I've been on the same lane.

You miss gravity, which gives you one extra. And in case of curving you miss the G-force from turning - the 60 deg used in narrow thermals give you one further.

At http://da.wikipedia.org/wiki/Bruger:...Logfil-analyse I've started some deductions - I actually reached the point where the nett G-force is calculated (last formula). Wiki was choosen, because it has an easily accessible formula tool ... in my oppinion at least.

For those interested I can add, that the explaining text is in danish, but readers with flair for math should be able to follow the formulas; first I move into an metric vector space (ti, xi, yi, zi); then I look at three consecutive observations and treat x, y and z as parables in time, and hence calculate acceleration (a) and velocity (v) in each of the three dimensions. Adding gravity and combining it by pythagoras gives the nett G-force.

My further intention was to split the logfile into phases of climb and glide; climb can be identified in the xy-plane by the acceleration (ax, yx) beeing perpendicular to the velocity (vx, vy). This offcourse requires at least three logs per full turn, so logfiles whith more than five seconds between logs are poor for analytical purposes.

When the climb-phases are identified, wind can be deduced. The simplest way is to subtract the two vectors representing max and min speed within a limitted span of logs. More complete could be to assume constant turn-rate and do a OLS-model with sin and cos-components. An advanced version would allow for increasing wind-speed with altitude.

With wind known, the thermal can be projected down to the 'hot spot' on the ground feeding it. The z-values calculated from the logs might need some calibration, but that can be done from the QFE of the takeoff/landing airfield.

The net strength of the termal is somewhat more complicated to guess. Total energy is simple enough - we know the changes in speed. But the sink of the glider will depend on the G-load (as above) multiplied by a loadfactor (some assumptions are needed - on good days the hotshots bring lots of water) run through a polar (aircraft known from the header, if the pilot did declare his task) and somehow compensated for dirt on the wings (increasing with time) and unintended sideslipping (more with narrow turns, I think). Reasonable assumptions can be made and a fair guess on the nett value of the termal - including strength by altitude - could come out.

I suspect there are some hot spots offering lift in different possitions with varying wind-directions. With data from multiple fligths it would be possible to identyfy them by strength and wind direction. (An I havn't completely forgiven olc not answering my request to have access to som IGC-files.)

With the gaggles we see during competitions it might as well be possible to make an 3d image of a thermal. I've allways dreamt of making a emperical based visualisation of a thermal.

Yours,
/Poul

JohnDeRosa:
I thought it would be an interesting experiment to take an IGC trace

and figure out rates of climb. That much was pretty easy. I took

consecutive IGC file B-records and with just a little math I was able

to determine the ft/min or meters/min climb rates*.



I then thought it would be a good experiment to determine the G forces

as I pull up (decelerate) from cruise to lift or push over

(accelerate) from lift to cruise. Are there any physicists in the

house that can come up with a SIMPLE formula to calculate what a G

meter would have read based on the information I have?



Thanks, John



--------------------------------------------------------------



* The many individual b-records in an IGC file contains lots of good

information.



B1101355206343N00006198WA0158701558



110135: time tracklog entry was recorded at 11:01:35 i.e. just

after 11am (GMT)

5206343N: latitude i.e. 52 degrees 06.343 minutes North

00006198W: longitude i.e. 000 degrees 06.198 minutes West

A: altitude valid flag confirming this record has a valid

altitude value

01587: altitude in meters from pressure sensor

01558: altitude in meters from GPS



Rate of Climb per minute (m/sec) =

(Altitude #2 - Altitude #1) / (Time-Seconds #2 - Time-

Seconds #1) X 60 seconds



Rate of Climb per minute (ft/sec) = Rate of Climb per minute (m/sec) X

3.28084