Note - this is a document generated primarily for people within the AAD sea ice group. However, INS data users anywhere may find some useful things here.
Figure A |
Since helicopters don't always fly directly at their destination, or perfectly level, we can us the INS data record to determine where exactly the helicopter-based instruments are looking on the ground.
Figure A, to the right, shows the physical context of our problem. A tilted helicopter and some measurements: a is the GPS altitude, GPS is the point on the ground directly below the GPS, and nadir is where the instruments on the helicopter are actually looking, due to helicopter attitude, or tilt.
Figure B shows a theoretical rectangle with nadir and GPS defining opposite corners.
From these two figures, our problem is clearly a trigonmetry issue. So, what angles and sides can we use to start solving it?
We know GPS and a. We have also measured pitch [front-to-to back tilt], roll [side-to-side tilt], and heading - the angle at which the helicopter is pointing in degrees true.
Looking at figure B, we use pitch and a to calculate the pitch offset [x]: x=a(tan(pitch))
We can use roll to calculate a roll offset [y]: y=a(tan(roll))
That's enough to locate nadir in space, because we can offset GPS by x and y.
But wait! There's more. Right angle rules give us the distance between GPS and nadir on the ground [O, in figure B]: O = sqrt(x2+y2)
....which allows us to calculate dN, or the distance from the helicopter to nadir. It also allows us to use a nifty IDL function for spatially locating the nadir, as long as we know the apparent heading - or heading +- hN, depending on the direction of roll.
We might also want to know where instruments not located right at the INS are looking. For example, the radar. Radar nadir rN will vary from the GPS nadir point depending on helicopter pitch and roll. You could pin it right down by calculating the triangle tRt [theoretical radar triangle, figure A], and adding the vertical side of tRt to a for all of the other calculations[make sure you remove tRt's hypotenuse length to get true distance from radar to nadir dNr in the end]
All this is encapsulated in a one-page PDF:
helinadir.pdf [PDF, 14.6MB].Its quite big, but quite useful.
Figure B
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