Understanding Gravity Models
Before running a heatmap analysis, let's understand the theory behind gravity-based accessibility modeling.
What is a Gravity Model?
Gravity models in accessibility analysis are inspired by Newton's law of gravitation. The basic concept:
The attractiveness of a destination decreases with distance (or travel time)
The Formula
The accessibility score at any location is calculated as:
$$ Ai = \sum{j} \frac{Oj}{f(t{ij})} $$
Where:
- $A_i$ = Accessibility at location $i$
- $O_j$ = Opportunities at destination $j$ (e.g., number of jobs, shops)
- $t_{ij}$ = Travel time from $i$ to $j$
- $f()$ = Impedance function (how distance affects attractiveness)
Impedance Functions
GOAT supports several impedance functions:
| Function | Behavior | Best For |
|---|---|---|
| Linear | Gradual decrease | General analysis |
| Exponential | Sharp decay | Short-distance trips |
| Gaussian | Bell curve | Peak attractiveness at certain distance |
| Power | Customizable decay | Research applications |
Real-World Example
Imagine you're analyzing access to supermarkets:
Location A: Has 3 supermarkets within 5 minutes walking Location B: Has 1 supermarket at 3 minutes, 2 at 15 minutes
Even though both have access to 3 supermarkets, Location A has better accessibility because all stores are close by. The gravity model captures this nuance!
Why This Matters for Planning
Gravity-based heatmaps help planners:
- 🎯 Identify underserved areas with poor accessibility
- 📊 Quantify accessibility inequalities across neighborhoods
- 🏗️ Evaluate new facility locations before building
- 🔄 Compare scenarios to find optimal solutions
Unlike simple "count within buffer" approaches, gravity models recognize that a nearby facility is more valuable than a distant one.
Next Step
Now that you understand the theory, let's configure your heatmap analysis!
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