ECEF acceleration in straight and level flight

Chuck37

Hopefully this is the right forum. I'm trying to do something I think should be straightforward, which is to describe a straight and level flight over a WGS84 earth in ECEF coordinates. For example, pick a starting lat,lon,alt,heading and speed and just keep going at that heading and altitude. I'm trying to get evenly spaced time samples with ECEF position, velocity and acceleration.

I can compute ECEF position at the start, then compute a vector that is level to the ellipsoid at that point. If the time sampling is very close I can propagate to the next point and just move along like that and be close to the right answer (I'm slowly climbing because the velocity vectors point up). I'd like to get closer by computing the ECEF acceleration at each point and using that to propagate to the next point too, plus my data will be better if I can provide ECEF acceleration at each point anyway.

Can anyone help? If you know a smarter way to get all the points in one shot, that would be just as good too, I just couldn't figure it out that way.