climb rate – altitude correlation from analysis of igc files

Christof Maul, OSTIV Meteorology Panel Workshop, Pfaffstätten/A, 26.9.09 Climb Rate Altitude Correlation from Analysis of IGC Files

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Climb Rate – Altitude Correlation from Analysis of IGC Files

Christof MaulTechnische Universität BraunschweigJohann Wolfgang Goethe-Universität Frankfurt (Akaflieg Frankfurt)


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Source data: Competition flights

Advantages: Open accessWell-defined pilot strategyWell-defined terrain and weather conditions

B1400235136607N01245193EA016980181000208173008B1400475136514N01246159EA016790178000207169010

Convert data string to 5-dimensional flight vector V(t, y, x, h, w=dh/dt)

14.0064, 51.6101, 12.7532, 1698, -2.6714.0131, 51.6086, 12.7693, 1679, -0.79


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Competition data pre-treatment

removal of pre-start and post-finish data


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Analyzed competitions (2007):

1) Lilienthal Glide, Lüsse, Germany, July 14 to 2797 competitorsJuly 16, 23, 26254 flights127,000 data points

2) European Gliding Championships, Issoudun, France, Aug 6 to 19 91 competitorsAugust 9, 12, 13, 16, 18386 flights177,000 data points

3) Junior World Gliding Championships, Rieti, Italy, July 28 to Aug 1153 competitorsJuly 29, 30, August 4, 6, 7221 flights95,000 data points


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Basic results – tracks – y(x):

well defined geographical area with homogenous samplingLilienthal Glide


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From variograms w(t) to vertical speed distributions f(w):

projection of variogram onto w axis

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Climb and sink vertical speed distributions are general features

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0908

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1808

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Rieti Issoudun


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From barograms h(t) to altitude distributions f(h):

projection of barogram onto h axis

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abundance, %

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Circling vs. straight climb

sink fs (h)w = dh/dt < 0

climb fc (h)w = dh/dt > 0

thermal/circling fcc(h)w = dh/dt > 0

(dx/dh)2 + (dy/dh)2

0

aligned lift fcs(h)w = dh/dt > 0

(dx/dh)2 + (dy/dh)2

0

total f(h)


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Altitude distributions of thermal fcc(h) () vs. aligned fcs(h) () lift. Significant variations, aligned lift accounts for as much as 50% of total lift!

Rieti Issoudun

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circling climb straight climb

altitude, m

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altitude, m

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'dh)'h(f)'h(f)h(fh

0outin

cc

Description of circling climb altitude distributions fcc(h,w>0).

If w-h correlatins are absent, fcc(h,w>0) can be obtained by integrating over thermal entering and thermal exiting altitude distributions fin (h) and fout (h):

Consequently, fin (h) and fout (h) can be obtained by differentiating f(h):

)h(f)h(fdh

)h(dfoutin

cc

Alternatively, fin (h) and fout (h) can be directly obtained from identifying thermals from flight recorder data.

Both methods should give identical results!

(1)

(2)


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Excellent agreement between altitude distributions fcc(h) obtained from flight recorder data () and from integration of eq.1 ().

Rieti Issoudun

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altitude, m

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circling climb straight climb calculated circling climb

altitude, m

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Result corroborated by absence of w-h correlation.

Rieti Issoudun

Mean vertical speeds (black) are essentially independent of altitude. In contrast, maximum and minimum vertical speed values (blue) occur at medium altitudes.


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Result is in contradiction to accepted theory, see e.g. "Meteorology and Flight"by T. Bradbury:

"Average rates of climb may be onlyhalf these values."


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altitude, m

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systematicallytoo small

systematicallytoo large

A second look to altitude distributions


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GoodA second look to altitude distributions


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Strategy

fit 3rd order polynomial tomaximum climb rate data (black)

fix intercept at -0.5 m/s and compare to Bradbury

divide result by 2 (averagerates of climb may be only half these values) and compareto mean climb rate data (red)

A second look to w-h correlations


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3rd order polynomial fir tomaximum climb rate dataintercept -0.5 m/s

No fit! Result from abovedivided by 2, compared tomean climb rate data

Issoudun 20070809

Issoudun 20070809


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"Bradbury correlation" applied to mean thermaling climb ratesof Luesse and Issoudun competitions


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Iss1608 Iss1308 Iss1208 Iss0908 Iss1808 Lue1607 Lue2307 Lue2607

climb rate / ms-1

altit

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final comparison of statistical analysis to Bradbury's model

another excellent agreement!


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Another add-on to previous workconcerning vertical speed distributions

Gaussian or non-Gaussian?

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Bin Center (m/s)

f(w) straight f(w) circle

straight and circlingGaussian

straight flight onlyGaussian

same databut look non-Gaussian

Issoudun, 9.8.07

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straight circle


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altitude distributionstraight and circling

vertical speed distributionstraight and circling

more than 50% straight climbcircling climb rate distribution is Gaussian

Issoudun, 16.8.07

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straight flight circling


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Summary of new results

1) vertical speed – altitude correlation

A close look reveals very good agreement of evaluated datawith correlation reported by Bradbury.

2) vertical speed distribution

No deviation from Gaussian normal distributions is observed.Holds also for circling only climb data.

climb rate – altitude correlation from analysis of igc files

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