mojk}}{EV_{cmj}} * 1000$

so $ACO{cmok}= \sum{j}\frac{EC{cmoj}}{EV{cmj}} 1000 \sum{j} CRF{mojk} = BCO{cmo} * \sum{j} CRF_{mojk}$

(I think????) (In case that helps anything anyway)

mRaffill commented 12 months ago

Wait, what would EV for user-inputted crashes be set at? will the current EV estimates actually be consistent with the magnitude of the user-inputted crashes?

I guess I can just try and see what happens...

mRaffill commented 11 months ago

Evaluated in https://github.com/mRaffill/atp-bc-tool-analysis/issues/3#issuecomment-1746276557 and yes, the results are now (almost) all negative!