# Haversine Distance

**AISdb** includes a function called `aisdb.gis.delta_meters` that <mark style="background-color:yellow;">calculates the Haversine distance in meters between consecutive positions within a vessel track.</mark> This function is essential for analyzing vessel movement patterns and ensuring accurate distance calculations on the Earth's curved surface. It is also integrated into the [denoising encoder](https://aisdb.meridian.cs.dal.ca/doc/api/aisdb.denoising_encoder.html#aisdb.denoising_encoder.encode_greatcircledistance), which compares distances against a threshold to aid in the data-cleaning process.

Here is an example of calculating the Haversine distance between each pair of consecutive points on a track:

{% code lineNumbers="true" %}

```python
import aisdb
import numpy as np
from aisdb.gis import dt_2_epoch
from datetime import datetime

y1, x1 = 44.57039426840729, -63.52931373766157
y2, x2 = 44.51304767533133, -63.494075674952555
y3, x3 = 44.458038982492134, -63.535634138077945
y4, x4 = 44.393941339104074, -63.53826396955358
y5, x5 = 44.14245580737021, -64.16608964280064

t1 = dt_2_epoch( datetime(2021, 1, 1, 1) )
t2 = dt_2_epoch( datetime(2021, 1, 1, 2) )
t3 = dt_2_epoch( datetime(2021, 1, 1, 3) )
t4 = dt_2_epoch( datetime(2021, 1, 1, 4) )
t5 = dt_2_epoch( datetime(2021, 1, 1, 7) )

# Create a sample track
tracks_short = [
    dict(
        lon=np.array([x1, x2, x3, x4, x5]),
        lat=np.array([y1, y2, y3, y4, y5]),
        time=np.array([t1, t2, t3, t4, t5]),
        mmsi=123456789,
        dynamic=set(['lon', 'lat', 'time']),
        static=set(['mmsi'])
    )
]

# Calculate the Haversine distance
for track in tracks_short:
    print(aisdb.gis.delta_meters(track))
```

{% endcode %}

{% code lineNumbers="true" %}

```
[ 6961.401286 6948.59446128 7130.40147082 57279.94580704]
```

{% endcode %}

If we visualize this track on the map, we can observe:

<figure><img src="/files/ZIKPSY4sYQ3a74XmOwnZ" alt=""><figcaption></figcaption></figure>


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://aisviz.gitbook.io/documentation/tutorials/haversine-distance.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.