Modeling the Earth's Magnetic Field
Here's an arbitrary classification scheme we can use when talking about models. Which one will we end up using? Depends on how much accuracy we need, and how much the Earth's magnetic field changes given position (lat, long and altitude).
- Static model: Given a specific launch site, the Earth's magnetic field (magnitude and direction) is constant for the flight regime we're intereseted in so we can use a single static vector to represent the field.
- Linear model: Given a specific launch site, the field changes linearly with altitude but does not heavily depend on actual position except for altitude
- Nonlinear model: Same as the linear, except the field is modeled with an nth order polynomial instead of linearly.
- Full local model: a full model of the Earth's magnetic field, but possibily restriced to a certain hemisphere or location.
- Full Global Model: The full-on global model.
Using the USGS magnetic field calculator linked below set to the IGRF-2005 model and coordinates 45°31′12″N, 122°40′55″S (Portland so saith wikipedia) the difference between the magnetic field at 0m and 100km is about 2800nT in strength (~55800nT at 0m compared to ~53000nT at 100km) and 0.14° and 0.45° in inclination and declination respectively. Given that we expect about 0.5° accuracy from the magnetometer, the static model looks like a pretty good approximation.
Links:
- UK Magnetic field model pdf (35MB!): http://www.geomag.bgs.ac.uk/documents/wmm2000.pdf
- USGS (US Geological Survey) Geomagnetism Program
- http://geomag.usgs.gov/
- USGS Magentic field models: http://geomag.usgs.gov/models.html
- Java applet "model" calculator: http://intermagnetusa.org/geomag/geomagAWT.html
- http://public.tgf.tc.faa.gov/documentation/magneticDecl/Verification.pdf - FAA verification of the WMM. They claim less than "0.5 degrees"... must mean if you use it as a 2D compass.